Multiple-antennas and isotropically random unitary inputs: the received signal density in closed form

An important open problem in multiple-antenna communications theory is to compute the capacity of a wireless link subject to flat Rayleigh block-fading, with no channel-state information (CSI) available either to the transmitter or to the receiver. The isotropically random (i.r.) unitary matrix-having orthonormal columns, and a probability density that is invariant to premultiplication by an independent unitary matrix-plays a central role in the calculation of capacity and in some special cases happens to be capacity-achieving. We take an important step toward computing this capacity by obtaining, in closed form, the probability density of the received signal when transmitting i.r. unitary matrices. The technique is based on analytically computing the expectation of an exponential quadratic function of an i.r. unitary matrix and makes use of a Fourier integral representation of the constituent Dirac delta functions in the underlying density. Our formula for the received signal density enables us to evaluate the mutual information for any case of interest, something that could previously only be done for single transmit and receive antennas. Numerical results show that at high signal-to-noise ratio (SNR), the mutual information is maximized for M=min(N, T/2) transmit antennas, where N is the number of receive antennas and T is the length of the coherence interval, whereas at low SNR, the mutual information is maximized by allocating all transmit power to a single antenna

Space-time autocoding

Prior treatments of space-time communications in Rayleigh flat fading generally assume that channel coding covers either one fading interval-in which case there is a nonzero “outage capacity”-or multiple fading intervals-in which case there is a nonzero Shannon capacity. However, we establish conditions under which channel codes span only one fading interval and yet are arbitrarily reliable. In short, space-time signals are their own channel codes. We call this phenomenon space-time autocoding, and the accompanying capacity the space-time autocapacity. Let an M-transmitter antenna, N-receiver antenna Rayleigh flat fading channel be characterized by an M×N matrix of independent propagation coefficients, distributed as zero-mean, unit-variance complex Gaussian random variables. This propagation matrix is unknown to the transmitter, it remains constant during a T-symbol coherence interval, and there is a fixed total transmit power. Let the coherence interval and number of transmitter antennas be related as T=βM for some constant β. A T×M matrix-valued signal, associated with R·T bits of information for some rate R is transmitted during the T-symbol coherence interval. Then there is a positive space-time autocapacity Ca such that for all R<Ca, the block probability of error goes to zero as the pair (T, M)→∞ such that T/M=β. The autocoding effect occurs whether or not the propagation matrix is known to the receiver, and Ca=Nlog(1+ρ) in either case, independently of β, where ρ is the expected signal-to-noise ratio (SNR) at each receiver antenna. Lower bounds on the cutoff rate derived from random unitary space-time signals suggest that the autocoding effect manifests itself for relatively small values of T and M. For example, within a single coherence interval of duration T=16, for M=7 transmitter antennas and N=4 receiver antennas, and an 18-dB expected SNR, a total of 80 bits (corresponding to rate R=5) can theoretically be transmitted with a block probability of error less than 10^-9, all without any training or knowledge of the propagation matrix

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.Comment: Allerton Conference on Communication, Control, and Computing, Urbana-Champaign, Illinois, Oct. 201

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

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.Comment: Final manuscript, to appear in IEEE Communications Magazin

The academic and industrial embrace of space-time methods

[Guest Editors introduction to: Special issue on space-time transmission, reception, coding and signal processing] Every episode of the classic 1966–1969 television series Star Trek begins with Captain Kirk’s (played by William Shatner) famous words : “Space: The final frontier….” While space may not be the final frontier for the information and communication theory community, it is proving to be an important and fruitful one. In the information theory community, the notion of space can be broadly defined as the simultaneous use of multiple, possibly coupled, channels. The notions of space–time and multiple-input multiple-output (MIMO) channels are therefore often used interchangeably. The connection between space and MIMO is most transparent when we view the multiple channels as created by two or more spatially separated antennas at a wireless transmitter or receiver. A large component of the current interest in space–time methods can be attributed to discoveries in the late 1980s and early 1990s that a rich wireless scattering environment can be beneficial when multiple antennas are used on a point-to-point link. We now know that adding antennas in a rich environment provides proportional increases in point-to-point data rates, without extra transmitted power or bandwidth

Massive MIMO is a Reality -- What is Next? Five Promising Research Directions for Antenna Arrays

Massive MIMO (multiple-input multiple-output) is no longer a "wild" or "promising" concept for future cellular networks - in 2018 it became a reality. Base stations (BSs) with 64 fully digital transceiver chains were commercially deployed in several countries, the key ingredients of Massive MIMO have made it into the 5G standard, the signal processing methods required to achieve unprecedented spectral efficiency have been developed, and the limitation due to pilot contamination has been resolved. Even the development of fully digital Massive MIMO arrays for mmWave frequencies - once viewed prohibitively complicated and costly - is well underway. In a few years, Massive MIMO with fully digital transceivers will be a mainstream feature at both sub-6 GHz and mmWave frequencies. In this paper, we explain how the first chapter of the Massive MIMO research saga has come to an end, while the story has just begun. The coming wide-scale deployment of BSs with massive antenna arrays opens the door to a brand new world where spatial processing capabilities are omnipresent. In addition to mobile broadband services, the antennas can be used for other communication applications, such as low-power machine-type or ultra-reliable communications, as well as non-communication applications such as radar, sensing and positioning. We outline five new Massive MIMO related research directions: Extremely large aperture arrays, Holographic Massive MIMO, Six-dimensional positioning, Large-scale MIMO radar, and Intelligent Massive MIMO.Comment: 20 pages, 9 figures, submitted to Digital Signal Processin