# Towards Radio Designs with Non-Linear Processing for Next Generation Mobile
Systems

Konstantinos Nikitopoulos, Marcin Filo, Chathura Jayawardena and Rahim
Tafazolli The authors are with the Wireless Systems Lab, 5G Innovation Centre,
Institute for Communication Systems, University of Surrey, Guildford GU2 7XH,
UK e-mail: {k.nikitopoulos, m.filo, c.jayawardena, r<EMAIL_ADDRESS>
###### Abstract

MIMO mobile systems, with a large number of antennas at the base-station side,
enable the concurrent transmission of multiple, spatially separated
information streams and, therefore, enable improved network throughput and
connectivity both in uplink and downlink transmissions. Traditionally, to
efficiently facilitate such MIMO transmissions, linear base-station processing
is adopted, that translates the MIMO channel into several single-antenna
channels. Still, while such approaches are relatively easy to implement, they
can leave on the table a significant amount of unexploited MIMO capacity.
Recently proposed non-linear base-station processing methods claim this
unexplored capacity and promise a substantially increased network throughput.
Still, to the best of the authors’ knowledge, non-linear base-station
processing methods not only have not yet been adopted by actual systems, but
have not even been evaluated in a standard-compliant framework, involving of
all the necessary algorithmic modules required by a practical system. This
work, outlines our experience by trying to incorporate and evaluate the gains
of non-linear base-station processing in a 3GPP standard environment. We
discuss the several corresponding challenges and our adopted solutions,
together with their corresponding limitations. We report gains that we have
managed to verify, and we also discuss remaining challenges, missing
algorithmic components and future research directions that would be required
towards highly efficient, future mobile systems that can efficiently exploit
the gains of non-linear, base-station processing.

##  I Introduction

Much of the current communication systems research focuses on finding new,
breakthrough ways to increase the achievable throughout (both at a user and a
system level) and user connectivity capabilities, while meeting very tight
latency requirements. In this direction, a plethora of ideas have been
proposed. Still, very few of these ideas, and perhaps the simplest in terms of
practical realization, have finally been adopted by actual wireless systems
and standards. In the natural question “why is this happening?” someone can
give several answers. In many of the works published, the proposed ideas are
only evaluated via simulations and, therefore, the results may be heavily
assumption-depended. Namely, the showed gains can be a strong function of the
simulated environment that can sufficiently differ from the actual
transmission environment. To facilitate more realistic evaluations, many
researchers use “proof-of-concept” systems. However, this approach comes with
its own challenges and practical limitations. Such a challenge is the
availability of appropriate research platforms able to realize and validate
proposed novel ideas. In addition, in many cases and especially in physical
layer research, the proposed ideas are not evaluated in a complete, standard-
compliant environment. As a result, additional algorithmic components may be
required to make a new idea adoptable by a practical system or communication
standards. As we will discuss later in detail, such components are often
related to limitations imposed from the existing system design, as for example
limitations related to conventional signalling procedures or even other
mechanisms that are required for transmsission optimization, as for example
the transmission rate selection. As a result, implementing and evaluating new
physical layer concepts and ideas in a standard-compliant environment can be
of substantial importance, not only to verify the potential gains in more
realistic transmission scenarios, but also to identify any need for new
“building blocks” or required modifications in the standards (e.g., the
signalling, pilots, access methods). In other words, testing and verifying new
physical layer ideas in a research-grade, standard-compliant environment can
be an important step towards future systems design and evaluation, that can
highly increase our confidence on newly proposed approaches and can assist in
identifying further requirements and missing components that will enable the
adoption of novel ideas in actual systems.

