# A Nonlinear Autoregressive Neural Network for Interference Prediction and
Resource Allocation in URLLC Scenarios

Christian Padilla  Centre for Wireless Communications (CWC), University of
Oulu, Oulu, Finland,
Emails: {christian.padillaolivo, ramin.hashemi, nurulhuda.mahmood,
<EMAIL_ADDRESS>††thanks: This work was supported by the Academy of
Finland 6Genesis Flagship project under grant 318927. Ramin Hashemi  Centre
for Wireless Communications (CWC), University of Oulu, Oulu, Finland,
Emails: {christian.padillaolivo, ramin.hashemi, nurulhuda.mahmood,
<EMAIL_ADDRESS>††thanks: This work was supported by the Academy of
Finland 6Genesis Flagship project under grant 318927. Nurul Huda Mahmood
Centre for Wireless Communications (CWC), University of Oulu, Oulu, Finland,
Emails: {christian.padillaolivo, ramin.hashemi, nurulhuda.mahmood,
<EMAIL_ADDRESS>††thanks: This work was supported by the Academy of
Finland 6Genesis Flagship project under grant 318927. Matti Latva-aho  Centre
for Wireless Communications (CWC), University of Oulu, Oulu, Finland,
Emails: {christian.padillaolivo, ramin.hashemi, nurulhuda.mahmood,
<EMAIL_ADDRESS>††thanks: This work was supported by the Academy of
Finland 6Genesis Flagship project under grant 318927.

###### Abstract

Ultra reliable low latency communications (URLLC) is a new service class
introduced in 5G which is characterized by strict reliability ($1-10^{-5}$)
and low latency requirements ($1$ ms). To meet these requisites, several
strategies like over-provisioning of resources and channel-predictive
algorithms have been developed. This paper describes the application of a
Nonlinear Autoregressive Neural Network (NARNN) as a novel approach to
forecast interference levels in a wireless system for the purpose of efficient
resource allocation. Accurate interference forecasts also grant the
possibility of meeting specific outage probability requirements in URLLC
scenarios. Performance of this proposal is evaluated upon the basis of NARNN
predictions accuracy and system resource usage. Our proposed approach achieved
a promising mean absolute percentage error of 7.8 % on interference
predictions and also reduced the resource usage in up to 15 % when compared to
a recently proposed interference prediction algorithm.

###### Index Terms:

Interference prediction, Nonlinear Autoregressive Neural Network, ultra-
reliable low-latency communications (URLLC).

##  I Introduction

Ultra-reliable low-latency communication (URLLC) is a service class introduced
in 5G that targets strict quality of service (QoS) requirements: reliability
of $1-10^{-5}$ and latency of 1 ms [1]. These strict QoS guarantees can be
achieved by over-provisioning of resources, i.e., allocating a large amount of
resources in order to guarantee low outages [2]. However, such an approach is
neither resource efficient nor scalable. Therefore it is necessary to develop
a radio resource management (RRM) technique that overcomes these scalability
and resource usage (RU) challenges while enabling URLLC [3].

Interference management has always been a challenge in wireless systems design
[4]. Efficient interference management is among the possible ways to ensure
efficient resource allocation (and to ensure scalability) for URLLC services.
Having the ability to predict future interference is beneficial to tackle the
effects of interference [5], resources can be allocated efficiently using this
knowledge. Obtaining accurate forecasts of the interference power is a
challenging task due to the time varying nature of wireless channels. Various
researchers have proposed different interference prediction techniques.
Haenggi et al. [6] used stochastic geometry to derive mean interference and
probability distribution in wireless networks, Schmidt et al. [4] proposed the
use of a recursive predictor to estimate future interference values by
filtering the measured interference. Varma presented a two-staged machine
learning algorithm to remove multiple interference from wireless signals while
minimizing information loss in [7].

Methodologically speaking, the interference power prediction can be classified
into statistical and artificial intelligence (AI) methods. Statistical
interference power prediction implies that some statistical properties of the
interference power, such as mean interference, or even full probability
distributions, are used to estimate future interference values. AI-based
interference prediction consists of using a machine learning algorithm to
approximate the behavior of the channel with a model that uses past
interference values as inputs and future interference values as outputs. In
this proposal we consider an AI-based solution since there is a broad study of
statistics-based interference prediction techniques but there is scarcity in
the application of AI for the same purpose.

