# Towards Scalable Multi-Chip Wireless Networks with Near-Field Time Reversal
††thanks: *F. Rodríguez-Galán and A. Bandara contributed equally to this work.
Authors acknowledge support from the European Union’s Horizon 2020 research
and innovation program, grant agreement 863337 (WiPLASH), the European
Research Council (ERC) under grant agreement 101042080 (WINC) as well as the
European Innovation Council (EIC) PATHFINDER scheme, grant agreement No
101099697 (QUADRATURE). Corresponding author: Sergi Abadal<EMAIL_ADDRESS>
Ama Bandara  Fátima Rodríguez-Galán  Pau Talarn  Elana Pereira de Santana
Peter Haring Bolívar  Eduard Alarcón  Sergi Abadal A.Bandara, F. Rodríguez-
Galán, P. Talarn, E. Alarcón, S. Abadal are with Universitàt Politècnica de
Catalunya, Spain. E. Pereira de Santana and P. Haring Bolívar are with
University of Siegen, Germany

###### Abstract

The concept of Wireless Network-on-Chip (WNoC) has emerged as a potential
solution to address the escalating communication demands of modern computing
systems due to their low-latency, versatility, and reconfigurability. However,
for WNoC to fulfill its potential, it is essential to establish multiple high-
speed wireless links across chips. Unfortunately, the compact and enclosed
nature of computing packages introduces significant challenges in the form of
Co-Channel Interference (CCI) and Inter-Symbol Interference (ISI), which not
only hinder the deployment of multiple spatial channels but also severely
restrict the symbol rate of each individual channel. In this paper, we posit
that Time Reversal (TR) could be effective in addressing both impairments in
this static scenario thanks to its spatiotemporal focusing capabilities even
in the near field. Through comprehensive full-wave simulations and bit error
rate analysis in multiple scenarios and at multiple frequency bands, we
provide evidence that TR can increase the symbol rate by an order of
magnitude, enabling the deployment of multiple concurrent links and achieving
aggregate speeds exceeding 100 Gb/s. Finally, we evaluate the impact of
reducing the sampling rate of the TR filter on the achievable speeds, paving
the way to practical TR-based wireless communications at the chip scale.

###### Index Terms:

Time Reversal; Near-Field Communications; Wireless Interconnects; Network-on-
Chip

##  I Introduction

The end of Moore’s law has compelled computer architects to explore methods
for improving the performance and efficiency of microprocessors beyond mere
transistor scaling. One approach involves increasing the number of independent
processor cores within a chip, resulting in what are known as many-core
processors [1]. Alternatively, other strategies encompass the deployment of
specialized hardware accelerators and the integration of multiple such
specialized chips within a computing package [2]. Given the parallel nature of
these architectures and their requirement for internal data synchronization
and sharing, effective communication within and between chips emerges as a
pivotal factor determining the performance and efficiency of next-generation
computing systems.

Currently, numerous processor families in both academic and industrial
settings adopt the Network-on-Chip (NoC) as the prevailing solution for on-
chip communications [1]. A NoC functions as a packet-switched network
comprising on-chip routers and links co-integrated into the architecture. Its
widespread use is attributed to its simplicity and high performance,
particularly in moderately sized processors. However, as architectures scale
towards larger sizes and extend beyond the confines of a single chip, where
wired links experience significant slowdowns [2], NoC encounters notable
challenges related to latency and energy consumption. This becomes especially
problematic during collective communications, such as one-to-all and all-to-
one patterns, which can lead to severe congestion within the NoC.

In this context, Wireless Network-on-Chip (WNoC) is an emerging paradigm with
significant promise to enhance communications within computing packages. WNoC
are possible because of the advances in antennas and transceivers in the
millimeter-wave (mmWave) and THz bands that have made possible their
integration inside computing cores [3, 4]. They are expected to solve the
scalability and flexibility issues that come with the increment of the number
of processors, their integration on multiple interconnected chips, and the use
of wired NoC communication approaches [1, 5]. The goal is to augment the wired
backbone with wireless links within the package [6].

Due to the use of electromagnetic (EM) propagation nearly at the speed of
light, WNoC provides broadcast and multicast opportunities with reduced
latency and is expected to offer reconfigurable links able to operate at
speeds of tens of Gb/s or more. For the WNoC paradigm to be competitive,
though, it must deliver a reliability commensurate to that of their wired
counterpart. In particular, multiple works [7, 8, 9, 10] point towards a
latency of 1–10 nanoseconds, a throughput in the range of 10–100 Gb/s or
higher, and a Bit Error Rate (BER) of 10-12–10-15 as targets for WNoC.
Complying with these values while keeping low the area/power consumption calls
for affordable solutions, low order modulations, and simple physical layer
elements for implementation [11, 12, 9, 13, 14, 15].

However, several challenges arise when including wireless communications in a
package environment while trying to meet the target performance requirements.
Some examples include the antenna placement in the highly integrated
environment, design of transceivers with efficient coding schemes and
modulations, interference management, and medium access control [6, 16, 17,
18]. In particular, in this paper we focus on the problems of inter-symbol
interference (ISI) and co-channel interference (CCI). In the on-chip scenario,
the antennas radiate in a highly reverberant environment and are impaired by
near-field effects. As a result, on the one hand, signals are subject to
multiple reflections before reaching the receiver, leading to large delay
spreads dominated by the strong multipath components. This leads to severe
ISI, which degrades the performance of high-rate transmissions especially in
low-order modulations. On the other hand, reverberation causes the radiated
energy to spread across the entire space. This leads to strong CCI with non-
intended antennas and prevents the possibility of having multiple spatial
channels concurrently.

Time Reversal (TR) [19, 20, 21, 22, 23] is a technique that uses a time-
reversed version of the channel’s impulse response (CIR) to create a matched
filter that focuses energy in space and time in a targeted destination. Due to
the spatiotemporal focusing, TR can therefore considerably alleviate both ISI
and CCI, as shown in multiple works at multiple scales and including in the
near-field [24, 20].

In traditional large-scale wireless systems, this approach is expensive to
implement because the channel, being dynamic, would have to be estimated
continuously. In the chip scenario, however, the node position is fixed and
every element in the system is known. This works to our advantage because
regardless of the channel complexity, this will be almost fixed and static.
One estimation of the CIR of the wireless path between terminals of interest
will remain constant and can be used in every transmission. Moreover, the
near-field effects naturally arising in WNoC due to the small scale of the
chip environment are not an issue, since TR can be applied to channels with
near-field effects as long as their consequences are captured in the CIR [24,
20].

In previous work, we explored TR in a small set of chip configurations and
frequencies [25, 26]. In [25], we proposed TR in a flip-chip structure at
60GHz to mitigate the ISI of single-link communications. Moving forward, in
[26] we aimed for a TR approach for multiple simultaneous channels at 140GHz,
in a multi-core architecture to mitigate CCI (Figure 1). We were able to show
the superiority BER-wise of using TR to successfully transmit at high data
rates and get rid of undesired interference. However, in this past work,
besides assuming a limited set of environments, we considered an ideal TR
filter that can compensate perfectly for all the components of the channel.
Perfect filters are impossible to fabricate in practice, and in this scenario,
a high-resolution filter might be unfeasible due to area/power constraints.

In this work, we expand beyond our prior work with a deep exploration of the
effectiveness of TR in a broader set of settings and using filters with a
finite sampling rate. In particular, the contributions of this paper are as
follows:

  * •

We formulate, simulate, and evaluate the performance of wireless links in a
four-chiplet computing system at 140 GHz (Figure 1), in single-link and multi-
link settings, with and without time reversal. We observe order of magnitude
improvements on the speed of the links, and the possibility to deploy multiple
links concurrently.

  * •

We assess the impact of changing the frequency of operation of the wireless
link without modifying the environment. We observe that time reversal is
compatible with all frequencies in this environment, without large variations
in performance.

  * •

We assess the impact of changing the environment, by modifying the number of
chiplets and their size. We observe that these changes can have an impact on
the performance of the wireless links.

  * •

We consider filters with a finite sampling rate and evaluate the degradation
of performance as the sampling rate is reduced. We observe gradual reductions
in the achievable speeds due to an increasing mismatch between the CIR and the
TR filter.

Figure 1: Overview of the application of time reversal in a wireless network
within package. Modulated data is transmitted through the proposed TR filter
and focused on the intended receivers.

The rest of the paper is organized as follows. In Section II, we provide some
background related to the general problems of the on-chip scenario. In Section
III, we formulate the system model considered throughout this work. In Section
IV, we describe the overall evaluation methodology, including the simulation
pipeline, the simulated environment, and the evaluated variations. In Section
V, we present the results obtained from the base scenario, which is used as
base for the parametric characterization developed in this work. In Section
VI, we evaluate the performance of TR for changes in the operation frequency
and the geometry of the chip. Finally, in Section VII, we use a sample-and-
hold filter with variable sampling rate to assess the trade-off between
performance and feasibility of TR in this scenario.

##  II Background

###  II-A Wireless Communications at the Chip Scale

Wireless communications on chip-scale have been built with the foundation of
using millimeter wave technology for electromagnetic nano-communication, as an
overlay of wireless links on top of wired NoC architecture. A variety of
antennas and transceivers [27, 28, 29, 30, 31, 32] have been proposed to be
co-integrated as a system in package, where the wireless channel inside the
chip is chosen as the propagation medium. WNoC complements NoC nicely with
reconfigurability, low latency, and broadcasting capabilities for a high
number of cores ($>64$). In a dense wired routing network, WNoC can avoid
unnecessary hops when communicating distant cores.

To meet the expected performance of WNoC with high data rates and ultra-low
latency, the wireless channels have to be shared among the antennas or the
modulation order data transmissions have to be increased. Therefore MAC
protocols play an important role in maintaining reliable data communication,
where several attempts have been made [33, 34, 35, 17] to adapt token-passing,
CSMA to the chip environment by considering its unique requirements and
characteristics. On the other hand, although the modulations are also crucial
on enhancing the data rate, the area, power overhead of the chip scale
transceivers and stringent BER requirements have limited the modulations to On
off keying (OOK) [36], [6].

###  II-B Wireless Channel within the Chip Package

The controlled materials and dimensions within the chip package let us tailor
the wireless channel and know the nature of the medium beforehand [37, 13,
38]. A computer chip is created by stacking layers of lossy silicon, metal,
and dielectric [39]. In particular, the structure of the flip-chip
configurations widely used in nowadays processors is, from top to bottom: a
heat sink on top, the silicon substrate, a thin dielectric layer for the
interconnections, and a layer of solder bumps that connect the chip to the PCB
[40]. Recently, a trend in computer architecture consists in the
interconnection of multiple flipped chips in a co-planar configuration. To
this end, the chips are connected through a silicon interposer with a much
higher connection pin density than via a PCB [41, 42]. All the work developed
in this paper considers such a 2.5D integration scheme.

Regardless of the number of interconnected chips, communicating within the
chip package with electromagnetic radiation has its unique characteristics. A
large amount of the transmitted energy will be reflected by the metal
enclosure, the edges, and obstacles in the structure, leading to a large delay
spread with multi-path propagation while creating a distinctive CIR between
each transmitter and receiver [37, 13]. Fortunately, the structure is designed
beforehand, and all materials, nodes, and terminals will become fixed and
known. This offers a significant advantage since the wireless channel can be
treated as quasi-deterministic and time-invariant which enables a pre-
characterization of the CIR that will not change and that requires a single
estimation process and can be re-used moving forward.

###  II-C Time Reversal for On-Chip Communications

TR is a technique that can be used to compensate for the multipath effects
that occur in complex transmission mediums with the use of adaptive energy
focusing on the pre-characterized CIRs. The phase conjugate of the CIR is
obtained, pre-emphasized with the transmitting symbols, and propagated through
the same wireless medium such that the radiated energy is focused in both time
and space at a target receiver. TR acts as an ideal spatial matched filter
with the process of auto-correlation of the transmitted time-reversed channel
response with an equal wireless medium.

As the chip-scale wireless communications are conducted in quasi-deterministic
channels, TR is a promising technology to adapt as a solution to mitigate the
ISI effects that occur due to energy reverberation. With prior known wireless
channels, repetitive CIR characterization is not required.