In this work we focus on recently proposed ideas to improve base-station (BS)
processing in multiple-input multiple-output (MIMO) spatially multiplexed
systems. The use of a large number of antennas at the BS side has been shown
to be a very efficient way to increase the achievable throughput and the user
connectivity capabilities of mobile systems, both in uplink and downlink
transmissions, by enabling several concurrently transmitting, spatially
separated users (i.e., Multi-User MIMO)[1, 2, 3]. Traditionally, in such
systems, linear precoding (in the downlink) and detection (in the uplink)
approaches are employed at the BS, based on the zero-forcing (ZF) or on the
minimum-mean-square-error (MMSE) principles. Such linear approaches have two
major practical benefits. Their implementation is relatively simple, and since
they practically translate the mutually interfering information streams into
traditional, non-interfering ones, they can be easily adopted by standards
with minimum modifications. Still, their main drawback is that, in order for
these approaches to be efficient in terms of achievable throughput, the number
of BS antennas needs to be much larger than the number of concurrently
transmitted information streams, and, therefore, the number of served users
[2, 1]. However, since by increasing the number of antennas the capacity of
the MIMO channel generally increases [4], such an approach leaves on the table
a significant amount of unexploited capacity [5]. Equivalently, it
unnecessarily increases the number of BS antennas for a certain number of
users, significantly increasing the BS cost and reducing power efficiency. In
contrary, non-linear BS processing approaches, like “hard” and “soft” Maximum-
Likelihood detection, in the uplink [5, 6], and Vector-Perturbation in the
downlink [7], promise substantially increased achievable throughput and user
connectivity. Still, to the best of our knowledge, such approaches have not
yet been adopted by practical systems and have not even been validated in a
standard-compliant scenario. In addition, and perhaps as a consequence, it is
not obvious what further system changes are required to deliver the promised
gains in practice.

Contributions of this paper. In this work we present our experience by trying
to incorporate and validate the performance gains of advanced, non-linear
methods in a 3rd Generation Partnership Project (3GPP) compliant framework. We
outline the main challenges we have faced in order to realize and evaluate
such approaches, together with our adopted approaches and their limitations.
We report gains that we have been able to verify, and we describe missing
components, remaining challenges, potential solutions, and open research
directions that would enable the adoption of such approaches in practice.
Finally, we discuss some future research directions that have the potential to
substantially increase both the throughput and connectivity capabilities of
next generation wireless systems by adopting new forms of non-linear BS
processing.

##  II Outline of Non-linear Processing Techniques for Base-Station Processing

As discussed, current MIMO deployments mostly employ linear BS processing,
both for uplink and downlink transmissions, but such approaches may leave a
significant amount of capacity unexploited. Instead, non-linear BS processing
approaches promise consistent gains compared to the linear ones, both in terms
of achievable throughput and user connectivity. For uplink transmissions,
“hard” Maximum-Likelihood detection methods have been proposed, both exact and
approximate, and with most of them being realized in terms of sphere decoding
[8, 5, 9, 10, 11, 12]. Most of these approaches, though, have been evaluated
using simulations and by assuming “Rayleigh” or other mathematically modeled
MIMO channels. While such mathematical models are necessary for the
theoretical analysis of such systems, they do not necessary capture the
spatial multiplexing capabilities of the actual MIMO channels. In addition,
the provided performance of these methods is often presented in terms of
(uncoded) bit-error-rate, which is not adequate for evaluating systems
throughput gains. The sphere decoding approaches of [5, 13, 9] are evaluated
in actual transmission channel environments and in terms of achievable
throughput. Still, their evaluations are based on a very limited number of
transmission rates (i.e., combinations of QAM constellation size and coding
rates) that are selected based on their average performance. In addition,
since the processing takes place off-line, the reported achievable rates do
not include the impact of the higher layers of the protocol stack (e.g., the
impact of the hybrid automatic repeat request (HARQ) mechanism). In addition,
“hard” detection cannot be used jointly with state-of-the-art “soft” channel
encoding and decoding schemes (e.g., LDPC, Turbo) adopted in recent standards,
and therefore, are of limited practical interest.

For use with soft channel decoding schemes, soft-output sphere decoders have
been proposed to reduce the complexity of optimal soft detection [6, 14, 15,
16]. Again, most soft sphere decoding approaches, including the sequential
sphere decoder of [6] and the soft fixed complexity sphere decoder of [15],
are evaluated by assuming mathematically modelled MIMO channels. The massively
parallel hard and soft detectors of [17, 18], that enable practical low
complexity and low latency non-linear detection, are evaluated both in
mathematically modelled and measured channels. Still, these evaluations are
based on a limited number of transmission rates, and the performance is
reported for rates that have been chosen by an exhaustive search to maximize
the average throughput, across all positions, instead of optimizing rate per
packet transmission. In addition, similarly to the hard detection approaches,
they do not capture the impact of the higher layers of the protocol stack.

