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AoA-Based Physical Layer Authentication in Analog Arrays under Impersonation Attacks

Muralikrishnan Srinivasan1, Linda Senigagliesi2, Hui Chen3, Arsenia Chorti4, Marco Baldi2, Henk Wymeersch3

1Indian Institute of Technology (BHU), Varanasi, India 2Università Politecnica delle Marche, Italy

3Chalmers University of Technology, Sweden, 4ETIS UMR 8051 / CY Paris University, ENSEA, CNRS, FranceThis work was supported by the Swedish Research Council (VR grant 2023-03821), by Hexa-X-II, part of the European Union’s Horizon Europe research and innovation programme under Grant Agreement No 101095759 and by project SERICS (PE00000014) under the MUR National Recovery and Resilience Plan funded by the European Union - NextGenerationEU.

We discuss the use of AoA as an authentication measure in analog array MIMO systems. A base station equipped with an analog array authenticates users based on the AoA estimated from certified pilot transmissions, while active attackers manipulate their transmitted signals to mount impersonation attacks. We study several attacks of increasing intensity (captured through the availability of side information at the attackers) and assess the performance of AoA-based authentication using one-class classifiers. Our results show that some attack techniques with knowledge of the combiners at the verifier are effective in falsifying the AoA and compromising the security of the considered type of physical layer authentication.

Physical layer authentication, AoA-based authentication, Impersonation attack.

§ INTRODUCTION

PLA is gaining momentum in the realm of wireless communication systems due to its ability to be deployed relatively easily in device-to-device setups without the need for a cumbersome public key infrastructure [1]. Unlike conventional cryptographic methods, PLA authenticates devices or users based on unique signal characteristics observed at the physical layer.
In addition to its fast processing and high interoperability in heterogeneous systems, such as its ability to work jointly with or complement upper-layer authentication, PLA enables the construction of multi-factor authentication schemes for enhanced security[1, 2].

A typical PLA scenario is shown in Fig. <ref>: the training process involves acquisition of initial features from transmissions of a legitimate user (Alice), associating them with her identity by leveraging some manual process or higher-layer identification protocol. Subsequent transmissions from Alice are then recognized by comparison with the signals acquired during training, and possibly distinguished from those of an attacker (Eve) attempting to impersonate Alice by manipulating transmitted signals through precoding.

Considered physical layer authentication scenario: (a) Offline Training phase: Alice's transmission is guaranteed to be authentic, the corresponding signal is acquired by Bob and associated with her identity (b) Online classification phase: Alice is recognized by the classifier through comparison of the newly acquired signal with her original signal, collected during training (c) Authentication system under successful impersonation attack: Eve transmits a precoded signal with the aim to confuse Bob's classifier and make it recognize the received signal as being transmitted by Alice.

PLA can be used either in challenge-response authentication protocols or in tag-based authentication protocols [3], and includes hardware-based and channel-based authentication. As an example of challenge-response PLA, hardware fingerprints, referred to as physical unclonable functions (PUFs), serve as unclonable unique device identifiers [4, 5, 6]. Recently, channel controllability using reflective intelligent surfaces (RIS) has also been considered in challenge-response protocols [7].

Channel-based PLA employs various channel features for authentication [8, 9, 10, 11, 12, 13]. In some recent works on channel-based PLA, like [14, 15, 16], the use of the AoA as a unique identity feature has been proposed, and also used to identify Sybil attacks in robotic networks [17].

Significantly, there has been a surge of interest in integrating ML into PLA [16, 18, 12],
as well as model-based approaches for location spoofing [19, 20].

Similar to any authentication scheme, AoA-based PLA solutions are susceptible to active attacks, in particular to impersonation/spoofing. Such attacks aim to deceive the verifier (Bob) – possibly by employing suitable precoders – to mis-classify Eve as Alice due to induced errors in the estimated AoA. Robustness against such attacks has been explored only in a handful of works up to now, like [21, 22]. The former focuses on jamming attacks and discusses the optimality of maximum likelihood-based AoA estimation. The latter focuses on spoofing attacks on AoA estimation in MIMO systems with digital arrays at the verifier.

In digital arrays, each receive antenna corresponds to a dedicated RF chain and the verifier estimates the AoA by examining phase variation across the array.

In the case of analog arrays with a single RF chain, the AoA is estimated through multiple pilot transmissions, probing different angles with appropriate beamforming vectors for each transmission.
In view of the fact that low-cost IoT devices can possibly not afford digital array transceivers, the study of spoofing attacks in AoA-based PLA systems using analog arrays becomes very important and motivates the current study.

In this paper, we demonstrate that analog arrays are much more vulnerable to spoofing attacks. Our contributions are as follows: (i)

We consider a standard authentication protocol in a novel context, where a verifier, in this case the BS, is equipped with an analog array and identifies a node, exploiting a one-class classifier trained using the estimated AoA of the legitimate node; (ii)

We investigate impersonation attacks by a malicious node and study the impact of the impersonation attacks on the estimated AoA; (iii)

We study the impact of the impersonation attacks on the ML-based classifier's performance.

§.§.§ Notation
Vectors $\bm{x}$ are denoted in bold, transpose as $\bm{x}^\top$, Hermitian as $\bm{x}^{\mathsf{H}}$, and complex conjugate as  $\bm{x}^*$.

§ AUTHENTICATION MODEL

In this section, we first describe the system model, followed by an  authentication protocol, focusing on the AoA as the primary feature.

§.§ System Model

Consider Alice's single-antenna[We have opted for a simple yet non-trivial system model to gain fundamental insights. This approach allows us to establish foundational principles and understand core mechanisms without unnecessary complexities.]
UE located at coordinates $\bm{x}^{\text{A}}=[{x}^{\text{A}}_1, {x}^{\text{A}}_2]^\top$.
The BS, corresponding to Bob, is situated at the origin $[0, 0]^\top$ and is equipped with an analog array, i.e., $N$ receive antennas and a single RF chain, subject to the constraint $N>1$.

Alice transmits a sequence of $T>1$ uplink pilot signals $\bm s^{\text{A}} = [s^{\text{A}}_1, \ldots, s^{\text{A}}_T]^\top$ to Bob satisfying the constraint $\Vert\bm s^{\text{A}}\Vert^2= 1$, where $T$ is the number of pilot transmissions. The received signal at Bob can be expressed as

\begin{align}
y_t = \sqrt{P} h^{\text{A}} \bm{w}^{\mathsf{H}}_t \bm{a}(\theta^{\text{A}}) s^{\text{A}}_t + n_t, \quad t=1,2,\ldots, T, \label{eq:Observation_nominal}
\end{align}

where $P$ represents the transmitted power from Alice, $|h^{\text{A}}|=\lambda /(4 \pi d^{\text{A}})$  is the channel amplitude between Alice and Bob (as a function of the distance $d^{\text{A}} = \Vert\bm x^{\text{A}}\Vert$ and the wavelength $\lambda$),  $n_t$ is complex AWGN with variance $\sigma^2/2$ per real dimension, $\bm{w}_t$ is the beamforming vector at time $t$, and $\bm{a}(\theta^{\text{A}})$ stands for the array steering vector[For a linear antenna array, the $n$-th element of the array steering vector is given by $[\bm{a}(\theta^{\text{A}})]_n = \exp(\jmath \pi n \sin(\theta^{\text{A}}))$, for $n=1,2,\ldots, N$] determined by the angle-of-arrival (AoA) $\theta^{\text{A}}$, where $\theta^{\text{A}}=\arctan({x}^{\text{A}}_1/{x}^{\text{A}}_2)$.
The beamforming vectors
$\bm{w}_t$ are configured to directional beams, i.e., $\bm{w}_t=\bm{a}(\theta_t)$, where $\theta_t$ denotes the probing direction between $[-90 \degree, 90 \degree]$. Also, $\sigma^2 = N_0 W$, where $N_0$ is the noise power spectral density
and $W$ is the bandwidth.

It is assumed that Bob possesses knowledge of $\bm s^{\text{A}}$, based on which, the AoA $\hat \theta$ at the BS can be estimated.

§.§ Physical Layer Authentication Protocol

We consider a standard authentication protocol in which Bob needs to identify Alice, based on the estimated AoA. Authentication protocols include an offline training phase and an online verification phase, which are schematically depicted in Fig. <ref>-(a) and Fig. <ref>-(b), and described next.

* Offline Training Phase:
features (in our case estimated AoAs $\hat \theta$) are recorded by Bob for each legitimate user; a corresponding database of user/node identifiers (IDs) and features is then created.

The transmissions of Alice received by Bob are guaranteed to be authentic by higher-layer protocols.
From an authentication perspective, this corresponds to a OCC scenario, where only the positive class (target class) is present during training, while the negative classes (non-target classes) remain unknown [12].

* Online Verification Phase:
Alice begins by announcing her identity to Bob and transmitting pre-agreed pilot sequences. This allows Bob to estimate Alice's AoA and authenticate her using an OCC classifier trained in the previous phase.[In precise terms, we define identification as a process enabling the authenticator to recognize the node's identity without explicit inquiry. On the other hand, authentication refers to a procedure where the node initially declares its identity and subsequently provides proof to verify that they are indeed the claimed identity.]

The purpose of this work is to study the robustness of such a standard authentication protocol to several new impersonation attacks, tailored to AoA estimation with analog arrays.

§ IMPERSONATION ATTACKS

Any authentication system is subject to attacks, notably impersonation/spoofing attacks.
We assume that the attacker (Eve) is provided with a single-antenna UE and employs suitable precoding with the aim that the received signals prompt Bob's classifier to mis-classify them as originating from Alice, as schematically illustrated in Fig. <ref>-(c).

§.§ General Attack Model

Eve, located at coordinates $\bm{x}^{\text{E}}=[{x}^{\text{E}}_1, {x}^{\text{E}}_2]^\top$, induces an array steering vector  $\bm{a}(\theta^{\text{E}})$ at Bob, determined by the AoA $\theta^{\text{E}}$, where $\theta^{\text{E}}=\arctan({x}^{\text{E}}_1/{x}^{\text{E}}_2)$. Eve manipulates the AoA-based authentication of Alice by altering the transmitted signal $\bm s^{\text{E}} =[s^{\text{E}}_1, \ldots, s^{\text{E}}_T]^\top$ to Bob, while satisfying the constraint $\Vert\bm s^{\text{E}}\Vert^2= 1$.
The received signal at Bob originating from Eve can be expressed as:

\begin{align}
{y}_t = \sqrt{P} h^{\text{E}} \bm{w}^{\mathsf{H}}_t \bm{a}(\theta^{\text{E}}) s^{\text{E}}_t + {n}_t, \quad t=1,2,\ldots, T,
\end{align}

where $P$ is Eve's transmission power (here for simplicity set equal to the transmission power of Alice), $|h^{\text{E}}|=\lambda/(4 \pi d^{\text{E}})$ is the channel amplitude, in which $d^{\text{E}} = \Vert\bm x^{\text{E}}\Vert$ is the distance of Eve from Bob,

$\theta^{\text{E}}=\arctan({x}^{\text{E}}_1/{x}^{\text{E}}_2)$, and ${n}_t$ denotes the AWGN component  with variance $\sigma^2/2$ per real dimension.
Eve can manipulate the transmitted signal or its statistical properties in different ways, depending on the knowledge she has regarding Alice.
In the following we describe some strategies that Eve might follow to manipulate her signals and the corresponding assumptions on her knowledge about Alice.

§.§ Random Attack

Eve knows when to transmit and the duration of the transmission.

Eve generates $s^{\text{E}}_t=\exp(\jmath \phi_t)/\sqrt{T}$, where $\phi_t \sim \mathcal{U}[0,2\pi]$.

Since $s^{\text{E}}_t\neq s^{\text{A}}_t$, the AoA estimation capability at Bob is compromised. However, it is unlikely that Eve can impersonate Alice with this attack.

§.§ Code-based attack

Eve knows when to transmit, and the duration of the transmission.  Eve also knows the combiners $\bm{w}_t$ (which can be interpreted as a code, hence the name code-based attack), the pilot $\bm s^{\text{A}}$,   and  Alice's AoA $\theta^{\text{A}}$. Eve does not know  $\theta^{\text{E}}$.

Here, Eve can manipulate $s^{\text{E}}_t$ as

\begin{align}
s^{\text{E}}_t  = \alpha^{\text{E}} {\bm{w}^{\mathsf{H}}_t \bm{a}(\theta^{\text{A}})} s^{\text{A}}_t,
\end{align}

where $\alpha^{\text{E}}$ is a normalization value set to meet the constraint $\Vert\bm s^{\text{E}}\Vert^2= 1$, i.e., $\alpha^{\text{E}}=({{\sum_{t=1}^{T}|\bm{w}^{\mathsf{H}}_t \bm{a}(\theta^{\text{A}})s^{\text{A}}_t|^2}})^{-1/2}$.

Subsequently, the received signal at time $t$ at the BS is given by

\begin{align}
{y}_t & = \sqrt{P} h^{\text{E}} \alpha^{\text{E}} \bm{w}^{\mathsf{H}}_t \bm{a}(\theta^{\text{E}})  {\bm{w}^{\mathsf{H}}_t \bm{a}(\theta^{\text{A}})} s^{\text{A}}_t +n_t.
\end{align}

This manipulation causes the BS to perceive a signal arriving from both the impersonator AoA $\theta^{\text{E}}$ and the true AoA $\theta^{\text{A}}$, providing opportunities for Eve to impersonate Alice.

§.§ Location-based attack

In this case, Eve acquires knowledge of the combiners $\bm{w}_t$,  the pilot $\bm s^{\text{A}}$,  the target angle $\theta^{\text{A}}$ and her own angle $\theta^{\text{E}}$, leveraging information about both the BS and her own location.

Eve can manipulate $s^{\text{E}}_t$ as follows:

\begin{align}
s^{\text{E}}_t  = \alpha^{\text{E}} \frac{\bm{w}^{\mathsf{H}}_t \bm{a}( \theta^{\text{A}})(\bm{w}^{\mathsf{H}}_t \bm{a}(\theta^{\text{E}}))^*}{|\bm{w}^{\mathsf{H}}_t \bm{a}(\theta^{\text{E}})|^2}s^{\text{A}}_t,
\end{align}

where $\alpha^{\text{E}}$ is again a normalization value set to meet the constraint $\Vert\bm s^{\text{E}}\Vert^2= 1$.

The received signal at Bob at time $t$ is given by

\begin{align}
y_t &  =\sqrt{P} h^{\text{E}} \alpha^{\text{E}} \bm{w}^{\mathsf{H}}_t \bm{a}(\theta^{\text{E}})  \frac{\bm{w}^{\mathsf{H}}_t \bm{a}( \theta^{\text{A}})(\bm{w}^{\mathsf{H}}_t \bm{a}(\theta^{\text{E}}))^*}{|\bm{w}^{\mathsf{H}}_t \bm{a}(\theta^{\text{E}})|^2}s^{\text{A}}_t +n_t\\
& = \sqrt{P} h^{\text{E}} \alpha^{\text{E}}   \bm{w}^{\mathsf{H}}_t \bm{a}( \theta^{\text{A}}) s^{\text{A}}_t +n_t.
\end{align}

This manipulation causes the BS to perceive only a signal arriving from $\theta^{\text{A}}$, effectively eliminating any trace of the true angle $\theta^{\text{E}}$. However, the effectiveness of the attack depends on the power of $\alpha^{\text{E}}$, which Eve cannot control. In particular, if a combiner $\bm{w}_t$ is such that $|\bm{w}^{\mathsf{H}}_t \bm{a}(\theta^{\text{E}})| \ll |\bm{w}^{\mathsf{H}}_t \bm{a}( \theta^{\text{A}})|$,

the overall potency of the attack is reduced.

§ NUMERICAL RESULTS

In this section, we assess the impact of impersonation attacks on the considered authentication protocol.

§.§ Authentication Protocol and Performance Metrics

The authentication protocol comprises two stages: the AoA estimator and the OCC, generating the decisions.

§.§.§ AoA Estimation

We adopt maximum likelihood estimation of $\theta^{\text{A}}$   from (<ref>) in the presence of an unknown complex channel gain $h^{\text{A}}$, leading to

\begin{align} \label{eq:ML}
\hat{\theta}=\arg \min_{\theta} \Vert \bm{y}- \hat{h}(\theta) \bm z (\theta) \Vert^2,
\end{align}

where $\bm{y}= [y_{1}, y_{2}, \ldots, y_{T}]^\top$, $[\bm z]_t = \bm w_t^{\mathsf{H}} \bm a(\theta)$, and $\hat{h}(\theta) = {\bm {z}^{\mathsf{H}}(\theta) \bm y}/{\norm{\bm{z}(\theta)}^2}$.

§.§.§ Classifier

For authentication, we employ OC-SVM as the classifier at Bob [12]. OC-SVM aims to encapsulate the majority of training data within a hypersphere $R = \{\bm x \in \mathbb{R}^N | f_{\text{oc}}(\bm x) > 0 \}$, where $\bm x$ is the feature vector and $f_{\text{oc}}(\bm x)$ is the decision function. New samples are accepted or rejected based on the decision function $f_{\text{oc}}(\bm x)$: if $f_{\text{oc}}(\bm x) > 0$, the message is accepted; otherwise, it is rejected.
To assess the effectiveness of this decision process, we exploit the classical metrics based on the probability of FA and MD.
A FA occurs when Bob wrongly rejects a message from Alice, while an MD happens when a message from Eve is mistakenly accepted by Bob as authentic.
The probability of FA is calculated as:

\begin{equation}
P_{\textsc{FA}} = \frac{\textsc{FN}}{\textsc{TP}+\textsc{FN}},
\label{eq:pfa}
\end{equation}

where $\textsc{FN}$ and $\textsc{TP}$ represent the number of false negatives and true positives, respectively. Similarly, the probability of MD is computed as:

\begin{equation}
\label{eq:pmd}
P_{\textsc{MD}} = \frac{\textsc{FP}}{\textsc{FP}+\textsc{TN}},
\end{equation}

where $\textsc{FP}$ and $\textsc{TN}$ represent the number of false positives and true negatives, respectively. Finally, overall accuracy is defined as:

\begin{equation}
\label{eq:acc}
\text{Acc} = \frac{\textsc{TP}+ \textsc{TN}}{\textsc{TP}+\textsc{TN} + \textsc{FP}+\textsc{FN}}.
\end{equation}

§.§ Simulation Parameters

We consider a system operating at 2.5 GHz with $W=20~\text{MHz}$ bandwidth and a transmit power $P=10~\text{dBm}$. The noise power spectral density is $N_0=-174$ dBm/Hz. Bob is equipped with $N=16$ antennas and expects $T=17$ transmissions. The beamforming vectors $\bm{w}_t$ are set to directional beams, denoted as $\bm{w}_t=\bm{a}(\theta_t)$, where $\theta_t$ represents the $T$ probing directions, uniformly spanning from $-90 \degree$ to $90 \degree$. Alice is located at $d^{\text{A}}=10~\text{m}$ with  $\theta^{\text{A}}=0\degree$, while Eve will have a variable location.