Channel correlation plays a crucial role in TR processing and the energy
focusing could be for the merit or adverse based on the expected signal
transmission scenario. Even though TR was initially adapted for on-chip
communications to mitigate ISI, later it was proved that TR could be used to
reduce the co-channel interference in same frequency/time signal transmissions
[25, 26]. When the communicating channels are less correlated TR is capable of
reducing the non-orthogonal interference of nearby signal transmissions with
the use of destructive cancellation of energy components on focused CIR. In
return, it enables the wireless medium to have parallel concurrent signal
transmissions by sharing the same bandwidth, thus improving the aggregate data
rate of the system. However, this phenomenon is adverse with symmetric
channels where the co-channel interference could be high. In such cases, the
known CIR can be analyzed before the transmissions to optimize the
communication scheme. Nevertheless, the symmetric channels can be highly
useful to focus the energy on multiple nodes with single transmitter
excitation to enhance the broadcasting capabilities.

##  III System Model

In this section, we provide a detailed description of the TR process and its
influence on the transmission. The model is detailed for different scenarios
involving one or more concurrent TR links.

###  III-A TR with Single Input Single Output Link

We analyze the case of TR-based adaptive energy focusing on time domain. Let
us consider, for the purpose of characterisation, that an impulse is excited
from an arbitrary transmitter $i$ to an arbitrary receiver $k$. The
characterized CIR is recorded and used to transmit modulated information via
the channel $h_{ik}$, which is given by

$h_{ik}(t)=\sum_{n=1}^{N}A_{n}e^{j\theta_{n}}\delta(t-\tau_{n})\,,$ (1)

where $\\{A_{n},\theta_{n},\tau_{n}\\}$ are amplitude, phase, and propagation
delay of the multipath component $n$ of the CIR $h_{ik}$.

For simplicity, impulse radio OOK modulated symbols are assumed. Hence,
symbols $m_{ik}\in\\{1,0\\}$, are sent through the characterized time-reversed
filter and transported towards receiver $k$ from the transmitter $i$. The
transmitted signal can be expressed as

$s_{ik}(t)=h_{ik}^{*}(-t)\star m_{ik}$ (2)

where $(\cdot)^{*}$ represents the complex conjugate operator and $\star$
indicates the convolution operator respectively.

The resultant energy concentration resembles the autocorrelation of the CIR as

$\begin{split}y_{ik}(t)&=\\{s_{ik}(t)\\}\star h_{ik}+n_{k}\\\ &=m_{ik}\star
h_{ik}^{*}(-t)\star h_{ik}+n_{k}\\\ &=m_{ik}\star R_{ik}^{A}(t)+n_{k}\\\
\end{split}$ (3)

where $R_{ik}^{A}(t)$ denotes the autocorrelation function of the channel
$h_{ik}$ and $n_{k}$ is the Additive White Gaussian Noise (AWGN) component at
the receiver $k$. The autocorrelation property eliminates the multipath
effects with constructive and destructive interference cancellation while
improving the signal-to-noise ratio (SNR) at the respective receiver.

Next, we assume a case where the transmitted signal $s_{ik}$ is propagated
towards an off-target receiver $k^{\prime}$. Then,

$\begin{split}y_{ik^{\prime}}(t)&=\\{s_{ik}(t)\\}\star
h_{ik^{\prime}}+n_{j^{\prime}}\\\ &=m_{ik}\star
R_{ikk^{\prime}}^{C}(t)+n_{j^{\prime}}\\\ \end{split}$ (4)

where $R_{ijj^{\prime}}^{C}(t)$ represents the cross correlation function in
between the arbitrary channels $h_{ij}$ and $h_{ij^{\prime}}$. For further
analysis of the impact of channel correlation functions on TR, let us consider
the convolution of the CIR $h_{ik^{\prime}}$ with the time-reversed
$h_{ik}^{*}$:

$\begin{split}h_{ik^{\prime}}(t)\star
h_{ik}^{*}(-t)&=\int_{-\infty}^{\infty}h_{ik^{\prime}}(\tau)h_{ik}^{*}(-(t-\tau))d\tau\\\
\end{split}$ (5)

By substituting Equation (1) in Equation (5), the convolution operation can be
obtained as

$\begin{split}h_{ik^{\prime}}(t)\star
h_{ik}^{*}(-t)&=\int_{-\infty}^{\infty}\sum_{n^{\prime}=1}^{N^{\prime}}A_{n^{\prime}}e^{j\theta_{n^{\prime}}}\delta(\tau-\tau_{n^{\prime}})\\\
&\sum_{n=1}^{N}A_{n}e^{-j\theta_{n}}\delta(-(t-\tau)-\tau_{n})d\tau\\\
\end{split}$ (6)

where $\\{A_{n^{\prime}},\theta_{n^{\prime}},\tau_{n^{\prime}}\\}$ are
amplitude, phase, and propagation delay of the multipath component
$n^{\prime}$ of the CIR $h_{ik^{\prime}}$.

Thus the simplified cross-correlation expression can be obtained as

$\begin{split}R_{ikk^{\prime}}^{C}(t)&=\sum_{n^{\prime}=1}^{N^{\prime}}\sum_{n=1}^{N}A_{n^{\prime}}A_{n}e^{j(\theta_{n^{\prime}}-\theta_{n})}\delta(t-(\tau_{n^{\prime}}+\tau_{n}))\end{split}$
(7)

With the above expression, it is observed that when the transport signal is
passed through symmetric channels (autocorrelation index is high) the energy
components are constructively added with a null phase shift while having the
maximum energy concentration at the point of maximum propagation delay;
$max(\tau_{n})$. When the TR adopted CIR is dissimilar, the cross-correlation
index is phase shifted and the energy concentration will be controlled by the
shifted amount of phase. As the EM waves are propagated through an enclosed
chamber, it is complex to predict the randomness of the CIR. Thus, it is
important to measure each CIR before the transmissions and design the
protocols to optimize the paths in parallel communications.

###  III-B TR with Multiple Input Multiple Output Link

Subsequently, let us consider multiple input multiple output (MIMO)
communication with TR. In the cases that follow, suppose there are $N_{t}$
transmitters with $N_{r}$ receivers simultaneously communicating with each
other on an interposer package.

####  III-B1 Single Transmitter-Multiple Receivers

First, let us consider a _scatter_ operation from a single transmitter to
multiple receivers. In computer architecture, scatter refers to the
distribution of $P=\\{p_{1},\dots,p_{N}\\}$ pieces of data to $N$ receivers
with a one to one mapping, i.e. $p_{1}$ to node 1, $p_{2}$ to node 2, etc.
Assuming that all the wireless channels are pre-characterized, the TR
modulated symbols to be transmitted from $i^{th}$ single transmitter to the
$k^{th}$ receiver can be expressed as

$s^{t}_{ik}(t)=\sum^{N_{r}}_{k^{{}^{\prime}}=1,k^{{}^{\prime}}\neq
k}h_{ik^{{}^{\prime}}}^{*}(-t)\star m_{ik^{{}^{\prime}}}+h_{ik}^{*}(-t)\star
m_{ik}$ (8)

TR precoding is done based on the simultaneous transmissions utilized in the
particular transmitter to the intended receivers. Note that according to the
receiver selection, other TR-CIR can be assumed as zero.

The received signal from a single $i^{th}$ transmitter to $k^{th}$ receiver
can be obtained as

$\begin{split}&y^{t}_{ik}(t)=s^{t}_{ik}(t)\star h_{ik}+n_{k}\\\
&=\bigg{\\{}\sum^{N_{r}}_{k^{{}^{\prime}}=1,k^{{}^{\prime}}\neq
k}h_{ik^{{}^{\prime}}}^{*}(-t)\star m_{ik^{{}^{\prime}}}+h_{ik}^{*}(-t)\star
m_{ik}\bigg{\\}}\star h_{ik}\\\ &+n_{k}\\\
&=\underbrace{\sum^{N_{r}}_{k^{{}^{\prime}}=1,k^{{}^{\prime}}\neq
k}R_{ikk^{\prime}}^{C}(t)\star
m_{ik^{{}^{\prime}}}}_{\text{Interference}}+\underbrace{R_{ik}^{A}(t)\star
m_{ik}}_{\text{Signal}}+n_{k}\\\ \end{split}$ (9)

Based on the measurements of the channel correlation index among the
characterized CIR, the interference can be previously known. Although the
effects of interference could be decreased as discussed in Equation (6), it is
important to measure the amount of decrement to learn the number of
simultaneous transmissions that can be utilized.

####  III-B2 Multiple Transmitters-Multiple Receivers

Second, let us consider a scenario when multiple transmitters transmit to
multiple receivers. This scenario resembles a parallel information shared in
between cores, to improve the aggregate data rate of the system. Here, each
$i^{th}$ transmitter wishes to transmit the TR precoded modulated information
to the intended receiver $k$. Thus, the transmitted signal can be obtained as

$s^{r}_{ik}(t)=\sum^{N_{t}}_{i^{{}^{\prime}}=1,i^{{}^{\prime}}\neq
i}h_{i^{{}^{\prime}}k}^{*}(-t)\star m_{i^{{}^{\prime}}k}+h_{ik}^{*}(-t)\star
m_{ik}$ (10)

The received signal at a single $k^{th}$ receiver can be expressed as

$\begin{split}y^{r}_{ik}(t)&=s^{r}_{ik}(t)\star h_{ik}+n_{k}\\\
&=\bigg{\\{}\sum^{N_{t}}_{i^{{}^{\prime}}=1,i^{{}^{\prime}}\neq
i}h_{i^{{}^{\prime}}k}^{*}(-t)\star m_{i^{{}^{\prime}}k}+h_{ik}^{*}(-t)\ast
m_{ik}\bigg{\\}}\star h_{ik}\\\ &+n_{k}\\\
&=\underbrace{\sum^{N_{r}}_{k^{{}^{\prime}}=1,k^{{}^{\prime}}\neq
k}R_{i^{\prime}kk}^{C}(t)\star
m_{i^{\prime}k}}_{\text{Interference}}+\underbrace{R_{ik}^{A}(t)\star
m_{ik}}_{\text{Signal}}+n_{k}\\\ \end{split}$ (11)

As we observe in Equation (11), the interference is dependent on the channel
cross-relation between the focused channel CIR with the interference channels
(refer to Fig. 3) due to the non-orthogonality of the signal transmissions. It
is advisable to measure the correlation of each channel prior to the signal
transmissions and manage the communications with an adaptable MAC protocol.

###  III-C SINR Analysis with TR

To quantify the impact of TR on the effectiveness of the signal transmission,
the signal-to-noise plus interference ratio was measured for both single-link
and multi-link TR precoded communications. Even though ISI is highly mitigated
with TR, it is important to quantify the peak energy concentration
proportional to the data rate to measure how much concentration we could
achieve with closely packed energy peaks in higher data rates.

We detect the peak energy concentration inside a defined time domain window
with general energy detection [43] based on the data rate and consider the
energy outside the defined time duration as the interference due to low-
compressed energy components. The SINR is defined for three cases as
aforementioned in Section III-A and Section III-B. Therefore, SINR for single
input single output channel can be obtained as,

$\begin{split}SINR_{SISO}=\frac{\int^{t_{2}}_{t_{1}}y_{siso}(t)^{2}dt}{I_{siso}+n_{k}}\end{split}$
(12)

where,$y_{siso}(t)=m_{ik}\star R^{A}_{ik}(t)$,
$I_{siso}=\int^{t_{1}}_{0}y_{siso}(t)^{2}dt+\int^{2max(\tau_{n})}_{t_{1}}y_{siso}(t)^{2}dt,\,t_{1}=max(\tau_{n})-t_{rate}/2,$
$\,t_{2}=max(\tau_{n})+t_{rate}/2$. $t_{rate}$ is the defined time domain
window for the energy detection.

Figure 2: Summary of the proposed methodology: Characterisation of channel
impulse response and analyzing the proposed communication with MATLAB

Similarly, based on the received signals as in Equation (9) the SINR for
single transmitter multiple receivers can be obtained as

$\begin{split}SINR_{SIMO}=\frac{\int^{t_{2}}_{t_{1}}y_{simo}(t)^{2}dt}{I_{siso}+I^{t}_{CCI}+n_{k}}\end{split}$
(13)

where $y_{simo}(t)=m_{ik}\star R^{A}_{ik}(t)$,
$I_{simo}=\int^{t_{1}}_{0}y_{simo}(t)^{2}dt+\int^{max(\tau_{n}+\tau_{n^{\prime}})}_{t_{1}}y_{simo}(t)^{2}dt$,
$I^{t}_{CCI}=\int^{t_{2}}_{t_{1}}\\{R_{ikk^{\prime}}^{C}(t)\star
m_{ik^{{}^{\prime}}}\\}^{2}dt$.

