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Towards a Realistic Assessment of Multiple Antenna HCNs: Residual Additive Transceiver Hardware Impairments and Channel Aging
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Abstract
Given the critical dependence of broadcast channels by the accuracy of channel state information at the transmitter (CSIT), we develop a general downlink model with zero-forcing (ZF) precoding, applied in realistic heterogeneous cellular systems with multiple antenna base stations (BSs). Specifically, we take into consideration imperfect CSIT due to pilot contamination, channel aging due to users relative movement, and unavoidable residual additive transceiver hardware impairments (RATHIs). Assuming that the BSs are Poisson distributed, the main contributions focus on the derivations of the upper bound of the coverage probability and the achievable user rate for this general model. We show that both the coverage probability and the user rate are dependent on the imperfect CSIT and RATHIs. More concretely, we quantify the resultant performance loss of the network due to these effects. We depict that the uplink RATHIs have equal impact, but the downlink transmit BS distortion has a greater impact than the receive hardware impairment of the user. Thus, the transmit BS hardware should be of better quality than user's receive hardware. Furthermore, we characterise both the coverage probability and user rate in terms of the time variation of the channel. It is shown that both of them decrease with increasing user mobility, but after a specific value of the normalised Doppler shift, they increase again. Actually, the time variation, following the Jakes autocorrelation function, mirrors this effect on coverage probability and user rate. Finally, we consider space division multiple access (SDMA), single user beamforming (SU-BF), and baseline single-input single-output (SISO) transmission. A comparison among these schemes reveals that the coverage by means of SU-BF outperforms SDMA in terms of coverage.
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Rate-Splitting (RS) has recently been shown to provide significant performance benefits in various multi-user transmission scenarios. In parallel, the huge degrees-of-freedom provided by the appealing massive Multiple-Input Multiple- Output (MIMO) necessitate the employment of inexpensive hardware, being more prone to hardware imperfections, in order to be a cost-efficient technology. Hence, in this work, we focus on a realistic massive Multiple-Input Single-Output (MISO) Broadcast Channel (BC) hampered by the inevitable hardware impairments. We consider a general experimentally validated model of hardware impairments, accounting for the presence of multiplicative distortion due to phase noise, additive distortion noise and thermal noise amplification. Under both scenarios with perfect and imperfect channel state information at the transmitter (CSIT), we analyze the potential robustness of RS to each separate hardware imperfection. We analytically assess the sum-rate degradation due to hardware imperfections. Interestingly, in the case of imperfect CSIT, we demonstrate that RS is a robust strategy for multiuser MIMO in the presence of phase and amplified thermal noise, since its sum-rate does not saturate at high signal-to-noise ratio (SNR), contrary to conventional techniques. On the other hand, the additive impairments always lead to a sum-rate saturation at high SNR, even after the application of RS. However, RS still enhances the performance. Furthermore, as the number of users increases, the gains provided by RS decrease not only in ideal conditions, but in practical conditions with RTHIs as well. Notably, although a deterministic equivalent analysis is employed, the analytical and simulation results coincide even for finite system dimensions. As a consequence, the applicability of these results also holds for current “small-scale” multi-antenna systems.
Despite the deleterious effect of hardware impairments on communication
systems, most prior works have not investigated their impact on widely used
relay systems. Most importantly, the application of inexpensive transceivers,
being prone to hardware impairments, is the most cost-efficient way for the
implementation of massive multiple-input multiple-output (MIMO) systems.
Consequently, the direction of this paper is towards the investigation of the
impact of hardware impairments on MIMO relay networks with large number of
antennas. Specifically, we obtain the general expression for the ergodic
capacity of dual-hop (DH) amplify-and-forward (AF) relay systems. Next, given
the advantages of the free probability (FP) theory with comparison to other
known techniques in the area of large random matrix theory, we pursue a large
limit analysis in terms of number of antennas and users by shedding light to
the behavior of relay systems inflicted by hardware impairments.
Delayed channel state information at the transmitter (CSIT) due to time variation of the channel, coming from the users’ relative movement with regard to the BS antennas, is an inevitable degrading performance factor in practical systems. Despite its importance, little attention has been paid to the literature of multi-cellular multiple-input massive multiple-output (MIMO) system by investigating only the maximal ratio combining (MRC) receiver and the maximum ratio transmission (MRT) precoder. Hence, the contribution of this work is designated by the performance analysis/comparison of/with more sophisticated linear techniques, i.e., a minimum-mean-square-error (MMSE) detector for the uplink and a regularized zero-forcing (RZF) precoder for the downlink are assessed. In particular, we derive the deterministic equivalents of the signal-to-interference-plus-noise ratios (SINRs), which capture the effect of delayed CSIT, and make the use of lengthy Monte Carlo simulations unnecessary. Furthermore, prediction of the current CSIT after applying a Wiener filter allows to evaluate the mitigation capabilities of MMSE and RZF. Numerical results depict that the proposed achievable SINRs (MMSE/RZF) are more efficient than simpler solutions (MRC/MRT) in delayed CSIT conditions, and yield a higher prediction at no special computational cost due to their deterministic nature. Nevertheless, it is shown that massive MIMO are preferable even in time-varying channel conditions.