§.§ Results and Discussion

§.§.§ Impact of the Attacks on the Estimated AoA

To illustrate the effects of different attacks on the estimated AoA, we position Eve at a distance of $10$ meters from the BS with an AoA of $\theta^{\text{E}} = 45 \degree$, and we plot the negative log-likelihood cost $\Vert \bm{y}- \hat{h}(\theta) \bm z (\theta) \Vert^2$ from (<ref>) in Fig. <ref>.

The cost originating from Alice () has a distinct minimum at $\theta=0\degree$. Similarly, if Eve does not deploy any attack, the corresponding cost  () has a minimum at $\theta=45\degree$. Under the random attack  (), this minimum is attenuated and shifted but does not generate a minimum around $\theta^{\text{A}}$, and hence  Eve is incapable of impersonating Alice. Nonetheless, a sufficient number of random attacks could potentially facilitate successful Denial of Service Attacks, undermining Bob's capability to estimate the AoA. The code-based attack () does somewhat better and an additional minimum is created around $0$ degree apart from the one at $45 \degree$. Both minima are rather shallow and shifted from their nominal value. In this case, Eve has opportunities to impersonate Alice. Finally, with the location-based attack () a new minimum appears at $\theta=0 \degree$, while the original minimum at $\theta= 45\degree$ disappears. The minimum is pronounced and sharp, indicating that this attack can be highly effective at impersonating Alice.

Negative log-likelihood cost function (<ref>) as a function of the AoA  for different attacks for $d^{\text E}= 10~$m.

From now on, we will disregard the random attack and perform a more in-depth statistical analysis of the code-based and location-based attacks. To this end, we compute the RMSE, defined as $(\mathbb{E}\{ (\hat \theta - \theta^{\text A})^2\})^{1/2}$ based on 1000 Monte Carlo trials for various $d^{\text{E}}$ and  $\theta^{\text{E}}$.

The RMSE resulting from the code-based and location-based attacks is depicted in Fig. <ref>. For the location-based attack, we observe that as the distance $d^{\text{E}}$ increases, the RMSE increases due to a decrease in the SNR, leading to the failure of the attack. Additionally, the AoA estimation trend shows a predominantly monotonic behavior as $\theta^{\text{E}}$ increases but is also significantly influenced by nulls in the beam response. When the null of Eve's beam response precisely aligns with the main lobe of Alice's beam response, for example, at $\theta^{\text{E}} = 30 \degree$, achieving accurate emulation of Alice's response theoretically necessitates an infinite amount of power, resulting in $\alpha^{\text{E}}\to 0$.
Nevertheless, in a broader context, the overall trend suggests that with an increase in $\theta^{\text{E}}$, there is a corresponding increase in the RMSE of the estimated AoA. Notably, the RMSE is more pronounced in the code-based attack compared to the location-based attack. This increased error is attributed to the presence of dual minima in the negative log-likelihood function, leading to bias in the estimates, as discussed in the context of Fig. <ref>. The code-based attack thus introduces bias, resulting in increased RMSE; at angles exceeding $80 \degree$, a higher variance but reduced bias in AoA estimates occurs for larger distances, leading to an overall smaller RMSE compared to smaller distances.

[Code-based attack]

[Location-based attack]

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rgb(91pt)=(0.1429,0.618,0.9022); rgb(92pt)=(0.1408,0.6226,0.8998); rgb(93pt)=(0.1383,0.6272,0.8975); rgb(94pt)=(0.1354,0.6317,0.8953); rgb(95pt)=(0.1321,0.6363,0.8932); rgb(96pt)=(0.1288,0.6408,0.891); rgb(97pt)=(0.1253,0.6453,0.8887); rgb(98pt)=(0.1219,0.6497,0.8862); rgb(99pt)=(0.1185,0.6541,0.8834); rgb(100pt)=(0.1152,0.6584,0.8804); rgb(101pt)=(0.1119,0.6627,0.877); rgb(102pt)=(0.1085,0.6669,0.8734); rgb(103pt)=(0.1048,0.671,0.8695); rgb(104pt)=(0.1009,0.675,0.8653); rgb(105pt)=(0.0964,0.6789,0.8609); rgb(106pt)=(0.0914,0.6828,0.8562); rgb(107pt)=(0.0855,0.6865,0.8513); rgb(108pt)=(0.0789,0.6902,0.8462); rgb(109pt)=(0.0713,0.6938,0.8409); rgb(110pt)=(0.0628,0.6972,0.8355); rgb(111pt)=(0.0535,0.7006,0.8299); rgb(112pt)=(0.0433,0.7039,0.8242); rgb(113pt)=(0.0328,0.7071,0.8183); rgb(114pt)=(0.0234,0.7103,0.8124); rgb(115pt)=(0.0155,0.7133,0.8064); rgb(116pt)=(0.0091,0.7163,0.8003); rgb(117pt)=(0.0046,0.7192,0.7941); rgb(118pt)=(0.0019,0.722,0.7878); rgb(119pt)=(0.0009,0.7248,0.7815); rgb(120pt)=(0.0018,0.7275,0.7752); rgb(121pt)=(0.0046,0.7301,0.7688); rgb(122pt)=(0.0094,0.7327,0.7623); rgb(123pt)=(0.0162,0.7352,0.7558); rgb(124pt)=(0.0253,0.7376,0.7492); rgb(125pt)=(0.0369,0.74,0.7426); rgb(126pt)=(0.0504,0.7423,0.7359); rgb(127pt)=(0.0638,0.7446,0.7292); rgb(128pt)=(0.077,0.7468,0.7224); rgb(129pt)=(0.0899,0.7489,0.7156); rgb(130pt)=(0.1023,0.751,0.7088); rgb(131pt)=(0.1141,0.7531,0.7019); rgb(132pt)=(0.1252,0.7552,0.695); rgb(133pt)=(0.1354,0.7572,0.6881); rgb(134pt)=(0.1448,0.7593,0.6812); rgb(135pt)=(0.1532,0.7614,0.6741); rgb(136pt)=(0.1609,0.7635,0.6671); rgb(137pt)=(0.1678,0.7656,0.6599); rgb(138pt)=(0.1741,0.7678,0.6527); rgb(139pt)=(0.1799,0.7699,0.6454); rgb(140pt)=(0.1853,0.7721,0.6379); rgb(141pt)=(0.1905,0.7743,0.6303); rgb(142pt)=(0.1954,0.7765,0.6225); rgb(143pt)=(0.2003,0.7787,0.6146); rgb(144pt)=(0.2061,0.7808,0.6065); rgb(145pt)=(0.2118,0.7828,0.5983); rgb(146pt)=(0.2178,0.7849,0.5899); rgb(147pt)=(0.2244,0.7869,0.5813); rgb(148pt)=(0.2318,0.7887,0.5725); rgb(149pt)=(0.2401,0.7905,0.5636); rgb(150pt)=(0.2491,0.7922,0.5546); rgb(151pt)=(0.2589,0.7937,0.5454); rgb(152pt)=(0.2695,0.7951,0.536); rgb(153pt)=(0.2809,0.7964,0.5266); rgb(154pt)=(0.2929,0.7975,0.517); rgb(155pt)=(0.3052,0.7985,0.5074); rgb(156pt)=(0.3176,0.7994,0.4975); rgb(157pt)=(0.3301,0.8002,0.4876); rgb(158pt)=(0.3424,0.8009,0.4774); rgb(159pt)=(0.3548,0.8016,0.4669); rgb(160pt)=(0.3671,0.8021,0.4563); rgb(161pt)=(0.3795,0.8026,0.4454); rgb(162pt)=(0.3921,0.8029,0.4344); rgb(163pt)=(0.405,0.8031,0.4233); rgb(164pt)=(0.4184,0.803,0.4122); rgb(165pt)=(0.4322,0.8028,0.4013); rgb(166pt)=(0.4463,0.8024,0.3904); rgb(167pt)=(0.4608,0.8018,0.3797); rgb(168pt)=(0.4753,0.8011,0.3691); rgb(169pt)=(0.4899,0.8002,0.3586); rgb(170pt)=(0.5044,0.7993,0.348); rgb(171pt)=(0.5187,0.7982,0.3374); rgb(172pt)=(0.5329,0.797,0.3267); rgb(173pt)=(0.547,0.7957,0.3159); rgb(175pt)=(0.5748,0.7929,0.2941); rgb(176pt)=(0.5886,0.7913,0.2833); rgb(177pt)=(0.6024,0.7896,0.2726); rgb(178pt)=(0.6161,0.7878,0.2622); rgb(179pt)=(0.6297,0.7859,0.2521); rgb(180pt)=(0.6433,0.7839,0.2423); rgb(181pt)=(0.6567,0.7818,0.2329); rgb(182pt)=(0.6701,0.7796,0.2239); rgb(183pt)=(0.6833,0.7773,0.2155); rgb(184pt)=(0.6963,0.775,0.2075); rgb(185pt)=(0.7091,0.7727,0.1998); rgb(186pt)=(0.7218,0.7703,0.1924); rgb(187pt)=(0.7344,0.7679,0.1852); rgb(188pt)=(0.7468,0.7654,0.1782); rgb(189pt)=(0.759,0.7629,0.1717); rgb(190pt)=(0.771,0.7604,0.1658); rgb(191pt)=(0.7829,0.7579,0.1608); rgb(192pt)=(0.7945,0.7554,0.157); rgb(193pt)=(0.806,0.7529,0.1546); rgb(194pt)=(0.8172,0.7505,0.1535); rgb(195pt)=(0.8281,0.7481,0.1536); rgb(196pt)=(0.8389,0.7457,0.1546); rgb(197pt)=(0.8495,0.7435,0.1564); rgb(198pt)=(0.86,0.7413,0.1587); rgb(199pt)=(0.8703,0.7392,0.1615); rgb(200pt)=(0.8804,0.7372,0.165); rgb(201pt)=(0.8903,0.7353,0.1695); rgb(202pt)=(0.9,0.7336,0.1749); rgb(203pt)=(0.9093,0.7321,0.1815); rgb(204pt)=(0.9184,0.7308,0.189); rgb(205pt)=(0.9272,0.7298,0.1973); rgb(206pt)=(0.9357,0.729,0.2061); rgb(207pt)=(0.944,0.7285,0.2151); rgb(208pt)=(0.9523,0.7284,0.2237); rgb(209pt)=(0.9606,0.7285,0.2312); rgb(210pt)=(0.9689,0.7292,0.2373); rgb(211pt)=(0.977,0.7304,0.2418); rgb(212pt)=(0.9842,0.733,0.2446); rgb(213pt)=(0.99,0.7365,0.2429); rgb(214pt)=(0.9946,0.7407,0.2394); rgb(215pt)=(0.9966,0.7458,0.2351); rgb(216pt)=(0.9971,0.7513,0.2309); rgb(217pt)=(0.9972,0.7569,0.2267); rgb(218pt)=(0.9971,0.7626,0.2224); rgb(219pt)=(0.9969,0.7683,0.2181); rgb(220pt)=(0.9966,0.774,0.2138); rgb(221pt)=(0.9962,0.7798,0.2095); rgb(222pt)=(0.9957,0.7856,0.2053); rgb(223pt)=(0.9949,0.7915,0.2012); rgb(224pt)=(0.9938,0.7974,0.1974); rgb(225pt)=(0.9923,0.8034,0.1939); rgb(226pt)=(0.9906,0.8095,0.1906); rgb(227pt)=(0.9885,0.8156,0.1875); rgb(228pt)=(0.9861,0.8218,0.1846); rgb(229pt)=(0.9835,0.828,0.1817); rgb(230pt)=(0.9807,0.8342,0.1787); rgb(231pt)=(0.9778,0.8404,0.1757); rgb(232pt)=(0.9748,0.8467,0.1726); rgb(233pt)=(0.972,0.8529,0.1695); rgb(234pt)=(0.9694,0.8591,0.1665); rgb(235pt)=(0.9671,0.8654,0.1636); rgb(236pt)=(0.9651,0.8716,0.1608); rgb(237pt)=(0.9634,0.8778,0.1582); rgb(238pt)=(0.9619,0.884,0.1557); rgb(239pt)=(0.9608,0.8902,0.1532); rgb(240pt)=(0.9601,0.8963,0.1507); rgb(241pt)=(0.9596,0.9023,0.148); rgb(242pt)=(0.9595,0.9084,0.145); rgb(243pt)=(0.9597,0.9143,0.1418); rgb(244pt)=(0.9601,0.9203,0.1382); rgb(245pt)=(0.9608,0.9262,0.1344); rgb(246pt)=(0.9618,0.932,0.1304); rgb(247pt)=(0.9629,0.9379,0.1261); rgb(248pt)=(0.9642,0.9437,0.1216); rgb(249pt)=(0.9657,0.9494,0.1168); rgb(250pt)=(0.9674,0.9552,0.1116); rgb(251pt)=(0.9692,0.9609,0.1061); rgb(252pt)=(0.9711,0.9667,0.1001); rgb(253pt)=(0.973,0.9724,0.0938); rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805),

