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Performance analysis of large-scale MU-MIMO with AF relaying in the presence of interference
Abstract
This paper analyzes the performance of a large-scale multiuser multiple-input multiple-output (MU-MIMO) system with amplify-and-forward (AF) relaying in the presence of co-channel interference. Each user terminal (UT) has a single antenna while the relay is equipped with very large antenna arrays. To evaluate the impact of large number of relay antennas on the performance of the considered system, we derive a lower bound on the achievable rate. We also perform a large system analysis in the regimes of high signal-to-noise ratio (SNR), large number of relay antennas and large number of UTs. Numerical results are presented to verify the theoretical analysis.
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This paper analyzes the outage performance of a dual-hop relaying system in which the relay is equipped with multiple antennas, while the source and destination have a single antenna. New exact
closed-form expressions for the outage probability of both the amplify-and-forward (AF) and the decode-and-forward (DF) relaying systems are derived, assuming that the relay and destination are impaired by cochannel interferers and additive white Gaussian noise (AWGN). Numerical results are presented to verify the theoretical analysis.
We consider a multipair decode-and-forward relay channel, where multiple
sources transmit simultaneously their signals to multiple destinations with the
help of a full-duplex relay station. We assume that the relay station is
equipped with massive arrays, while all sources and destinations have a single
antenna. The relay station uses channel estimates obtained from received pilots
and zero-forcing (ZF) or maximum-ratio combining/maximum-ratio transmission
(MRC/MRT) to process the signals. To reduce significantly the loop interference
effect, we propose two techniques: i) using a massive receive antenna array; or
ii) using a massive transmit antenna array together with very low transmit
power at the relay station. We derive an exact achievable rate in closed-form
for MRC/MRT processing and an analytical approximation of the achievable rate
for ZF processing. This approximation is very tight, especially for large
number of relay station antennas. These closed-form expressions enable us to
determine the regions where the full-duplex mode outperforms the half-duplex
mode, as well as, to design an optimal power allocation scheme. This optimal
power allocation scheme aims to maximize the energy efficiency for a given sum
spectral efficiency and under peak power constraints at the relay station and
sources. Numerical results verify the effectiveness of the optimal power
allocation scheme. Furthermore, we show that, by doubling the number of
transmit/receive antennas at the relay station, the transmit power of each
source and of the relay station can be reduced by 1.5dB if the pilot power is
equal to the signal power, and by 3dB if the pilot power is kept fixed, while
maintaining a given quality-of-service.
This paper considers a dual-hop amplify-and-forward (AF) relaying system
where the relay is equipped with multiple antennas, while the source and the
destination are equipped with a single antenna. Assuming that the relay is
subjected to co-channel interference (CCI) and additive white Gaussian noise
(AWGN) while the destination is corrupted by AWGN only, we propose three
heuristic relay precoding schemes to combat the CCI, namely, 1) Maximum ratio
combining/maximal ratio transmission (MRC/MRT), 2) Zero-forcing/MRT (ZF/MRT),
3) Minimum mean-square error/MRT (MMSE/MRT). We derive new exact outage
expressions as well as simple high signal-to-noise ratio (SNR) outage
approximations for all three schemes. Our findings suggest that both the
MRC/MRT and the MMSE/MRT schemes achieve a full diversity of N, while the
ZF/MRT scheme achieves a diversity order of N-M, where N is the number of relay
antennas and M is the number of interferers. In addition, we show that the
MMSE/MRT scheme always achieves the best outage performance, and the ZF/MRT
scheme outperforms the MRC/MRT scheme in the low SNR regime, while becomes
inferior to the MRC/MRT scheme in the high SNR regime. Finally, in the large N
regime, we show that both the ZF/MRT and MMSE/MRT schemes are capable of
completely eliminating the CCI, while perfect interference cancelation is not
possible with the MRC/MRT scheme.