A Nonlinear Autoregressive Neural Network (NARNN) has been chosen for
interference prediction due to its high forecasting accuracy [8] and the fact
that there is no need of a mathematical model of the process other than its
own universal algorithm for future series prediction. A major benefit of
NARNNs is that they accept dynamic inputs represented by time series sets
where past values are used to predict future values in a time series set [9].
Several researchers have demonstrated promising prediction capabilities of
NARNNs. Gairaa et al. [10] used a NARNN to predict global solar radiation
levels, Ruiz et al. [9] used a NARNN to forecast energy consumption in public
buildings and Sarkar et al. [8] studied the performance of NARNNs for long-
term wind speed forecasting.

The layout of this paper is as follows: the system model is presented in
Section II. The NARNN design is described in Section III. In Section IV, the
results are discussed. The conclusion of this proposal is presented in Section
V.

##  II System Model

We consider the downlink of a typical multi-user wireless system in the two
dimensional space organized by $N$ transmitters (i.e., base stations (BS)),
each of which serves a single receiver. We focus our attention on a particular
receiver of choice (denoted as user $n$), which is receiving a URLLC
transmission in the presence of interference from the remaining $N-1$ BSs. We
assume that the transmitting BS of interest is the closest BS, while the
remaining $N-1$ interfering BSs are distributed across the service area at
varying distances from the receiver of interest.

The corresponding channel responses between a transmitter and a receiver
follows circularly symmetric complex Gaussian distribution. It is worth noting
that the adaption of the channels’ distribution can be generalized to more
practical and complex scenarios without loss of generality. In order to keep
the latency budget as low as possible, we assume a single-shot transmission
scheme. Therefore, the received signal at the receiver is given by

$\displaystyle
r=h_{n}x_{n}+\underset{\text{Interference}}{\underbrace{\sum_{k=1,k\neq
n}^{N}h_{k}x_{k}}}+w,$ (1)

where $h_{k}\sim\mathcal{C}\mathcal{N}(0,\beta_{k})$, $\forall
k\in\\{1,\ldots,N\\}$ denotes the channel response between the $k^{th}$ BS and
the user $n$ with path loss $\beta_{k}$. Also, the white Gaussian noise $w$
has variance $\mathbb{E}[|w|^{2}]=\sigma^{2}$ and the symbols transmitted from
BS to each user $x_{n}$ where $\mathbb{E}[|x_{n}|^{2}]=p_{n}$ denotes the
maximum transmit power. Thus, the signal-to-interference-plus-noise ratio
(SINR) is defined as

$\displaystyle\gamma_{n}=\frac{p_{n}|h_{n}|^{2}}{\sum_{k=1,k\neq
n}^{N}|h_{k}|^{2}p_{k}+\sigma^{2}},$ (2)

the objective of this work is to estimate the interference power such that the
transmitter can effectively adapt its rate to minimize the unexpected
interference power variations that affect the received signal quality and
SINR. More specifically, in URLLC systems the amount of resources needed must
be allocated depending on the outage probability requirement. URLLC packets
usually transmit control signals or other application messages where the
packet size is small. Due to the small packet size, conventional Shannon-rate
formula is not applicable. To address this, Polyanski et al. analyzed the
achievable rate and the decoding error probability for finite block-length
channels in [11]. The channel usage for user $n$ in the finite block-length
regime is approximated as

$R_{n}\approx\frac{D}{\text{C}(\hat{\gamma}_{n})}+\frac{Q^{-1}(\epsilon)^{2}\text{V}(\hat{\gamma}_{n})}{2\text{C}(\hat{\gamma}_{n})^{2}}\left[1+\sqrt{1+\frac{4D\text{C}(\hat{\gamma}_{n})}{Q^{-1}(\epsilon)^{2}\text{V}(\hat{\gamma}_{n})}}\right],$
(3)

where

$\displaystyle\hat{\gamma}_{n}=\frac{p_{n}|h_{n}|^{2}}{\hat{\text{I}}_{n}+\sigma^{2}},$
(4)

is the predicted SINR, $\hat{\text{I}}_{n}$ is the predicted interference, $D$
is the number of information bits with decoding probability $\epsilon$,
$\text{C}(\gamma)=\log_{2}(1+\gamma)$ is the Shannon capacity of AWGN channels
under infinite blocklength regime, $Q^{-1}(\cdot)$ is the inverse of the
Q-function and
$V(\gamma)=\frac{1}{\ln{(2)^{2}}}(1-\frac{1}{\left(1+\gamma\right)^{2}})$ is
the channel dispersion.