shader=interp, colormap=mymap[1pt] rgb(0pt)=(0.2422,0.1504,0.6603); rgb(1pt)=(0.2444,0.1534,0.6728); rgb(2pt)=(0.2464,0.1569,0.6847); rgb(3pt)=(0.2484,0.1607,0.6961); rgb(4pt)=(0.2503,0.1648,0.7071); rgb(5pt)=(0.2522,0.1689,0.7179); rgb(6pt)=(0.254,0.1732,0.7286); rgb(7pt)=(0.2558,0.1773,0.7393); rgb(8pt)=(0.2576,0.1814,0.7501); rgb(9pt)=(0.2594,0.1854,0.761); rgb(11pt)=(0.2628,0.1932,0.7828); rgb(12pt)=(0.2645,0.1972,0.7937); rgb(13pt)=(0.2661,0.2011,0.8043); rgb(14pt)=(0.2676,0.2052,0.8148); rgb(15pt)=(0.2691,0.2094,0.8249); rgb(16pt)=(0.2704,0.2138,0.8346); rgb(17pt)=(0.2717,0.2184,0.8439); rgb(18pt)=(0.2729,0.2231,0.8528); rgb(19pt)=(0.274,0.228,0.8612); rgb(20pt)=(0.2749,0.233,0.8692); rgb(21pt)=(0.2758,0.2382,0.8767); rgb(22pt)=(0.2766,0.2435,0.884); rgb(23pt)=(0.2774,0.2489,0.8908); rgb(24pt)=(0.2781,0.2543,0.8973); rgb(25pt)=(0.2788,0.2598,0.9035); rgb(26pt)=(0.2794,0.2653,0.9094); rgb(27pt)=(0.2798,0.2708,0.915); rgb(28pt)=(0.2802,0.2764,0.9204); rgb(29pt)=(0.2806,0.2819,0.9255); rgb(30pt)=(0.2809,0.2875,0.9305); rgb(31pt)=(0.2811,0.293,0.9352); rgb(32pt)=(0.2813,0.2985,0.9397); rgb(33pt)=(0.2814,0.304,0.9441); rgb(34pt)=(0.2814,0.3095,0.9483); rgb(35pt)=(0.2813,0.315,0.9524); rgb(36pt)=(0.2811,0.3204,0.9563); rgb(37pt)=(0.2809,0.3259,0.96); rgb(38pt)=(0.2807,0.3313,0.9636); rgb(39pt)=(0.2803,0.3367,0.967); rgb(40pt)=(0.2798,0.3421,0.9702); rgb(41pt)=(0.2791,0.3475,0.9733); rgb(42pt)=(0.2784,0.3529,0.9763); rgb(43pt)=(0.2776,0.3583,0.9791); rgb(44pt)=(0.2766,0.3638,0.9817); rgb(45pt)=(0.2754,0.3693,0.984); rgb(46pt)=(0.2741,0.3748,0.9862); rgb(47pt)=(0.2726,0.3804,0.9881); rgb(48pt)=(0.271,0.386,0.9898); rgb(49pt)=(0.2691,0.3916,0.9912); rgb(50pt)=(0.267,0.3973,0.9924); rgb(51pt)=(0.2647,0.403,0.9935); rgb(52pt)=(0.2621,0.4088,0.9946); rgb(53pt)=(0.2591,0.4145,0.9955); rgb(54pt)=(0.2556,0.4203,0.9965); rgb(55pt)=(0.2517,0.4261,0.9974); rgb(56pt)=(0.2473,0.4319,0.9983); rgb(57pt)=(0.2424,0.4378,0.9991); rgb(58pt)=(0.2369,0.4437,0.9996); rgb(59pt)=(0.2311,0.4497,0.9995); rgb(60pt)=(0.225,0.4559,0.9985); rgb(61pt)=(0.2189,0.462,0.9968); rgb(62pt)=(0.2128,0.4682,0.9948); rgb(63pt)=(0.2066,0.4743,0.9926); rgb(64pt)=(0.2006,0.4803,0.9906); rgb(65pt)=(0.195,0.4861,0.9887); rgb(66pt)=(0.1903,0.4919,0.9867); rgb(67pt)=(0.1869,0.4975,0.9844); rgb(68pt)=(0.1847,0.503,0.9819); rgb(69pt)=(0.1831,0.5084,0.9793); rgb(70pt)=(0.1818,0.5138,0.9766); rgb(71pt)=(0.1806,0.5191,0.9738); rgb(72pt)=(0.1795,0.5244,0.9709); rgb(73pt)=(0.1785,0.5296,0.9677); rgb(74pt)=(0.1778,0.5349,0.9641); rgb(75pt)=(0.1773,0.5401,0.9602); rgb(76pt)=(0.1768,0.5452,0.956); rgb(77pt)=(0.1764,0.5504,0.9516); rgb(78pt)=(0.1755,0.5554,0.9473); rgb(79pt)=(0.174,0.5605,0.9432); rgb(80pt)=(0.1716,0.5655,0.9393); rgb(81pt)=(0.1686,0.5705,0.9357); rgb(82pt)=(0.1649,0.5755,0.9323); rgb(83pt)=(0.161,0.5805,0.9289); rgb(84pt)=(0.1573,0.5854,0.9254); rgb(85pt)=(0.154,0.5902,0.9218); rgb(86pt)=(0.1513,0.595,0.9182); rgb(87pt)=(0.1492,0.5997,0.9147); rgb(88pt)=(0.1475,0.6043,0.9113); rgb(89pt)=(0.1461,0.6089,0.908); rgb(90pt)=(0.1446,0.6135,0.905); rgb(91pt)=(0.1429,0.618,0.9022); rgb(92pt)=(0.1408,0.6226,0.8998); rgb(93pt)=(0.1383,0.6272,0.8975); rgb(94pt)=(0.1354,0.6317,0.8953); rgb(95pt)=(0.1321,0.6363,0.8932); rgb(96pt)=(0.1288,0.6408,0.891); rgb(97pt)=(0.1253,0.6453,0.8887); rgb(98pt)=(0.1219,0.6497,0.8862); rgb(99pt)=(0.1185,0.6541,0.8834); rgb(100pt)=(0.1152,0.6584,0.8804); rgb(101pt)=(0.1119,0.6627,0.877); rgb(102pt)=(0.1085,0.6669,0.8734); rgb(103pt)=(0.1048,0.671,0.8695); rgb(104pt)=(0.1009,0.675,0.8653); rgb(105pt)=(0.0964,0.6789,0.8609); rgb(106pt)=(0.0914,0.6828,0.8562); rgb(107pt)=(0.0855,0.6865,0.8513); rgb(108pt)=(0.0789,0.6902,0.8462); rgb(109pt)=(0.0713,0.6938,0.8409); rgb(110pt)=(0.0628,0.6972,0.8355); rgb(111pt)=(0.0535,0.7006,0.8299); rgb(112pt)=(0.0433,0.7039,0.8242); rgb(113pt)=(0.0328,0.7071,0.8183); rgb(114pt)=(0.0234,0.7103,0.8124); rgb(115pt)=(0.0155,0.7133,0.8064); rgb(116pt)=(0.0091,0.7163,0.8003); rgb(117pt)=(0.0046,0.7192,0.7941); rgb(118pt)=(0.0019,0.722,0.7878); rgb(119pt)=(0.0009,0.7248,0.7815); rgb(120pt)=(0.0018,0.7275,0.7752); rgb(121pt)=(0.0046,0.7301,0.7688); rgb(122pt)=(0.0094,0.7327,0.7623); rgb(123pt)=(0.0162,0.7352,0.7558); rgb(124pt)=(0.0253,0.7376,0.7492); rgb(125pt)=(0.0369,0.74,0.7426); rgb(126pt)=(0.0504,0.7423,0.7359); rgb(127pt)=(0.0638,0.7446,0.7292); rgb(128pt)=(0.077,0.7468,0.7224); rgb(129pt)=(0.0899,0.7489,0.7156); rgb(130pt)=(0.1023,0.751,0.7088); rgb(131pt)=(0.1141,0.7531,0.7019); rgb(132pt)=(0.1252,0.7552,0.695); rgb(133pt)=(0.1354,0.7572,0.6881); rgb(134pt)=(0.1448,0.7593,0.6812); rgb(135pt)=(0.1532,0.7614,0.6741); rgb(136pt)=(0.1609,0.7635,0.6671); rgb(137pt)=(0.1678,0.7656,0.6599); rgb(138pt)=(0.1741,0.7678,0.6527); rgb(139pt)=(0.1799,0.7699,0.6454); rgb(140pt)=(0.1853,0.7721,0.6379); rgb(141pt)=(0.1905,0.7743,0.6303); rgb(142pt)=(0.1954,0.7765,0.6225); rgb(143pt)=(0.2003,0.7787,0.6146); rgb(144pt)=(0.2061,0.7808,0.6065); rgb(145pt)=(0.2118,0.7828,0.5983); rgb(146pt)=(0.2178,0.7849,0.5899); rgb(147pt)=(0.2244,0.7869,0.5813); rgb(148pt)=(0.2318,0.7887,0.5725); rgb(149pt)=(0.2401,0.7905,0.5636); rgb(150pt)=(0.2491,0.7922,0.5546); rgb(151pt)=(0.2589,0.7937,0.5454); rgb(152pt)=(0.2695,0.7951,0.536); rgb(153pt)=(0.2809,0.7964,0.5266); rgb(154pt)=(0.2929,0.7975,0.517); rgb(155pt)=(0.3052,0.7985,0.5074); rgb(156pt)=(0.3176,0.7994,0.4975); rgb(157pt)=(0.3301,0.8002,0.4876); rgb(158pt)=(0.3424,0.8009,0.4774); rgb(159pt)=(0.3548,0.8016,0.4669); rgb(160pt)=(0.3671,0.8021,0.4563); rgb(161pt)=(0.3795,0.8026,0.4454); rgb(162pt)=(0.3921,0.8029,0.4344); rgb(163pt)=(0.405,0.8031,0.4233); rgb(164pt)=(0.4184,0.803,0.4122); rgb(165pt)=(0.4322,0.8028,0.4013); rgb(166pt)=(0.4463,0.8024,0.3904); rgb(167pt)=(0.4608,0.8018,0.3797); rgb(168pt)=(0.4753,0.8011,0.3691); rgb(169pt)=(0.4899,0.8002,0.3586); rgb(170pt)=(0.5044,0.7993,0.348); rgb(171pt)=(0.5187,0.7982,0.3374); rgb(172pt)=(0.5329,0.797,0.3267); rgb(173pt)=(0.547,0.7957,0.3159); rgb(175pt)=(0.5748,0.7929,0.2941); rgb(176pt)=(0.5886,0.7913,0.2833); rgb(177pt)=(0.6024,0.7896,0.2726); rgb(178pt)=(0.6161,0.7878,0.2622); rgb(179pt)=(0.6297,0.7859,0.2521); rgb(180pt)=(0.6433,0.7839,0.2423); rgb(181pt)=(0.6567,0.7818,0.2329); rgb(182pt)=(0.6701,0.7796,0.2239); rgb(183pt)=(0.6833,0.7773,0.2155); rgb(184pt)=(0.6963,0.775,0.2075); rgb(185pt)=(0.7091,0.7727,0.1998); rgb(186pt)=(0.7218,0.7703,0.1924); rgb(187pt)=(0.7344,0.7679,0.1852); rgb(188pt)=(0.7468,0.7654,0.1782); rgb(189pt)=(0.759,0.7629,0.1717); rgb(190pt)=(0.771,0.7604,0.1658); rgb(191pt)=(0.7829,0.7579,0.1608); rgb(192pt)=(0.7945,0.7554,0.157); rgb(193pt)=(0.806,0.7529,0.1546); rgb(194pt)=(0.8172,0.7505,0.1535); rgb(195pt)=(0.8281,0.7481,0.1536); rgb(196pt)=(0.8389,0.7457,0.1546); rgb(197pt)=(0.8495,0.7435,0.1564); rgb(198pt)=(0.86,0.7413,0.1587); rgb(199pt)=(0.8703,0.7392,0.1615); rgb(200pt)=(0.8804,0.7372,0.165); rgb(201pt)=(0.8903,0.7353,0.1695); rgb(202pt)=(0.9,0.7336,0.1749); rgb(203pt)=(0.9093,0.7321,0.1815); rgb(204pt)=(0.9184,0.7308,0.189); rgb(205pt)=(0.9272,0.7298,0.1973); rgb(206pt)=(0.9357,0.729,0.2061); rgb(207pt)=(0.944,0.7285,0.2151); rgb(208pt)=(0.9523,0.7284,0.2237); rgb(209pt)=(0.9606,0.7285,0.2312); rgb(210pt)=(0.9689,0.7292,0.2373); rgb(211pt)=(0.977,0.7304,0.2418); rgb(212pt)=(0.9842,0.733,0.2446); rgb(213pt)=(0.99,0.7365,0.2429); rgb(214pt)=(0.9946,0.7407,0.2394); rgb(215pt)=(0.9966,0.7458,0.2351); rgb(216pt)=(0.9971,0.7513,0.2309); rgb(217pt)=(0.9972,0.7569,0.2267); rgb(218pt)=(0.9971,0.7626,0.2224); rgb(219pt)=(0.9969,0.7683,0.2181); rgb(220pt)=(0.9966,0.774,0.2138); rgb(221pt)=(0.9962,0.7798,0.2095); rgb(222pt)=(0.9957,0.7856,0.2053); rgb(223pt)=(0.9949,0.7915,0.2012); rgb(224pt)=(0.9938,0.7974,0.1974); rgb(225pt)=(0.9923,0.8034,0.1939); rgb(226pt)=(0.9906,0.8095,0.1906); rgb(227pt)=(0.9885,0.8156,0.1875); rgb(228pt)=(0.9861,0.8218,0.1846); rgb(229pt)=(0.9835,0.828,0.1817); rgb(230pt)=(0.9807,0.8342,0.1787); rgb(231pt)=(0.9778,0.8404,0.1757); rgb(232pt)=(0.9748,0.8467,0.1726); rgb(233pt)=(0.972,0.8529,0.1695); rgb(234pt)=(0.9694,0.8591,0.1665); rgb(235pt)=(0.9671,0.8654,0.1636); rgb(236pt)=(0.9651,0.8716,0.1608); rgb(237pt)=(0.9634,0.8778,0.1582); rgb(238pt)=(0.9619,0.884,0.1557); rgb(239pt)=(0.9608,0.8902,0.1532); rgb(240pt)=(0.9601,0.8963,0.1507); rgb(241pt)=(0.9596,0.9023,0.148); rgb(242pt)=(0.9595,0.9084,0.145); rgb(243pt)=(0.9597,0.9143,0.1418); rgb(244pt)=(0.9601,0.9203,0.1382); rgb(245pt)=(0.9608,0.9262,0.1344); rgb(246pt)=(0.9618,0.932,0.1304); rgb(247pt)=(0.9629,0.9379,0.1261); rgb(248pt)=(0.9642,0.9437,0.1216); rgb(249pt)=(0.9657,0.9494,0.1168); rgb(250pt)=(0.9674,0.9552,0.1116); rgb(251pt)=(0.9692,0.9609,0.1061); rgb(252pt)=(0.9711,0.9667,0.1001); rgb(253pt)=(0.973,0.9724,0.0938); rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805), mesh/rows=91]
table[row sep=crcr, point meta=c]