In the downlink, non-linear, theoretical precoding approaches exist which
claim the MIMO channel capacity that is currently unexploited by linear
precoders [7, 19, 20, 21, 22, 23]. These approaches are based on Dirty Paper
Coding principles which can achieve the capacity of the Gaussian broadcast
channel [24]. In this direction, the non-linear Tomlinson-Harashima precoding
[25] can substantially improve on the throughput achievable by traditional
linear precoding. Improving on the Tomlinson-Harashima precoding, vector
perturbation [7] precoding can further contribute into bridging the gap to the
MIMO channel capacity limit. In particular, efficiently perturbing the
transmitted constellation symbols in a way that the corresponding perturbation
effect can be efficiently compensated at the receiver side. Again, most
evaluations of vector perturbation precoding [7, 19] are limited to
simulations employing mathematically modelled channels. The massively parallel
vector perturbation precoder of [26], that promises practical non-linear
precoding, is evaluated by over-the-air experiments, but also with off-line
processing, inheriting the corresponding evaluation drawbacks.

As discussed, to the best of our knowledge, none of the above approaches has
been evaluated in a standard-compliant framework, neither a corresponding
attempt has been reported that would identify missing algorithmic components,
and further challenges that need to be resolved.

##  III Challenges, Adopted Approaches & Lessons Learned

Here we describe our experience by trying to incorporate and validate the
performance of non-linear processing approaches in a 3GPP compliant
environment. We outline some of the main challenges we have faced, as well as
our adopted solutions together with their corresponding limitations, and the
related lessons we have learned. As we will discuss in detail, such an attempt
came with numerous challenges, ranging from finding (and extending) an
appropriate software and hardware platform to perform our evaluations, to
challenges related to missing components and practical aspects of the
algorithms that, to the best of our knowledge, have not been
highlighted/identified before.

###  III-A Seeking for the appropriate software platform

There is a number of software platforms which aim at providing a 3GPP
compliant protocol stack, capable of running on general-purpose processors.
They can be broadly classified as commercial and open-source. The commercial
solutions include, among others, the LTE and NR Network Software Suit by
Amarisoft [27], the National Instruments LTE Application Framework for LabVIEW
Communications System Design Suite [28] and Intel’s FlexRAN [29]. The most
complete is perhaps the solution provided by Amarisoft which, in contrast to
other options, provides a full protocol stack implementation on BS side and
user equipment (UE) side. Although it supports many features and transmission
modes, due to its closed-source nature, Amarisoft solution cannot be openly
used for physical layer research. In contrast to commercial platforms, open-
source solutions which include srsLTE [30], openLTE [31] and OpenAirInterface
(OAI) [32] are freely available to the public. Among those, it seems that the
most advanced platform is OAI which is the open-source solution with the
largest developer community actively working towards adding new features into
the existing code base (e.g. support for 5G New Radio (NR)).

Our adopted solution. For our evaluations, we extended our recently proposed
SoftWare Open Radio Design (SWORD) platform [33], that overcomes the missing
support for large/massive MIMO setups, as well as the inherent inability of
existing approaches to investigate non-linear processing without prohibitive
software and hardware optimization necessary. To support downlink and uplink
MU-MIMO transmission schemes, which were in our main interest for testing non-
linear processing approaches, SWORD significantly extends the OAI code base
[34] and introduces a completely new mode of operation which we call pseudo-
real-time (RT). This new mode combines the properties and builds upon two
existing modes of operations already supported by the OAI which permit RT
over-the-air (OTA) transmission and emulation of an entire radio access
network without the use of software-defined radio (SDR) modules. Compared to
the generally adopted method of the offline processing in which a received
signal is stored in a raw format on the receiver side and then processed, the
pseudo-RT can be effectively used to evaluate the impact of advanced physical
layer approaches on the overall system performance. In contrast to the offline
processing, the pseudo-RT mode makes use of a pause period between each
transmission to facilitate signal processing on both sides. As a result, it
preserves the dependence between consecutive events, allowing for a more
realistic setting in which the full-protocol stack is executed.

In order to enable pseudo-RT processing, a mechanism is required to ensure
that processing of a subframe at a receiver side begins only after processing
at a transmitter side is completed. For this purpose, the subframe processing
synchronization mechanism developed as part of the OAI emulation mode was
reused and extended. The extensions include a number of changes in the OAI
device library responsible for handling communication with SDR modules to
allow for appropriate handling of multiple UEs and multiple BS radio chains.
Further, to account for various aspects related to transmission over a real
channel (e.g. propagation delay), a subset of routines used in OAI RT mode
were also modified. It is worth noting that the subframe processing
synchronization mechanism does not ensure the exact time when transmission and
reception is initiated on each SDR module. To circumvent this, additional
synchronization between SDR modules is required. This can be achieved with an
external reference clock source which is common for all SDR modules on the BS
side and UE side.

