arXiv subjects

Thomas L. Marzetta

Publications and source records attributed to Thomas L. Marzetta.

36 records · Page 2Linked to original sources

arXiv2017

Max-Min Fair Transmit Precoding for Multi-group Multicasting in Massive MIMO

This paper considers the downlink precoding for physical layer multicasting in massive multiple-input-multiple-output (MIMO) systems. We study the max-min fairness (MMF) problem, where channel state information (CSI) at the transmitter is used to design precoding vectors that maximize the minimum spectral efficiency (SE) of the system, given fixed power budgets for uplink training and downlink transmission. Our system model accounts for channel estimation, pilot contamination, arbitrary pathlosses, and multi-group multicasting. We consider six scenarios with different transmission technologies (unicast and multicast), different pilot assignment strategies (dedicated or shared pilot assignments), and different precoding schemes (maximum ratio transmission and zero forcing), and derive achievable spectral efficiencies for all possible combinations. Then we solve the MMF problem for each of these scenarios and for any given pilot length we find the SE maximizing uplink pilot and downlink data transmission policies, all in closed-forms. We use these results to draw a general guideline for massive MIMO multicasting design, where for a given number of base station antennas, number of users, and coherence interval length, we determine the multicasting scheme that shall be used.

cs.IT↗

arXiv2017

Channel Training for Analog FDD Repeaters: Optimal Estimators and Cramér-Rao Bounds

For frequency division duplex channels, a simple pilot loop-back procedure has been proposed that allows the estimation of the UL & DL channels at an antenna array without relying on any digital signal processing at the terminal side. For this scheme, we derive the maximum likelihood (ML) estimators for the UL & DL channel subspaces, formulate the corresponding Cramér-Rao bounds and show the asymptotic efficiency of both (SVD-based) estimators by means of Monte Carlo simulations. In addition, we illustrate how to compute the underlying (rank-1) SVD with quadratic time complexity by employing the power iteration method. To enable power control for the data transmission, knowledge of the channel gains is needed. Assuming that the UL & DL channels have on average the same gain, we formulate the ML estimator for the channel norm, and illustrate its robustness against strong noise by means of simulations.

cs.IT↗

arXiv2017

Performance of Cell-Free Massive MIMO Systems with MMSE and LSFD Receivers

Cell-Free Massive MIMO comprises a large number of distributed single-antenna access points (APs) serving a much smaller number of users. There is no partitioning into cells and each user is served by all APs. In this paper, the uplink performance of cell-free systems with minimum mean squared error (MMSE) and large scale fading decoding (LSFD) receivers is investigated. The main idea of LSFD receiver is to maximize achievable throughput using only large scale fading coefficients between APs and users. Capacity lower bounds for MMSE and LSFD receivers are derived. An asymptotic approximation for signal-to-interference-plus-noise ratio (SINR) of MMSE receiver is derived as a function of large scale fading coefficients only. The obtained approximation is accurate even for a small number of antennas. MMSE and LSFD receivers demonstrate five-fold and two-fold gains respectively over matched filter (MF) receiver in terms of 5%-outage rate.

cs.IT↗

arXiv2017

Uplink Interference Reduction in Large Scale Antenna Systems

A massive MIMO system entails a large number (tens or hundreds) of base station antennas serving a much smaller number of terminals. These systems demonstrate large gains in spectral and energy efficiency compared with conventional MIMO technology. As the number of antennas grows, the performance of a massive MIMO system gets limited by the interference caused by pilot contamination. Earlier A. Ashikhmin and T. Marzetta proposed (under the name of Pilot Contamination Precoding) Large Scale Fading Precoding (LSFP) and Decoding (LSFD) based on limited cooperation between base stations. They showed that Zero-Forcing LSFP and LSFD eliminate pilot contamination entirely and lead to an infinite throughput as the number of antennas grows. In this paper, we focus on the uplink and show that even in the case of a finite number of base station antennas, LSFD yields a very large performance gain. In particular, one of our algorithms gives a more than 140 fold increase in the 5% outage data transmission rate! We show that the performance can be improved further by optimizing the transmission powers of the users. Finally, we present decentralized LSFD that requires limited cooperation only between neighboring cells.