This paper studies the impact of co-channel interferences (CCIs) on the
system performance of multi-hop amplify-and-forward (AF) relaying, in a simple
and explicit way. For generality, the desired channels along consecutive
relaying hops and the CCIs at all nodes are subject to Nakagami-$m$ fading with
different shape factors. This study reveals that the diversity gain is
determined only by the fading shape factor of the desired channels, regardless
of the interference and the number of relaying hops. On the other hand,
although the coding gain is in general a complex function of various system
parameters, if the desired channels are subject to Rayleigh fading, the coding
gain is inversely proportional to the accumulated interference at the
destination, i.e. the product of the number of relaying hops and the average
interference-to-noise ratio, irrespective of the fading distribution of the
CCIs.
Multi-user Multiple-Input Multiple-Output (MIMO) offers big advantages over
conventional point-to-point MIMO: it works with cheap single-antenna terminals,
a rich scattering environment is not required, and resource allocation is
simplified because every active terminal utilizes all of the time-frequency
bins. However, multi-user MIMO, as originally envisioned with roughly equal
numbers of service-antennas and terminals and frequency division duplex
operation, is not a scalable technology. Massive MIMO (also known as
"Large-Scale Antenna Systems", "Very Large MIMO", "Hyper MIMO", "Full-Dimension
MIMO" & "ARGOS") makes a clean break with current practice through the use of a
large excess of service-antennas over active terminals and time division duplex
operation. Extra antennas help by focusing energy into ever-smaller regions of
space to bring huge improvements in throughput and radiated energy efficiency.
Other benefits of massive MIMO include the extensive use of inexpensive
low-power components, reduced latency, simplification of the media access
control (MAC) layer, and robustness to intentional jamming. The anticipated
throughput depend on the propagation environment providing asymptotically
orthogonal channels to the terminals, but so far experiments have not disclosed
any limitations in this regard. While massive MIMO renders many traditional
research problems irrelevant, it uncovers entirely new problems that urgently
need attention: the challenge of making many low-cost low-precision components
that work effectively together, acquisition and synchronization for
newly-joined terminals, the exploitation of extra degrees of freedom provided
by the excess of service-antennas, reducing internal power consumption to
achieve total energy efficiency reductions, and finding new deployment
scenarios. This paper presents an overview of the massive MIMO concept and
contemporary research.
We consider a multi-pair relay channel where multiple sources simultaneously
communicate with destinations using a relay. Each source or destination has
only a single antenna, while the relay is equipped with a very large antenna
array. We investigate the power efficiency of this system when maximum ratio
combining/maximal ratio transmission (MRC/MRT) or zero-forcing (ZF) processing
is used at the relay. Using a very large array, the transmit power of each
source or relay (or both) can be made inversely proportional to the number of
relay antennas while maintaining a given quality-of-service. At the same time,
the achievable sum rate can be increased by a factor of the number of
source-destination pairs. We show that when the number of antennas grows to
infinity, the asymptotic achievable rates of MRC/MRT and ZF are the same if we
scale the power at the sources. Depending on the large scale fading effect,
MRC/MRT can outperform ZF or vice versa if we scale the power at the relay.
Random matrix theory has found many applications in physics, statistics and engineering since its inception. Although early developments were motivated by practical experimental problems, random matrices are now used in fields as diverse as Riemann hypothesis, stochastic differential equations, condensed matter physics, statistical physics, chaotic systems, numerical linear algebra, neural networks, multivariate statistics, information theory, signal processing and small-world networks. This article provides a tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained. Furthermore, the application of random matrix theory to the fundamental limits of wireless communication channels is described in depth.
This paper surveys recent advances in the area of very large MIMO systems.
With very large MIMO, we think of systems that use antenna arrays with an
order of magnitude more elements than in systems being built today, say a
hundred antennas or more. Very large MIMO entails an unprecedented number of
antennas simultaneously serving a much smaller number of terminals. The
disparity in number emerges as a desirable operating condition and a practical
one as well. The number of terminals that can be simultaneously served is
limited, not by the number of antennas, but rather by our inability to acquire
channel-state information for an unlimited number of terminals. Larger numbers
of terminals can always be accommodated by combining very large MIMO technology
with conventional time- and frequency-division multiplexing via OFDM. Very
large MIMO arrays is a new research field both in communication theory,
propagation, and electronics and represents a paradigm shift in the way of
thinking both with regards to theory, systems and implementation. The ultimate
vision of very large MIMO systems is that the antenna array would consist of
small active antenna units, plugged into an (optical) fieldbus.