Lessons learned. The effective investigation of advanced physical layer
approaches requires supporting large/massive MIMO setups and pseudo-RT mode of
operation, which are not yet available in existing platforms. While our
platform provides these features, the current implementation of the pseudo-RT
mode of operation mandates that processing for all UEs and BS is preformed by
a single process, executed on a single workstation. Although beneficial during
development and debugging of new features, we found that this architecture
does not scale well for a higher number of UEs and BSs due to limited
computational power. In the next iteration of our software platform we intend
to adopt a new architecture which permits UE processing to be executed in a
separate process (and a separate machine) to allow for better flexibility in
allocation of resources for processing. Note that this is also a key enabler
in providing more flexibility in interconnecting SDR modules, as the current
software architecture mandates that all radio modules are connected to the
same workstation. As a result, in order to conduct measurements under various
channel conditions, long, low-attenuation cables are required which
interconnect UE antennas with SDR modules on the UE side. We noticed that
these cables, due to their limited length, can significantly restrict the set
of scenarios that can be investigated. To address this we foresee to rework
the subframe processing synchronization mechanism which constitutes the core
of the pseudo-RT mode, and thus eliminate the need for such cables. Given the
new architecture, the reworked mechanism would allow for the flexibility in
interconnecting SDR modules used on the UE side with any workstation dedicated
for UE processing.

###  III-B Seeking for the appropriate hardware platform.

There is a number of hardware platforms capable of supporting MIMO setups
which aim to be open to everyone for experimentation and can be potentially
used for evaluation of new physical layer solutions. One example of such a
hardware platform is COSMOS [35] which is a city-scale testbed deployed in the
city of New York aimed at providing means for real-world experimentation on
next generation wireless technologies and applications. Another example is
POWDER [36] which is also a cite-scale testbed run by the University of Utah.
Contrary to COSMOS, POWDER provides hardware components specifically dedicated
for large/massive MIMO experimentation, with up to 64 antennas per
site/sector. Interestingly, both COSMOS and POWDER allow for the use of
various open-source software platforms such as OAI, srsLTE, or openLTE. Yet
another example of a hardware platform is LuMaMi [37] of Lund University.
LuMaMi is much smaller in scale compared to COSMOS and POWDER, but in contrast
to the other two testbeds, it is specifically dedicated for conducting
large/massive MIMO related research and supports up to 128 radio chains.

Although all three setups have a broad range of capabilities, they come with
certain limitations, that make them non appropriate for meeting our
objectives, at least at their current design stage. For instance, in case of
COSMOS, the capabilities of SDR modules used in the deployed nodes are limited
to a maximum of four radio chains per site/sector. This can be potentially
circumvented by considering a distributed MIMO setup, however, due to
additional challenges, this type of setup currently is not our main focus.
Situation is slightly different in case of POWDER. In this case the limitation
resides on the UE side, as only two SDR modules in POWDER’s massive MIMO setup
seems to be currently dedicated to run as UEs. This means that the non-linear
processing gains would be difficult to demonstrate since they target
supporting numbers of users that is similar to the numbers of BS antennas [5,
13, 26]. The main limitation of LuMaMi is that, contrary to the other
testbeds, it heavily relies on proprietary hardware and software solutions
from National Instruments [38]. This means that any experiments would have to
be based on National Instruments’ software. Note that LuMaMi was not designed
to be used for evaluation of physical layer approaches as part of a full 3GPP
compliant protocol stack and it is not clear if LuMaMi would support the
National Instruments software extensions which could potentially bridge this
gap. In addition to the above, in all three cases, the lack of physical access
to nodes dedicated for experimentation on the UE side, restricts investigation
to a limited set of scenarios.

Our adopted solution. The identified limitations of the existing publicly
available hardware platforms convinced us to invest in development of our own
hardware platform which can be easily moved around and which permits
investigation of scenarios with different number of BS antennas, and different
number of UEs. The main hardware component of our SWORD hardware platform is a
multi-core x86_64 workstation with a large number of PCIe lanes. The large
number of PCIe lanes is necessary to host multiple NICs, which in turn we use
to interface with SDR modules of our choice. The SDR module selected is the
Universal Software Radio Peripheral (USRP) X series with UBX daughterboard.
USRP X series hosts two independent radio chains and is one of the SDR modules
recommended by Ettus for applications which require phase alignment [39]. In
order to synchronize and maintain phase alignment across multiple SDR modules
we exploit the Ettus Research Octoclock-G CDA-2990 [40] which is a highly-
accurate external clock reference and pulse distribution module. The
synchronized USRPs on the BS side are connected to a 3.4-3.8GHz antenna array
which is composed of 64 half wavelength-spaced elements in a dual-polarized,
8x8 configuration. Circulators are used to connect TX and RX paths of each
radio chain to an antenna port. More detailed description with a rational
behind using specific building blocks can be found in [33].