Subsequently, with the received signal in equation (11) the SINR for multiple
transmitters and multiple receivers can be expressed as below.

$\begin{split}SINR_{MIMO}=\frac{\int^{t_{2}}_{t_{1}}y_{mimo}(t)^{2}dt}{I_{mimo}+I^{r}_{CCI}+n_{k}}\end{split}$
(14)

Where, $y_{mimo}(t)=m_{ik}\star R^{A}_{ik}(t)$,
$I_{mimo}=\int^{t_{1}}_{0}y_{mimo}(t)^{2}dt+\int^{max(\tau_{n}+\tau_{n^{\prime}})}_{t_{1}}y_{mimo}(t)^{2}dt$,
$I^{r}_{CCI}=\int^{t_{2}}_{t_{1}}\\{R_{i^{\prime}kk}^{C}(t)\star
m_{i^{\prime}k}\\}^{2}dt$.

##  IV Methodology

The overview of the proposed methodology is shown in Fig. 2. We follow a
sequential methodology for this work to (1) systematically pre-characterize
the wireless channel with CIR by using CST Microwave Studio [44] and (2) model
the communication system on MATLAB to analyze the performance of the TR
technique on modulated streams of data. We detail them next.

###  IV-A Full-wave Simulation

The simulations made in this work are conducted in an interposer. The detailed
configuration of the flip-chip layers is seen in Table I. To create the
interposer we placed a number of flip-chip structures on top of a stack of
silicon interposer and two layers of copper. The space between chiplets is
filled with vacuum and the configuration is completely enclosed by a Perfect
Electric Conductor (PEC). Each chiplet is augmented with a number of antennas
placed in symmetrical positions in a Trough-Silicon-Vias (TSV) approach [25]
as vertical monopoles. Unless noted, we consider four chiplets with three
antennas per chiplet tuned at a frequency of 140 GHz.

TABLE I: Evaluated Structure and Dimensions. Parameter | Thickness | Materials | Units
---|---|---|---
Lateral Spacer | - | Vacuum | N/A
Heat Spreader | 0.5 | Aluminum Nitride | mm
Silicon die | 0.5 | High-res. Silicon | mm
Chiplet insulator | 0.01 | SiO2 | mm
Bumps | 0.0875 | Copper | mm
TABLE II: Evaluation Scenarios. Variables | Default | Section | Variations | Section
---|---|---|---|---
No. chiplets | 4 | Sec. V | 4–16 | Sec. VI
Frequency (GHz) | 140 | 140–170 | Sec. VI
Sampling Rate (GHz) | Ideal | 80–400 | Sec. VII

Moving forward we developed several simulations to study the TR technique, its
behavior, and application possibilities for changes in the base scenario in
terms of frequency of operation and changes in the structure’s geometry. We
refer the reader to Table II for details on the evaluated variations.

The structures where the parametric sweep takes place are seen in Figure 3. We
illustrate the location of the antennas and the links used for measurement of
the quality of transmission. As observed, we change the number of chiplets to
study the impact of the layout on the effectiveness of TR. In particular, we
introduce more chips in the same amount of space, hence decreasing the chiplet
size and only placing one antenna per chiplet.

Figure 3: Evaluated multi-receiver time-reversal scenarios for four and
sixteen chiplets in an ineterposer package, with multiple concurrent
transmitters at the same time, different data to different receivers.

Each scenario is simulated in CST Microwave Studio using the time-domain
solver. The length of the vertical monopole antennas is adjusted to resonate
in frequencies close to 140, 170, and 200 GHz (Fig. 4(a)). We can also see
several notches, which suggest that we are indeed in a reverberant scenario
with significant near-field effects; the antenna can couple with nearby and
distant elements, changing the impedance and hence mismatching the antenna. As
a result, we also need to adapt the antenna when varying the dimensions of the
chiplet (Fig. 4(b)).

Once the antennas are modeled correctly, we apply an impulse to the
transmitting antenna to obtain the CIR at the output. Hence, the outcome of
the simulations is the CIR from a given port to all others. Hence, we obtain
information to evaluate any wireless link we consider for transmission. This
can be extracted from the software and further processed in MATLAB.

Finally, we note that, to validate the time reversal approach, we record the
CIR and excite the transmitting antenna with the reversed version of the CIR.
This simulation is used to obtain the field distribution and see the
spatiotemporal focusing, as well as to later compare the results with that of
a simple convolution between the filter and the actual channel in MATLAB.

###  IV-B PHY Layer Simulation

As the next step, the characterized CIR is used to process the proposed
communication scheme with TR. First, we generate a pseudo-random string of
bits with the preferred data rate. The data is then modulated with impulse
radio (IR) on-off keying (OOK) modulation to create a train of impulses,
although the methodology is easily applicable to continuous-wave modulations,
in which case the data would be multiplied by a continuous time carrier wave
with a frequency matching the antenna resonance frequency.

(a) Return loss for antennas at 140/170/200 GHz, four chiplets.

(b) Return loss for antenna at 140 GHz, sixteen chiplets.

Figure 4: Return loss of the simulated antennas in the multiple evaluated
scenarios.

In transmission, the modulated symbols are convoluted with the TR filters and
transported in the wireless channel. AWGN noise is added to the transport
signal and the noise power is modeled as $P_{AWGN}=KTB$, where $K$ is the
Boltzmann constant, $T$ is the chip temperature and $B$ is bandwidth. The TR
filter is initially modeled as the ideal (continuous) time-reversed CIR
perfectly matching the characterized channel. However, in Section VII, we also
perform a gradual degradation of the filter sampling rate in the default
simulated scenario to consider a more realistic filtering approach and observe
the resulting degradation in performance of the wireless link.

At the receiver, Energy Detection (ED) is implemented by integrating the
received signals (aforementioned in Section III) over the respective time
intervals based on the data rate. The computed energy values are compared with
a threshold to decode the data stream. The threshold value is decided a
posteriori and on a per-link basis to minimize the BER.

##  V Time Reversal in a Multi-Chip Scenario

For the baseline scenario, the simulations have been executed for several
transmission cases in a four-chiplet scenario at 140 GHz and assuming ideal
filters. Also, the links contemplated are within the same chip and among
different chips. The results entail single-link and multiple-link
transmissions. Within the multiple links scenario, we made simulations for
multiple transmitters and multiple receivers.

Figure 5 shows a summary of the results of TR obtained with our end-to-end
methodology. Fig. 5(a) illustrates the spatiotemporal focusing of the
technique (right) in comparison with normal transmission (left). We can see
the cleanness of the TR transmission with high concentration in targeted spots
and low concentration elsewhere, except for symmetric points. On the other
hand, the electrical field in the non-TR case is completely scattered, with
some concentration in the desired target but surrounded by large amounts of
interference, which tarnishes any concurrent transmission attempt.

As we further show in Fig. 5(b), the TR signal at the receiver is focused in
the time domain, showing a large and very concentrated peak of 45 mW; whereas
the non-TR signal appears spread and with the peak only reaching 0.2 mW.

With respect to co-channel interference, an important conclusion can be drawn
from Fig.5(c). This image shows the ability of TR to compress the energy
concentration in non-desired targets if and when the channel impulse response
of each wireless path is not correlated with the targeted receiver. In this
particular case, node $C$ is placed in a relatively symmetric position with
respect to the targeted node $B$ and, hence, receives a relatively large
interference. An opposite behavior is observed for nodes $D$ to $F$, for which
the interference is largely suppressed.

(a)

(b)

(c)

(d)

Figure 5: Single-link time-reversal with vertical monopoles in an interposer
package at 140 GHz. (a) Spatial distribution of field before and applying TR.
(b) Signal received over time in node $B$ before and after applying TR. (c)
Total received power in the intended receiver $B$ and non-intended receivers
$C$–$F$, (d) BER as a function of the aggregated data rate for a total power
of 10 dBm in the TR case. See [26] for more details.

To evaluate the performance of TR with parallel communications, the BER as a
function of the aggregated data rate (i.e. the sum of the data rates of all
parallel transmissions) is measured as illustrated in Fig. 5(d). It was
observed that even with three concurrent communications, the SINR is higher
than non-time reversal transmissions, and thus the BER is improved at the
receiver. In terms of data rate, a significantly high aggregate data rate can
be obtained with time reversal. In particular, a speed of 50 Gb/s is obtained
with an error rate below 0.01 with a single-link transmission. Compared with
the non-TR transmission (not shown here), the TR case achieves an order of
magnitude higher speed for the same BER. Further, as we add new concurrent
links to the simulation, we observe that the aggregate data rate increases
with the number of deployed, although the system starts to saturate with three
concurrent links in this particular case. In summary, these results are
indicative of the capacities of TR.

##  VI Sensitivity Analysis

Next, we want to determine the limits of our model and explore possible
shortcomings that arise from changes in the structure as well as variations
with the frequency.

(a)

(b)

(c)

(d)

Figure 6: Impact of the resonant frequency of the antennas on the validity of
the TR approach. (a) CIR for the $AE$ link without time reversal and (b) with
time reversal. (c) Power concentrated on the desired target node $E$ divided
by the power received at the rest of the terminals. (d) Aggregated data rate
with different techniques and number of concurrent links for BER of 0.1 and 0
dBm per transmitter.

###  VI-A Impact of Communication Frequency

As it is beneficial to count with multiple frequencies for transmission, the
TR evaluation is made also for multiple frequencies, maintaining the rest of
the interposer landscape intact. The peak energy concentration with TR on the
focused receiver is based on two main factors such as the delay spread and the
received signal strength of the characterized CIR. When the center frequency
of the antenna is increased, the delay spread generally tends to get shorter,
and based on the scattered energy components on the chip package, the received
signal strength on each antenna could be increased or decreased. This
variation in frequency affects the receiver’s peak energy concentration and
thus the system’s bit error rate. We evaluate these effects next.

Fig. 6 shows the general behavior of characterized CIR and the received peak
energy concentration with different antenna resonance frequencies. It is
observed that, even with a short delay spread, a clean focused energy peak is
obtained at all frequencies. The specific peak instantaneous power and the
width of the response depends on the length of the CIR and total energy of the
CIR. While we observe some variations on these values, there is not an
specific trend or large impact. This is because the scenario keeps being
fairly reverberant at all frequencies, and the TR filter is adapted to each
new measured CIR.

To assess the degree of spatial focusing of our technique, we evaluate the
ratio of the power in the desired target to the power of the rest of ports of
the system. As observed in Figure 6(c) for a particular link, we observe how
TR focuses the energy on the target destination, as the power is superior to
the sum of the powers in all the other ports. In contrast, the non-TR case
will probably lead to large co-channel interference, since the power at the
intended destination is just a small fraction of the power arriving to all
other ports. The difference between both cases is around 3$\times$ with small
variation when changing the operation frequency of the wireless network.
Hence, this confirms that TR could be used simultaneously to frequency
multiplexing in a single package.

The TR capabilities have been further tested by obtaining the BER as a
function of the data rate of an OOK modulated stream in all frequencies. The
results, summarized in Fig. 6(d) for a fixed BER of 0.1, show a consistent
behavior of the TR technique. In general, it is observed that TR works well at
all frequencies, with a large gap between the non-TR and TR achievable rates.
As the frequency increases, the performance of TR can increase or decrease
depending on the particular shape of the channel at that particular link at
the specific frequency, as well as the interference pattern it generates.
Interestingly, the single-link performance decreases from 140 GHz to 170 GHz
and then rises again. Whereas the three-link performance decreases sharply
when shifting from 140 GHz to higher frequencies.

(a)

(b)

(c)

(d)

Figure 7: Impact of the number of chiplets and their dimensions on the
validity of the TR approach. (a) Power concentrated on the desired target to
the power received by the rest of the terminals for links $AE$ and $GC$, and
(b) for links $GH$ and $HF$ in the four-chiplet and sixteen-chiplet case,
respectively. (c) BER as a function of aggregate data rate for 0dBm per
transmission for sixteen chiplets. (d) Aggregate data rates for BER = 0.1 and
0 dBm per transmission.