x	y	c

-90	1	40.0112681205615

-90	5	40.2267961502458

-90	10	39.7999815382949

-90	50	39.2125660111337

-90	100	39.1422443767582

-90	150	39.7607133807726

-90	200	39.0040040987966

-90	250	38.5070552692723

-90	400	39.2919721086533

-90	500	39.3515394245885

-90	1000	39.5423308938729

-90	2000	39.4574387035272

-88	1	0.548260039977393

-88	5	14.6591090489271

-88	10	32.0746051012122

-88	50	39.4231918659769

-88	100	40.086259015402

-88	150	38.6666739026744

-88	200	40.1119656541755

-88	250	39.8320127457574

-88	400	40.5068444072123

-88	500	40.3962132621703

-88	1000	38.3228481983191

-88	2000	40.9268630441441

-86	1	0.147762047787846

-86	5	0.682305406030392

-86	10	1.27745057366931

-86	50	33.4167006666802

-86	100	38.3909160459005

-86	150	38.992428752326

-86	200	39.2110117943245

-86	250	40.398268852491

-86	400	39.5844128920911

-86	500	40.1519412066841

-86	1000	39.4332432774239

-86	2000	39.5725992075691

-84	1	0.072744930650287

-84	5	0.292982387703354

-84	10	0.591368024651295

-84	50	16.1978639200346

-84	100	33.0203675241894

-84	150	37.6572248086114

-84	200	38.3560795795313

-84	250	39.6080258203639

-84	400	38.6573768332021

-84	500	38.9006836813853

-84	1000	40.0818008753405

-84	2000	39.9186587190121

-82	1	0.0455181893315704

-82	5	0.17881122124075

-82	10	0.358319213025017

-82	50	1.99165615953552

-82	100	21.590922980006

-82	150	31.5613327800415

-82	200	35.3997818199851

-82	250	36.8907913491822

-82	400	39.3134714961366

-82	500	38.5837697692713

-82	1000	38.6482590002325

-82	2000	38.7802923509025

-80	1	0.0344803165392929

-80	5	0.122978157020556

-80	10	0.232635080647571

-80	50	1.09949419483621

-80	100	7.61198031981105

-80	150	19.1809384853809

-80	200	29.1344438325828

-80	250	31.2828429284563

-80	400	35.1029595546634

-80	500	37.4415468381477

-80	1000	37.5142949931749

-80	2000	38.6911062332968

-78	1	0.0329577951308233

-78	5	0.0950726876745109

-78	10	0.164360665451672

-78	50	0.819339198564186

-78	100	1.58301619039709

-78	150	8.17188461281712

-78	200	19.8772007087205

-78	250	24.6648310326994

-78	400	35.2972971643942

-78	500	35.4709363957422

-78	1000	38.5943236208874

-78	2000	39.1864693499638

-76	1	0.0329577951308233

-76	5	0.0788236721523769

-76	10	0.137159265104936

-76	50	0.631384980764391

-76	100	1.22543905770965

-76	150	3.49779143780775

-76	200	10.3817775623626

-76	250	18.5365519318224

-76	400	30.7676736218081

-76	500	33.2166935370693

-76	1000	38.2291436985428

-76	2000	38.4590939753088

-74	1	0.0329577951308233

-74	5	0.0702363394924012

-74	10	0.123119083225127

-74	50	0.556057706951754

-74	100	1.1144566015429

-74	150	1.6179407035287

-74	200	6.37677830774491

-74	250	15.8877891158051

-74	400	29.4877039354332

-74	500	33.0964631280935

-74	1000	38.3159992676699

-74	2000	39.0794660871668

-72	1	0.076140969657274

-72	5	0.304718736959505

-72	10	0.62174827414663

-72	50	17.9406941545631

-72	100	33.0764911390725

-72	150	35.9232741203294

-72	200	39.1225890803979

-72	250	38.4955952149195

-72	400	38.8737989276106

-72	500	39.4979553178408

-72	1000	39.9773429595803

-72	2000	39.862774006429

-70	1	0.0329577951308233

-70	5	0.0900716741564089

-70	10	0.172218937106014

-70	50	0.809092529356351

-70	100	2.80054065629495

-70	150	9.31081380167799

-70	200	18.3543119935356

-70	250	26.2508447284421

-70	400	35.5951683429624

-70	500	36.2846821116465

-70	1000	38.5981081310814

-70	2000	38.9092618433192

-68	1	0.0362229677299812

-68	5	0.137002802450111

-68	10	0.265473278947747

-68	50	1.32435793159524

-68	100	11.5726751352728

-68	150	25.162698516864

-68	200	30.8198961620035

-68	250	34.2750121370077

-68	400	37.8392226564296

-68	500	37.9896828221538

-68	1000	39.1973480019352

-68	2000	39.6233087116217

-66	1	0.0329577951308233

-66	5	0.0716737514123246

-66	10	0.126719182191995

-66	50	0.569949586628029

-66	100	1.13776844273034

-66	150	2.72787260924081

-66	200	6.31735393104031

-66	250	14.9728385956399

-66	400	29.3207837345903

-66	500	33.6369654406624

-66	1000	36.7891884333139

-66	2000	39.364165187477

-64	1	0.0332678741977636

-64	5	0.0897010632484486

-64	10	0.154304962729375

-64	50	0.725713335121564

-64	100	1.67718646607863

-64	150	7.34532596487817

-64	200	15.9591282591209

-64	250	22.4775785364659

-64	400	32.2363147322985

-64	500	36.5591078077558

-64	1000	38.6899511606366

-64	2000	39.5043011695929

-62	1	0.0565118014015359

-62	5	0.222967500962221

-62	10	0.458761220221722

-62	50	6.69892015043732

-62	100	27.9309854109758

-62	150	34.0438431761466

-62	200	37.0587815877548

-62	250	37.6137674080229

-62	400	39.07705868209

-62	500	38.8198512813762

-62	1000	40.4677498169291

-62	2000	38.4937240161647

-60	1	0.0450647886106091

-60	5	0.184567887894385

-60	10	0.363925467031574

-60	50	2.00648991346913

-60	100	23.0743227475306

-60	150	31.192886581775

-60	200	36.3059376535013

-60	250	37.959386733743

-60	400	38.3590579831779

-60	500	39.2272329904364

-60	1000	39.1124001230222

-60	2000	39.6830052345707

-58	1	0.0329577951308233

-58	5	0.0818819104585983

-58	10	0.139200206507312

-58	50	0.660238056999459

-58	100	1.29887309551585

-58	150	3.11105104020062

-58	200	12.4915957505565

-58	250	19.1358847339267

-58	400	31.7866392688334

-58	500	34.2329304692169

-58	1000	38.0750807473104

-58	2000	40.4812756201401

-56	1	0.0329577951308233

-56	5	0.0738222029463746

-56	10	0.128907802412863

-56	50	0.574336353768722

-56	100	1.10978682853021

-56	150	2.40265537596363

-56	200	8.9905717656186

-56	250	15.3036001003445

-56	400	30.2913007316168

-56	500	33.5336449272989

-56	1000	36.5121372204493

-56	2000	39.0163787708466

-54	1	0.0338795194939956

-54	5	0.106853668562845

-54	10	0.196883992455807

-54	50	0.941321802210565

-54	100	2.78409294281557

-54	150	15.8405970070293

-54	200	26.7879053731688

-54	250	30.3141035652971

-54	400	34.8765661606938

-54	500	37.1817541205881

-54	1000	39.2455793508008

-54	2000	39.6563762563657

-52	1	0.0329577951308233

-52	5	0.0686327230463077

-52	10	0.121080319820971

-52	50	0.546755188159749

-52	100	1.11917151686428

-52	150	1.60846460597423

-52	200	7.30831262632943

-52	250	15.4876489686424

-52	400	29.6907511654669

-52	500	30.8213458711148

-52	1000	38.0172012070071

-52	2000	39.4954069859325

-50	1	0.0335750896855262

-50	5	0.110409629693976

-50	10	0.201630422070114

-50	50	0.99287013996924

-50	100	4.156072202867

-50	150	17.6332925001057

-50	200	26.4447201944934

-50	250	31.0201407788824

-50	400	35.8472716270432

-50	500	38.3824019106439

-50	1000	39.6408977626781

-50	2000	39.5783854564089

-48	1	0.0583942426331972

-48	5	0.233567915800919

-48	10	0.441202655680376

-48	50	7.28599205342963

-48	100	29.6571533957086

-48	150	34.7456150995924

-48	200	38.0773633345908

-48	250	39.2634015550439

-48	400	38.0751234684994

-48	500	38.6192812149797

-48	1000	39.4685676689985

-48	2000	39.9436154368202

-46	1	0.0329577951308233

-46	5	0.0690106730715331

-46	10	0.119100545644806

-46	50	0.556792537428158

-46	100	1.13332661622139

-46	150	1.78289597095312

-46	200	5.45259157532305

-46	250	15.0333210368289

-46	400	29.2050089028784

-46	500	32.431278548294

-46	1000	36.5208675441116

-46	2000	38.9356717049

-44	1	0.157640327955083

-44	5	0.738300850300303

-44	10	1.42768632316114

-44	50	35.6054289129975

-44	100	37.4119050837466

-44	150	38.5869656996429

-44	200	39.0619053902061

-44	250	39.7418767950996

-44	400	39.3830522949481

-44	500	40.4397128259037

-44	1000	39.7562159890195

-44	2000	39.3170829669351

-42	1	0.0392172222684014

-42	5	0.150670420551946

-42	10	0.289719826930067

-42	50	1.36473155555135

-42	100	13.9003282714443

-42	150	27.3464973778966

-42	200	32.2057788966865

-42	250	34.8038044776907

-42	400	36.5912323055286

-42	500	38.9413501382265

-42	1000	38.8931096878522

-42	2000	39.1162727580415

-40	1	0.0329577951308233

-40	5	0.0996106737712425

-40	10	0.177483039395402

-40	50	0.839462015131366

-40	100	1.64396447984646

-40	150	10.2449186262033

-40	200	20.6163174777171

-40	250	26.6067026781218

-40	400	35.4605387287197

-40	500	36.9427541182415

-40	1000	39.1387592345784

-40	2000	40.5328883487674

-38	1	0.0410089853412581

-38	5	0.15290718816177

-38	10	0.291426147073112

-38	50	1.4386701875879

-38	100	16.2496012934379

-38	150	28.7932599296126

-38	200	33.7464429401991

-38	250	35.3561137988545

-38	400	38.1286351224531

-38	500	38.6615404670575

-38	1000	40.126418531679

-38	2000	38.936290218165

-36	1	0.0329577951308233

-36	5	0.0598911245318795

-36	10	0.102849617636376

-36	50	0.446194420527593

-36	100	0.90280749730553

-36	150	1.34882708937831

-36	200	2.38289472905153

-36	250	6.41845841018558

-36	400	23.8152191063217

-36	500	27.5068421125331

-36	1000	37.2266158128093

-36	2000	38.4887505538968

-34	1	0.0329577951308233

-34	5	0.096702672910293

-34	10	0.166027790156264

-34	50	0.815807708266458

-34	100	1.57480293275612

-34	150	10.1400314319027

-34	200	19.9135318417179

-34	250	26.3660248907474

-34	400	35.5467452630637

-34	500	36.1513850387849

-34	1000	38.5197342250001

-34	2000	39.9286881362373

-32	1	0.0329577951308233

-32	5	0.0638732451638618

-32	10	0.110795403888942

-32	50	0.468236047080399

-32	100	0.922492063524791

-32	150	1.42612533511799

-32	200	3.37673294926896

-32	250	8.13741576176687

-32	400	23.8739569498133

-32	500	29.670952551177

-32	1000	36.7574765965631

-32	2000	39.3399317970057

-30	1	38.8802286768917

-30	5	40.3163094255646

-30	10	39.0045984508714

-30	50	40.1229146124547

-30	100	39.343060349617

-30	150	40.1604856558597

-30	200	40.1443106871871

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66	200	5.95359251110578

66	250	13.7063528459123

66	400	28.8484994855317

66	500	32.2706645487175

66	1000	38.9198592035642

66	2000	40.0373979823236

68	1	0.0362229677299812

68	5	0.140899462109929

68	10	0.275859749450217

68	50	1.33572980968183

68	100	12.3053548645846

68	150	26.0009242063529

68	200	31.3894812677568

68	250	34.1222828484801

68	400	36.8246314283671

68	500	39.0788070888811

68	1000	38.7865534388633

68	2000	39.2529301064943

70	1	0.0329577951308233

70	5	0.0937093468075155

70	10	0.165908183637733

70	50	0.831546189485389

70	100	1.61769501896549

70	150	9.32677846192799

70	200	20.0316944574302

70	250	26.1128122375765

70	400	35.169857352244

70	500	35.7628684856097

70	1000	38.6828983501487

70	2000	38.9851684251264

72	1	0.0753366098197792

72	5	0.307341675081325

72	10	0.610053097042019

72	50	16.8061487822648

72	100	33.676106575173

72	150	37.0448774915164

72	200	38.9086739533646

72	250	38.6373775019131

72	400	38.9020917924343

72	500	39.3036288270285

72	1000	38.4907580843732

72	2000	38.7603431285686

74	1	0.0329577951308233

74	5	0.0662061647734551

74	10	0.125334164702242

74	50	0.575559450228995

74	100	1.14552857755081

74	150	3.06122137479971

74	200	5.52929732153224

74	250	15.1589026940371

74	400	27.6182496328753

74	500	32.6737455243366

74	1000	37.5372565170408

74	2000	38.5607866015609

76	1	0.0329577951308233

76	5	0.0748352182982022

76	10	0.136906175551286

76	50	0.628135046803748

76	100	1.18462650607081

76	150	2.88219444052273

76	200	8.76010865922213

76	250	18.4166694913642

76	400	31.1863349014333

76	500	35.1602293969074

76	1000	37.4776873828288

76	2000	39.2784569990866

78	1	0.0329577951308233

78	5	0.0930741296850003

78	10	0.162749367791911

78	50	0.821758117413874

78	100	1.86044831751429

78	150	8.66123567014117

78	200	19.3175035585628

78	250	25.8036813226864

78	400	33.6841372331791

78	500	36.5068437163274

78	1000	38.1499733342463

78	2000	39.8222517901077

80	1	0.0341812380538934

80	5	0.11828161299581

80	10	0.22444438990606

80	50	1.12384899113094

80	100	7.18118837625529

80	150	20.195459468323

80	200	27.5767445851287

80	250	31.724558710353

80	400	36.3330621727223

80	500	37.9194597024488

80	1000	38.8607800413415

80	2000	40.5086190889832

82	1	0.0464117047202137

82	5	0.181969582101991

82	10	0.333886680595375

82	50	1.88435789087688

82	100	22.404150987119

82	150	31.5633347488775

82	200	35.3786145107298

82	250	35.5700969784565

82	400	38.6209058383737

82	500	38.0314256309712

82	1000	39.1437221414516

82	2000	38.926147451786

84	1	0.0743887367838939

84	5	0.292828147817842

84	10	0.594116489359209

84	50	18.3743891209877

84	100	34.039737689098

84	150	36.6882896620411

84	200	37.5022744423547

84	250	38.8399063798324

84	400	39.1915522074305

84	500	39.2109520606911

84	1000	38.4949106305146

84	2000	40.4220950788641

86	1	0.139414767279155

86	5	0.672148042805871

86	10	1.35387049789843

86	50	35.2371988446183

86	100	38.148327881176

86	150	38.2815785655739

86	200	38.650535880379

86	250	38.0187577726088

86	400	39.8067449424786

86	500	39.8046286700561

86	1000	39.4975877949186

86	2000	39.921423416008

88	1	0.542955271734397

88	5	12.2271557951253

88	10	32.9479193309578

88	50	38.9428756747686

88	100	39.0183406897801

88	150	39.7405365317631

88	200	39.2014465664972

88	250	40.7409232114578

88	400	39.4800592341353

88	500	39.4483702646739

88	1000	39.3690341866395

88	2000	39.3014347129666

90	1	39.35326316275

90	5	39.2791117277447

90	10	39.5321881735709

90	50	39.4179685580207

90	100	38.0285775051165

90	150	39.6762703332448

90	200	38.7099326326667

90	250	38.9525448636934

90	400	37.9603741625058

90	500	40.5901841498982

90	1000	38.4848456043996

90	2000	38.5204054935508

RMSE in estimated angle in degrees vs distance of Eve from Bob and various AoA of Eve.

§.§.§ Impact of the Attacks on the Classifier

The OC-SVM classifier was trained on 1,000 AoA samples from Alice, considering a distance between Alice and Bob equal to 10 meters. The test set consisted of 200,000 samples evenly split between Alice and Eve, comprising 100,000 legitimate signals and 100,000 attack signals. The reported results are averaged over 100 randomly selected training and test sets. Fig. <ref> compares the accuracy achieved by the OC-SVM under both code-based and location-based attacks.

width=7 cm,
height=4 cm,
scale only axis,
point meta min=0.45,
point meta max=1,
xlabel style=font=,
xlabel=Angle of Eve in degrees,
ylabel style=font=,
ylabel=Distance of Eve in metres,
axis background/.style=fill=white,
axis x line*=bottom,
axis y line*=left,
colormap=mymap[1pt] rgb(0pt)=(0.2422,0.1504,0.6603); rgb(1pt)=(0.2444,0.1534,0.6728); rgb(2pt)=(0.2464,0.1569,0.6847); rgb(3pt)=(0.2484,0.1607,0.6961); rgb(4pt)=(0.2503,0.1648,0.7071); rgb(5pt)=(0.2522,0.1689,0.7179); rgb(6pt)=(0.254,0.1732,0.7286); rgb(7pt)=(0.2558,0.1773,0.7393); rgb(8pt)=(0.2576,0.1814,0.7501); rgb(9pt)=(0.2594,0.1854,0.761); rgb(11pt)=(0.2628,0.1932,0.7828); rgb(12pt)=(0.2645,0.1972,0.7937); rgb(13pt)=(0.2661,0.2011,0.8043); rgb(14pt)=(0.2676,0.2052,0.8148); rgb(15pt)=(0.2691,0.2094,0.8249); rgb(16pt)=(0.2704,0.2138,0.8346); rgb(17pt)=(0.2717,0.2184,0.8439); rgb(18pt)=(0.2729,0.2231,0.8528); rgb(19pt)=(0.274,0.228,0.8612); rgb(20pt)=(0.2749,0.233,0.8692); rgb(21pt)=(0.2758,0.2382,0.8767); rgb(22pt)=(0.2766,0.2435,0.884); rgb(23pt)=(0.2774,0.2489,0.8908); rgb(24pt)=(0.2781,0.2543,0.8973); rgb(25pt)=(0.2788,0.2598,0.9035); rgb(26pt)=(0.2794,0.2653,0.9094); rgb(27pt)=(0.2798,0.2708,0.915); rgb(28pt)=(0.2802,0.2764,0.9204); rgb(29pt)=(0.2806,0.2819,0.9255); rgb(30pt)=(0.2809,0.2875,0.9305); rgb(31pt)=(0.2811,0.293,0.9352); rgb(32pt)=(0.2813,0.2985,0.9397); rgb(33pt)=(0.2814,0.304,0.9441); rgb(34pt)=(0.2814,0.3095,0.9483); rgb(35pt)=(0.2813,0.315,0.9524); rgb(36pt)=(0.2811,0.3204,0.9563); rgb(37pt)=(0.2809,0.3259,0.96); rgb(38pt)=(0.2807,0.3313,0.9636); rgb(39pt)=(0.2803,0.3367,0.967); rgb(40pt)=(0.2798,0.3421,0.9702); rgb(41pt)=(0.2791,0.3475,0.9733); rgb(42pt)=(0.2784,0.3529,0.9763); rgb(43pt)=(0.2776,0.3583,0.9791); rgb(44pt)=(0.2766,0.3638,0.9817); rgb(45pt)=(0.2754,0.3693,0.984); rgb(46pt)=(0.2741,0.3748,0.9862); rgb(47pt)=(0.2726,0.3804,0.9881); rgb(48pt)=(0.271,0.386,0.9898); rgb(49pt)=(0.2691,0.3916,0.9912); rgb(50pt)=(0.267,0.3973,0.9924); rgb(51pt)=(0.2647,0.403,0.9935); rgb(52pt)=(0.2621,0.4088,0.9946); rgb(53pt)=(0.2591,0.4145,0.9955); rgb(54pt)=(0.2556,0.4203,0.9965); rgb(55pt)=(0.2517,0.4261,0.9974); rgb(56pt)=(0.2473,0.4319,0.9983); rgb(57pt)=(0.2424,0.4378,0.9991); rgb(58pt)=(0.2369,0.4437,0.9996); rgb(59pt)=(0.2311,0.4497,0.9995); rgb(60pt)=(0.225,0.4559,0.9985); rgb(61pt)=(0.2189,0.462,0.9968); rgb(62pt)=(0.2128,0.4682,0.9948); rgb(63pt)=(0.2066,0.4743,0.9926); rgb(64pt)=(0.2006,0.4803,0.9906); rgb(65pt)=(0.195,0.4861,0.9887); rgb(66pt)=(0.1903,0.4919,0.9867); rgb(67pt)=(0.1869,0.4975,0.9844); rgb(68pt)=(0.1847,0.503,0.9819); rgb(69pt)=(0.1831,0.5084,0.9793); rgb(70pt)=(0.1818,0.5138,0.9766); rgb(71pt)=(0.1806,0.5191,0.9738); rgb(72pt)=(0.1795,0.5244,0.9709); rgb(73pt)=(0.1785,0.5296,0.9677); rgb(74pt)=(0.1778,0.5349,0.9641); rgb(75pt)=(0.1773,0.5401,0.9602); rgb(76pt)=(0.1768,0.5452,0.956); rgb(77pt)=(0.1764,0.5504,0.9516); rgb(78pt)=(0.1755,0.5554,0.9473); rgb(79pt)=(0.174,0.5605,0.9432); rgb(80pt)=(0.1716,0.5655,0.9393); rgb(81pt)=(0.1686,0.5705,0.9357); rgb(82pt)=(0.1649,0.5755,0.9323); rgb(83pt)=(0.161,0.5805,0.9289); rgb(84pt)=(0.1573,0.5854,0.9254); rgb(85pt)=(0.154,0.5902,0.9218); rgb(86pt)=(0.1513,0.595,0.9182); rgb(87pt)=(0.1492,0.5997,0.9147); rgb(88pt)=(0.1475,0.6043,0.9113); rgb(89pt)=(0.1461,0.6089,0.908); rgb(90pt)=(0.1446,0.6135,0.905); rgb(91pt)=(0.1429,0.618,0.9022); rgb(92pt)=(0.1408,0.6226,0.8998); rgb(93pt)=(0.1383,0.6272,0.8975); rgb(94pt)=(0.1354,0.6317,0.8953); rgb(95pt)=(0.1321,0.6363,0.8932); rgb(96pt)=(0.1288,0.6408,0.891); rgb(97pt)=(0.1253,0.6453,0.8887); rgb(98pt)=(0.1219,0.6497,0.8862); rgb(99pt)=(0.1185,0.6541,0.8834); rgb(100pt)=(0.1152,0.6584,0.8804); rgb(101pt)=(0.1119,0.6627,0.877); rgb(102pt)=(0.1085,0.6669,0.8734); rgb(103pt)=(0.1048,0.671,0.8695); rgb(104pt)=(0.1009,0.675,0.8653); rgb(105pt)=(0.0964,0.6789,0.8609); rgb(106pt)=(0.0914,0.6828,0.8562); rgb(107pt)=(0.0855,0.6865,0.8513); rgb(108pt)=(0.0789,0.6902,0.8462); rgb(109pt)=(0.0713,0.6938,0.8409); rgb(110pt)=(0.0628,0.6972,0.8355); rgb(111pt)=(0.0535,0.7006,0.8299); rgb(112pt)=(0.0433,0.7039,0.8242); rgb(113pt)=(0.0328,0.7071,0.8183); rgb(114pt)=(0.0234,0.7103,0.8124); rgb(115pt)=(0.0155,0.7133,0.8064); rgb(116pt)=(0.0091,0.7163,0.8003); rgb(117pt)=(0.0046,0.7192,0.7941); rgb(118pt)=(0.0019,0.722,0.7878); rgb(119pt)=(0.0009,0.7248,0.7815); rgb(120pt)=(0.0018,0.7275,0.7752); rgb(121pt)=(0.0046,0.7301,0.7688); rgb(122pt)=(0.0094,0.7327,0.7623); rgb(123pt)=(0.0162,0.7352,0.7558); rgb(124pt)=(0.0253,0.7376,0.7492); rgb(125pt)=(0.0369,0.74,0.7426); rgb(126pt)=(0.0504,0.7423,0.7359); rgb(127pt)=(0.0638,0.7446,0.7292); rgb(128pt)=(0.077,0.7468,0.7224); rgb(129pt)=(0.0899,0.7489,0.7156); rgb(130pt)=(0.1023,0.751,0.7088); rgb(131pt)=(0.1141,0.7531,0.7019); rgb(132pt)=(0.1252,0.7552,0.695); rgb(133pt)=(0.1354,0.7572,0.6881); rgb(134pt)=(0.1448,0.7593,0.6812); rgb(135pt)=(0.1532,0.7614,0.6741); rgb(136pt)=(0.1609,0.7635,0.6671); rgb(137pt)=(0.1678,0.7656,0.6599); rgb(138pt)=(0.1741,0.7678,0.6527); rgb(139pt)=(0.1799,0.7699,0.6454); rgb(140pt)=(0.1853,0.7721,0.6379); rgb(141pt)=(0.1905,0.7743,0.6303); rgb(142pt)=(0.1954,0.7765,0.6225); rgb(143pt)=(0.2003,0.7787,0.6146); rgb(144pt)=(0.2061,0.7808,0.6065); rgb(145pt)=(0.2118,0.7828,0.5983); rgb(146pt)=(0.2178,0.7849,0.5899); rgb(147pt)=(0.2244,0.7869,0.5813); rgb(148pt)=(0.2318,0.7887,0.5725); rgb(149pt)=(0.2401,0.7905,0.5636); rgb(150pt)=(0.2491,0.7922,0.5546); rgb(151pt)=(0.2589,0.7937,0.5454); rgb(152pt)=(0.2695,0.7951,0.536); rgb(153pt)=(0.2809,0.7964,0.5266); rgb(154pt)=(0.2929,0.7975,0.517); rgb(155pt)=(0.3052,0.7985,0.5074); rgb(156pt)=(0.3176,0.7994,0.4975); rgb(157pt)=(0.3301,0.8002,0.4876); rgb(158pt)=(0.3424,0.8009,0.4774); rgb(159pt)=(0.3548,0.8016,0.4669); rgb(160pt)=(0.3671,0.8021,0.4563); rgb(161pt)=(0.3795,0.8026,0.4454); rgb(162pt)=(0.3921,0.8029,0.4344); rgb(163pt)=(0.405,0.8031,0.4233); rgb(164pt)=(0.4184,0.803,0.4122); rgb(165pt)=(0.4322,0.8028,0.4013); rgb(166pt)=(0.4463,0.8024,0.3904); rgb(167pt)=(0.4608,0.8018,0.3797); rgb(168pt)=(0.4753,0.8011,0.3691); rgb(169pt)=(0.4899,0.8002,0.3586); rgb(170pt)=(0.5044,0.7993,0.348); rgb(171pt)=(0.5187,0.7982,0.3374); rgb(172pt)=(0.5329,0.797,0.3267); rgb(173pt)=(0.547,0.7957,0.3159); rgb(175pt)=(0.5748,0.7929,0.2941); rgb(176pt)=(0.5886,0.7913,0.2833); rgb(177pt)=(0.6024,0.7896,0.2726); rgb(178pt)=(0.6161,0.7878,0.2622); rgb(179pt)=(0.6297,0.7859,0.2521); rgb(180pt)=(0.6433,0.7839,0.2423); rgb(181pt)=(0.6567,0.7818,0.2329); rgb(182pt)=(0.6701,0.7796,0.2239); rgb(183pt)=(0.6833,0.7773,0.2155); rgb(184pt)=(0.6963,0.775,0.2075); rgb(185pt)=(0.7091,0.7727,0.1998); rgb(186pt)=(0.7218,0.7703,0.1924); rgb(187pt)=(0.7344,0.7679,0.1852); rgb(188pt)=(0.7468,0.7654,0.1782); rgb(189pt)=(0.759,0.7629,0.1717); rgb(190pt)=(0.771,0.7604,0.1658); rgb(191pt)=(0.7829,0.7579,0.1608); rgb(192pt)=(0.7945,0.7554,0.157); rgb(193pt)=(0.806,0.7529,0.1546); rgb(194pt)=(0.8172,0.7505,0.1535); rgb(195pt)=(0.8281,0.7481,0.1536); rgb(196pt)=(0.8389,0.7457,0.1546); rgb(197pt)=(0.8495,0.7435,0.1564); rgb(198pt)=(0.86,0.7413,0.1587); rgb(199pt)=(0.8703,0.7392,0.1615); rgb(200pt)=(0.8804,0.7372,0.165); rgb(201pt)=(0.8903,0.7353,0.1695); rgb(202pt)=(0.9,0.7336,0.1749); rgb(203pt)=(0.9093,0.7321,0.1815); rgb(204pt)=(0.9184,0.7308,0.189); rgb(205pt)=(0.9272,0.7298,0.1973); rgb(206pt)=(0.9357,0.729,0.2061); rgb(207pt)=(0.944,0.7285,0.2151); rgb(208pt)=(0.9523,0.7284,0.2237); rgb(209pt)=(0.9606,0.7285,0.2312); rgb(210pt)=(0.9689,0.7292,0.2373); rgb(211pt)=(0.977,0.7304,0.2418); rgb(212pt)=(0.9842,0.733,0.2446); rgb(213pt)=(0.99,0.7365,0.2429); rgb(214pt)=(0.9946,0.7407,0.2394); rgb(215pt)=(0.9966,0.7458,0.2351); rgb(216pt)=(0.9971,0.7513,0.2309); rgb(217pt)=(0.9972,0.7569,0.2267); rgb(218pt)=(0.9971,0.7626,0.2224); rgb(219pt)=(0.9969,0.7683,0.2181); rgb(220pt)=(0.9966,0.774,0.2138); rgb(221pt)=(0.9962,0.7798,0.2095); rgb(222pt)=(0.9957,0.7856,0.2053); rgb(223pt)=(0.9949,0.7915,0.2012); rgb(224pt)=(0.9938,0.7974,0.1974); rgb(225pt)=(0.9923,0.8034,0.1939); rgb(226pt)=(0.9906,0.8095,0.1906); rgb(227pt)=(0.9885,0.8156,0.1875); rgb(228pt)=(0.9861,0.8218,0.1846); rgb(229pt)=(0.9835,0.828,0.1817); rgb(230pt)=(0.9807,0.8342,0.1787); rgb(231pt)=(0.9778,0.8404,0.1757); rgb(232pt)=(0.9748,0.8467,0.1726); rgb(233pt)=(0.972,0.8529,0.1695); rgb(234pt)=(0.9694,0.8591,0.1665); rgb(235pt)=(0.9671,0.8654,0.1636); rgb(236pt)=(0.9651,0.8716,0.1608); rgb(237pt)=(0.9634,0.8778,0.1582); rgb(238pt)=(0.9619,0.884,0.1557); rgb(239pt)=(0.9608,0.8902,0.1532); rgb(240pt)=(0.9601,0.8963,0.1507); rgb(241pt)=(0.9596,0.9023,0.148); rgb(242pt)=(0.9595,0.9084,0.145); rgb(243pt)=(0.9597,0.9143,0.1418); rgb(244pt)=(0.9601,0.9203,0.1382); rgb(245pt)=(0.9608,0.9262,0.1344); rgb(246pt)=(0.9618,0.932,0.1304); rgb(247pt)=(0.9629,0.9379,0.1261); rgb(248pt)=(0.9642,0.9437,0.1216); rgb(249pt)=(0.9657,0.9494,0.1168); rgb(250pt)=(0.9674,0.9552,0.1116); rgb(251pt)=(0.9692,0.9609,0.1061); rgb(252pt)=(0.9711,0.9667,0.1001); rgb(253pt)=(0.973,0.9724,0.0938); rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805),