Lessons learned. In order to investigate and demonstrate the benefits of non-
linear processing, a movable hardware platform which can run multiple UEs and
support large / massive MIMO setup is needed. While our SWORD hardware
solution meets these requirements, maintaining phase alignment through
reference clock sharing across multiple USRPs proved to be difficult and
required frequent execution of time-division duplexing (TDD) reciprocity
calibration to compensate for any drifts. We observed that such drifts had a
significant negative impact on system performance, in particular when number
of UEs in a setup was approaching number of BS antennas. In order to improve
this we plan to achieve phase alignment through the local oscillator (LO)
sharing, rather than reference clock sharing. As highlighted by Ettus in [41],
the LO sharing can significantly reduce short term and long term phase drift.
Note that USRP N32X series would be required for this purpose. Further, our
existing hardware setup is currently based on the use of circulators which,
due to the limited output power of USRP X series, significantly limits the
range of scenarios which can be investigated. In order to overcome this we
intend to replace circulators with external power amplifiers in the next
iteration of our platform.

###  III-C Remaining system challenges and tweaks around them

While trying to evaluate the non-linear approaches we came across a number of
practical issues that needed either to be resolved or to bypassed. These are:

Enabling non-linear processing. As many non-linear decoding approaches are
designed for OFDM transmission, in order to test non-linear processing in the
uplink, we modified the processing of physical uplink shared channel (PUSCH)
in our LTE-based platform by making transform precoding optional (see LTE
PUSCH processing in [42]). To inform UEs about the use of transform precoding
we extended radio resource control (RRC) signaling in line with the 5G-NR
specification (note that transform precoding in 5G-NR is optional and can be
dynamically enabled or disabled using RRC signaling). We faced similar issues
with non-linear precoding approaches in the downlink which adopt vector
perturbation and thus require a modulo operation to be applied at the
transmitter side [7, 22]. To revert this operation on the receiver side, we
modified UE processing of physical downlink shared channel (PDSCH)
accordingly. Furthermore, we extended RRC signaling to inform UEs about the
use of vector perturbation. Note that to enable more dynamic switching
existing set of downlink control informations (DCIs) in LTE and 5G-NR used for
scheduling transmission opportunities could be extended to include information
on whether the incoming transmission underwent vector perturbation.

Transmission rate selection. Adaptive modulation and coding (AMC) is an
important aspect of 3GPP systems that enables the efficient utilization of the
available spectrum resources. However, AMC for non-linear is still an open
problem. As discussed before, in order to evaluate performance of non-linear
algorithms, the research community usually conducts an exhaustive search by
running experiments for a small number of rates (i.e., QAM constellations and
channel coding rates) and shows the average performance per rate. Although
useful, the number of rates is in general very limited. In order to better
evaluate the performance of non-linear approaches, and in the absence of AMC,
we have applied an “adaptive” rate adaptation algorithm which selects the
employed modulation and coding scheme (MCS) based on the reported ACK/NACK
information. More specifically, the employed algorithm tracks the erroneous
and correctly received transmissions in both uplink and downlink. Based on
this information, and given a maximum and minimum MCS, the algorithm attempts
to adjust the MCS value after a predefined number of consecutive ACKs, or
NACKs is received (resetting a ACK counter, when a NACK is received, and NACK
counter, when an ACK is received). To prevent excessive MCS switching, the
proposed MCS selection approach exploits also a simple “cool-off period
mechanism” that prevents any MCS changes for a specific number of frames after
the last MCS change. Still, while our adopted approach can provide an improved
throughput evaluation compared to traditionally used approaches that use a
limited number of rates (and they depict the rate that maximizes the average
performance across channels), it is far from being realistic, and can only be
used to reliably evaluate the performance in a static environment where
channel remains relatively unchanged over multiple radio frames.