###  VI-B Impact of Number of Chiplets

Next, we evaluate the TR technique in a 16 chiplets interposer. For this, some
changes are made in the original configuration presented in Section II, while
maintaining 140 GHz as the frequency of operation. The changes come mainly in
the size of the chiplets, reduced in this case to fit 16 in the same system
dimensions, and in the location of the antennas. We distribute one antenna per
chiplet. Similar to the analysis done in Section VI-A, here we evaluate the
ratio of the power in the target destination with respect to that of the rest
of antennas, as well as the BER as a function of the data rate and the data
rate at a specific BER.

Figure 7(a) and 7(b) show the comparison of the power ratio for 4 and 16
chiplets in two differnt links. For the 4 chiplet case, we take the channels
$AE$ and $GH$ as examples. To perform a fair comparison with the 16 chiplet
case, we find links that are in a close physical position to their 4-chiplet
counterparts, which would be links $GC$ and $FH$ in this case. In Figure 3 we
can see the position of the antennas for both scenarios.

Although the increase of chiplet-package interfaces in the sixteen-chiplet
case significantly and complicates the propagation, the results from Figure
7(a) illustrate that TR can still improve the field concentration. However,
there is a strong dependence on the relative positions of the chiplets, as we
can see in Figure 7(b) for sixteen chiplets. In that case, both the power of
the non-TR and TR are reduced as propagation impairments prevent a large part
of the energy to reach the chiplet of node $H$ from node $F$. The difference
among both shrinks.

Next, Figure 7(c) plots the BER as a function of the data rate. We observe
that, as a consequence of the better spatial and temporal focusing suggested
in previous figures, the achievable data rate is higher in the TR case. The
sixteen-chiplet case admits two concurrent transmissions with relative ease,
at least for the two links selected here. However, as we add a third link,
noise and interference seems to dominate, to the point of not achieving a
better performance than in the two-link case. The comparison made in Figure
7(d) for BER=0.1 further illustrates the difference between the two analyzed
cases. This result indeed suggests that the more complex channel leads to the
existence of higher correlations and, hence, higher interference even with TR.
Also, the losses in the channel may be increasing, leading to a higher impact
of the noise existing in all receivers. That would also explain the lower data
rate in the single-link case.

##  VII Performance Degradation with Non-Ideal Filters

The spatial-temporal concentration of ideal TR filters has demonstrated
superior performance on higher bandwidths up to 50 Gb/s thanks to the
mitigation of ISI effects. However, so far we assumed that the TR filters have
been implemented with perfect synchronized sampling of the pre-characterized
CIR with infinite sampling speed. In practice, however, a digital filter
implementing TR would need to have a finite sampling rate to be feasible.

Ideally, the filter needs to capture all the temporal variations of the
channel to perfectly apply TR on a given channel. However, our full-wave
simulations have shown that due to the high frequencies involved and the
densely integrated environment being simulated, changes in the response in
picosecond time intervals, which would need sampling frequencies in the THz
range to be captured. Implementation of filters with such resolution is
unfeasible. Therefore, based on realistic constraints, it is important to
analyze the impact of TR with non-ideal filters and evaluate the spatial-
temporal focusing based on the trade-off between the resource constraints and
the received signal strength.

###  VII-A Zero-Order Hold Filter

Inspired by the standard interpolation technique of sample and hold [45], here
were propose a simple analysis considering the ideal TR estimation and hold
the amplitude to the period of reduced sampling frequency. With this method,
the sampled amplitudes are being held constant at the point of sampling
operation is performed simply by introducing a synchronized square wave to the
sampled signal with equal sampling frequency. This operation is identified as
zero-order hold (ZOH) filtering. ZOH filter holds each sampled value for a
duration of one sampling interval, as it is illustrated in Figure 8.

Since the nearest received multi-path components on the CIR have approximately
equal amplitudes, the preserved amplitudes with ZOH filtering have a similar
effect on the concentrated energy with reduced sample rates along with a minor
degradation of energy concentration. We next evaluate the impact of reducing
the sampling frequency.

Figure 8: Overview of zero-order hold filtering.

###  VII-B Performance Evaluation

The general behavior of the ZOH filtering of the CIR is illustrated in Figure
9. As can be observed, the ideal TR response which acts as the perfect filter
has a quickly oscillating behavior. The second chart shows how the ZOH filter
has reduced the sampling frequency down to 100GHz, with noticeable non-
linearities appearing due to the ZOH operation. Still, at 100 GHz, we still
can see the high-energy components of the filter around 1.4 ns and 1.6 ns are
still distinguishable. As ZOH acts as a typical low pass filter in the time
domain, the frequency domain response corresponds to a $sinc(\cdot)$ function,
which in return could limit the frequency components. Hence, if the sampling
frequency is reduced further, significant portions of the CIR could be lost in
the filter. Finally, Figure 9(c) illustrates the difference between the
convolution of the filter and the channel in both cases. We observe how the
ideal TR has a higher energy in the peak and in the surroundings, whereas the
ZOH version, even sampled at a very high frequency, has a slight broadening of
the response.

(a)

(b)

(c)

Figure 9: Impact of the use of non-ideal filters on the response of the TR
channel. (a) Response of the ideal TR filter. (b) Response of the TR filter
with ZOH at 100 GHz sampling frequency. (c) Comparison of energy concentration
with ideal TR filter and ZOH.

To evaluate the performance of the technique sample and hold, we summarize the
results of several evaluations in Figure 10. First, we integrate the energy
around the peak with a window of 0.4 ns (corresponding to a modulation speed
of 2.5 Gb/s) and compare it to the energy outside of the peak, as an
indication of how well the temporal concentration is maintained when sampling
at different frequencies. As shown in Figure 10(a), the energy is rather
constant until the sampling rate drops below 350 GHz. As we shift further
down, there is a degradation of the ratio, yet without a drop of more than 7
dB until 50GHz sampling frequency.

Furthermore, the effect of $I_{SISO}$ was measured by varying the window size
of the interference measurement. This result provides us with an approximate
idea on measured signal strength when the data rate is increased (and then the
window reduced). From the results of Figure 10(b), it is apparent that when
the window size is increased, the amount of captured energy also increases
proportionally. In the figure we see that the impact of the window size is
more noticeable at small sizes, since the finite sampling rates causes the
peak to broaden. The impact of the resonance frequency is mild.

Finally, to analyze the performance of the filter with BER, the data rates
were evaluated with varied sampling frequencies (i.e. 400 GHz, 300 GHz, 200
GHz, 100 GHz, and 80 GHz) for three resonance frequencies. As illustrated in
Figure 10(c) for a fixed BER of 0.1, the achievable data rates seem to degrade
gracefully as we reduce the sampling rate by significant amounts, still
achieving remarkable speeds for a sampling rate of 80 GHz.

(a)

(b)

(c)

Figure 10: Impact of the TR filter properties on the performance of TR for the
140 GHz, 170 GHz, and 200 GHz channels. (a) Ratio of energy within a window of
0.4 ns centered in the peak of the response, to that outside the window as a
function of the sampling frequency. (b) Ratio of energy within a window of
variable size to that outside the window as a function of the window size, for
a sampling rate of 100 GHz. (c) Achievable data rate as a function of the
sampling rate of the TR filter at 0.1 BER and 0 dBm.

##  VIII Conclusion

In this paper, we have presented the idea of applying time reversal to
mitigate the sources of interference in static wireless communication
scenarios within computing packages. To explore the effect of TR in varied
setups, we evaluated the technique in a base scenario with four chiplets and
antennas operating at 140 GHz, assuming idea TR filters, as well as for
multiple variations in frequency, geometry, and also employing TR filters with
finite sampling rate. Overall, the results proved the superior capabilities of
TR in transmission, obtaining a remarkable amount of power concentration in
targeted destinations. The performance of TR in transmission was assessed by
calculating the error rate as a function of the data rate. We observed that TR
provides an order-of-magnitude improvement with respect to non-TR
transmissions, and that allows to perform 2–3 concurrent transmissions to
further boost the data rate. We did not observe a clear variation with
frequency, because the environment under evaluation is reverberant at all the
evaluated frequencies. When increasing the number of chiplets, the changes
were significant due to the higher complexity of a channel with numerous
changes of propagation medium. Finally, we evaluated the impact of a finite
sampling frequency in the TR filter on the performance of the technique. We
observed a rather graceful degradation of the achievable data rate. In future
work, we aim to explore the limits of the technique as we further reduce the
sampling rate and further simplify the filter.