shader=interp, colormap=mymap[1pt] rgb(0pt)=(0.2422,0.1504,0.6603); rgb(1pt)=(0.2444,0.1534,0.6728); rgb(2pt)=(0.2464,0.1569,0.6847); rgb(3pt)=(0.2484,0.1607,0.6961); rgb(4pt)=(0.2503,0.1648,0.7071); rgb(5pt)=(0.2522,0.1689,0.7179); rgb(6pt)=(0.254,0.1732,0.7286); rgb(7pt)=(0.2558,0.1773,0.7393); rgb(8pt)=(0.2576,0.1814,0.7501); rgb(9pt)=(0.2594,0.1854,0.761); rgb(11pt)=(0.2628,0.1932,0.7828); rgb(12pt)=(0.2645,0.1972,0.7937); rgb(13pt)=(0.2661,0.2011,0.8043); rgb(14pt)=(0.2676,0.2052,0.8148); rgb(15pt)=(0.2691,0.2094,0.8249); rgb(16pt)=(0.2704,0.2138,0.8346); rgb(17pt)=(0.2717,0.2184,0.8439); rgb(18pt)=(0.2729,0.2231,0.8528); rgb(19pt)=(0.274,0.228,0.8612); rgb(20pt)=(0.2749,0.233,0.8692); rgb(21pt)=(0.2758,0.2382,0.8767); rgb(22pt)=(0.2766,0.2435,0.884); rgb(23pt)=(0.2774,0.2489,0.8908); rgb(24pt)=(0.2781,0.2543,0.8973); rgb(25pt)=(0.2788,0.2598,0.9035); rgb(26pt)=(0.2794,0.2653,0.9094); rgb(27pt)=(0.2798,0.2708,0.915); rgb(28pt)=(0.2802,0.2764,0.9204); rgb(29pt)=(0.2806,0.2819,0.9255); rgb(30pt)=(0.2809,0.2875,0.9305); rgb(31pt)=(0.2811,0.293,0.9352); rgb(32pt)=(0.2813,0.2985,0.9397); rgb(33pt)=(0.2814,0.304,0.9441); rgb(34pt)=(0.2814,0.3095,0.9483); rgb(35pt)=(0.2813,0.315,0.9524); rgb(36pt)=(0.2811,0.3204,0.9563); rgb(37pt)=(0.2809,0.3259,0.96); rgb(38pt)=(0.2807,0.3313,0.9636); rgb(39pt)=(0.2803,0.3367,0.967); rgb(40pt)=(0.2798,0.3421,0.9702); rgb(41pt)=(0.2791,0.3475,0.9733); rgb(42pt)=(0.2784,0.3529,0.9763); rgb(43pt)=(0.2776,0.3583,0.9791); rgb(44pt)=(0.2766,0.3638,0.9817); rgb(45pt)=(0.2754,0.3693,0.984); rgb(46pt)=(0.2741,0.3748,0.9862); rgb(47pt)=(0.2726,0.3804,0.9881); rgb(48pt)=(0.271,0.386,0.9898); rgb(49pt)=(0.2691,0.3916,0.9912); rgb(50pt)=(0.267,0.3973,0.9924); rgb(51pt)=(0.2647,0.403,0.9935); rgb(52pt)=(0.2621,0.4088,0.9946); rgb(53pt)=(0.2591,0.4145,0.9955); rgb(54pt)=(0.2556,0.4203,0.9965); rgb(55pt)=(0.2517,0.4261,0.9974); rgb(56pt)=(0.2473,0.4319,0.9983); rgb(57pt)=(0.2424,0.4378,0.9991); rgb(58pt)=(0.2369,0.4437,0.9996); rgb(59pt)=(0.2311,0.4497,0.9995); rgb(60pt)=(0.225,0.4559,0.9985); rgb(61pt)=(0.2189,0.462,0.9968); rgb(62pt)=(0.2128,0.4682,0.9948); rgb(63pt)=(0.2066,0.4743,0.9926); rgb(64pt)=(0.2006,0.4803,0.9906); rgb(65pt)=(0.195,0.4861,0.9887); rgb(66pt)=(0.1903,0.4919,0.9867); rgb(67pt)=(0.1869,0.4975,0.9844); rgb(68pt)=(0.1847,0.503,0.9819); rgb(69pt)=(0.1831,0.5084,0.9793); rgb(70pt)=(0.1818,0.5138,0.9766); rgb(71pt)=(0.1806,0.5191,0.9738); rgb(72pt)=(0.1795,0.5244,0.9709); rgb(73pt)=(0.1785,0.5296,0.9677); rgb(74pt)=(0.1778,0.5349,0.9641); rgb(75pt)=(0.1773,0.5401,0.9602); rgb(76pt)=(0.1768,0.5452,0.956); rgb(77pt)=(0.1764,0.5504,0.9516); rgb(78pt)=(0.1755,0.5554,0.9473); rgb(79pt)=(0.174,0.5605,0.9432); rgb(80pt)=(0.1716,0.5655,0.9393); rgb(81pt)=(0.1686,0.5705,0.9357); rgb(82pt)=(0.1649,0.5755,0.9323); rgb(83pt)=(0.161,0.5805,0.9289); rgb(84pt)=(0.1573,0.5854,0.9254); rgb(85pt)=(0.154,0.5902,0.9218); rgb(86pt)=(0.1513,0.595,0.9182); rgb(87pt)=(0.1492,0.5997,0.9147); rgb(88pt)=(0.1475,0.6043,0.9113); rgb(89pt)=(0.1461,0.6089,0.908); rgb(90pt)=(0.1446,0.6135,0.905); rgb(91pt)=(0.1429,0.618,0.9022); rgb(92pt)=(0.1408,0.6226,0.8998); rgb(93pt)=(0.1383,0.6272,0.8975); rgb(94pt)=(0.1354,0.6317,0.8953); rgb(95pt)=(0.1321,0.6363,0.8932); rgb(96pt)=(0.1288,0.6408,0.891); rgb(97pt)=(0.1253,0.6453,0.8887); rgb(98pt)=(0.1219,0.6497,0.8862); rgb(99pt)=(0.1185,0.6541,0.8834); rgb(100pt)=(0.1152,0.6584,0.8804); rgb(101pt)=(0.1119,0.6627,0.877); rgb(102pt)=(0.1085,0.6669,0.8734); rgb(103pt)=(0.1048,0.671,0.8695); rgb(104pt)=(0.1009,0.675,0.8653); rgb(105pt)=(0.0964,0.6789,0.8609); rgb(106pt)=(0.0914,0.6828,0.8562); rgb(107pt)=(0.0855,0.6865,0.8513); rgb(108pt)=(0.0789,0.6902,0.8462); rgb(109pt)=(0.0713,0.6938,0.8409); rgb(110pt)=(0.0628,0.6972,0.8355); rgb(111pt)=(0.0535,0.7006,0.8299); rgb(112pt)=(0.0433,0.7039,0.8242); rgb(113pt)=(0.0328,0.7071,0.8183); rgb(114pt)=(0.0234,0.7103,0.8124); rgb(115pt)=(0.0155,0.7133,0.8064); rgb(116pt)=(0.0091,0.7163,0.8003); rgb(117pt)=(0.0046,0.7192,0.7941); rgb(118pt)=(0.0019,0.722,0.7878); rgb(119pt)=(0.0009,0.7248,0.7815); rgb(120pt)=(0.0018,0.7275,0.7752); rgb(121pt)=(0.0046,0.7301,0.7688); rgb(122pt)=(0.0094,0.7327,0.7623); rgb(123pt)=(0.0162,0.7352,0.7558); rgb(124pt)=(0.0253,0.7376,0.7492); rgb(125pt)=(0.0369,0.74,0.7426); rgb(126pt)=(0.0504,0.7423,0.7359); rgb(127pt)=(0.0638,0.7446,0.7292); rgb(128pt)=(0.077,0.7468,0.7224); rgb(129pt)=(0.0899,0.7489,0.7156); rgb(130pt)=(0.1023,0.751,0.7088); rgb(131pt)=(0.1141,0.7531,0.7019); rgb(132pt)=(0.1252,0.7552,0.695); rgb(133pt)=(0.1354,0.7572,0.6881); rgb(134pt)=(0.1448,0.7593,0.6812); rgb(135pt)=(0.1532,0.7614,0.6741); rgb(136pt)=(0.1609,0.7635,0.6671); rgb(137pt)=(0.1678,0.7656,0.6599); rgb(138pt)=(0.1741,0.7678,0.6527); rgb(139pt)=(0.1799,0.7699,0.6454); rgb(140pt)=(0.1853,0.7721,0.6379); rgb(141pt)=(0.1905,0.7743,0.6303); rgb(142pt)=(0.1954,0.7765,0.6225); rgb(143pt)=(0.2003,0.7787,0.6146); rgb(144pt)=(0.2061,0.7808,0.6065); rgb(145pt)=(0.2118,0.7828,0.5983); rgb(146pt)=(0.2178,0.7849,0.5899); rgb(147pt)=(0.2244,0.7869,0.5813); rgb(148pt)=(0.2318,0.7887,0.5725); rgb(149pt)=(0.2401,0.7905,0.5636); rgb(150pt)=(0.2491,0.7922,0.5546); rgb(151pt)=(0.2589,0.7937,0.5454); rgb(152pt)=(0.2695,0.7951,0.536); rgb(153pt)=(0.2809,0.7964,0.5266); rgb(154pt)=(0.2929,0.7975,0.517); rgb(155pt)=(0.3052,0.7985,0.5074); rgb(156pt)=(0.3176,0.7994,0.4975); rgb(157pt)=(0.3301,0.8002,0.4876); rgb(158pt)=(0.3424,0.8009,0.4774); rgb(159pt)=(0.3548,0.8016,0.4669); rgb(160pt)=(0.3671,0.8021,0.4563); rgb(161pt)=(0.3795,0.8026,0.4454); rgb(162pt)=(0.3921,0.8029,0.4344); rgb(163pt)=(0.405,0.8031,0.4233); rgb(164pt)=(0.4184,0.803,0.4122); rgb(165pt)=(0.4322,0.8028,0.4013); rgb(166pt)=(0.4463,0.8024,0.3904); rgb(167pt)=(0.4608,0.8018,0.3797); rgb(168pt)=(0.4753,0.8011,0.3691); rgb(169pt)=(0.4899,0.8002,0.3586); rgb(170pt)=(0.5044,0.7993,0.348); rgb(171pt)=(0.5187,0.7982,0.3374); rgb(172pt)=(0.5329,0.797,0.3267); rgb(173pt)=(0.547,0.7957,0.3159); rgb(175pt)=(0.5748,0.7929,0.2941); rgb(176pt)=(0.5886,0.7913,0.2833); rgb(177pt)=(0.6024,0.7896,0.2726); rgb(178pt)=(0.6161,0.7878,0.2622); rgb(179pt)=(0.6297,0.7859,0.2521); rgb(180pt)=(0.6433,0.7839,0.2423); rgb(181pt)=(0.6567,0.7818,0.2329); rgb(182pt)=(0.6701,0.7796,0.2239); rgb(183pt)=(0.6833,0.7773,0.2155); rgb(184pt)=(0.6963,0.775,0.2075); rgb(185pt)=(0.7091,0.7727,0.1998); rgb(186pt)=(0.7218,0.7703,0.1924); rgb(187pt)=(0.7344,0.7679,0.1852); rgb(188pt)=(0.7468,0.7654,0.1782); rgb(189pt)=(0.759,0.7629,0.1717); rgb(190pt)=(0.771,0.7604,0.1658); rgb(191pt)=(0.7829,0.7579,0.1608); rgb(192pt)=(0.7945,0.7554,0.157); rgb(193pt)=(0.806,0.7529,0.1546); rgb(194pt)=(0.8172,0.7505,0.1535); rgb(195pt)=(0.8281,0.7481,0.1536); rgb(196pt)=(0.8389,0.7457,0.1546); rgb(197pt)=(0.8495,0.7435,0.1564); rgb(198pt)=(0.86,0.7413,0.1587); rgb(199pt)=(0.8703,0.7392,0.1615); rgb(200pt)=(0.8804,0.7372,0.165); rgb(201pt)=(0.8903,0.7353,0.1695); rgb(202pt)=(0.9,0.7336,0.1749); rgb(203pt)=(0.9093,0.7321,0.1815); rgb(204pt)=(0.9184,0.7308,0.189); rgb(205pt)=(0.9272,0.7298,0.1973); rgb(206pt)=(0.9357,0.729,0.2061); rgb(207pt)=(0.944,0.7285,0.2151); rgb(208pt)=(0.9523,0.7284,0.2237); rgb(209pt)=(0.9606,0.7285,0.2312); rgb(210pt)=(0.9689,0.7292,0.2373); rgb(211pt)=(0.977,0.7304,0.2418); rgb(212pt)=(0.9842,0.733,0.2446); rgb(213pt)=(0.99,0.7365,0.2429); rgb(214pt)=(0.9946,0.7407,0.2394); rgb(215pt)=(0.9966,0.7458,0.2351); rgb(216pt)=(0.9971,0.7513,0.2309); rgb(217pt)=(0.9972,0.7569,0.2267); rgb(218pt)=(0.9971,0.7626,0.2224); rgb(219pt)=(0.9969,0.7683,0.2181); rgb(220pt)=(0.9966,0.774,0.2138); rgb(221pt)=(0.9962,0.7798,0.2095); rgb(222pt)=(0.9957,0.7856,0.2053); rgb(223pt)=(0.9949,0.7915,0.2012); rgb(224pt)=(0.9938,0.7974,0.1974); rgb(225pt)=(0.9923,0.8034,0.1939); rgb(226pt)=(0.9906,0.8095,0.1906); rgb(227pt)=(0.9885,0.8156,0.1875); rgb(228pt)=(0.9861,0.8218,0.1846); rgb(229pt)=(0.9835,0.828,0.1817); rgb(230pt)=(0.9807,0.8342,0.1787); rgb(231pt)=(0.9778,0.8404,0.1757); rgb(232pt)=(0.9748,0.8467,0.1726); rgb(233pt)=(0.972,0.8529,0.1695); rgb(234pt)=(0.9694,0.8591,0.1665); rgb(235pt)=(0.9671,0.8654,0.1636); rgb(236pt)=(0.9651,0.8716,0.1608); rgb(237pt)=(0.9634,0.8778,0.1582); rgb(238pt)=(0.9619,0.884,0.1557); rgb(239pt)=(0.9608,0.8902,0.1532); rgb(240pt)=(0.9601,0.8963,0.1507); rgb(241pt)=(0.9596,0.9023,0.148); rgb(242pt)=(0.9595,0.9084,0.145); rgb(243pt)=(0.9597,0.9143,0.1418); rgb(244pt)=(0.9601,0.9203,0.1382); rgb(245pt)=(0.9608,0.9262,0.1344); rgb(246pt)=(0.9618,0.932,0.1304); rgb(247pt)=(0.9629,0.9379,0.1261); rgb(248pt)=(0.9642,0.9437,0.1216); rgb(249pt)=(0.9657,0.9494,0.1168); rgb(250pt)=(0.9674,0.9552,0.1116); rgb(251pt)=(0.9692,0.9609,0.1061); rgb(252pt)=(0.9711,0.9667,0.1001); rgb(253pt)=(0.973,0.9724,0.0938); rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805), mesh/rows=19]
table[row sep=crcr, point meta=c]