cs.IT↗

arXiv2017

Cell-Free Massive MIMO versus Small Cells

A Cell-Free Massive MIMO (multiple-input multiple-output) system comprises a very large number of distributed access points (APs)which simultaneously serve a much smaller number of users over the same time/frequency resources based on directly measured channel characteristics. The APs and users have only one antenna each. The APs acquire channel state information through time-division duplex operation and the reception of uplink pilot signals transmitted by the users. The APs perform multiplexing/de-multiplexing through conjugate beamforming on the downlink and matched filtering on the uplink. Closed-form expressions for individual user uplink and downlink throughputs lead to max-min power control algorithms. Max-min power control ensures uniformly good service throughout the area of coverage. A pilot assignment algorithm helps to mitigate the effects of pilot contamination, but power control is far more important in that regard. Cell-Free Massive MIMO has considerably improved performance with respect to a conventional small-cell scheme, whereby each user is served by a dedicated AP, in terms of both 95%-likely per-user throughput and immunity to shadow fading spatial correlation. Under uncorrelated shadow fading conditions, the cell-free scheme provides nearly 5-fold improvement in 95%-likely per-user throughput over the small-cell scheme, and 10-fold improvement when shadow fading is correlated.

cs.IT↗

arXiv2015

Massive MIMO: Ten Myths and One Critical Question

Wireless communications is one of the most successful technologies in modern years, given that an exponential growth rate in wireless traffic has been sustained for over a century (known as Cooper's law). This trend will certainly continue driven by new innovative applications; for example, augmented reality and internet-of-things. Massive MIMO (multiple-input multiple-output) has been identified as a key technology to handle orders of magnitude more data traffic. Despite the attention it is receiving from the communication community, we have personally witnessed that Massive MIMO is subject to several widespread misunderstandings, as epitomized by following (fictional) abstract: "The Massive MIMO technology uses a nearly infinite number of high-quality antennas at the base stations. By having at least an order of magnitude more antennas than active terminals, one can exploit asymptotic behaviors that some special kinds of wireless channels have. This technology looks great at first sight, but unfortunately the signal processing complexity is off the charts and the antenna arrays would be so huge that it can only be implemented in millimeter wave bands." The statements above are, in fact, completely false. In this overview article, we identify ten myths and explain why they are not true. We also ask a question that is critical for the practical adoption of the technology and which will require intense future research activities to answer properly. We provide references to key technical papers that support our claims, while a further list of related overview and technical papers can be found at the Massive MIMO Info Point: http://massivemimo.eu

cs.IT↗

arXiv2015

Cell-Free Massive MIMO: Uniformly Great Service For Everyone

We consider the downlink of Cell-Free Massive MIMO systems, where a very large number of distributed access points (APs) simultaneously serve a much smaller number of users. Each AP uses local channel estimates obtained from received uplink pilots and applies conjugate beamforming to transmit data to the users. We derive a closed-form expression for the achievable rate. This expression enables us to design an optimal max-min power control scheme that gives equal quality of service to all users. We further compare the performance of the Cell-Free Massive MIMO system to that of a conventional small-cell network and show that the throughput of the Cell-Free system is much more concentrated around its median compared to that of the small-cell system. The Cell-Free Massive MIMO system can provide an almost $20-$fold increase in 95%-likely per-user throughput, compared with the small-cell system. Furthermore, Cell-Free systems are more robust to shadow fading correlation than small-cell systems.

cs.IT↗

arXiv2014

Interference Reduction in Multi-Cell Massive MIMO Systems I: Large-Scale Fading Precoding and Decoding

A wireless massive MIMO system entails a large number (tens or hundreds) of base station antennas serving a much smaller number of users, with large gains in spectral-efficiency and energy-efficiency compared with conventional MIMO technology. Until recently it was believed that in multi-cellular massive MIMO system, even in the asymptotic regime, as the number of service antennas tends to infinity, the performance is limited by directed inter-cellular interference. This interference results from unavoidable re-use of reverse-link training sequences (pilot contamination) by users in different cells. We devise a new concept that leads to the effective elimination of inter-cell interference in massive MIMO systems. This is achieved by outer multi-cellular precoding, which we call Large-Scale Fading Precoding (LSFP). The main idea of LSFP is that each base station linearly combines messages aimed to users from different cells that re-use the same training sequence. Crucially, the combining coefficients depend only on the slow-fading coefficients between the users and the base stations. Each base station independently transmits its LSFP-combined symbols using conventional linear precoding that is based on estimated fast-fading coefficients. Further, we derive estimates for downlink and uplink SINRs and capacity lower bounds for the case of massive MIMO systems with LSFP and a finite number of base station antennas.