## References

  * [1] G. Nychis, C. Fallin, T. Moscibroda, O. Mutlu, and S. Seshan, “On-chip networks from a networking perspective: congestion and scalability in many-core interconnects,” in _Proceedings of the SIGCOMM_ , 2012, pp. 407–18.
  * [2] B. Zimmer, R. Venkatesan, Y. S. Shao, J. Clemons, M. Fojtik, N. Jiang, B. Keller, A. Klinefelter, N. Pinckney, P. Raina _et al._ , “A 0.32–128 tops, scalable multi-chip-module-based deep neural network inference accelerator with ground-referenced signaling in 16 nm,” _IEEE Journal of Solid-State Circuits_ , vol. 55, no. 4, pp. 920–932, 2020.
  * [3] F. Lemic, S. Abadal, W. Tavernier, P. Stroobant, D. Colle, E. Alarcón, J. Marquez-Barja, and J. Famaey, “Survey on terahertz nanocommunication and networking: A top-down perspective,” _IEEE Journal on Selected Areas in Communications_ , vol. 39, no. 6, pp. 1506–1543, 2021.
  * [4] H. Elayan, R. M. Shubair, J. M. Jornet, and P. Johari, “Terahertz channel model and link budget analysis for intrabody nanoscale communication,” _IEEE transactions on nanobioscience_ , vol. 16, no. 6, pp. 491–503, 2017.
  * [5] A. Todri-Sanial, R. Ramos, H. Okuno, J. Dijon, A. Dhavamani, M. Wislicenus, K. Lilienthal, B. Uhlig, T. Sadi, V. Georgiev, A. Asenov, S. Amoroso, A. Pender, A. Brown, C. Millar, F. Motzfeld, B. Gotsmann, J. Liang, G. Gonçalves, N. Rupesinghe, and K. Teo, “A Survey of Carbon Nanotube Interconnects for Energy Efficient Integrated Circuits,” _IEEE Circuits and Systems Magazine_ , vol. 17, no. 2, pp. 47–62, 2017.
  * [6] X. Timoneda, S. Abadal, A. Franques, D. Manessis, J. Zhou, J. Torrellas, E. Alarcón, and A. Cabellos-Aparicio, “Engineer the channel and adapt to it: Enabling wireless intra-chip communication,” _IEEE Transactions on Communications_ , vol. 68, no. 5, pp. 3247–3258, 2020.
  * [7] S. Deb, A. Ganguly, P. P. Pande, B. Belzer, and D. Heo, “Wireless NoC as Interconnection Backbone for Multicore Chips: Promises and Challenges,” _IEEE Journal on Emerging and Selected Topics in Circuits and Systems_ , vol. 2, no. 2, pp. 228–239, 2012.
  * [8] A. K. Kodi, A. I. Sikder, D. Ditomaso, S. Kaya, D. Matolak, and W. Rayess, “Kilo-core Wireless Network-on-Chips (NoCs) Architectures,” in _Proceedings of the NANOCOM ’15_ , 2015, p. Art. 33.
  * [9] S. Shamim, N. Mansoor, R. S. Narde, V. Kothandapani, A. Ganguly, and J. Venkataraman, “A Wireless Interconnection Framework for Seamless Inter and Intra-chip Communication in Multichip Systems,” _IEEE Transactions on Computers_ , vol. 66, no. 3, pp. 389–402, 2017.
  * [10] S. Abadal, A. Mestres, J. Torrellas, E. Alarcón, and A. Cabellos-Aparicio, “Medium access control in wireless network-on-chip: A context analysis,” _IEEE Communications Magazine_ , vol. 56, no. 6, pp. 172–178, 2018.
  * [11] V. Pano, I. Tekin, I. Yilmaz, Y. Liu, K. R. Dandekar, and B. Taskin, “TSV antennas for multi-band wireless communication,” _IEEE Journal on Emerging and Selected Topics in Circuits and Systems_ , vol. 10, no. 1, pp. 100–113, 2020.
  * [12] A. Karkar, T. Mak, K.-F. Tong, and A. Yakovlev, “A Survey of Emerging Interconnects for On-Chip Efficient Multicast and Broadcast in Many-Cores,” _IEEE Circuits and Systems Magazine_ , vol. 16, no. 1, pp. 58–72, 2016.
  * [13] D. Matolak, S. Kaya, and A. Kodi, “Channel modeling for wireless networks-on-chips,” _IEEE Communications Magazine_ , vol. 51, no. 6, pp. 180–186, 2013.
  * [14] J. W. Holloway, G. C. Dogiamis, and R. Han, “A 105Gb/s Dielectric-Waveguide Link in 130nm BiCMOS Using Channelized 220-to-335GHz Signal and Integrated Waveguide Coupler,” in _Proceedings of the ISSCC ’21_ , 2021, pp. 27–29.
  * [15] C. Yi, D. Kim, S. Solanki, J. H. Kwon, M. Kim, S. Jeon, Y. C. Ko, and I. Lee, “Design and Performance Analysis of THz Wireless Communication Systems for Chip-to-Chip and Personal Area Networks Applications,” _IEEE Journal on Selected Areas in Communications_ , vol. 39, no. 6, pp. 1785–1796, 2021.
  * [16] J. M. Jornet and I. F. Akyildiz, “Femtosecond-long pulse-based modulation for terahertz band communication in nanonetworks,” _IEEE Transactions on Communications_ , vol. 62, no. 5, pp. 1742–1754, 2014.
  * [17] A. Franques, S. Abadal, H. Hassanieh, and J. Torrellas, “Fuzzy-token: An adaptive mac protocol for wireless-enabled manycores,” in _2021 Design, Automation & Test in Europe Conference & Exhibition (DATE)_. IEEE, 2021, pp. 1657–1662.
  * [18] D. Bertozzi, G. Dimitrakopoulos, J. Flich, and S. Sonntag, “The fast evolving landscape of on-chip communication,” _Design Automation for Embedded Systems_ , vol. 19, no. 1, pp. 59–76, 2015.
  * [19] G. Lerosey, J. De Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, “Time reversal of electromagnetic waves,” _Physical review letters_ , vol. 92, no. 19, p. 193904, 2004.
  * [20] G. Lerosey, J. De Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” _Science_ , vol. 315, no. 5815, pp. 1120–1122, 2007.
  * [21] F. Han, Y. H. Yang, B. Wang, Y. Wu, and K. J. Liu, “Time-reversal division multiple access over multi-path channels,” _IEEE Transactions on Communications_ , vol. 60, no. 7, pp. 1953–1965, 2012.
  * [22] Q. Xu, C. Jiang, Y. Han, B. Wang, and K. J. Liu, “Waveforming: An Overview With Beamforming,” _IEEE Communications Surveys and Tutorials_ , vol. 20, no. 1, pp. 132–149, 2018.
  * [23] G. C. Alexandropoulos, A. Mokh, R. Khayatzadeh, J. de Rosny, M. Kamoun, A. Ourir, A. Tourin, M. Fink, and M. Debbah, “Time reversal for 6g spatiotemporal focusing: Recent experiments, opportunities, and challenges,” _IEEE Vehicular Technology Magazine_ , 2022.
  * [24] M. J. Chabalko and A. P. Sample, “Electromagnetic time reversal focusing of near field waves in metamaterials,” _Applied Physics Letters_ , vol. 109, no. 26, 2016.
  * [25] A. Bandara, F. Rodríguez-Galán, E. P. de Santana, P. H. Bolívar, E. Alarcón, and S. Abadal, “Exploration of time reversal for wireless communications within computing packages,” _Proceedings of the 10th ACM International Conference on Nanoscale Computing and Communication (NANOCOM)_ , 2023.
  * [26] F. Rodríguez-Galán, A. Bandara, E. P. de Santana, P. H. Bolívar, S. Abadal, and E. Alarcón, “Collective communication patterns using time-reversal terahertz links at the chip scale,” in _Proceedings of IEEE Global Communications Conference (GLOBECOM)_ , 2023.
  * [27] G. Bellanca, G. Calò, A. E. Kaplan, P. Bassi, and V. Petruzzelli, “Integrated vivaldi plasmonic antenna for wireless on-chip optical communications,” _Optics express_ , vol. 25, no. 14, pp. 16 214–16 227, 2017.
  * [28] W. Rayess, D. W. Matolak, S. Kaya, and A. K. Kodi, “Antennas and Channel Characteristics for Wireless Networks on Chips,” _Wireless Personal Communications_ , vol. 95, no. 4, pp. 5039–5056, 2017.
  * [29] X. Timoneda, A. Cabellos-Aparicio, D. Manessis, E. Alarcón, and S. Abadal, “Channel characterization for chip-scale wireless communications within computing packages,” in _2018 Twelfth IEEE/ACM International Symposium on Networks-on-Chip (NOCS)_. IEEE, 2018, pp. 1–8.
  * [30] F. Gutierrez, S. Agarwal, K. Parrish, and T. S. Rappaport, “On-chip integrated antenna structures in cmos for 60 ghz wpan systems,” _IEEE Journal on Selected Areas in Communications_ , vol. 27, no. 8, pp. 1367–1378, 2009.
  * [31] H.-H. Yeh, N. Hiramatsu, and K. L. Melde, “The design of broadband 60 ghz amc antenna in multi-chip rf data transmission,” _IEEE Transactions on Antennas and Propagation_ , vol. 61, no. 4, pp. 1623–1630, 2012.
  * [32] S. Hwangbo, R. Bowrothu, H.-i. Kim, and Y.-K. Yoon, “Integrated compact planar inverted-f antenna (pifa) with a shorting via wall for millimeter-wave wireless chip-to-chip (c2c) communications in 3d-sip,” in _2019 IEEE 69th Electronic Components and Technology Conference (ECTC)_. IEEE, 2019, pp. 983–988.
  * [33] K. Duraisamy, R. G. Kim, and P. P. Pande, “Enhancing performance of wireless nocs with distributed mac protocols,” in _Sixteenth International Symposium on Quality Electronic Design_. IEEE, 2015, pp. 406–411.
  * [34] N. Mansoor and A. Ganguly, “Reconfigurable wireless network-on-chip with a dynamic medium access mechanism,” in _Proceedings of the 9th International Symposium on Networks-on-Chip_ , 2015, pp. 1–8.
  * [35] B. Ollé, P. Talarn, A. Cabellos-Aparicio, F. Lemic, E. Alarcón, and S. Abadal, “Multi-channel medium access control protocols for wireless networks within computing packages,” in _2023 IEEE International Symposium on Circuits and Systems (ISCAS)_ , 2023, pp. 1–5.
  * [36] A. Ganguly, S. Abadal, I. Thakkar, N. E. Jerger, M. Riedel, M. Babaie, R. Balasubramonian, A. Sebastian, S. Pasricha, and B. Taskin, “Interconnects for dna, quantum, in-memory, and optical computing: Insights from a panel discussion,” _IEEE micro_ , vol. 42, no. 3, pp. 40–49, 2022.
  * [37] S. Abadal, C. Han, and J. M. Jornet, “Wave propagation and channel modeling in chip-scale wireless communications: A survey from millimeter-wave to terahertz and optics,” _IEEE access_ , vol. 8, pp. 278–293, 2019.
  * [38] Y. Chen and C. Han, “Channel modeling and characterization for wireless networks-on-chip communications in the millimeter wave and terahertz bands,” _IEEE Transactions on Molecular, Biological and Multi-Scale Communications_ , vol. 5, no. 1, pp. 30–43, 2019.
  * [39] O. Markish, O. Katz, B. Sheinman, D. Corcos, and D. Elad, “On-chip millimeter wave antennas and transceivers,” in _Proceedings of the 9th International Symposium on Networks-on-Chip_ , 2015, pp. 1–7.
  * [40] S. Wright, R. Polastre, H. Gan, L. Buchwalter, R. Horton, P. Andry, E. Sprogis, C. Patel, C. Tsang, J. Knickerbocker _et al._ , “Characterization of micro-bump c4 interconnects for si-carrier sop applications,” in _56th Electronic Components and Technology Conference 2006_. IEEE, 2006, pp. 8–pp.
  * [41] X. Zhang, J. K. Lin, S. Wickramanayaka, S. Zhang, R. Weerasekera, R. Dutta, K. F. Chang, K.-J. Chui, H. Y. Li, D. S. Wee Ho _et al._ , “Heterogeneous 2.5 d integration on through silicon interposer,” _Applied physics reviews_ , vol. 2, no. 2, 2015.
  * [42] A. Kannan, N. E. Jerger, and G. H. Loh, “Enabling interposer-based disintegration of multi-core processors,” in _Proceedings of the 48th international symposium on Microarchitecture_ , 2015, pp. 546–558.
  * [43] M. F. Imani, S. Abadal, and P. del Hougne, “Metasurface-programmable wireless network-on-chip,” _Advanced Science_ , 2022.
  * [44] Computer Simulation Technology (CST), “CST Microwave Studio,” 2022. [Online]. Available: http://www.cst.com
  * [45] A. Oppenheim, A. Willsky, and I. Young, _Signals and Systems_. Prentice-Hall, Englewood Cliffs, New Jersey, 1983.