This paper considers a downlink heterogeneous network, where different types of multi-antenna base stations (BSs) communicate with a number of single-antenna users. Multiple BSs can serve the users by spatial multiflow transmission techniques. Assuming imperfect channel state information at both BSs and users, the precoding, load balancing, and BS operation mode are jointly optimized for improving the network energy efficiency. We minimize the weighted total power consumption while satisfying quality of service constraints at the users. This problem is non-convex, but we prove that for each BS mode combination, the considered problem has a hidden convexity structure. Thus, the optimal solution is obtained by an exhaustive search over all possible BS mode combinations. Furthermore, by iterative convex approximations of the non-convex objective function, a heuristic algorithm is proposed to obtain a suboptimal solution of low complexity. We show that although multi-cell joint transmission is allowed, in most cases, it is optimal for each user to be served by a single BS. The optimal BS association condition is parameterized, which reveals how it is impacted by different system parameters. Simulation results indicate that putting a BS into sleep mode by proper load balancing is an important solution for energy savings.
The escalating tele-traffic growth imposed by the proliferation of smart-phones and tablet computers outstrips the capacity increase of wireless communications networks. Furthermore, it results in substantially increased carbon dioxide emissions. As a powerful countermeasure, in the case of full-rank channel matrices, MIMO techniques are potentially capable of linearly increasing the capacity or decreasing the transmit power upon commensurately increasing the number of antennas. Hence, the recent concept of Large-Scale MIMO (LS-MIMO) systems has attracted substantial research attention and been regarded as a promising technique for next-generation wireless communications networks. Therefore, this paper surveys the state-of-the-art of LS-MIMO systems. Firstly, we discuss the measurement and modeling of LS-MIMO channels. Then, some typical application scenarios are classified and analyzed. Key techniques of both the physical layer and network layer are also detailed. Finally, we conclude with a range of challenges and future research topics.
Massive multiple-input multiple-output (MIMO) networks, where the base
stations (BSs) are equipped with large number of antennas and serve a number of
users simultaneously, are very promising, but suffer from pilot contamination.
Despite its importance, delayed channel state information (CSI) due to user
mobility, being another degrading factor, lacks investigation in the
literature. Hence, we consider an uplink model, where each BS applies
zero-forcing decoder, accounting for both effects, but with the focal point on
the relative users' movement with regard to the BS antennas. In this setting,
analytical closed-form expressions for the sum-rate with finite number of BS
antennas, and the asymptotic limits with infinite number of BS antennas
epitomize the main contributions. In particular, the probability density
function of the signal-to-interference-plus-noise ratio and the ergodic
sum-rate are derived for any finite number of antennas. Insights of the impact
of the arising Doppler shift due to user mobility into the low signal-to-noise
ratio regime as well as the outage probability are obtained. Moreover,
asymptotic analysis performance results in terms of infinitely increasing
number of antennas, power, and both numbers of antennas and users (while their
ratio is fixed) are provided. The numerical results demonstrate the performance
loss in various Doppler shifts. An interesting observation is that massive MIMO
is favorable even in time-varying channel conditions.
Massive multiple-input multiple-output (MIMO) systems are cellular networks
where the base stations (BSs) are equipped with unconventionally many antennas,
deployed on co-located or distributed arrays. Huge spatial degrees-of-freedom
are achieved by coherent processing over these massive arrays, which provide
strong signal gains, resilience to imperfect channel knowledge, and low
interference. This comes at the price of more infrastructure; the hardware cost
and circuit power consumption scale linearly/affinely with the number of BS
antennas N. Hence, the key to cost-efficient deployment of large arrays is
low-cost antenna branches with low circuit power, in contrast to today's
conventional expensive and power-hungry BS antenna branches. Such low-cost
transceivers are prone to hardware imperfections, but it has been conjectured
that the huge degrees-of-freedom would bring robustness to such imperfections.
We prove this claim for a generalized uplink system with multiplicative
phase-drifts, additive distortion noise, and noise amplification. Specifically,
we derive closed-form expressions for the user rates and a scaling law that
shows how fast the hardware imperfections can increase with N while
maintaining high rates. The connection between this scaling law and the power
consumption of different transceiver circuits is rigorously exemplified. This
reveals that one can make the circuit power increase as , instead of
linearly, by careful circuit-aware system design.
Radio-frequency (RF) impairments in the transceiver hardware of communication
systems (e.g., phase noise (PN), high power amplifier (HPA) nonlinearities, or
in-phase/quadrature-phase (I/Q) imbalance) can severely degrade the performance
of traditional multiple-input multiple-output (MIMO) systems. Although
calibration algorithms can partially compensate these impairments, the
remaining distortion still has substantial impact. Despite this, most prior
works have not analyzed this type of distortion. In this paper, we investigate
the impact of residual transceiver hardware impairments on the MIMO system
performance. In particular, we consider a transceiver impairment model, which
has been experimentally validated, and derive analytical ergodic capacity
expressions for both exact and high signal-to-noise ratios (SNRs). We
demonstrate that the capacity saturates in the high-SNR regime, thereby
creating a finite capacity ceiling. We also present a linear approximation for
the ergodic capacity in the low-SNR regime, and show that impairments have only
a second-order impact on the capacity. Furthermore, we analyze the effect of
transceiver impairments on large-scale MIMO systems; interestingly, we prove
that if one increases the number of antennas at one side only, the capacity
behaves similar to the finite-dimensional case. On the contrary, if the number
of antennas on both sides increases with a fixed ratio, the capacity ceiling
vanishes; thus, impairments cause only a bounded offset in the capacity
compared to the ideal transceiver hardware case.
Small cell networks are regarded as a promising candidate to meet the
exponential growth of mobile data traffic in cellular networks. With a dense
deployment of access points, spatial reuse will be improved, and uniform
coverage can be provided. However, such performance gains cannot be achieved
without effective intercell interference management. In this paper, a novel
interference coordination strategy, called user-centric intercell interference
nulling, is proposed for small cell networks. A main merit of the proposed
strategy is its ability to effectively identify and mitigate the dominant
interference for each user. Different from existing works, each user selects
the coordinating base stations (BSs) based on the relative distance between the
home BS and the interfering BSs, called the interference nulling (IN) range,
and thus interference nulling adapts to each user's own interference situation.