cs.IT↗

arXiv2014

Aspects of Favorable Propagation in Massive MIMO

Favorable propagation, defined as mutual orthogonality among the vector-valued channels to the terminals, is one of the key properties of the radio channel that is exploited in Massive MIMO. However, there has been little work that studies this topic in detail. In this paper, we first show that favorable propagation offers the most desirable scenario in terms of maximizing the sum-capacity. One useful proxy for whether propagation is favorable or not is the channel condition number. However, this proxy is not good for the case where the norms of the channel vectors may not be equal. For this case, to evaluate how favorable the propagation offered by the channel is, we propose a ``distance from favorable propagation'' measure, which is the gap between the sum-capacity and the maximum capacity obtained under favorable propagation. Secondly, we examine how favorable the channels can be for two extreme scenarios: i.i.d. Rayleigh fading and uniform random line-of-sight (UR-LoS). Both environments offer (nearly) favorable propagation. Furthermore, to analyze the UR-LoS model, we propose an urns-and-balls model. This model is simple and explains the singular value spread characteristic of the UR-LoS model well.

cs.IT↗

arXiv2014

Massive MIMO for Next Generation Wireless Systems

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.

cs.IT↗

arXiv2013

Five Disruptive Technology Directions for 5G

New research directions will lead to fundamental changes in the design of future 5th generation (5G) cellular networks. This paper describes five technologies that could lead to both architectural and component disruptive design changes: device-centric architectures, millimeter Wave, Massive-MIMO, smarter devices, and native support to machine-2-machine. The key ideas for each technology are described, along with their potential impact on 5G and the research challenges that remain.

cs.NI↗

arXiv2013

Massive MU-MIMO Downlink TDD Systems with Linear Precoding and Downlink Pilots

We consider a massive MU-MIMO downlink time-division duplex system where a base station (BS) equipped with many antennas serves several single-antenna users in the same time-frequency resource. We assume that the BS uses linear precoding for the transmission. To reliably decode the signals transmitted from the BS, each user should have an estimate of its channel. In this work, we consider an efficient channel estimation scheme to acquire CSI at each user, called beamforming training scheme. With the beamforming training scheme, the BS precodes the pilot sequences and forwards to all users. Then, based on the received pilots, each user uses minimum mean-square error channel estimation to estimate the effective channel gains. The channel estimation overhead of this scheme does not depend on the number of BS antennas, and is only proportional to the number of users. We then derive a lower bound on the capacity for maximum-ratio transmission and zero-forcing precoding techniques which enables us to evaluate the spectral efficiency taking into account the spectral efficiency loss associated with the transmission of the downlink pilots. Comparing with previous work where each user uses only the statistical channel properties to decode the transmitted signals, we see that the proposed beamforming training scheme is preferable for moderate and low-mobility environments.

cs.IT↗

arXiv2012

Energy and Spectral Efficiency of Very Large Multiuser MIMO Systems

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. A 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. 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.

cs.IT↗

arXiv2012

Scaling up MIMO: Opportunities and Challenges with Very Large Arrays

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.