DL channel estimation. As indicated in [7] non-linear precoding approaches,
such as vector perturbation, results in a higher transmitted symbol
constellation. As we have here identified this makes non-linear approaches
more sensitive to the channel estimation errors than linear approaches. In
order to evaluate the performance of non-linear precoding approaches adopting
vector-perturbation, we compensated for the impact of the channel estimation
errors by boosting the transmit power of UE specific demodulation reference
signal (DM-RS) used in LTE and 5G-NR for channel estimation. We note that DM-
RS is only used for detection at the UE side and not for beamforming that is
based on the sounding reference signal (SRS). We also note that LTE and 5G-NR
already support power boosting for UE specific DM-RS, however, only a
predefined set of power boosting values can be used for this purpose. In case
of LTE, a 3dB power boosting is used when more than 2 layers are transmitted.
In case of 5G-NR 3dB, or 4.77dB power boosting can be applied, depending on
the DM-RS configuration used [43]. To inform UEs about the non-standard
compliant values we also extended RRC signaling. Figure 1 presents data for a
single indoor measurement position and depicts the impact of UE specific DM-RS
power boosting on downlink sum spectral efficiency for a 4x4 MU-MIMO
configuration. As seen, power boosting of UE specific DM-RS can lead to
significant performance improvements when non-linear precoding is used.

Figure 1: The impact of UE specific DM-RS power boosting on system
performance.

Channel state information (CSI) estimation. Another issue that we came across,
independent of processing type (i.e. linear or non-linear), is related to
estimation of channel state information (CSI). For the purpose of CSI
estimation 5G-NR and LTE employ a special signal transmitted in uplink termed
SRS. Existing implementation of SRS transmit power control (TPC) mechanism may
result, however, in a partial loss of CSI, which in turn can limit performance
of a precoder. In particular, the signal amplitude difference between multiple
UEs in a cell is lost. The fundamental objective of the TPC mechanism is to
assure that signals transmitted by multiple UEs arrive at BS with
approximately the same strength, which in turn results in a mentioned loss of
information. In order to circumvent this, as a first attempt solution, we set
the SRS transmit power to a constant value. To achieve it, and at the same
time retain the benefits of TPC for uplink, we separated TPC for SRS and other
uplink signals so that they are not conducted jointly. Note that in 5G-NR
separate TPC for SRS and other uplink signals is already part of the standard.
Separate TPC for a new variant of SRS (termed “additional” SRS) has been also
recently introduced in LTE release 16.

Lessons learned. Adapting non-linear processing in real system requires a
number of changes in 3GPP standards which include changes in PUSCH and PDSCH
processing. Additional changes are also required in the signaling procedures.
These primarily include extensions of RRC signaling which is used to inform
UEs about the settings of non-linear processing (e.g. additional power
boosting for UE specific DM-RS), but can also affect DCIs, e.g., to allow for
a “per transmission” parameter selection. In addition, AMC for non-linear
systems is a critical missing component that, as we also discuss later in more
detail, can determine systems performance. In this context, its absence may be
one of the main reasons preventing from adopting non-linear approaches to
actual systems.

##  IV Evaluation results

This section presents results obtained by the OTA measurements that validate
our design and provide some indicative performance evaluation of advanced non-
linear (NL) processing against linear (i.e., ZF) approaches that serves as the
baseline approach for linear processing. Without a loss of generality we
employed the soft, near-optimal, non-linear detection algorithm discussed in
[17] and vector-perturbation-based, non-linear precoder introduced in [26]
since they are the most promising in terms of processing latency and
complexity. The number of processing elements assumed are 40 and 32 for uplink
and downlink, respectively, that have been observed to provide a good trade-
off between error performance and computational complexity. The measurements
were conducted using the developed hardware and software SWORD platform for a
MU-MIMO setup with 4 and 8-antenna BS setup and 4 single antenna UEs. While
the examined MIMO dimensions are small, and as we will discuss later in
detail, they have been sufficient to verify the gains of non-linear
processing. It is also significant to note, that the aim of this short
evaluation is not only to validate the gains of non-linear approaches compared
to linear, but primarily to reveal hidden challenges in the system design that
can affect performance.

Measurement setup. Several indicative locations were selected for
measurements, including three outdoor locations (for uplink measurements only)
and four indoor locations (for uplink and downlink measurements). Note that
our platform does not currently integrate external power amplifiers. As a
result, due to the limited output power, all selected locations had a line-of-
sight (LOS), and the signal-to-noise ratios (SNRs) was in range of 15dB or
below. The platform was set in TDD mode, with 5 MHz channel bandwidth and
operating frequency of 3.55 GHz. The LTE downlink/uplink slot configuration
number 3 which includes 6 downlink slots, 3 uplink slots and 1 special slot
was selected for measurements [42]. A subset of antenna array elements with
the same polarisation and equivalent to a uniform linear array (ULA) was used.
Furthermore, the scheduler for MU-MIMO was set to always schedule transmission
to all UEs with the same number of resource blocks. CSI at the transmitter
were obtained using SRS transmitted in every frame, with a moving average
filter applied to reduce the effect of thermal noise. To compensate for any
thermal phase drift, each measurement instance was preceded by the TDD
reciprocity calibration procedure.