By adopting a random spatial network model, we derive an approximate expression
of the successful transmission probability to the typical user, which is then
used to determine the optimal IN range. Simulation results shall confirm the
tightness of the approximation, and demonstrate significant performance gains
(about 35%-40%) of the proposed coordination strategy, compared with the
non-coordination case. Moreover, it is shown that the proposed strategy
outperforms other interference nulling methods. Finally, the effect of
imperfect channel state information (CSI) is investigated, where CSI is assumed
to be obtained via limited feedback. It is shown that the proposed coordination
strategy still provides significant performance gains even with a moderate
number of feedback bits.
Multiple-input multiple-output (MIMO) communication may provide high spectral efficiency through the deployment of a very large number of antenna elements at the base stations. The gains from massive MIMO communication come from the use of multiuser MIMO on the uplink and downlink, but with a large excess of antennas at the base station compared to the number of served users. Initial work on massive MIMO did not fully address several practical issues associated with its deployment. This paper considers the impact of channel aging on the performance of massive MIMO systems. The effects of channel variation are characterized as a function of different system parameters assuming a simple model for the channel time variations at the transmitter. Channel prediction is proposed to overcome channel aging effects. The analytical results on aging show how capacity is lost due to time variation in the channel. Numerical results in a multiceli network show that massive MIMO works even with some channel variation and that channel prediction could partially overcome channel aging effects.
Cellular networks are in a major transition from a carefully planned set of large tower-mounted base-stations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In this paper, we develop a tractable, flexible, and accurate model for a downlink heterogeneous cellular network (HCN) consisting of K tiers of randomly located BSs, where each tier may differ in terms of average transmit power, supported data rate and BS density. Assuming a mobile user connects to the strongest candidate BS, the resulting Signal-to-Interference-plus-Noise-Ratio (SINR) is greater than 1 when in coverage, Rayleigh fading, we derive an expression for the probability of coverage (equivalently outage) over the entire network under both open and closed access, which assumes a strikingly simple closed-form in the high SINR regime and is accurate down to -4 dB even under weaker assumptions. For external validation, we compare against an actual LTE network (for tier 1) with the other K-1 tiers being modeled as independent Poisson Point Processes. In this case as well, our model is accurate to within 1-2 dB. We also derive the average rate achieved by a randomly located mobile and the average load on each tier of BSs. One interesting observation for interference-limited open access networks is that at a given sinr, adding more tiers and/or BSs neither increases nor decreases the probability of coverage or outage when all the tiers have the same target-SINR.
Cellular networks are usually modeled by placing the base stations on a grid, with mobile users either randomly scattered or placed deterministically. These models have been used extensively but suffer from being both highly idealized and not very tractable, so complex system-level simulations are used to evaluate coverage/outage probability and rate. More tractable models have long been desirable. We develop new general models for the multi-cell signal-to-interference-plus-noise ratio (SINR) using stochastic geometry. Under very general assumptions, the resulting expressions for the downlink SINR CCDF (equivalent to the coverage probability) involve quickly computable integrals, and in some practical special cases can be simplified to common integrals (e.g., the Q-function) or even to simple closed-form expressions. We also derive the mean rate, and then the coverage gain (and mean rate loss) from static frequency reuse. We compare our coverage predictions to the grid model and an actual base station deployment, and observe that the proposed model is pessimistic (a lower bound on coverage) whereas the grid model is optimistic, and that both are about equally accurate. In addition to being more tractable, the proposed model may better capture the increasingly opportunistic and dense placement of base stations in future networks.
In the last year or so, significant momentum has started to build around the idea of a fifth generation (5G) for wireless communications technology. New research projects have started internationally, and research centers devoted to 5G technology have begun to open. At the ICC 2013 conference in Budapest, there were a number of keynote talks and special invited sessions addressing some of the key concepts around 5G technology. This Special Issue was created by IEEE Communications Magazine to help readers understand the current perspectives on 5G technology from both industry and academic standpoints.
Oscillator phase noise limits the performance of high speed communication systems since it results in time varying channels and rotation of the signal constellation from symbol to symbol. In this paper, joint estimation of channel gains and Wiener phase noise in multi-input multi-output (MIMO) systems is analyzed. The signal model for the estimation problem is outlined in detail and new expressions for the Cramér-Rao lower bounds (CRLBs) for the multi-parameter estimation problem are derived. A data-aided least-squares (LS) estimator for jointly obtaining the channel gains and phase noise parameters is derived. Next, a decision-directed weighted least-squares (WLS) estimator is proposed, where pilots and estimated data symbols are employed to track the time-varying phase noise parameters over a frame. In order to reduce the overhead and delay associated with the estimation process, a new decision-directed extended Kalman filter (EKF) is proposed for tracking the MIMO phase noise throughout a frame. Numerical results show that the proposed LS, WLS, and EKF estimators' performances are close to the CRLB. Finally, simulation results demonstrate that by employing the proposed channel and time-varying phase noise estimators the bit-error rate performance of a MIMO system can be significantly improved.