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arXiv2010

A Random Matrix--Theoretic Approach to Handling Singular Covariance Estimates

In many practical situations we would like to estimate the covariance matrix of a set of variables from an insufficient amount of data. More specifically, if we have a set of $N$ independent, identically distributed measurements of an $M$ dimensional random vector the maximum likelihood estimate is the sample covariance matrix. Here we consider the case where $N<M$ such that this estimate is singular and therefore fundamentally bad. We present a radically new approach to deal with this situation. Let $X$ be the $M\times N$ data matrix, where the columns are the $N$ independent realizations of the random vector with covariance matrix $Σ$. Without loss of generality, we can assume that the random variables have zero mean. We would like to estimate $Σ$ from $X$. Let $K$ be the classical sample covariance matrix. Fix a parameter $1\leq L\leq N$ and consider an ensemble of $L\times M$ random unitary matrices, $\{Φ\}$, having Haar probability measure. Pre and post multiply $K$ by $Φ$, and by the conjugate transpose of $Φ$ respectively, to produce a non--singular $L\times L$ reduced dimension covariance estimate. A new estimate for $Σ$, denoted by $\mathrm{cov}_L(K)$, is obtained by a) projecting the reduced covariance estimate out (to $M\times M$) through pre and post multiplication by the conjugate transpose of $Φ$, and by $Φ$ respectively, and b) taking the expectation over the unitary ensemble. Another new estimate (this time for $Σ^{-1}$), $\mathrm{invcov}_L(K)$, is obtained by a) inverting the reduced covariance estimate, b) projecting the inverse out (to $M\times M$) through pre and post multiplication by the conjugate transpose of $Φ$, and by $Φ$ respectively, and c) taking the expectation over the unitary ensemble. We have a closed analytical expression for $\mathrm{invcov}_L(K)$ and $\mathrm{cov}_L(K)$ in terms of its eigenvalue decomposition.

math.PR↗

arXiv2010

Pilot Contamination and Precoding in Multi-Cell TDD Systems

This paper considers a multi-cell multiple antenna system with precoding used at the base stations for downlink transmission. For precoding at the base stations, channel state information (CSI) is essential at the base stations. A popular technique for obtaining this CSI in time division duplex (TDD) systems is uplink training by utilizing the reciprocity of the wireless medium. This paper mathematically characterizes the impact that uplink training has on the performance of such multi-cell multiple antenna systems. When non-orthogonal training sequences are used for uplink training, the paper shows that the precoding matrix used by the base station in one cell becomes corrupted by the channel between that base station and the users in other cells in an undesirable manner. This paper analyzes this fundamental problem of pilot contamination in multi-cell systems. Furthermore, it develops a new multi-cell MMSE-based precoding method that mitigate this problem. In addition to being a linear precoding method, this precoding method has a simple closed-form expression that results from an intuitive optimization problem formulation. Numerical results show significant performance gains compared to certain popular single-cell precoding methods.

cs.IT↗

arXiv2009

What is the Value of Joint Processing of Pilots and Data in Block-Fading Channels?

The spectral efficiency achievable with joint processing of pilot and data symbol observations is compared with that achievable through the conventional (separate) approach of first estimating the channel on the basis of the pilot symbols alone, and subsequently detecting the data symbols. Studied on the basis of a mutual information lower bound, joint processing is found to provide a non-negligible advantage relative to separate processing, particularly for fast fading. It is shown that, regardless of the fading rate, only a very small number of pilot symbols (at most one per transmit antenna and per channel coherence interval) should be transmitted if joint processing is allowed.

cs.IT↗

arXiv2005

Capacity of Differential versus Non-Differential Unitary Space-Time Modulation for MIMO channels

Differential Unitary Space-Time Modulation (DUSTM) and its earlier nondifferential counterpart, USTM, permit high-throughput MIMO communication entirely without the possession of channel state information (CSI) by either the transmitter or the receiver. For an isotropically random unitary input we obtain the exact closed-form expression for the probability density of the DUSTM received signal, which permits the straightforward Monte Carlo evaluation of its mutual information. We compare the performance of DUSTM and USTM through both numerical computations of mutual information and through the analysis of low- and high-SNR asymptotic expressions. In our comparisons the symbol durations of the equivalent unitary space-time signals are both equal to T, as are the number of receive antennas N. For DUSTM the number of transmit antennas is constrained by the scheme to be M = T/2, while USTM has no such constraint. If DUSTM and USTM utilize the same number of transmit antennas at high SNR's the normalized mutual information of the differential and the nondifferential schemes expressed in bits/sec/Hz are asymptotically equal, with the differential scheme performing somewhat better, while at low SNR's the normalized mutual information of DUSTM is asymptotically twice the normalized mutual information of USTM. If, instead, USTM utilizes the optimum number of transmit antennas then USTM can outperform DUSTM at sufficiently low SNR's.

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