x	y	c

0	1	0.48969

0	5	0.48833

0	10	0.49105

0	25	0.49587

0	50	0.51878

0	100	0.54584

0	150	0.60867

0	200	0.65044

0	250	0.70181

0	400	0.81087

0	500	0.83715

0	750	0.90869

0	1000	0.94909

0	2000	0.9803

0	5000	0.98491

0	10000	0.98425

5	1	0.49223

5	5	0.48884

5	10	0.48902

5	25	0.50183

5	50	0.53188

5	100	0.58879

5	150	0.6356

5	200	0.68986

5	250	0.75456

5	400	0.84011

5	500	0.88134

5	750	0.93836

5	1000	0.97191

5	2000	0.98231

5	5000	0.98723

5	10000	0.98575

10	1	0.4903100

10	5	0.4940700

10	10	0.5137400

10	25	0.5479900

10	50	0.6817100

10	100	0.8289800

10	150	0.8647800

10	200	0.8975600

10	250	0.9117200

10	400	0.9556900

10	500	0.9706900

10	750	0.9755700

10	1000	0.9811500

10	2000	0.9837700

10	5000	0.9908700

10	10000	0.989

15	1	0.488360

15	5	0.486940

15	10	0.488200

15	25	0.509310

15	50	0.540500

15	100	0.623410

15	150	0.710030

15	200	0.801250

15	250	0.807100

15	400	0.891960

15	500	0.936450

15	750	0.963350

15	1000	0.978360

15	2000	0.987290

15	5000	0.963460

15	10000	0.987340

20	1	0.490290

20	5	0.488100

20	10	0.489840

20	25	0.517450

20	50	0.560760

20	100	0.659220

20	150	0.718370

20	200	0.782820

20	250	0.828160

20	400	0.904520

20	500	0.931580

20	750	0.972460

20	1000	0.978850

20	2000	0.980200

20	5000	0.985170

20	10000	0.986350

25	1	0.4894400

25	5	0.5179000

25	10	0.5330000

25	25	0.6980500

25	50	0.8314800

25	100	0.9122500

25	150	0.9372900

25	200	0.9449800

25	250	0.9609400

25	400	0.9800600

25	500	0.9763300

25	750	0.9842500

25	1000	0.9888900

25	2000	0.9891000

25	5000	0.9874700

25	10000	0.9880800

30	1	0.487360

30	5	0.524120

30	10	0.612280

30	25	0.778430

30	50	0.870450

30	100	0.92650

30	150	0.954160

30	200	0.960560

30	250	0.978180

30	400	0.980990

30	500	0.982370

30	750	0.990130

30	1000	0.985190

30	2000	0.990490

30	5000	0.978570

30	10000	0.986920

35	1	0.4874300

35	5	0.4944600

35	10	0.4996300

35	25	0.5377900

35	50	0.5905600

35	100	0.7350800

35	150	0.8064100

35	200	0.8640700

35	250	0.9106500

35	400	0.9562300

35	500	0.96930

35	750	0.9805500

35	1000	0.9828900

35	2000	0.9847400

35	5000	0.9819200

35	10000	0.9881700

40	1	0.491150000

40	5	0.522880000

40	10	0.600350000

40	25	0.778720000

40	50	0.873340000

40	100	0.934950000

40	150	0.948530000

40	200	0.960510000

40	250	0.967530000

40	400	0.979090000

40	500	0.984170000

40	750	0.982470000

40	1000	0.985590000

40	2000	0.989150000

40	5000	0.989230000

40	10000	0.99174

45	1	0.49263

45	5	0.52588

45	10	0.58619

45	25	0.76570

45	50	0.86291

45	100	0.93082

45	150	0.95716

45	200	0.95616

45	250	0.96896

45	400	0.97783

45	500	0.98041

45	750	0.98641

45	1000	0.98537

45	2000	0.99044

45	5000	0.98714

45	10000	0.98930

50	1	0.4917400

50	5	0.4905800

50	10	0.5142200

50	25	0.5921100

50	50	0.7196600

50	100	0.8477600

50	150	0.8869500

50	200	0.9054800

50	250	0.9273300

50	400	0.9639500

50	500	0.9745100

50	750	0.99030

50	1000	0.9747600

50	2000	0.9861200

50	5000	0.9885400

50	10000	0.98580

55	1	0.4860600

55	5	0.5447000

55	10	0.5848300

55	25	0.7722700

55	50	0.8690500

55	100	0.9371000

55	150	0.9481900

55	200	0.9595300

55	250	0.9657700

55	400	0.9766500

55	500	0.9797000

55	750	0.9898600

55	1000	0.9878200

55	2000	0.9922000

55	5000	0.9908900

55	10000	0.9868100

60	1	0.488870

60	5	0.493460

60	10	0.505330

60	25	0.561810

60	50	0.657610

60	100	0.79750

60	150	0.871460

60	200	0.885070

60	250	0.908840

60	400	0.954050

60	500	0.971130

60	750	0.983020

60	1000	0.983590

60	2000	0.98970

60	5000	0.983020

60	10000	0.987120

65	1	0.492420

65	5	0.506270

65	10	0.543870

65	25	0.651560

65	50	0.796190

65	100	0.886920

65	150	0.921640

65	200	0.93690

65	250	0.959030

65	400	0.978470

65	500	0.977810

65	750	0.982930

65	1000	0.986810

65	2000	0.985020

65	5000	0.984350

65	10000	0.988780

70	1	0.493230

70	5	0.52020

70	10	0.593560

70	25	0.759730

70	50	0.863670

70	100	0.931250

70	150	0.942590

70	200	0.950250

70	250	0.973860

70	400	0.98140

70	500	0.984230

70	750	0.985080

70	1000	0.988480

70	2000	0.986930

70	5000	0.986840

70	10000	0.989570

75	1	0.490290

75	5	0.490530

75	10	0.507320

75	25	0.55870

75	50	0.660860

75	100	0.793740

75	150	0.863970

75	200	0.890560

75	250	0.912630

75	400	0.965730

75	500	0.97770

75	750	0.978650

75	1000	0.988090

75	2000	0.988640

75	5000	0.991750

75	10000	0.98789

80	1	0.492350

80	5	0.491620

80	10	0.50600

80	25	0.559510

80	50	0.662510

80	100	0.789710

80	150	0.869560

80	200	0.889370

80	250	0.908880

80	400	0.960340

80	500	0.96660

80	750	0.985160

80	1000	0.986650

80	2000	0.982430

80	5000	0.9888

80	10000	0.98956

85	1	0.492330

85	5	0.489610

85	10	0.505870

85	25	0.562290

85	50	0.674270

85	100	0.796240

85	150	0.849230

85	200	0.899880

85	250	0.914210

85	400	0.949810

85	500	0.975610

85	750	0.980740

85	1000	0.974350

85	2000	0.985950

85	5000	0.987040

85	10000	0.99086

90	1	0.491090

90	5	0.49840

90	10	0.515270

90	25	0.589870

90	50	0.733530

90	100	0.833660

90	150	0.893160

90	200	0.924330

90	250	0.930910

90	400	0.962650

90	500	0.974690

90	750	0.983050

90	1000	0.986320

90	2000	0.986180

90	5000	0.986190

90	10000	0.988430

scale only axis,
point meta min=0,
point meta max=1,
xlabel style=font=,
xlabel=Angle of Eve in degrees,
ylabel style=font=,
ylabel=Distance of Eve in metres,
axis background/.style=fill=white,
axis x line*=bottom,
axis y line*=left,
colormap=mymap[1pt] rgb(0pt)=(0.2422,0.1504,0.6603); rgb(1pt)=(0.2444,0.1534,0.6728); rgb(2pt)=(0.2464,0.1569,0.6847); rgb(3pt)=(0.2484,0.1607,0.6961); rgb(4pt)=(0.2503,0.1648,0.7071); rgb(5pt)=(0.2522,0.1689,0.7179); rgb(6pt)=(0.254,0.1732,0.7286); rgb(7pt)=(0.2558,0.1773,0.7393); rgb(8pt)=(0.2576,0.1814,0.7501); rgb(9pt)=(0.2594,0.1854,0.761); rgb(11pt)=(0.2628,0.1932,0.7828); rgb(12pt)=(0.2645,0.1972,0.7937); rgb(13pt)=(0.2661,0.2011,0.8043); rgb(14pt)=(0.2676,0.2052,0.8148); rgb(15pt)=(0.2691,0.2094,0.8249); rgb(16pt)=(0.2704,0.2138,0.8346); rgb(17pt)=(0.2717,0.2184,0.8439); rgb(18pt)=(0.2729,0.2231,0.8528); rgb(19pt)=(0.274,0.228,0.8612); rgb(20pt)=(0.2749,0.233,0.8692); rgb(21pt)=(0.2758,0.2382,0.8767); rgb(22pt)=(0.2766,0.2435,0.884); rgb(23pt)=(0.2774,0.2489,0.8908); rgb(24pt)=(0.2781,0.2543,0.8973); rgb(25pt)=(0.2788,0.2598,0.9035); rgb(26pt)=(0.2794,0.2653,0.9094); rgb(27pt)=(0.2798,0.2708,0.915); rgb(28pt)=(0.2802,0.2764,0.9204); rgb(29pt)=(0.2806,0.2819,0.9255); rgb(30pt)=(0.2809,0.2875,0.9305); rgb(31pt)=(0.2811,0.293,0.9352); rgb(32pt)=(0.2813,0.2985,0.9397); rgb(33pt)=(0.2814,0.304,0.9441); rgb(34pt)=(0.2814,0.3095,0.9483); rgb(35pt)=(0.2813,0.315,0.9524); rgb(36pt)=(0.2811,0.3204,0.9563); rgb(37pt)=(0.2809,0.3259,0.96); rgb(38pt)=(0.2807,0.3313,0.9636); rgb(39pt)=(0.2803,0.3367,0.967); rgb(40pt)=(0.2798,0.3421,0.9702); rgb(41pt)=(0.2791,0.3475,0.9733); rgb(42pt)=(0.2784,0.3529,0.9763); rgb(43pt)=(0.2776,0.3583,0.9791); rgb(44pt)=(0.2766,0.3638,0.9817); rgb(45pt)=(0.2754,0.3693,0.984); rgb(46pt)=(0.2741,0.3748,0.9862); rgb(47pt)=(0.2726,0.3804,0.9881); rgb(48pt)=(0.271,0.386,0.9898); rgb(49pt)=(0.2691,0.3916,0.9912); rgb(50pt)=(0.267,0.3973,0.9924); rgb(51pt)=(0.2647,0.403,0.9935); rgb(52pt)=(0.2621,0.4088,0.9946); rgb(53pt)=(0.2591,0.4145,0.9955); rgb(54pt)=(0.2556,0.4203,0.9965); rgb(55pt)=(0.2517,0.4261,0.9974); rgb(56pt)=(0.2473,0.4319,0.9983); rgb(57pt)=(0.2424,0.4378,0.9991); rgb(58pt)=(0.2369,0.4437,0.9996); rgb(59pt)=(0.2311,0.4497,0.9995); rgb(60pt)=(0.225,0.4559,0.9985); rgb(61pt)=(0.2189,0.462,0.9968); rgb(62pt)=(0.2128,0.4682,0.9948); rgb(63pt)=(0.2066,0.4743,0.9926); rgb(64pt)=(0.2006,0.4803,0.9906); rgb(65pt)=(0.195,0.4861,0.9887); rgb(66pt)=(0.1903,0.4919,0.9867); rgb(67pt)=(0.1869,0.4975,0.9844); rgb(68pt)=(0.1847,0.503,0.9819); rgb(69pt)=(0.1831,0.5084,0.9793); rgb(70pt)=(0.1818,0.5138,0.9766); rgb(71pt)=(0.1806,0.5191,0.9738); rgb(72pt)=(0.1795,0.5244,0.9709); rgb(73pt)=(0.1785,0.5296,0.9677); rgb(74pt)=(0.1778,0.5349,0.9641); rgb(75pt)=(0.1773,0.5401,0.9602); rgb(76pt)=(0.1768,0.5452,0.956); rgb(77pt)=(0.1764,0.5504,0.9516); rgb(78pt)=(0.1755,0.5554,0.9473); rgb(79pt)=(0.174,0.5605,0.9432); rgb(80pt)=(0.1716,0.5655,0.9393); rgb(81pt)=(0.1686,0.5705,0.9357); rgb(82pt)=(0.1649,0.5755,0.9323); rgb(83pt)=(0.161,0.5805,0.9289); rgb(84pt)=(0.1573,0.5854,0.9254); rgb(85pt)=(0.154,0.5902,0.9218); rgb(86pt)=(0.1513,0.595,0.9182); rgb(87pt)=(0.1492,0.5997,0.9147); rgb(88pt)=(0.1475,0.6043,0.9113); rgb(89pt)=(0.1461,0.6089,0.908); rgb(90pt)=(0.1446,0.6135,0.905); rgb(91pt)=(0.1429,0.618,0.9022); rgb(92pt)=(0.1408,0.6226,0.8998); rgb(93pt)=(0.1383,0.6272,0.8975); rgb(94pt)=(0.1354,0.6317,0.8953); rgb(95pt)=(0.1321,0.6363,0.8932); rgb(96pt)=(0.1288,0.6408,0.891); rgb(97pt)=(0.1253,0.6453,0.8887); rgb(98pt)=(0.1219,0.6497,0.8862); rgb(99pt)=(0.1185,0.6541,0.8834); rgb(100pt)=(0.1152,0.6584,0.8804); rgb(101pt)=(0.1119,0.6627,0.877); rgb(102pt)=(0.1085,0.6669,0.8734); rgb(103pt)=(0.1048,0.671,0.8695); rgb(104pt)=(0.1009,0.675,0.8653); rgb(105pt)=(0.0964,0.6789,0.8609); rgb(106pt)=(0.0914,0.6828,0.8562); rgb(107pt)=(0.0855,0.6865,0.8513); rgb(108pt)=(0.0789,0.6902,0.8462); rgb(109pt)=(0.0713,0.6938,0.8409); rgb(110pt)=(0.0628,0.6972,0.8355); rgb(111pt)=(0.0535,0.7006,0.8299); rgb(112pt)=(0.0433,0.7039,0.8242); rgb(113pt)=(0.0328,0.7071,0.8183); rgb(114pt)=(0.0234,0.7103,0.8124); rgb(115pt)=(0.0155,0.7133,0.8064); rgb(116pt)=(0.0091,0.7163,0.8003); rgb(117pt)=(0.0046,0.7192,0.7941); rgb(118pt)=(0.0019,0.722,0.7878); rgb(119pt)=(0.0009,0.7248,0.7815); rgb(120pt)=(0.0018,0.7275,0.7752); rgb(121pt)=(0.0046,0.7301,0.7688); rgb(122pt)=(0.0094,0.7327,0.7623); rgb(123pt)=(0.0162,0.7352,0.7558); rgb(124pt)=(0.0253,0.7376,0.7492); rgb(125pt)=(0.0369,0.74,0.7426); rgb(126pt)=(0.0504,0.7423,0.7359); rgb(127pt)=(0.0638,0.7446,0.7292); rgb(128pt)=(0.077,0.7468,0.7224); rgb(129pt)=(0.0899,0.7489,0.7156); rgb(130pt)=(0.1023,0.751,0.7088); rgb(131pt)=(0.1141,0.7531,0.7019); rgb(132pt)=(0.1252,0.7552,0.695); rgb(133pt)=(0.1354,0.7572,0.6881); rgb(134pt)=(0.1448,0.7593,0.6812); rgb(135pt)=(0.1532,0.7614,0.6741); rgb(136pt)=(0.1609,0.7635,0.6671); rgb(137pt)=(0.1678,0.7656,0.6599); rgb(138pt)=(0.1741,0.7678,0.6527); rgb(139pt)=(0.1799,0.7699,0.6454); rgb(140pt)=(0.1853,0.7721,0.6379); rgb(141pt)=(0.1905,0.7743,0.6303); rgb(142pt)=(0.1954,0.7765,0.6225); rgb(143pt)=(0.2003,0.7787,0.6146); rgb(144pt)=(0.2061,0.7808,0.6065); rgb(145pt)=(0.2118,0.7828,0.5983); rgb(146pt)=(0.2178,0.7849,0.5899); rgb(147pt)=(0.2244,0.7869,0.5813); rgb(148pt)=(0.2318,0.7887,0.5725); rgb(149pt)=(0.2401,0.7905,0.5636); rgb(150pt)=(0.2491,0.7922,0.5546); rgb(151pt)=(0.2589,0.7937,0.5454); rgb(152pt)=(0.2695,0.7951,0.536); rgb(153pt)=(0.2809,0.7964,0.5266); rgb(154pt)=(0.2929,0.7975,0.517); rgb(155pt)=(0.3052,0.7985,0.5074); rgb(156pt)=(0.3176,0.7994,0.4975); rgb(157pt)=(0.3301,0.8002,0.4876); rgb(158pt)=(0.3424,0.8009,0.4774); rgb(159pt)=(0.3548,0.8016,0.4669); rgb(160pt)=(0.3671,0.8021,0.4563); rgb(161pt)=(0.3795,0.8026,0.4454); rgb(162pt)=(0.3921,0.8029,0.4344); rgb(163pt)=(0.405,0.8031,0.4233); rgb(164pt)=(0.4184,0.803,0.4122); rgb(165pt)=(0.4322,0.8028,0.4013); rgb(166pt)=(0.4463,0.8024,0.3904); rgb(167pt)=(0.4608,0.8018,0.3797); rgb(168pt)=(0.4753,0.8011,0.3691); rgb(169pt)=(0.4899,0.8002,0.3586); rgb(170pt)=(0.5044,0.7993,0.348); rgb(171pt)=(0.5187,0.7982,0.3374); rgb(172pt)=(0.5329,0.797,0.3267); rgb(173pt)=(0.547,0.7957,0.3159); rgb(175pt)=(0.5748,0.7929,0.2941); rgb(176pt)=(0.5886,0.7913,0.2833); rgb(177pt)=(0.6024,0.7896,0.2726); rgb(178pt)=(0.6161,0.7878,0.2622); rgb(179pt)=(0.6297,0.7859,0.2521); rgb(180pt)=(0.6433,0.7839,0.2423); rgb(181pt)=(0.6567,0.7818,0.2329); rgb(182pt)=(0.6701,0.7796,0.2239); rgb(183pt)=(0.6833,0.7773,0.2155); rgb(184pt)=(0.6963,0.775,0.2075); rgb(185pt)=(0.7091,0.7727,0.1998); rgb(186pt)=(0.7218,0.7703,0.1924); rgb(187pt)=(0.7344,0.7679,0.1852); rgb(188pt)=(0.7468,0.7654,0.1782); rgb(189pt)=(0.759,0.7629,0.1717); rgb(190pt)=(0.771,0.7604,0.1658); rgb(191pt)=(0.7829,0.7579,0.1608); rgb(192pt)=(0.7945,0.7554,0.157); rgb(193pt)=(0.806,0.7529,0.1546); rgb(194pt)=(0.8172,0.7505,0.1535); rgb(195pt)=(0.8281,0.7481,0.1536); rgb(196pt)=(0.8389,0.7457,0.1546); rgb(197pt)=(0.8495,0.7435,0.1564); rgb(198pt)=(0.86,0.7413,0.1587); rgb(199pt)=(0.8703,0.7392,0.1615); rgb(200pt)=(0.8804,0.7372,0.165); rgb(201pt)=(0.8903,0.7353,0.1695); rgb(202pt)=(0.9,0.7336,0.1749); rgb(203pt)=(0.9093,0.7321,0.1815); rgb(204pt)=(0.9184,0.7308,0.189); rgb(205pt)=(0.9272,0.7298,0.1973); rgb(206pt)=(0.9357,0.729,0.2061); rgb(207pt)=(0.944,0.7285,0.2151); rgb(208pt)=(0.9523,0.7284,0.2237); rgb(209pt)=(0.9606,0.7285,0.2312); rgb(210pt)=(0.9689,0.7292,0.2373); rgb(211pt)=(0.977,0.7304,0.2418); rgb(212pt)=(0.9842,0.733,0.2446); rgb(213pt)=(0.99,0.7365,0.2429); rgb(214pt)=(0.9946,0.7407,0.2394); rgb(215pt)=(0.9966,0.7458,0.2351); rgb(216pt)=(0.9971,0.7513,0.2309); rgb(217pt)=(0.9972,0.7569,0.2267); rgb(218pt)=(0.9971,0.7626,0.2224); rgb(219pt)=(0.9969,0.7683,0.2181); rgb(220pt)=(0.9966,0.774,0.2138); rgb(221pt)=(0.9962,0.7798,0.2095); rgb(222pt)=(0.9957,0.7856,0.2053); rgb(223pt)=(0.9949,0.7915,0.2012); rgb(224pt)=(0.9938,0.7974,0.1974); rgb(225pt)=(0.9923,0.8034,0.1939); rgb(226pt)=(0.9906,0.8095,0.1906); rgb(227pt)=(0.9885,0.8156,0.1875); rgb(228pt)=(0.9861,0.8218,0.1846); rgb(229pt)=(0.9835,0.828,0.1817); rgb(230pt)=(0.9807,0.8342,0.1787); rgb(231pt)=(0.9778,0.8404,0.1757); rgb(232pt)=(0.9748,0.8467,0.1726); rgb(233pt)=(0.972,0.8529,0.1695); rgb(234pt)=(0.9694,0.8591,0.1665); rgb(235pt)=(0.9671,0.8654,0.1636); rgb(236pt)=(0.9651,0.8716,0.1608); rgb(237pt)=(0.9634,0.8778,0.1582); rgb(238pt)=(0.9619,0.884,0.1557); rgb(239pt)=(0.9608,0.8902,0.1532); rgb(240pt)=(0.9601,0.8963,0.1507); rgb(241pt)=(0.9596,0.9023,0.148); rgb(242pt)=(0.9595,0.9084,0.145); rgb(243pt)=(0.9597,0.9143,0.1418); rgb(244pt)=(0.9601,0.9203,0.1382); rgb(245pt)=(0.9608,0.9262,0.1344); rgb(246pt)=(0.9618,0.932,0.1304); rgb(247pt)=(0.9629,0.9379,0.1261); rgb(248pt)=(0.9642,0.9437,0.1216); rgb(249pt)=(0.9657,0.9494,0.1168); rgb(250pt)=(0.9674,0.9552,0.1116); rgb(251pt)=(0.9692,0.9609,0.1061); rgb(252pt)=(0.9711,0.9667,0.1001); rgb(253pt)=(0.973,0.9724,0.0938); rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805),