In this paper, we study physical layer security for the downlink of cellular
networks, where the confidential messages transmitted to each mobile user can
be eavesdropped by both (i) the other users in the same cell and (ii) the users
in the other cells. The locations of base stations and mobile users are modeled
as two independent two-dimensional Poisson point processes. Using the proposed
model, we analyze the secrecy rates achievable by regularized channel inversion
(RCI) precoding by performing a large-system analysis that combines tools from
stochastic geometry and random matrix theory. We obtain approximations for the
probability of secrecy outage and the mean secrecy rate, and characterize
regimes where RCI precoding achieves a nonzero secrecy rate. We find that
unlike isolated cells, the secrecy rate in a cellular network does not grow
monotonically with the transmit power, and the network tends to be in secrecy
outage if the transmit power grows unbounded. Furthermore, we show that there
is an optimal value for the base station deployment density that maximizes the
secrecy rate, and this value is a decreasing function of the signal-to-noise
ratio.
The use of large-scale antenna arrays can bring substantial improvements in
energy and/or spectral efficiency to wireless systems due to the greatly
improved spatial resolution and array gain. Recent works in the field of
massive multiple-input multiple-output (MIMO) show that the user channels
decorrelate when the numbers of antennas at base stations (BSs) increase, thus
strong signal gains are achievable with little inter-user interference. Since
these results rely on asymptotics, it is important to investigate whether the
conventional channel models are reasonable in the asymptotic regimes. This
paper considers a new generalized channel model that incorporates transceiver
hardware impairments at both the BSs (equipped with large antenna arrays) and
the single-antenna user equipments (UEs). As opposed to the conventional case
of ideal hardware, we show that hardware impairments create finite ceilings on
the estimation accuracy and the downlink/uplink capacity of each user.
Surprisingly, the capacity is mainly limited by the hardware at the UE, while
the impact of impairments in the large-scale arrays vanishes asymptotically and
inter-user interference (e.g., pilot contamination) becomes negligible.
Furthermore, we prove that an arbitrarily high energy efficiency can be
achieved by reducing the transmit power while increasing the number of
antennas. Alternatively, a non-zero capacity can be retained while the hardware
quality is decreased as the array grows, thus enabling the use of inexpensive
antenna elements.
The capacity of ideal MIMO channels has a high-SNR slope that equals the
minimum of the number of transmit and receive antennas. This letter analyzes if
this result holds when there are distortions from physical transceiver
impairments. We prove analytically that such physical MIMO channels have a
finite upper capacity limit, for any channel distribution and SNR. The high-SNR
slope thus collapses to zero. This appears discouraging, but we prove the
encouraging result that the relative capacity gain of employing MIMO is at
least as large as with ideal transceivers.
Physical wireless transceivers suffer from a variety of impairments that
distort the transmitted and received signals. Their degrading impact is
particularly evident in modern systems with multiuser transmission, high
transmit power, and low-cost devices, but their existence is routinely ignored
in the optimization literature for multicell transmission. This paper provides
a detailed analysis of coordinated beamforming in the multicell downlink. We
solve two optimization problems under a transceiver impairment model and derive
the structure of the optimal solutions. We show numerically that these
solutions greatly reduce the impact of impairments, compared with beamforming
developed for ideal transceivers. Although the so-called multiplexing gain is
zero under transceiver impairments, we show that the gain of multiplexing can
be large at practical SNRs.
Femtocells, despite their name, pose a potentially large disruption to the carefully planned cellular networks that now connect a majority of the planet's citizens to the Internet and with each other. Femtocells – which by the end of 2010 already outnumbered traditional base stations and at the time of publication are being deployed at a rate of about five million a year – both enhance and interfere with this network in ways that are not yet well understood. Will femtocells be crucial for offloading data and video from the creaking traditional network? Or will femtocells prove more trouble than they are worth, undermining decades of careful base station deployment with unpredictable interference while delivering only limited gains? Or possibly neither: are femtocells just a "flash in the pan"; an exciting but short-lived stage of network evolution that will be rendered obsolete by improved WiFi offloading, new backhaul regulations and/or pricing, or other unforeseen technological developments? This tutorial article overviews the history of femtocells, demystifies their key aspects, and provides a preview of the next few years, which the authors believe will see a rapid acceleration towards small cell technology. In the course of the article, we also position and introduce the articles that headline this special issue.
Physical transceiver implementations for multiple-input multiple-output (MIMO) wireless communication systems suffer from transmit-RF (Tx-RF) impairments. In this paper, we study the effect on channel capacity and error-rate performance of residual Tx-RF impairments that defy proper compensation. In particular, we demonstrate that such residual distortions severely degrade the performance of (near-)optimum MIMO detection algorithms. To mitigate this performance loss, we propose an efficient algorithm, which is based on an i.i.d. Gaussian model for the distortion caused by these impairments. In order to validate this model, we provide measurement results based on a 4-stream Tx-RF chain implementation for MIMO orthogonal frequency-division multiplexing (OFDM).
In this paper we develop a tractable framework for SINR analysis in downlink
heterogeneous cellular networks (HCNs) with flexible cell association policies.
The HCN is modeled as a multi-tier cellular network where each tier's base
stations (BSs) are randomly located and have a particular transmit power, path
loss exponent, spatial density, and bias towards admitting mobile users. For
example, as compared to macrocells, picocells would usually have lower transmit
power, higher path loss exponent (lower antennas), higher spatial density (many
picocells per macrocell), and a positive bias so that macrocell users are
actively encouraged to use the more lightly loaded picocells. In the present
paper we implicitly assume all base stations have full queues; future work
should relax this. For this model, we derive the outage probability of a
typical user in the whole network or a certain tier, which is equivalently the
downlink SINR cumulative distribution function. The results are accurate for
all SINRs, and their expressions admit quite simple closed-forms in some
plausible special cases. We also derive the \emph{average ergodic rate} of the
typical user, and the \emph{minimum average user throughput} -- the smallest
value among the average user throughputs supported by one cell in each tier. We
observe that neither the number of BSs or tiers changes the outage probability
or average ergodic rate in an interference-limited full-loaded HCN with
unbiased cell association (no biasing), and observe how biasing alters the
various metrics.