A model-based approach for interference prediction was recently presented by
Mahmood et al. in [3]. The interference distribution was modeled using a DTMC
and predictions were made in such a way that predicted interference is greater
than the actual interference with probability greater than or equal to the
confidence level $\eta$; resources are calculated using (3). The performance
results presented in [3] will be used as performance benchmarks for the
proposed NARNN and this approach will be referred to as statistics-based
prediction since it considers the entire distribution of interference values;
similar assumptions to this statistics-based prediction are considered in this
paper: the desired channel has a mean SNR $\gamma_{D}$ and the mean
interference to noise ratio (INR) of each interfering link is uniformly
distributed in the range $[\gamma_{I,\text{min}},\gamma_{I,\text{max}}]$, the
desired transmitter transmits packets of $D$ bits with a target block error
rate (BLER) $\epsilon$.

Different from the aforementioned paper, we propose to employ a novel method
to precisely estimate the interference power based on NARNNs. To do so, we
first review fundamental concepts of NARNNs in the next section.

##  III NAR Model

Interference power in a time series is difficult to forecast accurately due to
the random nature of the wireless channel. A linear model would not be able to
model the random variations in the wireless channel. For this reason, a NARNN
has been used for effective time series prediction of interference. The NARNN
is a recurrent dynamic network with feedback connections enclosing layers of
the network; thus, the current output depends on the values of the past output
[12]. The NARNN can be defined as [13]

$y(t)=f(y(t-1),y(t-2),y(t-3),...y(t-n))+\epsilon(t),$ (5)

where $y$ is the data series for the combined interference values of N-1
interferers, $f(\cdot)$ is a transfer function that can be approximated by the
neural network, $n$ is the input delay of interference time series and
$\epsilon$ is the approximation error.

Fig. 1 shows the architecture of the NARNN. It is composed of three layers:
input, hidden and output layers. The NARNN architecture requires specific
number of delays, hidden nodes, activation functions and a efficient training
algorithm [14]. All these parameters can be optimized by trial and error [9].
We found 20 delays to be accurate enough for prediction of Rayleigh channel
interference values. In addition, 16 neurons for hidden layer and both
_logsigmoid_ ($f_{1}$) and linear activation ($f_{2}$) functions were used in
hidden and output layers, respectively. Levenberg-Marquadt back propagation
(LMBP) was chosen as the training algorithm because of its fast convergence
speed and accuracy [15, 16].

Figure 1: NARNN architecture.

The necessary steps for implementing the NARNN are shown in Fig. 2. First, the
time series data sets obtained in simulation was divided in two different
sets: training and testing sets, this is the data pre-processing. NARNN
weights and bias are later initialized with random values. LMBP was used to
adjust their values in every iteration (epoch); as many iterations as needed
should be performed to achieve a target error. The final step consists in
using the test data to evaluate the performance and forecasting ability of the
NARNN. Details about the performance of the NARNN will be discussed in the
following sections. The open loop architecture (no feedback loop) was chosen
over the closed-loop architecture because predictions were made one-step-
ahead. Closed loop architecture is typically used for multistep-ahead
predictions [8]. For this proposal, the NARNN training data sets consist of
interference power time series obtained from computer simulations of downlink
transmission with N-1 interferers, all of which are Rayleigh faded. Details on
performance evaluation of the NARNN and resource allocation are discussed in
the next section.

Figure 2: NARNN training procedure.

##  IV Results and Discussion

This AI-based approach has two objectives. The first one is to predict the
interference values using the developed NARNN; performance of the NARNN is
evaluated by means of MAPE and MSE metrics. The second objective is to
allocate resources depending on the NARNN output; the performance is evaluated
again after allocating resources by studying the resource usage and outage
probabilities achieved by the NAR-based approach and comparing it to the
statistics-based prediction in [3] where interference power value is predicted
using a discrete time Markov chain (DTMC) and a configurable confidence level.
With respect to resource allocation, the predicted interference power needs to
be over-estimated to allow the system to meet target outage probabilities
ranging from $10^{-1}$ to $10^{-5}$. This over-estimation can be accomplished
by using an adjustable factor $1<\alpha<2$ to scale the NARNN output. We
denominate this procedure as the Resource Control stage.