Figure 2:  Relative gain of NL over Linear processing in uplink for 4x4 and
8x4 MU-MIMO configuration for indoor measurement positions.  Figure 3:
Relative gain of NL over Linear processing in uplink for 4x4 and 8x4 MU-MIMO
configuration for outdoor measurement positions.

Uplink results. As can be seen in Figure 2 for our indicative indoor
evaluations, and in Figure 3 for outdoor ones, the use of NL detection results
in a consistent increase in overall system performance compared to linear. In
case of the indoor scenario the average gains of NL approaches 57% and 9% for
4-antenna, and 8-antenna setup, respectively. In case of the outdoor scenario
the average gains of approx. 47% and 5% was achieved. The reduced gain in the
8-antenna setup is expected, since increasing the number of BS antennas while
maintaining the same number of UEs, allows simplifying the signal detection
processing, at the cost of highly under-utilizing the MIMO channel [17].
Still, in contrast to what has been expected, the gains of the NL processing
in the 8x4 MU-MIMO case are non-negligible.

Figure 4:  Relative gain of NL over Linear processing in downlink for 4x4 and
8x4 MU-MIMO configuration for indoor measurement positions.

Downlink results. As seen in Figure 4, similarly to the uplink case, an
increase in system performance through the use of NL precoding was obtained in
all measured positions, with an average relative gain of approx. 50% and 2% in
case of 4x4 and 8x4 MIMO configurations, respectively. While the downlink NL
gains compared to linear processing are consistent, they are less prominent
compared to the uplink. This is due to reasons like channel aging, as well as
because of the imperfections of the SRS-based channel estimation and TDD
calibration, that can be further improved.

##  V Remaining Challenges and Way Forward

Here we discuss some of the remaining challenges that need to be addressed in
order to develop future BSs that can benefit from the non-linear processing
approaches.

Transmission Rate Adaptation. As it has become obvious, one of the important
missing components in order to make non-linear processing both practical and
efficient, is how to perform efficient rate adaptation. In this direction, two
approaches can be potentially examined. The first one is to try to develop
non-linear-specific AMC methods, and the other is to adopt rateless (or
fountain) channel encoding.

The direction towards developing non-linear-specific AMC methods is
particularly challenging in the uplink. In this case, the per-user SNR would
typically differ and, therefore, each user should transmit using its own
transmission rate. This issue could be partially handled by retaining the
transmit power control mechanism of SRS signals (see discussion in Section
III-C). Still, the maximum achievable transmission rate is a function of the
MIMO channel and the adopted detection method that makes the AMC problem even
more complicated. A promising direction towards non-linear-specific AMC would
be to consider the mathematical framework used for identifying the “most
promising” vector solutions in the massively parallel methods of [17, 13]
since the corresponding metrics-of-promise is related to the achievable error-
rate probability. In the downlink, predicting the modulation order and the
coding rate that maximizes the throughput could perhaps be easier, since
typical non-linear precoding approaches result into the same SNR per user.
Still, if a per-user “power-loading” approach is adopted (that by itself is an
interesting research direction) the problem becomes similar to the uplink
case, and then the duality between uplink and downlink transmissions could
perhaps be explored.

Instead of a non-linear-specific AMC, rateless codes can be used, that negate
the need for choosing an MCS mode [44, 45, 46]. This is achieved by initially
transmitting high-rate information, and then by transmitting parity
information, that decreases the effective information rate, until the
transmitted information is correctly decoded. Still, such approaches will
require revisiting of the way we transmit ACK/NACK signalling. It is noted,
that a kin to the rate adoption problem, that is still open and perhaps needs
to be considered jointly with AMC, is the one of “user-selection” that
allocates users to MIMO transmissions (or MIMO antennas) in order to maximize
systems performance.