Transmit channel side information (CSIT) can significantly increase MIMO wireless capacity. Due to delay in acquiring this information, however, the time-selective fading wireless channel often induces incomplete, or partial, CSIT. In this paper, we first construct a dynamic CSIT model that takes into account channel temporal variation. It does so by using a potentially outdated channel measurement and the channel statistics, including the mean, covariance, and temporal correlation. The dynamic CSIT model consists of an effective channel mean and an effective channel covariance, derived as a channel estimate and its error covariance. Both parameters are functions of the temporal correlation factor, which indicates the CSIT quality. Depending on this quality, the model covers smoothly from perfect to statistical CSIT. We then summarize and further analyze the capacity gains and the optimal input with dynamic CSIT, asymptotically at low and high SNRs. At low SNRs, dynamic CSIT often multiplicatively increases the capacity for all multi-input systems. The optimal input is typically simple single-mode beamforming. At high SNRs, for systems with equal or fewer transmit than receive antennas, it is well-known that the capacity gain diminishes to zero because of equi-power optimal input. With more transmit than receive antennas, however, the capacity gain is additive. The optimal input then is highly dependent on the CSIT. In contrast to equi-power, it can drop modes for channels with a strong mean or strongly correlated transmit antennas. For such mode-dropping at high SNRs in special cases, simple conditions on the channel K factor or the transmit covariance condition number are subsequently quantified. Next, using a convex optimization program, we study the MIMO capacity with dynamic CSIT non-asymptotically. Particularly, we numerically analyze effects on the capacity of the CSIT quality, the relative number of transmit and receive antennas, and the channel K factor. Fo-
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r example, the capacity gain based on dynamic CSIT is more sensitive to the CSIT quality at higher qualities. The program also helps to evaluate a simple, analytical capacity lower-bound based on the Jensen optimal input. The bound is tight at all SNRs for systems with equal or fewer transmit than receive antennas, and at low SNRs for others.
As the theoretical foundations of multiple-antenna techniques evolve and as these multiple-input multiple-output (MIMO) techniques become essential for providing high data rates in wireless systems, there is a growing need to understand the performance limits of MIMO in practical networks. To address this need, MIMO Communication for Cellular Networks presents a systematic description of MIMO technology classes and a framework for MIMO system design that takes into account the essential physical-layer features of practical cellular networks. In contrast to works that focus on the theoretical performance of abstract MIMO channels, MIMO Communication for Cellular Networks emphasizes the practical performance of realistic MIMO systems. A unified set of system simulation results highlights relative performance gains of different MIMO techniques and provides insights into how best to use multiple antennas in cellular networks under various conditions. MIMO Communication for Cellular Networks describes single-user, multiuser, network MIMO technologies and system-level aspects of cellular networks, including channel modeling, resource scheduling, interference mitigation, and simulation methodologies. The key concepts are presented with sufficient generality to be applied to a wide range of wireless systems, including those based on cellular standards such as LTE, LTE-Advanced, WiMAX, and WiMAX2. The book is intended for use by graduate students, researchers, and practicing engineers interested in the physical-layer design of state-of-the-art wireless systems.
Wireless communication systems are persistently applying wider bandwidths, larger signal dynamics and higher carrier frequencies to fulfil the demand for higher data rates. This results in an ever increasing demand on the performance of low-cost and power-efficient radio frequency (RF) front-ends. Since the RF technology is, consequently, pushed to its operation boundaries, the intrinsic imperfections of the RF IC technology are more and more governing the system performance of wireless modems. RF Imperfections in High-rate Wireless Systems therefore presents a new vision on the design of wireless communication systems. In this approach the imperfections of the RF front-ends are accepted and digital signal processing algorithms are designed to suppress their impact on system performance. To illustrate this approach, the book focuses on multiple-antenna orthogonal frequency division multiplexing (MIMO OFDM), which will be applied as basis for the majority of near-future high-rate wireless systems. The basics of MIMO OFDM are introduced and the typically required signal processing in the implementation of such systems is elucidated. The book treats several of the front-end impairments that seriously affect the performance of MIMO OFDM systems: carrier frequency offset, phase noise, IQ imbalance and nonlinearities. To provide an in-depth understanding of the impact of these RF imperfections, analytical performance results are presented in the book. These results are then used to design different compensation approaches based on digital baseband processing. RF Imperfections in High-rate Wireless Systems is of interest to wireless system designers, who want to familiarise with the digital compensation of RF imperfections. For researchers in the field of wireless communications this book provides a valuable overview of this emerging research topic. © 2008 Springer Science + Business Media B.V. All Rights Reserved.
Despite the inevitable presence of transceiver impairments, most prior work on multiple-input multiple-output (MIMO) wireless systems assumes perfect transceiver hardware which is unrealistic in practice. In this direction, motivated by the increasing interest in MIMO relay systems due to their improved spectral efficiency and coverage, this paper investigates the impact of residual hardware impairments on the ergodic capacity of dual-hop (DH) amplify-and-forward (AF) MIMO relay systems. Specifically, a thorough characterization of the ergodic channel capacity of DH AF relay systems in the presence of hardware impairments is presented herein for both the finite and large antenna regimes by employing results from finite-dimensional and large random matrix theory, respectively. Regarding the former setting, we derive the exact ergodic capacity as well as closed-form expressions for tight upper and lower bounds. Furthermore, we provide an insightful study for the low signalto- noise ratio (SNR) regimes. Next, the application of the free probability (FP) theory allows us to study the effects of the hardware impairments in future 5G deployments including a large number of antennas. While these results are obtained for the large system limit, simulations show that the asymptotic results are quite precise even for conventional system dimensions.