Fig. 3 shows the 2-stage process of the proposed NAR-based RRM technique. The
NARNN is used in the first step for interference forecasting (namely
prediction stage) and the adjustable factor $\alpha$ is used in the second
step for regulating resource utilization.

Figure 3: Resource Management Model Proposal.

Regarding prediction stage, the NARNN was trained using data sets that consist
of interference power time series obtained from computer simulations of a
downlink with N-1 interferers operating in a Rayleigh channel. The prediction
performance of the NARNN was evaluated using mean squared error (MSE) and mean
absolute percentage error (MAPE). Mean square error is given by

$\text{MSE}=\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2},$ (6)

MAPE makes comparisons easier because it is percentage-based [17]. Mean
absolute percentage error is defined as

$\text{MAPE}=\frac{1}{n}\sum_{i=1}^{n}\frac{|y_{i}-\hat{y_{i}}|}{y_{i}}\times
100,$ (7)

The variables $y_{i}$ and $\hat{y_{i}}$ represent real and predicted
interference values respectively. Impulse response corresponding to the NARNN
in Prediction Stage is shown in Fig. 4. The best-performing NARNN was used to
forecast interference power. For comparison purposes, the true values from
simulations have also been plotted. The NARNN achieved a promising MSE of
0.5447 and MAPE of 7.816% in the optimal configuration. To find the optimal
number of neurons tests were made with both _log-sigmoid_ (namely logsig) and
_tangent hyperbolic sigmoid_ (namely tansig) functions. Table I shows the
results of the test with a variable number of neurons with _logsig_ and
_tansig_ functions as activation functions in the hidden layer. These results
show that there is not a significant benefit of increasing the number of
neurons. _Logsig_ performed at its best using 16 neurons with an MSE of 0.5447
while _tansig_ reached peak performance with 14 neurons and an MSE of 0.5446.
While there is a slight improvement with the _tansig_ function with 14
neurons, we observed a higher number of epochs needed for training when
compared to the _logsig_ function. _Tansig_ function required 64 epochs while
_logsig_ was trained with 19 epochs. It was concluded from these experiments
that the developed NARNN required 16 neurons for the best overall performance.

Figure 4: NARNN predictions for a fixed range of time steps. TABLE I: MSE and
MAPE for different Number of Neurons

Activat. | Metric | Number of Neurons
---|---|---
Funct. |  | 8 | 12 | 14 | 16 | 18
Logsig | MSE | 0.5449 | 0.5458 | 0.5455 | 0.5447 | 0.545
| MAPE | 7.828 | 7.836 | 7.832 | 7.816 | 7.829
Tansig | MSE | 0.5452 | 0.5449 | 0.5446 | 0.5454 | 0.5450
| MAPE | 7.830 | 7.824 | 7.831 | 7.825 | 7.826

To study the effect of increasing the number of delays in the performance,
multiple NARNN versions were trained with a different number of delay taps,
specifically: 2, 20 and 50 delay taps. MSE was almost identical for these 3:
0.546, 0.5447 and 0.545 respectively with MAPEs around 7.8%. These results
demonstrate that the NARNN is capable of modelling the Rayleigh channel with a
small number of neurons and delays and that gains in performance are almost
nonexistent when tuning these parameters. Given these results, 20 delays and
16 neurons were chosen to get a marginal improvement while keeping the
complexity of the NARNN low.

With respect to the Resource Control Stage, $\alpha$ can be adjusted once a
sufficient forecasting performance has been attained at the prediction stage,
it is important to note that regulating $\alpha$ leads to changes in resource
usage and outage probability. Since Resource Control Stage consists on a
factor multiplication, it is not possible to evaluate its performance, we
rather exhibit the performance of the entire NAR-based approach in two ways.
The first one, consists in adjusting the $\alpha$ factor to get the NARNN
resource usage to equal the statistics-based estimate resource usage; in this
scenario, the objective is to study the mean outage probability of these two
techniques having the resource usage fixed. The second experiment is similar
but instead of targeting the resource usage with $\alpha$, we aim at the mean
outage probability. The factor $\alpha$ is tuned to lower the resource usage
of the NARNN while matching the statistics-based estimate mean outage
probability. The objective is analogous to the first experiment, to study the
resource usage of both techniques with a fixed mean outage probability.