shader=interp, colormap=mymap[1pt] rgb(0pt)=(0.2422,0.1504,0.6603); rgb(1pt)=(0.2444,0.1534,0.6728); rgb(2pt)=(0.2464,0.1569,0.6847); rgb(3pt)=(0.2484,0.1607,0.6961); rgb(4pt)=(0.2503,0.1648,0.7071); rgb(5pt)=(0.2522,0.1689,0.7179); rgb(6pt)=(0.254,0.1732,0.7286); rgb(7pt)=(0.2558,0.1773,0.7393); rgb(8pt)=(0.2576,0.1814,0.7501); rgb(9pt)=(0.2594,0.1854,0.761); rgb(11pt)=(0.2628,0.1932,0.7828); rgb(12pt)=(0.2645,0.1972,0.7937); rgb(13pt)=(0.2661,0.2011,0.8043); rgb(14pt)=(0.2676,0.2052,0.8148); rgb(15pt)=(0.2691,0.2094,0.8249); rgb(16pt)=(0.2704,0.2138,0.8346); rgb(17pt)=(0.2717,0.2184,0.8439); rgb(18pt)=(0.2729,0.2231,0.8528); rgb(19pt)=(0.274,0.228,0.8612); rgb(20pt)=(0.2749,0.233,0.8692); rgb(21pt)=(0.2758,0.2382,0.8767); rgb(22pt)=(0.2766,0.2435,0.884); rgb(23pt)=(0.2774,0.2489,0.8908); rgb(24pt)=(0.2781,0.2543,0.8973); rgb(25pt)=(0.2788,0.2598,0.9035); rgb(26pt)=(0.2794,0.2653,0.9094); rgb(27pt)=(0.2798,0.2708,0.915); rgb(28pt)=(0.2802,0.2764,0.9204); rgb(29pt)=(0.2806,0.2819,0.9255); rgb(30pt)=(0.2809,0.2875,0.9305); rgb(31pt)=(0.2811,0.293,0.9352); rgb(32pt)=(0.2813,0.2985,0.9397); rgb(33pt)=(0.2814,0.304,0.9441); rgb(34pt)=(0.2814,0.3095,0.9483); rgb(35pt)=(0.2813,0.315,0.9524); rgb(36pt)=(0.2811,0.3204,0.9563); rgb(37pt)=(0.2809,0.3259,0.96); rgb(38pt)=(0.2807,0.3313,0.9636); rgb(39pt)=(0.2803,0.3367,0.967); rgb(40pt)=(0.2798,0.3421,0.9702); rgb(41pt)=(0.2791,0.3475,0.9733); rgb(42pt)=(0.2784,0.3529,0.9763); rgb(43pt)=(0.2776,0.3583,0.9791); rgb(44pt)=(0.2766,0.3638,0.9817); rgb(45pt)=(0.2754,0.3693,0.984); rgb(46pt)=(0.2741,0.3748,0.9862); rgb(47pt)=(0.2726,0.3804,0.9881); rgb(48pt)=(0.271,0.386,0.9898); rgb(49pt)=(0.2691,0.3916,0.9912); rgb(50pt)=(0.267,0.3973,0.9924); rgb(51pt)=(0.2647,0.403,0.9935); rgb(52pt)=(0.2621,0.4088,0.9946); rgb(53pt)=(0.2591,0.4145,0.9955); rgb(54pt)=(0.2556,0.4203,0.9965); rgb(55pt)=(0.2517,0.4261,0.9974); rgb(56pt)=(0.2473,0.4319,0.9983); rgb(57pt)=(0.2424,0.4378,0.9991); rgb(58pt)=(0.2369,0.4437,0.9996); rgb(59pt)=(0.2311,0.4497,0.9995); rgb(60pt)=(0.225,0.4559,0.9985); rgb(61pt)=(0.2189,0.462,0.9968); rgb(62pt)=(0.2128,0.4682,0.9948); rgb(63pt)=(0.2066,0.4743,0.9926); rgb(64pt)=(0.2006,0.4803,0.9906); rgb(65pt)=(0.195,0.4861,0.9887); rgb(66pt)=(0.1903,0.4919,0.9867); rgb(67pt)=(0.1869,0.4975,0.9844); rgb(68pt)=(0.1847,0.503,0.9819); rgb(69pt)=(0.1831,0.5084,0.9793); rgb(70pt)=(0.1818,0.5138,0.9766); rgb(71pt)=(0.1806,0.5191,0.9738); rgb(72pt)=(0.1795,0.5244,0.9709); rgb(73pt)=(0.1785,0.5296,0.9677); rgb(74pt)=(0.1778,0.5349,0.9641); rgb(75pt)=(0.1773,0.5401,0.9602); rgb(76pt)=(0.1768,0.5452,0.956); rgb(77pt)=(0.1764,0.5504,0.9516); rgb(78pt)=(0.1755,0.5554,0.9473); rgb(79pt)=(0.174,0.5605,0.9432); rgb(80pt)=(0.1716,0.5655,0.9393); rgb(81pt)=(0.1686,0.5705,0.9357); rgb(82pt)=(0.1649,0.5755,0.9323); rgb(83pt)=(0.161,0.5805,0.9289); rgb(84pt)=(0.1573,0.5854,0.9254); rgb(85pt)=(0.154,0.5902,0.9218); rgb(86pt)=(0.1513,0.595,0.9182); rgb(87pt)=(0.1492,0.5997,0.9147); rgb(88pt)=(0.1475,0.6043,0.9113); rgb(89pt)=(0.1461,0.6089,0.908); rgb(90pt)=(0.1446,0.6135,0.905); rgb(91pt)=(0.1429,0.618,0.9022); rgb(92pt)=(0.1408,0.6226,0.8998); rgb(93pt)=(0.1383,0.6272,0.8975); rgb(94pt)=(0.1354,0.6317,0.8953); rgb(95pt)=(0.1321,0.6363,0.8932); rgb(96pt)=(0.1288,0.6408,0.891); rgb(97pt)=(0.1253,0.6453,0.8887); rgb(98pt)=(0.1219,0.6497,0.8862); rgb(99pt)=(0.1185,0.6541,0.8834); rgb(100pt)=(0.1152,0.6584,0.8804); rgb(101pt)=(0.1119,0.6627,0.877); rgb(102pt)=(0.1085,0.6669,0.8734); rgb(103pt)=(0.1048,0.671,0.8695); rgb(104pt)=(0.1009,0.675,0.8653); rgb(105pt)=(0.0964,0.6789,0.8609); rgb(106pt)=(0.0914,0.6828,0.8562); rgb(107pt)=(0.0855,0.6865,0.8513); rgb(108pt)=(0.0789,0.6902,0.8462); rgb(109pt)=(0.0713,0.6938,0.8409); rgb(110pt)=(0.0628,0.6972,0.8355); rgb(111pt)=(0.0535,0.7006,0.8299); rgb(112pt)=(0.0433,0.7039,0.8242); rgb(113pt)=(0.0328,0.7071,0.8183); rgb(114pt)=(0.0234,0.7103,0.8124); rgb(115pt)=(0.0155,0.7133,0.8064); rgb(116pt)=(0.0091,0.7163,0.8003); rgb(117pt)=(0.0046,0.7192,0.7941); rgb(118pt)=(0.0019,0.722,0.7878); rgb(119pt)=(0.0009,0.7248,0.7815); rgb(120pt)=(0.0018,0.7275,0.7752); rgb(121pt)=(0.0046,0.7301,0.7688); rgb(122pt)=(0.0094,0.7327,0.7623); rgb(123pt)=(0.0162,0.7352,0.7558); rgb(124pt)=(0.0253,0.7376,0.7492); rgb(125pt)=(0.0369,0.74,0.7426); rgb(126pt)=(0.0504,0.7423,0.7359); rgb(127pt)=(0.0638,0.7446,0.7292); rgb(128pt)=(0.077,0.7468,0.7224); rgb(129pt)=(0.0899,0.7489,0.7156); rgb(130pt)=(0.1023,0.751,0.7088); rgb(131pt)=(0.1141,0.7531,0.7019); rgb(132pt)=(0.1252,0.7552,0.695); rgb(133pt)=(0.1354,0.7572,0.6881); rgb(134pt)=(0.1448,0.7593,0.6812); rgb(135pt)=(0.1532,0.7614,0.6741); rgb(136pt)=(0.1609,0.7635,0.6671); rgb(137pt)=(0.1678,0.7656,0.6599); rgb(138pt)=(0.1741,0.7678,0.6527); rgb(139pt)=(0.1799,0.7699,0.6454); rgb(140pt)=(0.1853,0.7721,0.6379); rgb(141pt)=(0.1905,0.7743,0.6303); rgb(142pt)=(0.1954,0.7765,0.6225); rgb(143pt)=(0.2003,0.7787,0.6146); rgb(144pt)=(0.2061,0.7808,0.6065); rgb(145pt)=(0.2118,0.7828,0.5983); rgb(146pt)=(0.2178,0.7849,0.5899); rgb(147pt)=(0.2244,0.7869,0.5813); rgb(148pt)=(0.2318,0.7887,0.5725); rgb(149pt)=(0.2401,0.7905,0.5636); rgb(150pt)=(0.2491,0.7922,0.5546); rgb(151pt)=(0.2589,0.7937,0.5454); rgb(152pt)=(0.2695,0.7951,0.536); rgb(153pt)=(0.2809,0.7964,0.5266); rgb(154pt)=(0.2929,0.7975,0.517); rgb(155pt)=(0.3052,0.7985,0.5074); rgb(156pt)=(0.3176,0.7994,0.4975); rgb(157pt)=(0.3301,0.8002,0.4876); rgb(158pt)=(0.3424,0.8009,0.4774); rgb(159pt)=(0.3548,0.8016,0.4669); rgb(160pt)=(0.3671,0.8021,0.4563); rgb(161pt)=(0.3795,0.8026,0.4454); rgb(162pt)=(0.3921,0.8029,0.4344); rgb(163pt)=(0.405,0.8031,0.4233); rgb(164pt)=(0.4184,0.803,0.4122); rgb(165pt)=(0.4322,0.8028,0.4013); rgb(166pt)=(0.4463,0.8024,0.3904); rgb(167pt)=(0.4608,0.8018,0.3797); rgb(168pt)=(0.4753,0.8011,0.3691); rgb(169pt)=(0.4899,0.8002,0.3586); rgb(170pt)=(0.5044,0.7993,0.348); rgb(171pt)=(0.5187,0.7982,0.3374); rgb(172pt)=(0.5329,0.797,0.3267); rgb(173pt)=(0.547,0.7957,0.3159); rgb(175pt)=(0.5748,0.7929,0.2941); rgb(176pt)=(0.5886,0.7913,0.2833); rgb(177pt)=(0.6024,0.7896,0.2726); rgb(178pt)=(0.6161,0.7878,0.2622); rgb(179pt)=(0.6297,0.7859,0.2521); rgb(180pt)=(0.6433,0.7839,0.2423); rgb(181pt)=(0.6567,0.7818,0.2329); rgb(182pt)=(0.6701,0.7796,0.2239); rgb(183pt)=(0.6833,0.7773,0.2155); rgb(184pt)=(0.6963,0.775,0.2075); rgb(185pt)=(0.7091,0.7727,0.1998); rgb(186pt)=(0.7218,0.7703,0.1924); rgb(187pt)=(0.7344,0.7679,0.1852); rgb(188pt)=(0.7468,0.7654,0.1782); rgb(189pt)=(0.759,0.7629,0.1717); rgb(190pt)=(0.771,0.7604,0.1658); rgb(191pt)=(0.7829,0.7579,0.1608); rgb(192pt)=(0.7945,0.7554,0.157); rgb(193pt)=(0.806,0.7529,0.1546); rgb(194pt)=(0.8172,0.7505,0.1535); rgb(195pt)=(0.8281,0.7481,0.1536); rgb(196pt)=(0.8389,0.7457,0.1546); rgb(197pt)=(0.8495,0.7435,0.1564); rgb(198pt)=(0.86,0.7413,0.1587); rgb(199pt)=(0.8703,0.7392,0.1615); rgb(200pt)=(0.8804,0.7372,0.165); rgb(201pt)=(0.8903,0.7353,0.1695); rgb(202pt)=(0.9,0.7336,0.1749); rgb(203pt)=(0.9093,0.7321,0.1815); rgb(204pt)=(0.9184,0.7308,0.189); rgb(205pt)=(0.9272,0.7298,0.1973); rgb(206pt)=(0.9357,0.729,0.2061); rgb(207pt)=(0.944,0.7285,0.2151); rgb(208pt)=(0.9523,0.7284,0.2237); rgb(209pt)=(0.9606,0.7285,0.2312); rgb(210pt)=(0.9689,0.7292,0.2373); rgb(211pt)=(0.977,0.7304,0.2418); rgb(212pt)=(0.9842,0.733,0.2446); rgb(213pt)=(0.99,0.7365,0.2429); rgb(214pt)=(0.9946,0.7407,0.2394); rgb(215pt)=(0.9966,0.7458,0.2351); rgb(216pt)=(0.9971,0.7513,0.2309); rgb(217pt)=(0.9972,0.7569,0.2267); rgb(218pt)=(0.9971,0.7626,0.2224); rgb(219pt)=(0.9969,0.7683,0.2181); rgb(220pt)=(0.9966,0.774,0.2138); rgb(221pt)=(0.9962,0.7798,0.2095); rgb(222pt)=(0.9957,0.7856,0.2053); rgb(223pt)=(0.9949,0.7915,0.2012); rgb(224pt)=(0.9938,0.7974,0.1974); rgb(225pt)=(0.9923,0.8034,0.1939); rgb(226pt)=(0.9906,0.8095,0.1906); rgb(227pt)=(0.9885,0.8156,0.1875); rgb(228pt)=(0.9861,0.8218,0.1846); rgb(229pt)=(0.9835,0.828,0.1817); rgb(230pt)=(0.9807,0.8342,0.1787); rgb(231pt)=(0.9778,0.8404,0.1757); rgb(232pt)=(0.9748,0.8467,0.1726); rgb(233pt)=(0.972,0.8529,0.1695); rgb(234pt)=(0.9694,0.8591,0.1665); rgb(235pt)=(0.9671,0.8654,0.1636); rgb(236pt)=(0.9651,0.8716,0.1608); rgb(237pt)=(0.9634,0.8778,0.1582); rgb(238pt)=(0.9619,0.884,0.1557); rgb(239pt)=(0.9608,0.8902,0.1532); rgb(240pt)=(0.9601,0.8963,0.1507); rgb(241pt)=(0.9596,0.9023,0.148); rgb(242pt)=(0.9595,0.9084,0.145); rgb(243pt)=(0.9597,0.9143,0.1418); rgb(244pt)=(0.9601,0.9203,0.1382); rgb(245pt)=(0.9608,0.9262,0.1344); rgb(246pt)=(0.9618,0.932,0.1304); rgb(247pt)=(0.9629,0.9379,0.1261); rgb(248pt)=(0.9642,0.9437,0.1216); rgb(249pt)=(0.9657,0.9494,0.1168); rgb(250pt)=(0.9674,0.9552,0.1116); rgb(251pt)=(0.9692,0.9609,0.1061); rgb(252pt)=(0.9711,0.9667,0.1001); rgb(253pt)=(0.973,0.9724,0.0938); rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805), mesh/rows=19]
table[row sep=crcr, point meta=c]