The downlink performance of two-tier (macro/pico) multi-antenna cellular heterogeneous networks (HetNets) employing space division multiple access (SDMA) technique with zero-forcing (ZF) precoding is analyzed in this paper. The number of users simultaneously served with SDMA by a base-station (BS) depends on the number of active users in its cell, with the maximum served users limited to Lmax. To protect the pico users from severe macro interference, part of the antennas at each macro BS is proposed to be utilized towards interference nulling to pico users. The partitioning of macro antenna resources to serve macro users and to null interference to pico users for optimal performance is investigated in this paper. Biased-nearestdistance based user association scheme is proposed where the bias value accounts for the natural bias due to the differences in multi-antenna transmission schemes across tiers, as well as the artificial bias for load balancing. The signal-to-interference-ratio (SIR) coverage probability, rate distribution and average rate of a typical user are then derived. Our results demonstrate that the proposed interference nulling scheme has strong potential for improving performance if the macro antennas partitioning is carefully done. The optimal L max for both macro and pico tier which maximize the average data rate is also investigated and it is found to outperform both single-user beamforming (SU-BF) and full-SDMA. Finally, the impact of imperfect channel state information (CSI) due to limited feedback is analyzed.
In this paper, we analyze the performance of the uplink communication of massive multi-cell multiple-input multiple-output (MIMO) systems under the effects of pilot contamination and delayed channels because of terminal mobility. The base stations (BSs) estimate the channels through the uplink training, and then use zero-forcing processing to decode the transmit signals from the users. The probability density function (PDF) of the signal-to-interference-plus-noise ratio is derived for any finite number of antennas. From this PDF, we derive an achievable ergodic rate with a finite number of BS antennas in closed form. Insights of the impact of the Doppler shift (due to terminal mobility) at the low signal-to-noise ratio regimes are exposed. In addition, the effects on the outage probability are investigated. Furthermore, the power scaling law and the asymptotic performance result by infinitely increasing the numbers of antennas and terminals (while their ratio is fixed) are provided. The numerical results demonstrate the performance loss for various Doppler shifts. Among the interesting observations revealed is that massive MIMO is favorable even in channel aging conditions.
A major limitation of heterogeneous cellular networks (HCNs) is the neglect of the additive residual transceiver hardware impairments (ARTHIs). The assumption of perfect hardware is quite strong and results in misleading conclusions. This paper models a general multiple-input multiple-output (MIMO) HCN with cell association by incorporating the RTHIs. We derive the coverage probability and shed light on the impact of the ARTHIs, when various transmission methods are applied. As the hardware quality decreases, the coverage probability worsens. Especially, this effect is more severe as the transmit power increases. Furthermore, we verify that in an HCN, it is better to employ at each base station as few transmit antennas as possible.
This paper proposes a stochastic geometry framework to analyze the signal-to-noise-and-interference ratio (SINR) and rate performance in a large-scale uplink massive multiple-input and multiple-output (MIMO) network. Based on the model, expressions are derived for spatial average SINR distributions over user and base station distributions with maximum ratio combining (MRC) and zero-forcing (ZF) receivers. We show that, using massive MIMO, the uplink SINR in certain urban marcocell scenarios is limited by interference. In the interference-limited regime, the results reveal that for MRC receivers, a superlinear (polynomial) scaling law between the number of base station antennas and scheduled users per cell preserves the uplink signal-to-interference ratio (SIR) distribution, while a linear scaling applies to ZF receivers. ZF receivers are shown to outperform MRC receivers in the SIR coverage, and the performance gap is quantified in terms of the difference in the number of antennas to achieve the same SIR distribution. Numerical results verify the analysis. It is found that the optimal compensation fraction in fractional power control to optimize rate is generally different for MRC and ZF receivers. Besides, simulations show that the scaling results derived from the proposed framework apply to the networks, where base stations are distributed according to a hexagonal lattice.
This paper aims at a realistic evaluation of Rayleigh-product multiple-input multiple-output (MIMO) systems. Specifically, by considering the residual transceiver hardware impairments into account, we derive the ergodic channel capacity of a MIMO system with optimal receivers in the case of insufficient scattering. Actually, motivated by the increasing interest for massive MIMO systems, we investigate the impact of transceiver hardware imperfections in systems with both finite (conventional) and large number of antennas under rank deficient channel matrix conditions by varying the severity of hardware quality. Among the interesting outcomes, we emphasize that the residual hardware transceiver impairments result to a saturation of the ergodic channel capacity within the high signal-to-noise ratio (SNR) regime. Furthermore, we observe that the higher the “richness” of the scattering environment, the higher the ergodic channel capacity till it gets saturated.
Recent works have identified massive multiple-input-multiple-output (MIMO) as a key technology for achieving substantial gains in spectral and energy efficiency. Additionally, the turn to low-cost transceivers, being prone to hardware impairments is the most effective and attractive way for cost-efficient applications concerning massive MIMO systems. In this context, the impact of channel aging, which severely affects the performance, is investigated herein by considering a generalized model. Specifically, we show that both Doppler shift because of the users' relative movement as well as phase noise due to noisy local oscillators (LOs) contribute to channel aging. To this end, we first propose a joint model, encompassing both effects, in order to investigate the performance of a massive MIMO system based on the inevitable time-varying nature of realistic mobile communications. Then, we derive the deterministic equivalents (DEs) for the signal-to-noise-and-interference ratios (SINRs) with maximum ratio transmission (MRT) and regularized zero-forcing precoding (RZF). Our analysis not only demonstrates a performance comparison between MRT and RZF under these conditions, but most importantly, it reveals interesting properties regarding the effects of user mobility and phase noise. In particular, the large antenna limit behavior depends profoundly on both effects, but the burden due to user mobility is much more detrimental than phase noise even for moderate user velocities ( km/h), while the negative impact of phase noise is noteworthy at lower mobility conditions.