Scaling to large numbers of users. Channel estimation is an important aspect
of every MIMO system. In order to allow for effective channel estimation in
3GPP systems, each stream is assigned with a DM-RS which is orthogonal with
respect to DM-RS allocated for other streams. As 3GPP systems have not been
specifically designed for non-linear processing (which enables supporting very
large numbers of users), the number of orthogonal DM-RS allocations in 3GPP is
limited to 8 in LTE [42] and 12 in 5G-NR [47]. Whilst these limits seem
reasonable when systems are based on linear processing, for which a number of
antennas grows rapidly with a number of streams (making deployment of sites
supporting large number of streams impractical), such limits may become a
bottleneck in case of systems with non-linear processing (in particular, when
number of concurrently supported UEs is larger than the number BS antennas, as
discussed in the next Section). Note also that SRS capability to support
multiple users, is highly dependent on the channel delay spread and there is
only a limited number of cyclic shifts that can be used in practice. As a
result, and given that the SRS periodicity needs to reflect changes in the
channel coherence time, the SRS capacity may not be sufficient to maintain the
CSI reliability.

##  VI Conclusions & Future Research

We have, for the first time, verified in a 3GPP compliant framework that non-
linear processing is a promising approach for increasing the achievable
throughput and user connectivity of mobile systems. Still, there is a lot of
research yet to be done before such approaches are adopted by actual wireless
systems and standards. Among them, two of the most significant open questions
are how to perform rate adaption and how to redesign the corresponding
wireless systems in order to be able to support a much larger number of users.
Especially since, as has already been shown in the literature, the gains of
non-linear processing increase when increasing the number of concurrently
supported users.

Despite the already verified gains, the most interesting capabilities that
non-linear BS processing can offer, and perhaps revolutionize future wireless
systems, have not yet been explored. In this direction, we can identify two
promising research pathways: (a) non-linear processing for supporting numbers
of transmitted information streams that are larger than the number of BS
antennas, and (b) practical, non-linear, iterative, BS processing for further
bridging the gap between the theoretical capacity and the achievable
throughput of systems with large connectivity.

Transmitting more streams than base-station antennas. In a “fully connected”
wireless ecosystem, future communication systems will need to be able to
support a very large number of users. Traditional wireless system designs with
linear processing are not capable of supporting more information streams than
the number of BS antennas and, in practice, can efficiently support only a
much smaller number of information streams. Non-linear processing approaches
can negate this limitation, at least theoretically, and can promise a
supported number of information streams that is much larger than the number of
users [10, 48], even without the need for specifically designated Non-
Orthogonal Multiple Access (NOMA) techniques [49, 50, 51]. Still, as already
discussed, for developing such systems we will need to revisit the signalling
procedures, as well as the way we perform channel estimation.

Non-linear, iterative, base-station processing. Iterative systems that
exchange “soft” information between a non-linear detector and a “soft” channel
decoder promise substantial gains [52, 53, 54]. Still, such approaches are not
scalable to large number of information streams due to their exponentially
increased complexity and latency requirements. For example, the approximate
non-linear approach of [54] would require a $10^{14}$ multiplications for a
$12\times 12$ MIMO system. On the other hand, currently proposed massively
parallel, soft-output approaches that can substantially reduce the
corresponding complexity and processing latency requirements [17, 48] are not
applicable to the iterative case. This is because such approaches are heavily
based on the geometrical properties of the transmitted signal constellation
which is destroyed by the existence of prior (from previous iterations)
information. Furthermore, existing iterative schemes, cannot currently support
a larger number of information streams than the BS antennas. Developing non-
linear, massively-parallel, iterative detection, decoding techniques, able to
support more users than BS antennas, could give a significant connectivity
boost, and allows us to access unexploited capacity resources.

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## Glossary

3GPP

    3rd Generation Partnership Project
AMC

    adaptive modulation and coding
BS

    base-station
CSI

    channel state information
DCI

    downlink control information
DM-RS

    demodulation reference signal
HARQ

    hybrid automatic repeat request
LO

    local oscillator
LOS

    line-of-sight
MCS

    modulation and coding scheme
MIMO

    multiple-input multiple-output
MMSE

    minimum-mean-square-error
NL

    non-linear
NR

    New Radio
OAI

    OpenAirInterface
OTA

    over-the-air
PDSCH

    physical downlink shared channel
PUSCH

    physical uplink shared channel
RRC

    radio resource control
RT

    real-time
SDR

    software-defined radio
SNR

    signal-to-noise ratio
SRS

    sounding reference signal
SWORD

    SoftWare Open Radio Design
TDD

    time-division duplexing
TPC

    transmit power control
UE

    user equipment
ULA

    uniform linear array
USRP

    Universal Software Radio Peripheral
ZF

    zero-forcing