This correspondence studies the statistical distribution of the signal-to-interference-plus-noise ratio (SINR) for the minimum mean-square error (MMSE) receiver in multiple-input multiple-output (MIMO) wireless communications. The channel model is assumed to be (transmit) correlated Rayleigh flat-fading with unequal powers. The SINR can be decomposed into two independent random variables: SINR=SINR<sup>ZF</sup>+T, where SINR<sup>ZF</sup> corresponds to the SINR for a zero-forcing (ZF) receiver and has an exact Gamma distribution. This correspondence focuses on characterizing the statistical properties of T using the results from random matrix theory. First three asymptotic moments of T are derived for uncorrelated channels and channels with equicorrelations. For general correlated channels, some limiting upper bounds for the first three moments are also provided. For uncorrelated channels and correlated channels satisfying certain conditions, it is proved that T converges to a Normal random variable. A Gamma distribution and a generalized Gamma distribution are proposed as approximations to the finite sample distribution of T. Simulations suggest that these approximate distributions can be used to estimate accurately the probability of errors even for very small dimensions (e.g., two transmit antennas).
We consider a multipair two-way relay network where multiple communication pairs simultaneously exchange information with the help of a single relay. Each terminal has only a single antenna, while the relay is equipped with a very large antenna array. We further assume that channel state information is available at the relay node. We investigate the power efficiency of this network when very simple signal processing, i.e., maximum ratio combining (MRC) or zero-forcing (ZF), is used at the relay. When the number of relay antennas grows infinite, the transmit power of each terminal or relay (or both) can be made inversely proportional to the number of relay antennas while maintaining a given quality-of-service. We show that with very large antenna arrays, the two-way relaying scheme outperforms both the orthogonal scheme and the one-way relaying scheme.
We consider a system with a source, a relay, and a destination with an arbitrary number of cochannel interferers and thermal noise at both the relay and the destination. The relay is equipped with multiple antennas, whereas the destination has a single antenna with limited interference mitigation capabilities. For such a system, we propose a two-hop amplify-and-forward (AF) relaying scheme, where the relay performs optimum combining to maximize the signal-to-interference-plus-noise ratio (SINR) and forwards the soft symbols to the destination. We derive the cumulative distribution function of an upper bound on the end-to-end SINR achievable with such relay in Rayleigh fading channels. The achievable diversity and outage probability performance are analyzed using the bound and simulations. Block error rate performance at the destination is studied and a practical application in cellular networks is discussed. The results show that the proposed relay can assist a destination with a single antenna, which was experiencing lower SINR in the absence of the relay, to achieve higher values of SINR.
We consider a multipair two-way relay network where multiple communication pairs simultaneously exchange information with the help of multiple relay nodes. All nodes are equipped with a single antenna and channel state information is available at the relay nodes. Each relay uses very simple signal processing in a distributed manner, called distributed amplify-and-forward (AF) relaying. A closed-form expression for the achievable rate is derived. We show that the distributed AF scheme outperforms conventional orthogonal relaying. When the number of relays is large, the distributed AF relaying scheme can achieve the capacity scaling given by the cut-set upper bound. Furthermore, when the number of relays grows large, the transmit powers of each terminal and of the relay can be made inversely proportional to the number of relays while maintaining a given quality-of-service. If the transmit power of each terminal is kept fixed, the transmit power of each relay can be scaled down inversely proportional to the square of the number of relays.