x	y	c

0   1   1

0   5   1

0   10  1

0   25  0.990380000000000

0   50  0.944280000000000

0   100 0.889040000000000

0   150 0.760400000000000

0   200 0.679840000000000

0   250 0.578320000000000

0   400 0.355820000000000

0   500 0.309160000000000

0   750 0.152400000000000

0   1000 0.0755600000000000

0   2000 0.0211000000000000

0   5000 0.00910000000000000

0   10000 0.00816000000000000

5 1	1

5 5	1

5 10	1

5 25	0.977040000000000

5 50	0.911240000000000

5 100	0.796240000000000

5 150	0.713520000000000

5 200	0.607620000000000

5 250	0.467020000000000

5 400	0.294820000000000

5 500	0.221960000000000

5 750	0.102700000000000

5 1000	0.0394800000000000

5 2000	0.0146800000000000

5 5000	0.00638000000000000

5 10000	0.00498000000000000

10 1	1

10 5	0.996700000000000

10 10	0.949000000000000

10 25	0.887140000000000

10 50	0.617260000000000

10 100	0.315680000000000

10 150	0.247020000000000

10 200	0.185780000000000

10 250	0.165640000000000

10 400	0.0691600000000000

10 500	0.0505200000000000

10 750	0.0197000000000000

10 1000	0.00768000000000000

10 2000	0.00738000000000000

10 5000	0.00284000000000000

10 10000	0

15 1	1

15 5	1

15 10	0.998920000000000

15 25	0.964480000000000

15 50	0.898100000000000

15 100	0.737980000000000

15 150	0.559200000000000

15 200	0.364240000000000

15 250	0.365200000000000

15 400	0.205020000000000

15 500	0.110400000000000

15 750	0.0444000000000000

15 1000	0.0172000000000000

15 2000	0.00880000000000000

15 5000	0.00200000000000000

15 10000	0.00616000000000000

20 1	1

20 5	1

20 10	0.996940000000000

20 25	0.942720000000000

20 50	0.848440000000000

20 100	0.653600000000000

20 150	0.542320000000000

20 200	0.410760000000000

20 250	0.318480000000000

20 400	0.172740000000000

20 500	0.118800000000000

20 750	0.0359000000000000

20 1000	0.0243600000000000

20 2000	0.0132000000000000

20 5000	0.00482000000000000

20 10000	0.00784000000000000

25 1	1

25 5	0.944860000000000

25 10	0.924400000000000

25 25	0.584420000000000

25 50	0.317300000000000

25 100	0.150540000000000

25 150	0.0989400000000000

25 200	0.0949000000000000

25 250	0.0656200000000000

25 400	0.0244800000000000

25 500	0.0181200000000000

25 750	0.00518000000000000

25 1000	0.00552000000000000

25 2000	0.00100000000000000

25 5000	0

25 10000	0.00168000000000000

30	1	0.999240000000000

30	5	0.935120000000000

30	10	0.748900000000000

30	25	0.421400000000000

30	50	0.241220000000000

30	100	0.130300000000000

30	150	0.0669600000000000

30	200	0.0558000000000000

30	250	0.0325000000000000

30	400	0.0146000000000000

30	500	0.00852000000000000

30	750	0.00202000000000000

30	1000	0.00336000000000000

30	2000	0.00100000000000000

30	5000	0.00204000000000000

30	10000	0.00400000000000000

35	1	1

35	5	0.999840000000000

35	10	0.983140000000000

35	25	0.899440000000000

35	50	0.803680000000000

35	100	0.510640000000000

35	150	0.347960000000000

35	200	0.256680000000000

35	250	0.159360000000000

35	400	0.0628400000000000

35	500	0.0395800000000000

35	750	0.0167400000000000

35	1000	0.0136000000000000

35	2000	0.00692000000000000

35	5000	0.00416000000000000

35	10000	0.00844000000000000

40	1	0.999740000000000

40	5	0.939420000000000

40	10	0.774740000000000

40	25	0.419380000000000

40	50	0.231240000000000

40	100	0.113380000000000

40	150	0.0766200000000000

40	200	0.0639000000000000

40	250	0.0383600000000000

40	400	0.0140000000000000

40	500	0.0111800000000000

40	750	0.00474000000000000

40	1000	0.00120000000000000

40	2000	0.00242000000000000

40	5000	0.00110000000000000

40	10000	0.000140000000000000

45	1	0.999780000000000

45	5	0.929880000000000

45	10	0.806760000000000

45	25	0.446640000000000

45	50	0.254640000000000

45	100	0.118860000000000

45	150	0.0620400000000000

45	200	0.0640800000000000

45	250	0.0330400000000000

45	400	0.0221800000000000

45	500	0.0102200000000000

45	750	0.00504000000000000

45	1000	0.00324000000000000

45	2000	0.000900000000000000

45	5000	0.000640000000000000

45	10000	0.00200000000000000

50	1	1

50	5	0.985780000000000

50	10	0.955120000000000

50	25	0.793760000000000

50	50	0.539900000000000

50	100	0.282560000000000

50	150	0.199780000000000

50	200	0.171220000000000

50	250	0.130440000000000

50	400	0.0472800000000000

50	500	0.0301200000000000

50	750	0.00412000000000000

50	1000	0.00668000000000000

50	2000	0.00572000000000000

50	5000	0.0760000000000000

50	10000	0.00100000000000000

55	1	1

55	5	0.880280000000000

55	10	0.811040000000000

55	25	0.438960000000000

55	50	0.237200000000000

55	100	0.104700000000000

55	150	0.0814800000000000

55	200	0.0687200000000000

55	250	0.0396000000000000

55	400	0.0188800000000000

55	500	0.0103600000000000

55	750	0.00500000000000000

55	1000	0.00354000000000000

55	2000	0.00170000000000000

55	5000	0.00176000000000000

55	10000	0.00168000000000000

60	1	1

60	5	0.997800000000000

60	10	0.972640000000000

60	25	0.851640000000000

60	50	0.662960000000000

60	100	0.381380000000000

60	150	0.234920000000000

60	200	0.216240000000000

60	250	0.165540000000000

60	400	0.0728400000000000

60	500	0.0395000000000000

60	750	0.0103000000000000

60	1000	0.0107800000000000

60	2000	0.00556000000000000

60	5000	0.00744000000000000

60	10000	0.00218000000000000

65	1	1

65	5	0.967000000000000

65	10	0.887040000000000

65	25	0.677320000000000

65	50	0.388080000000000

65	100	0.205660000000000

65	150	0.136940000000000

65	200	0.108300000000000

65	250	0.0626600000000000

65	400	0.0236400000000000

65	500	0.0235800000000000

65	750	0.00804000000000000

65	1000	0.00300000000000000

65	2000	0.00200000000000000

65	5000	0.000560000000000000

65	10000	0.00170000000000000

70	1	0.979800000000000

70	5	0.941560000000000

70	10	0.793800000000000

70	25	0.458500000000000

70	50	0.262960000000000

70	100	0.112560000000000

70	150	0.0882600000000000

70	200	0.0614800000000000

70	250	0.0354000000000000

70	400	0.0163000000000000

70	500	0.0109000000000000

70	750	0.00494000000000000

70	1000	0.00262000000000000

70	2000	0.00102000000000000

70	5000	0.00164000000000000

70	10000	0.00172000000000000

75	1	1

75	5	0.996800000000000

75	10	0.970080000000000

75	25	0.856160000000000

75	50	0.641760000000000

75	100	0.388960000000000

75	150	0.243160000000000

75	200	0.199760000000000

75	250	0.152440000000000

75	400	0.0393400000000000

75	500	0.0238000000000000

75	750	0.0180000000000000

75	1000	0.00562000000000000

75	2000	0.00734000000000000

75	5000	0.00402000000000000

75	10000	0.00484000000000000

80	1	1

80	5	0.996400000000000

80	10	0.974200000000000

80	25	0.853400000000000

80	50	0.653120000000000

80	100	0.401060000000000

80	150	0.237460000000000

80	200	0.199120000000000

80	250	0.157240000000000

80	400	0.0617400000000000

80	500	0.0452200000000000

80	750	0.0144800000000000

80	1000	0.0101600000000000

80	2000	0.00756000000000000

80	5000	0.000140000000000000

80	10000	0.00556000000000000

85	1	1

85	5	0.997280000000000

85	10	0.970440000000000

85	25	0.847800000000000

85	50	0.627640000000000

85	100	0.392160000000000

85	150	0.282000000000000

85	200	0.175080000000000

85	250	0.149600000000000

85	400	0.0740200000000000

85	500	0.0307600000000000

85	750	0.0160800000000000

85	1000	0.0116000000000000

85	2000	0.00328000000000000

85	5000	0.00368000000000000

85	10000	0.00160000000000000

90	1	1

90	5	0.993560000000000

90	10	0.951900000000000

90	25	0.799540000000000

90	50	0.509360000000000

90	100	0.309000000000000

90	150	0.188920000000000

90	200	0.130500000000000

90	250	0.117320000000000

90	400	0.0510600000000000

90	500	0.0380800000000000

90	750	0.00926000000000000

90	1000	0.00644000000000000

90	2000	0.00264000000000000

90	5000	0.00124000000000000

90	10000	0.00376000000000000

width=8 cm,
height=4 cm,
scale only axis,
xlabel style=font=,
xlabel=$d^{\text E}$ (m),
ymin=0.4    ,
ylabel style=yshift=-0.2cm,
ylabel style=font=,
axis background/.style=fill=white,
legend style=legend cell align=left, align=left,legend columns=2, fill opacity=0.8, draw=white!15!black, at=(0.99,0.4)

[color=mycolor1, line width=2.0pt, mark=+, mark options=solid, mycolor1]
table[row sep=crcr]
1	0.49699824120603

5	0.505656633165829

10	0.573579497487437

25	0.754206633165829

50	0.858873216080402

100	0.929519346733669

150	0.956029497487437

200	0.961489346733668

250	0.959329849246231

400	0.963544020100503

500	0.986735728643216

750	0.988740804020101

1000	0.986384271356784

2000	0.993675628140703

$\text{LBA }\theta{}^\text{E}\text{ = 5}^\circ$

[color=mycolor2, line width=2.0pt, mark=o, mark options=solid, mycolor2]
table[row sep=crcr]
1	0.496967336683417

5	0.515865025125628

10	0.601536733668342

25	0.785336582914573

50	0.877422060301507

100	0.939385326633166

150	0.958023266331659

200	0.961081557788945

250	0.977115226130654

400	0.981645427135678

500	0.985456331658292

750	0.995548341708543

1000	0.992369648241206

2000	0.983985879396985

$\text{LBA }\theta{}^\text{E}\text{ = 20}^\circ$

[color=mycolor3, line width=2.0pt, mark=square, mark options=solid, mycolor3]
table[row sep=crcr]
1	0.974263266331658

5	0.989137688442211

10	0.984208542713568

25	0.989232462311558

50	0.994157638190955

100	0.994314924623116

150	0.989204170854271

200	0.999015979899497

250	0.994137587939699

400	0.989162663316583

500	0.98423487437186

750	0.994161959798995

1000	0.999094824120603

2000	0.994335979899498

$\text{LBA }\theta{}^\text{E}\text{ = 30}^\circ$

[color=red, line width=2.0pt, mark=asterisk, mark options=solid, red]
table[row sep=crcr]
1	0.497089296482412

5	0.583415879396985

10	0.715945226130653

25	0.865008291457286

50	0.931723567839196

100	0.95869959798995

150	0.968863567839196

200	0.984313718592965

250	0.988473316582914

400	0.990032211055276

500	0.991775376884422

750	0.993111155778895

1000	0.998693316582915

2000	0.998941256281407

$\text{LBA }\theta{}^\text{E}\text{ = 45}^\circ$

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table[row sep=crcr]
1	0.525102613065327

5	0.803360954773869

10	0.890751708542714

25	0.959383015075377

50	0.979358643216081

100	0.987401055276382

150	0.996205879396985

200	0.992898844221105

250	0.983384623115578

400	0.994042763819095

500	0.99884743718593

750	0.993879095477387

1000	0.994079798994975

2000	0.984090452261306

$\text{LBA }\theta{}^\text{E}\text{ = 60}^\circ$

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table[row sep=crcr]
1	0.994408140703518

5	0.999552914572864

10	0.994377688442211

25	0.994499849246231

50	0.994484572864322

100	0.994484572864322

150	0.989479497487437

200	0.989504673366835

250	0.988978291457286

400	0.993371206030151

500	0.993242060301507

750	0.983969296482412

1000	0.993794271356784

2000	0.994015326633166

$\text{CBA }\theta^\text{E}\text{ = 45}^\circ$

Comparison of accuracy under code-based attack (CBA) and location-based attack (LBA), using OC-SVM, $\theta^{\text{A}} = 0\degree$.

In the context of the location-based attack, a parallel trend to the observed RMSE patterns is evident: as the distance $d^{\text{E}}$ between Eve and the verifier increases, the classification accuracy improves. This improvement occurs because Eve's ability to execute a successful impersonation attack diminishes at greater distances due to power limitations. Similarly, smaller values of $\theta^{\text{E}}$ lead to more successful attacks, resulting in reduced classification accuracy. This trend is  evident in the lower classification accuracy observed for $\theta^{\text{E}}= 5 \degree$ in comparison to that observed for $\theta^{\text{E}}= 20 \degree$, which in turn is smaller when compared to that of $\theta^{\text{E}}= 45 \degree$, aligning with the RMSE trends illustrated in Fig. <ref>. For the case of $\theta^{\text{E}}= 30 \degree$, the null of Eve's beam response aligns precisely with the main lobe of Alice's beam response, leading to the failure of impersonation attempts and consequently achieving the highest authentication accuracy.
For the code-based attack,

the impersonation attempt is less effective, resulting in a  high classifier accuracy even with a smaller RMSE for $\theta^{\text E}$. This disparity arises because the location-based attack causes the disappearance of the original minimum and introduces a new minimum at $\theta^{\text A}$, providing unbiased estimates with a variance dependent on Eve's angle and distance. Conversely, the code-based attack introduces bias into the estimates, making them easier to detect.

width=8 cm,
height=4 cm,
scale only axis,
ylabel style=yshift=-0.2cm,
xlabel style=font=,
xlabel=$d^{\text E}$ (m),
ylabel style=font=,
axis background/.style=fill=white,
legend style=legend cell align=left, align=left, legend columns=2, fill opacity=0.6, draw=white!15!black, at=(0.99,0.99)
[color=mycolor1, line width=2.0pt, mark=+, mark options=solid, mycolor1]
table[row sep=crcr]
1	0.99

5	0.9729522

10	0.8178016

25	0.4682832

50	0.2500369

100	0.1296801

150	0.08661

200	0.0657558

250	0.0502815

400	0.0320256

500	0.02523

750	0.0114314

1000	0.0061278

2000	0.0016709

LBA $\theta{}^\text{E}\text{ = 5}^\circ$

[color=mycolor2, line width=2.0pt, mark=o, mark options=solid, mycolor2]
table[row sep=crcr]
1	0.99

5	0.9425836

10	0.7622277

25	0.4061512

50	0.2134

100	0.1097415

150	0.0727749

200	0.0566949

250	0.04431

400	0.0256113

500	0.0183348

750	0.00806000000000001

1000	0.0044253

2000	0.001247

LBA $\theta{}^\text{E}\text{ = 20}^\circ$

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table[row sep=crcr]
1	0.000703

5	0.0008022

10	0.0007725

25	0.0006454

50	0.0008062

100	0.0006138

150	0.0005782

200	0.00067

250	0.0007524

400	0.0007211

500	0.0006596

750	0.0006435

1000	0.00088

2000	0.0006039

LBA $\theta{}^\text{E}\text{ = 30}^\circ$

[color=red, line width=2.0pt, mark=asterisk, mark options=solid, red]
table[row sep=crcr]
1	0.99

5	0.8085882

10	0.5245344

25	0.2379507

50	0.1250804

100	0.0614656

150	0.0411796

200	0.03011

250	0.0220794

400	0.0091377

500	0.0053001

750	0.0027324

1000	0.00177

2000	0.00094

LBA $\theta{}^\text{E}\text{ = 45}^\circ$

[color=mycolor4, line width=2.0pt, mark=x, mark options=solid, mycolor4]
table[row sep=crcr]
1	0.92414

5	0.3705282

10	0.1964367

25	0.08003

50	0.04

100	0.0144045

150	0.00629

200	0.0031878

250	0.0024735

400	0.001188

500	0.00116

750	0.0009009

1000	0.0007765

2000	0.0008245

LBA $\theta{}^\text{E}\text{ = 60}^\circ$

[color=black, line width=2.0pt, mark=diamond, dashed, mark options=solid, black]
table[row sep=crcr]
1	0

5	0

10	0

25	0

50	0

100	0

150	0

200	0.0002254

250	0.0013034

400	0.0022473

500	0.0022275

750	0.0014356

1000	0.0011286

2000	0.0008118

CBA $\theta{}^\text{E}\text{ = 45}^\circ$

Comparison of the probability of MD under code-based attack (CBA) and location-based attack (LBA), using OC-SVM , $\theta^{\text{A}} = 0\degree$.

We also analyze the probability of MD, which is illustrated in Fig. <ref> for both types of attacks. With a location-based attack, a similar trend is observed in terms of MD probability as in accuracy: the probability of MD for $5 \degree$  is larger than that for $20 \degree$, which in turn is larger than that for $ 45 \degree$. Notably, for $\theta^{\text{E}}= 30 \degree$, the probability of MD is lower, aligning with the already observed accuracy trends. The probability of FA is not illustrated in the figures, as it remains consistently around 0.014 regardless of changes in Eve's distance and AoA.[In the specific scenario under consideration, an OCC is trained solely on samples from Alice. Given that these samples remain unchanged from the training phase to the verification phase, except for the random noise affecting AoA estimation, Eve's parameters have no impact on the probability of false alarm.]

§ CONCLUSIONS

We studied a physical layer authentication protocol in which a BS equipped with an analog array aims at identifying a legitimate transmitting node using an OC-SVM classifier trained on the estimated AoA of the same node.
We introduced several attack techniques that could be exploited by a malicious node to forge the estimated AoA and impersonate the legitimate node.
We studied the effectiveness of these attacks on an ML-based classifier's performance for various distances and angles, observing that location-based and code-based attacks can be successful in impersonating the AoA. Our study reveals that a successful impersonation requires knowledge of the location of the attacker and the victim, as well as the combiners at the verifier. The effectiveness of the attack depends on the available transmission power at the attacker, as well as the nulls of the verifier's beams. Future studies can include investigating authentication spoofing with location mismatches and exploring the impact of multipath channels.

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