m o m o #2#4#1short=#2,long=#3,#4 #1short=#2,long=#3 #4#1short=#1,long=#3,#4
#1short=#1,long=#3 2Dtwo-dimensional 3Dthree-dimensional 4Dfour-dimensional
6Dsix-dimensional 1Gfirst generation 2Gsecond generation 3Gthird generation
4Gfourth generation 5Gfifth generation 5GC5G core network 5G-StoRM5G
stochastic radio channel for dual mobility 6Gsixth generation 3GPP3rd
generation partnership project 3GPP23rd generation partnership project 2
A2Aair-to-air A2Gair-to-ground AAantenna array ACadmission control ADattack-
decay AEantenna element AFamplify and forward ABSalmost blank subframe
ACFautocorrelation function ADSLasymmetric digital subscriber line
AHWalternate hop-and-wait AIartificial intelligence AMCadaptive modulation and
coding APaccess point APAadaptive power allocation APIapplication protocol
interface ARQautomatic repeat request ATaveraged time ARMAautoregressive
moving average ASEaverage squared error ASCadaptive satisfaction control
ATESadaptive throughput-based efficiency-satisfaction trade-off AWGNadditive
white gaussian noise BAPbackhaul adaptation protocol BBbranch and bound
BCbranch and cut BDblock diagonalization BERbit error rate BFbest fit BLbit
loading BLERblock error rate BLPC-1bit loading with power constraint in hop 1
BLPC-2bit loading with power constraint in hop 2 BPCbinary power control
BPSKbinary phase-shift keying BRAbalanced random allocation BSbase station
BSP*BS placement BSRbuffer status report BoIband of interest C-linkcontrol
link CAPcombinatorial allocation problem CAPEXcapital expenditure CBcontextual
bandit CBFcoordinated beamforming CBRconstant bit rate CBSclass based
scheduling CCcongestion control CCLcommon cell list CDFcumulative distribution
function CDLclustered delay line CDMAcode-division multiple access CIRchannel
impulse response CHchannel hardening CHOconditional handover C-RANcloud-based
radio access network CLclosed loop CLTcentral limit theorem CLPCclosed loop
power control CNcore network CNRchannel-to-noise ratio CPcontrol plane
CPAcellular protection algorithm CPICHcommon pilot channel CoMPcoordinated
multi-point CQIchannel quality indicator CREcell range expansion
CRMconstrained rate maximization CRNcognitive radio network C-RNTIcell radio
network temporary identifier CRRMcentralized/common radio resource management
CRScell-specific reference signal CScoordinated scheduling CSIchannel state
information CSI-RSchannel state information reference signal CTSclear to send
CUcentralized unit CUEcellular user equipment CWNDcongestion window size
D2Ddevice-to-device D2Ndrone-to-network DAAdrone antenna array DAGdirected
acyclic graph DBSdrone mounted base station DCdual connectivity DCAdynamic
channel allocation DEdifferential evolution DFdecode and forward DFTdiscrete
fourier transform DISTdistance DLdownlink DMAdouble moving average
DMRSdemodulation reference signal D2DM*D2D mode DMS*D2D mode selection DPdata
plane DPCdirty paper coding DRAdynamic resource assignment DSAdynamic spectrum
access DSMdelay-based satisfaction maximization DUdistributed unit E2Eend-to-
end ECCelectronic communications committee EDFearliest deadline first EEenergy
efficiency EFLCerror feedback based load control EIefficiency indicator
e-ICICenhanced inter-cell interference coordination eMBBenhanced mobile
broadband EMelectromagnetic eNBevolved node B EXPexponential EPAequal power
allocation EPCevolved packet core EPSevolved packet system E-UTRANevolved
universal terrestrial radio access network ESexhaustive search FCPfundamental
counting principle FCAflow control algorithm FDfull duplex FDDfrequency
division duplex FDMfrequency division multiplexing FDMAfrequency division
multiple access FERframe erasure rate FIFOfirst in first out FoVfield-of-view
FFfast fading FRS[FS]fast-rat scheduling FSfast switching FSBfixed switched
beamforming FSTfixed *SNR target FTfourier transform FTPfile transfer protocol
Fwdforwarding GAgenetic algorithm GAPgeneralized assignment problem GAP-
MQgeneralized assignment problem with minimum quantities GATESgeneralized
adaptive throughput-based efficiency-satisfaction trade-off GBRguaranteed bit
rate GLRgain to leakage ratio gNBgNodeB GOSgenerated orthogonal sequence
GPgaussian process GPLGNU general public license GPSglobal positioning system
GRPgrouping GSMglobal system for mobile communications GTELwireless
telecommunications research group HARQhybrid automatic repeat request
HBFhybrid beamforming HCPPhardcore point process HetNetheterogeneous network
HDhalf duplex HFhigh-frequency HHhughes-hartogs HardH[HH]hard handover
HMSharmonic mode selection HOhandover HOLhead of line HPBWhalf power beamwidth
HSDPAhigh speed downlink packet access HSRhigh-speed railway HSPAhigh speed
packet access HTTPhypertext transfer protocol IABintegrated access and
backhaul ICMPinternet control message protocol ICIintercell interference
ICICinter-cell interference coordination IDidentification i.i.d.independent
and identically distributed IETFinternet engineering task force IPCindividual
power constraint UIDunique identification IIDindependent and identically
distributed IIRinfinite impulse response ILPinteger linear problem
IMTinternational mobile telecommunications INVinverted norm-based grouping
IoTinternet of things IPinternet protocol IPv6internet protocol version 6
IRAintegrated resource allocation IRSintelligent reflecting surface ISDinter-
site distance ISIinter symbol interference ISMindustrial, scientific and
medical ITUinternational telecommunication union JOASjoint opportunistic
assignment and scheduling JOSjoint opportunistic scheduling JPjoint processing
JRAPAPjoint rb assignment and power allocation problem JSjump-stay JSMjoint
satisfaction maximization KKTkarush-kuhn-tucker KPIkey performance indicator
LAClink admission control LAlink adaptation LBSlocation based service LCload
control LOSline of sight LPlinear programming LTElong term evolution
LTE-A*LTE-advanced LTE-AdvancedLTE-A LTE-RLTE railway LSPlarge scale parameter
MADRDPGmulti-agent deep recurrent deterministic policy gradient MeNBmaster
*ENB M2Mmachine-to-machine MACmedium access control MANETmobile ad hoc network
MEDSmethod of exact doppler spread MCmodular clock MCPminimal cost power
MCSmodulation and coding scheme MDBmeasured delay based MDIminimum *D2D
interference MDSMmodified delay-based satisfaction maximization MDUmax-delay-
utility METISmobile and wireless communications enablers for the twenty-twenty
information society *5G MFmatched filter MFAPmobile femtocell access point
MGmaximum gain MHmulti-hop mIABmobile IAB MILPmixed integer linear programming
MIMOmultiple input multiple output MINLPmixed integer nonlinear programming
MIPmixed integer programming MISOmultiple input single output MITmobility
interruption time MLmachine learning MLWDFmodified largest weighted delay
first MMEmobility management entity MMFmax-min fairness mmMAGICmillimetre-wave
based mobile radio access network for fifth generation integrated
communications MMRPmaximizing the minimal residual power MMRP-LBmaximizing the
minimal residual power with lower bound MMSEminimum mean square error
mMTCmassive machine-type communications mmWavemillimeter wave MNmaster node
MOSmean opinion score MPFmulticarrier proportional fair MPRPmaximization of
the product of the residual powers MRAmaximum rate allocation MRmaximum rate
MRCmaximum ratio combining MRNmobile relay node MRTmaximum ratio transmission
MRUSmaximum rate with user satisfaction MSmode selection MSEmean squared error
MCGmaster cell group MSImulti-stream interference MTmobile termination
MTCmachine-type communication IMS*IP multimedia subsystem MTSImultimedia
telephony services over *IMS MTSMmodified throughput-based satisfaction
maximization MU-MIMOmulti-user multiple input multiple output MUmulti-user
Multi-CUTmulti-cell and multi-user and multi-tier NASnon-access stratum NBnode
B nBSneighbor base station NCLneighbor cell list NCRnetwork-controlled
repeater NGnext generation NGCnext generation core network NLPnonlinear
programming NLOSnon-line of sight NMSEnormalized mean square error NNneural
network NOMAnon-orthogonal multiple access NORMnormalized projection-based
grouping NPnon-polynomial time NRnew radio NRTnon-real time NSAnon-stand-alone
NSPSnational security and public safety services OBFopportunistic beamforming
OFDMAorthogonal frequency division multiple access OFDMorthogonal frequency
division multiplexing OFPCopen loop with fractional path loss compensation
O2Ioutdoor-to-indoor OLopen loop OLPCopen-loop power control OL-PCopen-loop
power control OM[O&M]operational & maintenance OMAorthogonal multiple access
OPEXoperational expenditure ORAorthogonal resource allocation ORBorthogonal
random beamforming JO-PFjoint opportunistic proportional fair OSIopen systems
interconnection PApower allocation PAIR*D2D pair gain-based grouping PAPRpeak-
to-average power ratio P2Ppeer-to-peer PBCHphysical broadcast channel PBSpico
base station PCpower control PCIphysical cell *ID PDCPpacket data convergence
protocol PDFprobability density function PDUprotocol data unit PERpacket error
rate PFproportional fair PGRAprobabilistic graph based resource allocation
P-GWpacket data network gateway PHYphysical PLpathloss PLRpacket loss ratio
PRABEpower and resource allocation based on quality of experience PRBphysical
resource block PROJprojection-based grouping PSDpower spectral density
PSDepositive semi-definite ProSeproximity services PSpacket scheduling
PSOparticle swarm optimization PSSprimary synchronization signal
PTASpolynomial-time approximation scheme PTPpoint-to-point PZFprojected zero-
forcing QAMquadrature amplitude modulation QHMLWDFqueue-HOL-MLWDF QoEquality
of experience QoSquality of service QPSKquadri-phase shift keying QSMqueue-
based satisfaction maximization QuaDRiGaquasi deterministic radio channel
generator RACHrandom access RAISESreallocation-based assignment for improved
spectral efficiency and satisfaction RANradio access network RAresource
allocation RAPrb assignment problem RATradio access technology[long-plural-
form=radio access technologies] RATErate-based RAUremote antenna unit
RBresource block RBGresource block group REFreference grouping RETremote
electrical tilt RFradio frequency RLreinforcement learning RLCradio link
control RLFradio link failure RMrate maximization RMarural macro RMJ-SNRregion
of the minimum joint snr RMECrate maximization under experience constraints
RMSEroot-mean-square error RNCradio network controller RNDrandom grouping
RNNrecurrent neural network RRAradio resource allocation RRMradio resource
management RSCPreceived signal code power RSRPreference signal received power
RSRQreference signal received quality RRround robin RISreconfigurable
intelligent surfaces RRCradio resource control RSSIreceived signal strength
indicator RTreal time RTSrequest to send RUresource unit RUNErudimentary
network emulator RVrandom variable Rxreceiver RZFregularized zero-forcing
SAsubcarrier assignment SACsession admission control sBSserving base station
SCsmall cell SCIside control information SCon[SC]single connectivity
SCGsecondary cell group SCMspatial channel model SCSsubcarrier spacing SC-
FDMAsingle carrier - frequency division multiple access SCRVspatially
consistent random variable SDsoft dropping SDAPservice data adaptation
protocol S-Dsource-destination SDPCsoft dropping power control SDMspace-
division multiplexing SDMAspace-division multiple access SEsquared error
SFshadow fading SMDPsemi-markov decision problem SeNBsecondary *ENB SERsymbol
error rate SESsimple exponential smoothing S-GWserving gateway SICsuccessive
interference cancellation SelfIC[SIC]self interference cancellation SINRsignal
to interference-plus-noise ratio SLNRsignal to leakage-plus-noise ratio
SNNstrictly non-negative SIsatisfaction indicator SelfI[SI]self interference
SIPsession initiation protocol SISOsingle input single output SIMOsingle input
multiple output SIRsignal to interference ratio SMsubcarrier matching
SMAsimple moving average SMSEspatial-mean-square error SNsecondary node
SNRsignal to noise ratio SONself organizing networks SoAstate-of-the-art
SoSsum-of-sinusoids SORAsatisfaction oriented resource allocation SORA-
NRTsatisfaction-oriented resource allocation for non-real time services SORA-
RTsatisfaction-oriented resource allocation for real time services SPsignal
processing SPFsingle-carrier proportional fair SRsmart repeater ASRadvanced SR
SRAsequential removal algorithm SRB1signaling radio bearer 1 SRSsounding
reference signal SSBsynchronization signal block SSPsmall scale parameter
SSSsecondary synchronization signal STspanning tree STTDspace time transmit
diversity[long-plural-form=space time transmit diversities] SU-MIMOsingle-user
multiple input multiple output SUsingle-user tBStarget base station
SVDsingular value decomposition TCPtransmission control protocol TDDtime
division duplex TDMtime division multiplexing TDMAtime division multiple
access TDMedtime division multiplexed TETRAterrestrial trunked radio
TPtransmit power TPCtotal power constraint TRtechnical report TTItransmission
time interval TTRtime-to-rendezvous TTTtime-to-trigger TSMthroughput-based
satisfaction maximization TUtypical urban TVtelevision TVWS*TV white space
Txtransmitter UAVunmanned aerial vehicle UABSCuser-assisted bearer split
control UDPuser datagram protocol UDNultra-dense networks UEuser equipment
UBAUE-BS association UEPSurgency and efficiency-based packet scheduling
UFCfederal university of ceará ULAuniform linear array ULuplink UMaurban macro
UMiurban micro UMTSuniversal mobile telecommunications system UPuser plane
UPNuser provided network URAuniform rectangular array URIuniform resource
identifier URLLCultra-reliable low-latency communications URMunconstrained
rate maximization VBRvariable bit rate VETvariable electrical tilt VMRvehicle-
mounted relay VRvirtual resource VoIPvoice over *IP WCDMAwideband code
division multiple access WFwater-filling WIDwireless infrastructure drone Wi-
Fiwireless fidelity WiMAXworldwide interoperability for microwave access
WINNERwireless world initiative new radio WLANwireless local area network
WMPFweighted multicarrier proportional fair WPwork package WPFweighted
proportional fair WSNwireless sensor network WWWworld wide web WFQweighted
fair queuing XIXO(single or multiple) input (single or multiple) output
XPRcross-polarization power ratio ZFzero-forcing ZMCSCGzero mean circularly
symmetric complex gaussian

# System Level Evaluation of Network-Controlled
Repeaters: Performance Improvement of Serving
Cell and Interference Impact on Neighbor Cells

Gabriel C. M. da Silva, Erik R. B. Falcão, Victor F. Monteiro, Darlan C.
Moreira,
Diego A. Sousa, Tarcisio F. Maciel, Fco. Rafael M. Lima and Behrooz Makki
Behrooz Makki is with Ericsson Research, Sweden. The other authors are with
the Wireless Telecommunications Research Group (GTEL), Federal University of
Ceará (UFC), Fortaleza, Ceará, Brazil. Diego A. Sousa is also with Federal
Institute of Education, Science, and Technology of Ceará (IFCE), Paracuru,
Brazil. This work was supported by Ericsson Research, Sweden, and Ericsson
Innovation Center, Brazil, under UFC.51 Technical Cooperation Contract
Ericsson/UFC. The work of Victor F. Monteiro was supported by CNPq under Grant
308267/2022-2. The work of Tarcisio F. Maciel was supported by CNPq under
Grant 312471/2021-1. The work of Francisco R. M. Lima was supported by FUNCAP
(edital BPI) under Grant BP4-0172-00245.01.00/20.