In this paper, we investigate the performance of multi-pair two-way relaying, in which multiple pairs of users exchange information within pair, with the help of a shared relay. Each user has a single antenna, and the relay is equipped with very large number of antennas. The relay adopts the amplify-and-forward protocol, and the beamforming matrixes of maximum-ratio combining/maximum ratio transmission and zero-forcing reception/zero-forcing transmission are both considered. Due to array gain of antenna array, the power of each user or the relay (or both) can be made inversely proportional to the number of relay antennas, without compromising the performance. Thus, three power-scaling schemes are studied. Furthermore, the asymptotic spectral and energy efficiencies of the system are obtained analytically, when the number of relay antennas approaches to infinity. The asymptotic results are beneficial to provide more insightful understandings for the fundamental limits of the very large antenna system, and verified by the Monte-Carlo simulations. The analytical and simulation results reveal that very large antenna arrays in such system can average the small-scale fading, eliminate the inter-pair interference, and reduce the total power consumption.
A multiplicity of autonomous terminals simultaneously transmits data streams to a compact array of antennas. The array uses imperfect channel-state information derived from transmitted pilots to extract the individual data streams. The power radiated by the terminals can be made inversely proportional to the square-root of the number of base station antennas with no reduction in performance. In contrast if perfect channel-state information were available the power could be made inversely proportional to the number of antennas. Lower capacity bounds for maximum-ratio combining (MRC), zero-forcing (ZF) and minimum mean-square error (MMSE) detection are derived. An MRC receiver normally performs worse than ZF and MMSE. However as power levels are reduced, the cross-talk introduced by the inferior maximum-ratio receiver eventually falls below the noise level and this simple receiver becomes a viable option. The tradeoff between the energy efficiency (as measured in bits/J) and spectral efficiency (as measured in bits/channel use/terminal) is quantified for a channel model that includes small-scale fading but not large-scale fading. It is shown that the use of moderately large antenna arrays can improve the spectral and energy efficiency with orders of magnitude compared to a single-antenna system.
We consider the uplink (UL) and downlink (DL) of non-cooperative multi-cellular time-division duplexing (TDD) systems, assuming that the number N of antennas per base station (BS) and the number K of user terminals (UTs) per cell are large. Our system model accounts for channel estimation, pilot contamination, and an arbitrary path loss and antenna correlation for each link. We derive approximations of achievable rates with several linear precoders and detectors which are proven to be asymptotically tight, but accurate for realistic system dimensions, as shown by simulations. It is known from previous work assuming uncorrelated channels, that as N→∞ while K is fixed, the system performance is limited by pilot contamination, the simplest precoders/detectors, i.e., eigenbeamforming (BF) and matched filter (MF), are optimal, and the transmit power can be made arbitrarily small. We analyze to which extent these conclusions hold in the more realistic setting where N is not extremely large compared to K. In particular, we derive how many antennas per UT are needed to achieve η% of the ultimate performance limit with infinitely many antennas and how many more antennas are needed with MF and BF to achieve the performance of minimum mean-square error (MMSE) detection and regularized zero-forcing (RZF), respectively.
A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval. Time-division duplex operation combined with reverse-link pilots enables the base station to estimate the reciprocal forward- and reverse-link channels. The conjugate-transpose of the channel estimates are used as a linear precoder and combiner respectively on the forward and reverse links. Propagation, unknown to both terminals and base station, comprises fast fading, log-normal shadow fading, and geometric attenuation. In the limit of an infinite number of antennas a complete multi-cellular analysis, which accounts for inter-cellular interference and the overhead and errors associated with channel-state information, yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve. In particular the effects of uncorrelated noise and fast fading vanish, throughput and the number of terminals are independent of the size of the cells, spectral efficiency is independent of bandwidth, and the required transmitted energy per bit vanishes. The only remaining impairment is inter-cellular interference caused by re-use of the pilot sequences in other cells (pilot contamination) which does not vanish with unlimited number of antennas.
In this letter, we investigate the outage performance of a two-hop fixed-gain relay system in the presence of multiple unequal-power Rayleigh interference at both relay and destina- tion. The closed-form expression for the outage probability is derived. We also show that the equal-power interference at the relay and destination leads to the worst outage performance. Index Terms—Fixed-gain relay, outage probability, unequal- power interference.