To keep the hardware costs of future communications systems manageable, the use of low-cost hardware components is desirable. This is particularly true for the emerging massive multiple-input multiple-output (MIMO) systems which equip base stations (BSs) with a large number of antenna elements. However, low-cost transceiver designs will further accentuate the hardware impairments which are present in any practical communication system. In this paper, we investigate the impact of hardware impairments on the secrecy performance of downlink massive MIMO systems in the presence of a passive multiple-antenna eavesdropper. Thereby, for the BS and the legitimate users, the joint effects of multiplicative phase noise, additive distortion noise, and amplified receiver noise are taken into account, whereas the eavesdropper is assumed to employ ideal hardware. We derive a lower bound for the ergodic secrecy rate of a given user when matched filter (MF) data precoding and artificial noise (AN) transmission are employed at the BS. Based on the derived analytical expression, we investigate the impact of the various system parameters on the secrecy rate and optimize both the pilot sets used for uplink training and the AN precoding. Our analytical and simulation results reveal that 1) the additive distortion noise at the BS may be beneficial for the secrecy performance, especially if the power assigned for AN emission is not sufficient; 2) all other hardware impairments have a negative impact on the secrecy performance; 3) so-called spatially orthogonal pilot sequences are preferable unless the phase noise is very strong; 4) the proposed generalized null-space (NS) AN precoding method can efficiently mitigate the negative effects of phase noise.
We propose a cell-edge-aware (CEA) zero forcing (ZF) precoder that exploits the excess spatial degrees of freedom provided by a large number of base station (BS) antennas to suppress inter-cell interference at the most vulnerable user equipments (UEs). We evaluate the downlink performance of CEA-ZF, as well as that of a conventional cell-edge-unaware (CEU) ZF precoder in a network with a random BS topology. Our analysis and simulations show that the proposed CEA-ZF precoder outperforms CEU-ZF precoding in terms of (i) aggregate per-cell data rate, (ii) coverage probability, and (iii) 95%-likely, or edge user, rate. In particular, when both perfect channel state information and a large number of antennas N are available at the BSs, we demonstrate that the outage probability under CEA-ZF and CEU-ZF decay as 1/N
2
and 1/N, respectively. This result identifies CEA-ZF as a more effective precoding scheme for massive multiple-input multiple-output (MIMO) cellular networks. Our framework also reveals the importance of scheduling the optimal number of UEs per BS, and confirms the necessity to control the amount of pilot contamination received during the channel estimation phase.
We consider a multi-cell multi-user downlink channel of a time-division duplex (TDD) MIMO system, where the base stations (BSs) employ the concept of massive MIMO, i.e., they are equipped with a large number of antennas. In addition, the number of users increases with the same speed. Focusing on the practical impairments of the channel such as pilot contamination and, in particular, delayed channel state information at the transmitter (CSIT), we derive an approximation of the sum rate with regularized zero-forcing (RZF) precoding, which provides a quantification of the capacity loss. As a result, it is deemed necessary to obtain the deterministic equivalent sum rate by incorporating in our analysis channel prediction circumventing the degradation due to delayed CSIT. The proposed results are accurate for realistic system dimensions, as simulations testify. Finally, we show the benefits of applying RZF in the sum rate against using eigenbeamforming (BF) for the same Doppler shift with no extra computational complexity.
This paper investigates the achievable sum-rate of massive multiple-input
multiple-output (MIMO) systems in the presence of channel aging. For the
uplink, by assuming that the base station (BS) deploys maximum ratio combining
(MRC) or zero-forcing (ZF) receivers, we present tight closed-form lower bounds
on the achievable sum-rate for both receivers with aged channel state
information (CSI). In addition, the benefit of implementing channel prediction
methods on the sum-rate is examined, and closed-form sum rate lower bounds are
derived. Moreover, the impact of channel aging and channel prediction on the
power scaling law is characterized. Extension to the downlink scenario and
multi-cell scenario are also considered. It is found that, for a system
with/without channel prediction, the transmit power of each user can be scaled
down at most by (where M is the number of BS antennas), which
indicates that aged CSI does not degrade the power scaling law, and channel
prediction does not enhance the power scaling law; instead, these phenomena
affect the achievable sum-rate by degrading or enhancing the effective signal
to interference and noise ratio, respectively.
The tremendous capacity gains promised by space division multiple access (SDMA) depend critically on the accuracy of the transmit channel state information. In the broadcast channel, even without any network interference, it is known that such gains collapse due to interstream interference if the feedback is delayed or low rate. In this paper, we investigate SDMA in the presence of interference from many other simultaneously active transmitters distributed randomly over the network. In particular we consider zero-forcing beamforming in a decentralized (ad hoc) network where each receiver provides feedback to its respective transmitter. We derive closed-form expressions for the outage probability, network throughput, transmission capacity, and average achievable rate and go on to quantify the degradation in network performance due to residual self-interference as a function of key system parameters. One particular finding is that as in the classical broadcast channel, the per-user feedback rate must increase linearly with the number of transmit antennas and SINR (in dB) for the full multiplexing gains to be preserved with limited feedback. We derive the throughput-maximizing number of streams, establishing that single-stream transmission is optimal in most practically relevant settings. In short, SDMA does not appear to be a prudent design choice for interference-limited wireless networks.