###### Abstract

Heterogeneous networks have been studied as one of the enablers of network
densification. These studies have been intensified to overcome some drawbacks
related to propagation in mmWave, such as severe path and penetration losses.
One of the promising heterogeneous nodes is NCR. It was proposed by the 3GPP
in Release 18 as a candidate solution to enhance network coverage. In this
context, this work performs a system level evaluation to analyze the
performance improvement that an NCR can cause in its serving cell as well as
its interference impact on neighbor cells. Particularly, the results show a
considerable improvement on the performance of UE served by the NCR, while
neighbor UE that receive the NCR signal as interference are negatively
impacted, but not enough to suffer from outage.

###### Index Terms:

NCR, wireless backhaul, coverage, 5G, 6G.

##  I Introduction

Compared to the previous generation of wireless cellular systems, 5G networks
have explored higher frequencies, e.g., mmWave [1]. Some of the reasons for
this interest are the fact that in mmWave there are larger portions of
available spectrum and that the required antenna arrays are smaller, which
allows the deployment of more antenna elements creating narrow beams with high
directional gain [1, 2, 3]. Nonetheless, there are some disadvantages, e.g.,
suffering from high path and penetration losses [2, 4].

One of the considered solutions to overcome the propagation losses is network
densification. However, building from scratch a completely new wired
infrastructure is expensive, takes time and, in some places, trenching may not
be allowed, like historical areas. Then, nodes with wireless backhaul have
emerged as a possible solution for the situations where wired backhaul is not
a viable solution [3, 5].

In this context, the present paper focuses on a new node with wireless
backhaul called NCR [6]. NCR was introduced by 3GPP in Release 18 [7]. It is
an enhanced version of traditional RF repeaters. One of the novelties of NCR
is the fact that they have beamforming capability that can be controlled by a
gNB via side control information to improve the communication.

In this paper, we introduce the concept of NCR and study the performance of
NCR-assisted networks. More specifically, this paper performs a system level
evaluation to analyze the performance improvement that an NCR can cause in its
serving cell. Also, we evaluate the effect of the interference that NCR can
have on the neighbor cells.

The rest of the paper is organized as follows. Section II presents the main
concepts related to NCR. The scenario considered in the performance evaluation
is presented in Section III. Section IV presents the performance evaluation
results. Finally, conclusions are presented in Section V.

##  II Network Controlled Repeater

Figure 1: NCR split in NCR-MT and NCR-Fwd.

Traditional RF repeaters used in previous generations of wireless
communications are non-regenerative nodes that amplify and forward a received
signal. A direct consequence of this is the increase of interference in the
system [8].

The NCR concept is an evolution of the RF repeaters that use side control
information to overcome the negative aspects of traditional repeaters. Side
control information that can be used by NCR are [8]:

  * •

ON/OFF information: turn on/off the amplify and forward on a given slot;

  * •

Timing information: dynamic DL/UL split;

  * •

Spatial Tx/ Rx: beamforming capability.

NCR can be split into NCR-MT and NCR-Fwd, as is shown in Fig. 1. The NCR-MT is
responsible for exchanging side control information with its controlling gNB.
Its link is called control link, and it is based on NR Uu interface. The NCR-
Fwd is responsible for executing the AF relaying [7].

##  III System model

As shown in Fig. 2, consider a scenario with two gNB, i.e., $b_{1}$ and
$b_{2}$. The ISD between them is equal to $2R$. Also, consider that there is
one UE close to each cell edge, i.e., UE $u_{1}$ and $u_{2}$ at cells of gNB
$b_{1}$ and $b_{2}$, respectively. In the cell of gNB $b_{2}$, an NCR is
deployed between $b_{2}$ and UE $u_{2}$ to enhance the link serving $u_{2}$ as
shown in Fig. 2.

Since we consider that the UE are close to the cell edge, the gNB antenna
array is deployed such that it steers to the middle point between its
respective UE and itself. Furthermore, the NCR backhaul antenna array is
always pointing towards the gNB $b_{2}$ direction, while its access antenna
array points towards the UE $u_{2}$.

Figure 2: Scenario with two gNB (distant 2$R$ from each other) and two UE,
connected to different gNB. Moreover, it is considered that one of the gNB
controls an NCR, which is deployed between its controller gNB and its serving
UE.

Regarding the SNR and SINR perceived by the UE in the DL, their expressions
are determined as follows.

Consider a PRB as the smallest allocable frequency unit, which consists of a
number of adjacent subcarriers in the frequency domain. The system bandwidth
is split into $K$ PRB. Moreover, consider that UE $u_{1}$ always connects
directly to gNB $b_{1}$, while UE $u_{2}$ connects to gNB $b_{2}$ either
directly or through the NCR.

The power received by a node $r$ from a signal that was transmitted by a node
$t$ at PRB $k$, where the pair $(t,r)$ can be, for example, $(b_{1},u_{1})$,
$(b_{2},u_{2})$, $(b_{2},\text{NCR})$, $(\text{NCR},u_{2})$, etc., is
expressed as

$p^{\text{R}}_{t,r,k}=\frac{p^{\text{T}}_{t,k}g^{\text{T}}_{t}g^{\text{R}}_{r}}{l_{t,r}},$
(1)

where $p^{\text{T}}_{t,k}$ is the power transmitted by node $t$ at PRB $k$,
$g^{\text{T}}_{t}$ is the transmit panel gain of node $t$, $g^{\text{R}}_{r}$
is the receive panel gain of node $r$, and $l_{t,r}$ is the pathloss between
nodes $t$ and $r$. Notice that, for the pairs
$(t,r)\in\\{(b_{1},u_{2}),(b_{2},u_{1}),(\text{NCR},u_{1})\\}$,
$p^{\text{R}}_{t,r,k}$ represents an interfering power, while, for the pairs
$(t,r)\in\\{(b_{1},u_{1}),(b_{2},u_{2}),(b_{2},\text{NCR}),(\text{NCR},u_{2})\\}$,
$p^{\text{R}}_{t,r,k}$ represents the useful power.

When gNB $b_{2}$ serves UE $u_{2}$ via NCR, the NCR transmit power on PRB $k$
$p^{\text{T}}_{\text{NCR},k}$ is equal to the NCR total receive power, i.e.,
the sum of the useful power $p^{\text{R}}_{b_{2},\text{NCR},k}$, the noise
$p_{n}$ and the interfering power
$p^{\text{I}}_{\text{NCR},k}=p^{\text{R}}_{b_{1},\text{NCR},k}$, amplified by
a gain $g^{\text{NCR}}$, limited by the NCR maximum transmit power per PRB
$p^{\text{NCR}}_{\text{MAX}}$. It can be expressed as

$p^{\text{T}}_{\text{NCR},k}=\text{min}\mathopen{}\mathclose{{}\left\\{p^{\text{NCR}}_{\text{MAX}},g^{\text{NCR}}\mathopen{}\mathclose{{}\left(p^{\text{R}}_{b_{2},\text{NCR},k}+p_{n}+p^{\text{I}}_{\text{NCR},k}}\right)}\right\\}.$
(2)

We consider that the NCR gain can be either fixed or dynamic111Only NCR fixed
gain has been specified by the 3GPP. So, while we try to mimic the model
specified by 3GPP Rel-18, the considered setup may have differences with
Rel-18 NCR.. When using the dynamic gain, the NCR transmit power
$p^{\text{T}}_{\text{NCR},k}$ is always equal to the NCR maximum transmit
power $p^{\text{NCR}}_{\text{MAX}}$. For this, the dynamic gain is defined as
the ratio between the NCR maximum transmit power, i.e.,
$p^{\text{NCR}}_{\text{MAX}}$, and NCR total receive power, i.e., the sum of
the useful power $p^{\text{R}}_{b_{2},\text{NCR},k}$, the noise $p_{n}$ and
the interfering power
$p^{\text{I}}_{\text{NCR},k}=p^{\text{R}}_{b_{1},\text{NCR},k}$. We remark
that the NCR does not need to know the values of
$p^{\text{R}}_{b_{2},\text{NCR},k}$, $p^{\text{I}}_{\text{NCR},k}$ and $p_{n}$
separately. It just need to know their sum, which is known since it is the
total input power that it receives. Thus, the dynamic gain can be expressed as

$g^{\text{NCR}}_{\text{DYN}}=\frac{p^{\text{NCR}}_{\text{MAX}}}{p^{\text{R}}_{b_{2},\text{NCR},k}+p^{\text{I}}_{\text{NCR},k}+p_{n}}.$
(3)

Regarding the fixed gain, i.e., $g^{\text{NCR}}_{\text{FIX}}$, it amplifies
the total received power with a fixed value, e.g., $90$ dB. When the fixed
gain implies an NCR total transmit power higher than its ceiling
$p^{\text{NCR}}_{\text{MAX}}$, the NCR works in a saturated mode. In this
mode, it behaves similar to the dynamic gain, where the NCR transmit power
$p^{\text{T}}_{\text{NCR},k}$ is equal to the NCR maximum transmit power
$p^{\text{NCR}}_{\text{MAX}}$.

Thus, the SNR and SINR perceived by UE $u_{i}$ at PRB $k$ are, respectively,
given by

$\rho_{u_{i},k}=\frac{p^{\text{R}}_{u_{i},k}}{p^{\text{N}}_{u_{i}}},$ (4)

and

$\eta_{u_{i},k}=\frac{p^{\text{R}}_{u_{i},k}}{p^{\text{I}}_{u_{i},k}+p^{\text{N}}_{u_{i}}},$
(5)

where $p^{\text{N}}_{u_{i}}$ is the receiver noise, $p^{\text{R}}_{u_{i},k}$
is the useful power received by $u_{i}$ at PRB $k$ and
$p^{\text{I}}_{u_{i},k}$ is the interference suffered by $u_{i}$ at PRB $k$.

Regarding $p^{\text{R}}_{u_{i},k}$, on the one hand, for $u_{1}$, the only
useful signal received is the one coming from $b_{1}$, thus

$p^{\text{R}}_{u_{1},k}=p^{\text{R}}_{b_{1},u_{1},k}.$ (6)

On the other hand, $u_{2}$ may receive two components of useful signal, one
coming directly from $b_{2}$ and other being amplified and forwarded by the
NCR. Thus,

$\displaystyle p^{\text{R}}_{u_{2},k}$ $\displaystyle=$ $\displaystyle
p^{\text{R}}_{b_{2},u_{2},k}+p^{\text{R}}_{\text{NCR},u_{2},k}$ (7)
$\displaystyle=$
$\displaystyle\frac{p^{\text{T}}_{b_{2},k}g^{\text{T}}_{b_{2}}g^{\text{R}}_{u_{2}}}{l_{b_{2},u_{2}}}+\frac{\mathopen{}\mathclose{{}\left(p^{\text{R}}_{b_{2},\text{NCR},k}g^{\text{NCR}}}\right)g^{\text{T}}_{\text{NCR}}g^{\text{R}}_{u_{2}}}{l_{\text{NCR},u_{2}}}$
$\displaystyle=$
$\displaystyle\frac{p^{\text{T}}_{b_{2},k}g^{\text{T}}_{b_{2}}g^{\text{R}}_{u_{2}}}{l_{b_{2},u_{2}}}+\frac{\mathopen{}\mathclose{{}\left(\frac{p^{\text{T}}_{b_{2},k}g^{\text{T}}_{b_{2}}g^{\text{R}}_{\text{NCR}}}{l_{b_{2},\text{NCR}}}}\right)g^{\text{NCR}}g^{\text{T}}_{\text{NCR}}g^{\text{R}}_{u_{2}}}{l_{\text{NCR},u_{2}}}$
$\displaystyle=$
$\displaystyle\frac{p^{\text{T}}_{b_{2},k}g^{\text{T}}_{b_{2}}g^{\text{R}}_{u_{2}}}{l_{b_{2},u_{2}}}+\frac{p^{\text{T}}_{b_{2},k}g^{\text{T}}_{b_{2}}g^{\text{R}}_{\text{NCR}}g^{\text{NCR}}g^{\text{T}}_{\text{NCR}}g^{\text{R}}_{u_{2}}}{l_{b_{2},\text{NCR}}l_{\text{NCR},u_{2}}}.$