Fig. 5 shows the ideal, statistics-based and the NAR-based prediction resource
usage for outage probabilities ranging from $10^{-1}$ to $10^{-5}$. It was
found empirically that a value of $\alpha=1.45$ equals the NARNN resource
usage with the statistics-based prediction resource usage. Note that ideal
resource usage has been calculated using a genie-aided estimator and is
considered to be the optimum performance bound while the average interference
is calculated using an IIR filter [3]. Also recall that the $\alpha$ factor
may be regulated dinamically to meet target outage probabilities of systems
that differ from our proposal; increasing $\alpha$ will lead to smaller outage
probabilities at the cost of higher resource usage.

Figure 5: Resource Usage of NAR-based estimate with $\alpha=1.45$.

The mean outage probability of the NAR and statistics-based approaches for
$\alpha=1.45$ and the same range of target probabilities ($10^{-1}$ to
$10^{-5}$) has been plotted in Fig. 6. This plot shows that the NAR-based
approach is capable of reducing the mean outage probability considerably by
using the same amount of resources as the statistical approach. There is a
reduction in outage probability of factor up to 1/10 when using the NARNN with
$\alpha=1.45$.

Figure 6: Outage probability of NAR-based estimate with $\alpha=1.45$.

It is possible to target the outage probability of the statistical approach
instead of the resource usage by choosing $\alpha=1.2$. Fig. 8 shows mean
outage probability for this $\alpha$ value. Both NAR and statistics-based
estimates have similar outage probabilities but the resource usage of the
NARNN went down by approximately 15% compared to the statistics-based estimate
as seen on Fig. 7.

Figure 7: Resource Usage of NAR-based estimate with $\alpha=1.2$. Figure 8:
Outage probability of NAR-based estimate with $\alpha=1.2$.

##  V Conclusion

Having knowledge of the channel is of major importance to avoid high error
rates and allocate resources accordingly. In addition, wireless channels
behaviour is chaotic which makes prediction approaches very appealing. The
focus of this proposal are URLLC scenarios, for this reason, predicting the
channel behaviour is not the only objective, meeting URLLC target outage
probabilities is also a major goal. To target these two objectives, we have
proposed the use of a NAR-based RRM technique with two stages: interference
prediction and resource control stages. For interference prediction, a NARNN
was used due to its promising prediction capabilities. For resource control, a
factor $1<\alpha<2$ is used to scale the output of the NARNN and to regulate
resource usage. The NARNN provided very accurate predictions showing a
promising MSE of 0.5447 and a MAPE of 7.816%. It was found by trial and error
that the optimal configuration for the NARNN was 16 neurons in hidden layer,
20 delays and a log-sigmoid activation function. The performance of the whole
system (NARNN prediction and resource control) was compared to an statistics-
based approach. For $\alpha=1.2$, the NAR-based prediction matched the outage
probability of the Statistics-based approach while using up to 15$\%$ less
resources. In addition, the outage probability is improved by an order of 10
times when using the NARNN with $\alpha=1.45$. In summary, the NARNN showed
promising predictions of interference and allowed a more efficient resource
allocation when compared to statistics-based estimates. In this study NARNNs
has been used to predict interference in a Rayleigh channel, however, we plan
to consider a more complex fading model in our future works.