We develop a general downlink model for multi-antenna heterogeneous cellular networks (HetNets), where base stations (BSs) across tiers may differ in terms of transmit power, target signal-to-interference-ratio (SIR), deployment density, number of transmit antennas and the type of multi-antenna transmission. In particular, we consider and compare space division multiple access (SDMA), single user beamforming (SU-BF), and baseline single-input single-output (SISO) transmission. For this general model, the main contributions are: (i) ordering results for both coverage probability and per user rate in closed form for any BS distribution for the three considered techniques, using novel tools from stochastic orders, (ii) upper bounds on the coverage probability assuming a Poisson BS distribution, and (iii) a comparison of the area spectral efficiency (ASE). The analysis concretely demonstrates, for example, that for a given total number of transmit antennas in the network, it is preferable to spread them across many single-antenna BSs vs. fewer multi-antenna BSs. Another observation is that SU-BF provides higher coverage and per user data rate than SDMA, but SDMA is in some cases better in terms of ASE.
An extensive update to a classic text
Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis.
The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital applications to spatial statistics and as a very interesting field of mathematics in its own right.
This edition: presents a wealth of models for spatial patterns and related statistical methods;
provides a great survey of the modern theory of random tessellations, including many new models that became tractable only in the last few years;
includes new sections on random networks and random graphs to review the recent ever growing interest in these areas;
provides an excellent introduction to theory and modelling of point processes, which covers some very latest developments;
illustrate the forefront theory of random sets, with many applications;
adds new results to the discussion of fibre and surface processes;
offers an updated collection of useful stereological methods;
includes 700 new references;
is written in an accessible style enabling non-mathematicians to benefit from this book;
provides a companion website hosting information on recent developments in the field www.wiley.com/go/cskm
Stochastic Geometry and its Applications is ideally suited for researchers in physics, materials science, biology and ecological sciences as well as mathematicians and statisticians. It should also serve as a valuable introduction to the subject for students of mathematics and statistics.
In this paper, single-carrier multiple-input multiple-output (MIMO) transmit beamforming (TB) systems in the presence of high-power amplifier (HPA) nonlinearity are investigated. Specifically, due to the suboptimality of the conventional maximal ratio transmission/maximal ratio combining (MRT/MRC) under HPA nonlinearity, we propose the optimal TB scheme with the optimal beamforming weight vector and combining vector, for MIMO systems with nonlinear HPAs. Moreover, an alternative suboptimal but much simpler TB scheme, namely, quantized equal gain transmission (QEGT), is proposed. The latter profits from the property that the elements of the beamforming weight vector have the same constant modulus. The performance of the proposed optimal TB scheme and QEGT/MRC technique in the presence of the HPA nonlinearity is evaluated in terms of the average symbol error probability and mutual information with the Gaussian input, considering the transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects on the performance of several system parameters, namely, the HPA parameters, numbers of antennas, quadrature amplitude modulation modulation order, number of pilot symbols, and cardinality of the beamforming weight vector codebook for QEGT.
Multiple-input multiple-output (MIMO) technology constitutes a breakthrough in the design of wireless communication systems, and is already at the core of several wireless standards. Exploiting multi-path scattering, MIMO techniques deliver significant performance enhancements in terms of data transmission rate and interference reduction. This book is a detailed introduction to the analysis and design of MIMO wireless systems. Beginning with an overview of MIMO technology, the authors then examine the fundamental capacity limits of MIMO systems. Transmitter design, including precoding and space-time coding, is then treated in depth, and the book closes with two chapters devoted to receiver design. Written by a team of leading experts, the book blends theoretical analysis with physical insights, and highlights a range of key design challenges. It can be used as a textbook for advanced courses on wireless communications, and will also appeal to researchers and practitioners working on MIMO wireless systems.
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.
A Wiley Interscience publication Incluye bibliografía e índice
Autoregressive stochastic models for the computer simulation of correlated Rayleigh fading processes are investigated. The unavoidable numerical difficulties inherent in this method are elucidated and a simple heuristic approach is adopted to enable the synthesis of accurately correlated, bandlimited Rayleigh variates. Startup procedures are presented, which allow autoregressive simulators to produce stationary channel gain samples from the first output sample. Performance comparisons are then made with popular fading generation techniques to demonstrate the merits of the approach. The general applicability of the method is demonstrated by examples involving the accurate synthesis of nonisotropic fading channel models.
A simple idealized linear (and planar) uplink cellular
multiple-access communication model, where only adjacent cell
interference is present and all signals may experience fading, is
considered. Shannon theoretic arguments are invoked to gain insight into
the implications on performance of the main system parameters and
multiple-access techniques. We specialize to the linear model and
address the case of practical importance where the cell-site receiver
processes only the signals received at this cell site, and where the
actively interfering users assigned to other cells (but not those within
the cell) are interpreted as Gaussian noise (worst case assumption). We
assume that the cell-site receiver is aware of the instantaneous
signal-to-noise ratios for all users assigned to that cell while the
users' transmitters do not have access to this side information. We
first investigate several different scenarios and focus on the effect of
fading and intercell interference and then provide a general formulation
for an achievable rate region (inner-bound) of which all the different
scenarios are special cases. The features of TDMA and wideband (WB)
intracell multiple-access techniques are examined as well as the role of
(optimized) fractional intercell time-sharing (ICTS) protocol. The cases
of: no fading, fading where intercell interference is not dominant, and
fading where intercell interference is present, are discussed
Key Technologies for 5G Wireless Systems
- V W Wong
- R Schober
- D W K Ng
- L.-C Wang
V. W. Wong, R. Schober, D. W. K. Ng, and L.-C. Wang, Key Technologies
for 5G Wireless Systems. Cambridge university press, 2017.