Concerning $p^{\text{I}}_{u_{i},k}$, with NCR, there are two sources of
interference for $u_{i}$, which are the signal from $b_{j}$, with $i\neq j$,
and this same signal amplified by the NCR, thus

$\displaystyle p^{\text{I}}_{u_{i},k}$ $\displaystyle=$
$\displaystyle\frac{p^{\text{T}}_{b_{j},k}g^{\text{T}}_{b_{j}}g^{\text{R}}_{u_{i}}}{l_{b_{j},u_{i}}}+\frac{p^{\text{T}}_{b_{j},k}g^{\text{T}}_{b_{j}}g^{\text{R}}_{\text{NCR}}g^{\text{NCR}}g^{\text{T}}_{\text{NCR}}g^{\text{R}}_{u_{i}}}{l_{b_{j},\text{NCR}}l_{\text{NCR},u_{i}}}.$
(8)

Finally, similarly to what has already been presented, regarding
$p^{\text{N}}_{u_{i}}$, we have

$\displaystyle p^{\text{N}}_{u_{1}}$ $\displaystyle=$ $\displaystyle
p_{n}\text{ and }$ (9) $\displaystyle p^{\text{N}}_{u_{2}}$ $\displaystyle=$
$\displaystyle
p_{n}\mathopen{}\mathclose{{}\left(1+\frac{g^{\text{NCR}}g^{\text{T}}_{\text{NCR}}g^{\text{R}}_{u_{2}}}{l_{\text{NCR},u_{2}}}}\right).$
(10)

##  IV Performance Evaluation

###  IV-A Simulation Assumptions

The simulations were conducted at 28 GHz. The frequency domain was split into
PRB consisting of 12 consecutive subcarriers, with subcarrier spacing of 60
kHz. It was adopted the RR scheduler for allocating the PRB.

Concerning the time domain, it was split into slots composed of 14 OFDM
symbols. Each slot had a duration of 0.25 ms. A TDD scheme was adopted, where
downlink and uplink slots were alternated in time.

Regarding the channel model, the adopted one is based on the 3GPP channel
model standardized in [9] and its implementation is described in [10]. In this
channel model, it is considered a distance-dependent pathloss, a lognormal
shadowing component, a small-scale fading, and it is spatially and time
consistent. The link types are described in Table I. The gNB and the NCR
transmissions were performed with a DFT codebook based beamforming, where for
each transmission a beam management was performed in order to identify the
best transmitter beam to be used when serving the UE.

TABLE I: Characteristic of the links Link | Scenario | LOS/NLOS
---|---|---
gNB - UE | Urban Macro | NLOS
gNB - NCR | Urban Macro | NLOS
NCR - UE | Urban Micro | LOS

It was used a CQI/MCS mapping curve standardized in [11] with a target BLER of
10 %. An outer loop strategy was considered to avoid the increase of the BLER,
i.e., when a transmission error occurred, the estimated SINR decreased 1 dB,
however, when a transmission occurred without error, the estimated SINR had
its value added by 0.1 dB. The most relevant simulation parameters are
summarized in Tables II and IV-A.

TABLE II: Entities characteristics. Parameter |  Macro gNB |  NCR |  UE
---|---|---|---
Height |  25 m |  10 m |  1.5 m
Transmit power |  16.8 dBm |  13.8 dBm |  5.8 dBm
Antenna array |  URA $8\times 8$ |  URA $8\times 8$ (2 panels) |  Single Antenna
Antenna element pattern |  3GPP 3D [9] |  3GPP 3D [9] |  Omni
Max. antenna element gain |  8 dBi |  8 dBi |  0 dBi
TABLE III: Simulation parameters.

Parameter |  Value
---|---
Carrier frequency |  28 GHz
Subcarrier spacing |  60 kHz
Number of subcarriers per RB |  $12$
Number of RB |  $1$
Slot duration |  0.25 ms
OFDM symbols per slot |  $14$
Channel generation procedure |  As described in [9, Fig.7.6.4-1]
Path loss |  Eqs. in [9, Table 7.4.1-1]
Fast fading |  As described in [9, Sec.7.5] and [9, Table 7.5-6]
AWGN density power per subcarrier |  -174 dBm/Hz
Noise figure |  9 dB
CBR packet size |  $3072$ bits
ISD |  400 m
Distance between gNB and UE |  150 m

###  IV-B Simulation Results

Figures 3 and 4 show the impact of NCR position on the SNR (quantiles 0.9 and
0.1, respectively) of UE $u_{1}$ and $u_{2}$. Both figures present the results
for the two possibilities of the NCR gain: dynamic and fixed. For the fixed
case, we considered two gain values: 70 dB and 90 dB. Considering the
positions of $u_{2}$ and $b_{2}$ fixed, the x-axis represents the possible
distance between the NCR and $b_{2}$. As expected, the SNR of $u_{1}$ does not
depend of the position of the NCR. Also, notice that the SNR of $u_{2}$, in
the beginning, increases and, after a certain distance, starts to decrease.
This is due to the product of the two pathlosses in (7), i.e.,
$l_{b_{2},\text{NCR}}l_{\text{NCR},u_{2}}$. Thus, unlike what one could
expect, deploying a NCR closer to the serving UE does not always mean a better
connection. In other words, one could expect that the closer a UE is to a NCR
the higher its SNR would be due to the shorter distance, and so lower path
loss, however as shown in Figs. 3 and 4, this is not true.

Due to the symmetry of the scenario presented in Fig. 2, without the NCR,
$u_{1}$ and $u_{2}$ should present similar values of SNR and SINR. Thus, by
comparing the curves in Fig. 3 and Fig. 4 related to $u_{1}$ and $u_{2}$, we
can see that the deployment of an NCR considerably improves the SNR perceived
by $u_{2}$. More specifically, the SNR perceived by $u_{2}$ increased in at
least 15 dB due to the deployment of the NCR. Moreover, notice that the case
with fixed NCR gain equal to 90 dB presented results similar to the dynamic
case, which means that for 90 dB, the NCR operated in its saturated mode.

Figure 3: Impact of NCR position on the SNR (quantile 90%) of both UE for two
types of NCR gain, i.e., dynamic and fixed. Figure 4: Impact of NCR position
on the SNR (quantile 10%) of both UE for two types of NCR gain, i.e., dynamic
and fixed.

Figures 5 and 6 are similar to Figs. 3 and 4, the main difference is that
Figs. 5 and 6 focus on SINR instead of SNR.

Notice, in Figs. 5 and 6, the trend discontinuity on the SINR of $u_{1}$ when
the distance between the NCR and $b_{2}$ is approximately 81 m. This is
explained by the change in the interference coming from the NCR. More
specifically, around that distance the beam used by the NCR to serve $u_{2}$
changes creating a new interference pattern on $u_{1}$. Fig. 7 illustrates
this behavior.

Fig. 7 presents the impact of the distance between $b_{2}$ and the NCR on the
interference suffered by $u_{1}$ (y-axis of left-hand side) and on the beam
index that is used to serve $u_{2}$ (y-axis of right-hand side). In this
figure, we can notice that the interference suffered by $u_{1}$ has a
discontinuity when the distance between $b_{2}$ and the NCR is around 81 m.
Around this position, the NCR beam serving $u_{2}$ changes from 0 to 1. Beam 0
points in a direction closer to $u_{1}$ than Beam 1, that is why when changing
from Beam 0 to Beam 1, the interference decreases. This can be seen as a
spatial filtering.

Furthermore, notice, in Fig. 7, that within the distance ranges 0 m to 81 m
and 81 m to 150 m, the interference suffered by $u_{1}$ increases when the NCR
distance between $b_{2}$ and the NCR increases. This is explained by the
approximation of the NCR to $u_{1}$.

Figure 5: Impact of NCR position on the SINR (quantile 90%) of both UE for two
types of NCR gain, i.e., dynamic and fixed. Figure 6: Impact of NCR position
on the SINR (quantile 10%) of both UE for two types of NCR gain, i.e., dynamic
and fixed. Figure 7: Comparison between the interference and amplified noise
by NCR in the $u_{1}$ and the change in the codebook indexes of the NCR-Fwd.

Finally, Figs. 8 and 9 present the impact of the distance between $b_{2}$ and
the NCR on the spectral efficiency of the transmissions to $u_{1}$ and
$u_{2}$. The maximum spectral efficiency that a transmission could achieve is:

$\displaystyle\frac{\text{subcarriers per PRB}\cdot\text{symbols per
PRB}\cdot\text{max. code rate}}{\text{PRB time}\cdot\text{PRB bandwidth}}$
(11) $\displaystyle=$ $\displaystyle\frac{12\cdot 14\cdot 5.5547}{0.25\cdot
10^{-3}\cdot 12\cdot 60\cdot 10^{3}}=5.18\text{ bits/s/Hz},$

where 5.5547 corresponds to the code rate associated to the CQI index 15 in
[11]. Remark that $u_{2}$ achieves the maximum spectral efficiency in the
majority of the considered cases, while $u_{1}$ achieves lower values, but
that are still high enough to allow the communication.

Figure 8: Spectral efficiency (quantile 90%) of the both UE and with different
types of NCR gain. Figure 9: Spectral efficiency (quantile 10%) of the both UE
and with different types of NCR gain.

##  V Conclusions

The paper presented a system level evaluation analyzing the performance
improvement due to the deployment of a NCR on a given cell and its
interference impact on neighbor cells. As expected, we have seen that the NCR
improves the link quality of its serving UE. However, unlike what one could
expect, deploying a NCR closer to its serving UE does not necessarily mean a
better connection. There is a trade-off given by the product between its
distance to its serving gNB and its distance to the UE that it is serving. We
have also seen that the interference caused on neighbor cells can be mitigated
by spatial filtering by means of appropriate beam management.

## References

  * [1] Kai Dong et al.  “Advanced Tri-Sectoral Multi-User Millimeter-Wave Smart Repeater”, 2022  arXiv:2210.04859
  * [2] Roberto Flamini et al.  “Towards a Heterogeneous Smart Electromagnetic Environment for Millimeter-Wave Communications: An Industrial Viewpoint”  In _IEEE Trans. Antennas Propag._ 70.10, 2022, pp. 8898–8910  DOI: 10.1109/TAP.2022.3151978
  * [3] Michele Polese et al.  “Integrated Access and Backhaul in 5G mmWave Networks: Potential and Challenges”  In _IEEE Commun. Mag._ 58.3, 2020, pp. 62–68  DOI: 10.1109/MCOM.001.1900346
  * [4] Reza Aghazadeh Ayoubi et al.  “Network-Controlled Repeaters vs. Reconfigurable Intelligent Surfaces for 6G mmW Coverage Extension”, 2022  arXiv:2211.08033
  * [5] Charitha Madapatha et al.  “On Integrated Access and Backhaul Networks: Current Status and Potentials”  In _IEEE Open J. Commu. Soc._ 1, 2020, pp. 1374–1389  DOI: 10.1109/OJCOMS.2020.3022529
  * [6] Hao Guo et al.  “A Comparison between Network-Controlled Repeaters and Reconfigurable Intelligent Surfaces”, 2022  arXiv:2211.06974
  * [7] 3GPP  “Study on NR network-controlled repeaters: Radio Interface Protocol Aspects” v.18.0.0, 2022  URL: http://www.3gpp.org/DynaReport/38867.htm
  * [8] “RWS-210019: NR Smart Repeaters”, Qualcomm, 2021
  * [9] 3GPP  “Study on Channel Model for Frequencies from 0.5 to 100 GHz” v.14.2.0, 2017  URL: http://www.3gpp.org/DynaReport/38901.htm
  * [10] Alexandre Matos Pessoa et al.  “A Stochastic Channel Model With Dual Mobility for 5G Massive Networks”  In _IEEE Access_ 7, 2019, pp. 149971–149987  DOI: 10.1109/ACCESS.2019.2947407
  * [11] 3GPP  “NR; Physical layer procedures for data” v.15.0.0, 2017  URL: http://www.3gpp.org/ftp/Specs/html-info/38214.htm