## References

  * [1] J. Sachs, G. Wikstrom, T. Dudda, R. Baldemair, and K. Kittichokechai, “5G Radio Network Design for Ultra-Reliable Low-Latency Communication,” _IEEE Network_ , vol. 32, no. 2, pp. 24–31, 2018.
  * [2] N. H. Mahmood, D. Laselva, D. Palacios, M. Emara, M. C. Filippou, D. M. Kim, and I. de-la Bandera, “Multi-channel access solutions for 5G new radio,” 2019\.
  * [3] N. H. Mahmood, O. A. López, H. Alves, and M. Latva-Aho, “A Predictive Interference Management Algorithm for URLLC in Beyond 5G Networks,” _IEEE Communications Letters_ , vol. 25, no. 3, pp. 995–999, 2021.
  * [4] J. Schmidt, U. Schilcher, M. Atiq, and C. Bettstetter, “Interference Prediction in Wireless Networks: Stochastic Geometry Meets Recursive Filtering,” _IEEE Transactions on Vehicular Technology_ , vol. PP, pp. 1–1, 02 2021.
  * [5] G. Zheng, I. Krikidis, C. Masouros, S. Timotheou, D.-A. Toumpakaris, and Z. Ding, “Rethinking the role of interference in wireless networks,” _IEEE Communications Magazine_ , vol. 52, no. 11, p. 152–158, Nov 2014. [Online]. Available: http://dx.doi.org/10.1109/MCOM.2014.6957156
  * [6] M. Haenggi, “Mean interference in hard-core wireless networks,” _Communications Letters, IEEE_ , vol. 15, pp. 792 – 794, 09 2011.
  * [7] S. Varma, “A machine learning algorithm for interference removal from a signal,” in _2015 National Conference on Recent Advances in Electronics Computer Engineering (RAECE)_ , 2015, pp. 211–215.
  * [8] R. Sarkar, S. Julai, S. Hossain, W. T. Chong, and M. Rahman, “A comparative study of activation functions of NAR and NARX neural network for long-term wind speed forecasting in malaysia,” _Mathematical Problems in Engineering_ , vol. 2019, p. 6403081, Mar 2019. [Online]. Available: https://doi.org/10.1155/2019/6403081
  * [9] L. G. B. Ruiz, M. P. Cuéllar, M. D. Calvo-Flores, and M. D. C. P. Jiménez, “An application of non-linear autoregressive neural networks to predict energy consumption in public buildings,” _Energies_ , vol. 9, no. 9, 2016\. [Online]. Available: https://www.mdpi.com/1996-1073/9/9/684
  * [10] K. Gairaa, F. Chellali, S. Benkaciali, Y. Messlem, and K. Abdallah, “Daily global solar radiation forecasting over a desert area using NAR neural networks comparison with conventional methods,” in _2015 International Conference on Renewable Energy Research and Applications (ICRERA)_ , 2015, pp. 567–571.
  * [11] Y. Polyanskiy, H. V. Poor, and S. Verdu, “Channel coding rate in the finite blocklength regime,” _IEEE Transactions on Information Theory_ , vol. 56, no. 5, pp. 2307–2359, 2010.
  * [12] F. da Costa Lopes, E. H. Watanabe, and L. G. B. Rolim, “A control-oriented model of a PEM fuel cell stack based on NARX and NOE neural networks,” _IEEE Transactions on Industrial Electronics_ , vol. 62, no. 8, pp. 5155–5163, 2015.
  * [13] Y. D. Nyanteh, S. K. Srivastava, C. S. Edrington, and D. A. Cartes, “Application of artificial intelligence to stator winding fault diagnosis in permanent magnet synchronous machines,” _Electric Power Systems Research_ , vol. 103, pp. 201–213, 2013. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0378779613001466
  * [14] R. Taherdangkoo, A. Tatomir, M. Taherdangkoo, P. Qiu, and M. Sauter, “Nonlinear Autoregressive Neural Networks to Predict Hydraulic Fracturing Fluid Leakage into Shallow Groundwater,” _Water_ , vol. 12, no. 3, 2020\. [Online]. Available: https://www.mdpi.com/2073-4441/12/3/841
  * [15] M. Hagan and M. Menhaj, “Training feedforward networks with the Marquardt algorithm,” _IEEE Transactions on Neural Networks_ , vol. 5, no. 6, pp. 989–993, 1994.
  * [16] D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” _Journal of the Society for Industrial and Applied Mathematics_ , vol. 11, no. 2, pp. 431–441, 1963. [Online]. Available: https://doi.org/10.1137/0111030
  * [17] R. G. Kavasseri and K. Seetharaman, “Day-ahead wind speed forecasting using f-ARIMA models,” _Renewable Energy_ , vol. 34, no. 5, pp. 1388–1393, 2009\. [Online]. Available: https://ideas.repec.org/a/eee/renene/v34y2009i5p1388-1393.html