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.

Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas

A multiplicity of autonomous terminals simultaneously transmits data streams to a compact array of antennas. The array uses imperfect channel-state information derived from transmitted pilots to extract the individual data streams. The power radiated by the terminals can be made inversely proportional to the square-root of the number of base station antennas with no reduction in performance. In contrast if perfect channel-state information were available the power could be made inversely proportional to the number of antennas. Lower capacity bounds for maximum-ratio combining (MRC), zero-forcing (ZF) and minimum mean-square error (MMSE) detection are derived. An MRC receiver normally performs worse than ZF and MMSE. However as power levels are reduced, the cross-talk introduced by the inferior maximum-ratio receiver eventually falls below the noise level and this simple receiver becomes a viable option. The tradeoff between the energy efficiency (as measured in bits/J) and spectral efficiency (as measured in bits/channel use/terminal) is quantified for a channel model that includes small-scale fading but not large-scale fading. It is shown that the use of moderately large antenna arrays can improve the spectral and energy efficiency with orders of magnitude compared to a single-antenna system.

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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.

Communication at millimeter wave (mmWave) frequencies is defining a new era of wireless communication. The mmWave band offers higher bandwidth communication channels versus those presently used in commercial wireless systems. The applications of mmWave are immense: wireless local and personal area networks in the unlicensed band, 5G cellular systems, not to mention vehicular area networks, ad hoc networks, and wearables. Signal processing is critical for enabling the next generation of mmWave communication. Due to the use of large antenna arrays at the transmitter and receiver, combined with radio frequency and mixed signal power constraints, new multiple-input multiple-output (MIMO) communication signal processing techniques are needed. Because of the wide bandwidths, low complexity transceiver algorithms become important. There are opportunities to exploit techniques like compressed sensing for channel estimation and beamforming. This article provides an overview of signal processing challenges in mmWave wireless systems, with an emphasis on those faced by using MIMO communication at higher carrier frequencies.

An Overview of Signal Processing Techniques for Millimeter Wave MIMO Systems

This paper presents an overview of the theory and currently known techniques for multi-cell MIMO (multiple input multiple output) cooperation in wireless networks. In dense networks where interference emerges as the key capacity-limiting factor, multi-cell cooperation can dramatically improve the system performance. Remarkably, such techniques literally exploit inter-cell interference by allowing the user data to be jointly processed by several interfering base stations, thus mimicking the benefits of a large virtual MIMO array. Multi-cell MIMO cooperation concepts are examined from different perspectives, including an examination of the fundamental information-theoretic limits, a review of the coding and signal processing algorithmic developments, and, going beyond that, consideration of very practical issues related to scalability and system-level integration. A few promising and quite fundamental research avenues are also suggested.

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Multi-Cell MIMO Cooperative Networks: A New Look at Interference

Multi-user MIMO (MU-MIMO) networks reveal the unique opportunities arising from a joint optimization of antenna combining techniques with resource allocation protocols. Furthermore, it brings robustness with respect to multipath richness, allowing for compact antenna spacing at the BS and, crucially, yielding the diversity and multiplexing gains without the need for multiple antenna user terminals. To realize these gains, however, the BS should be informed with the user's channel coefficients, which may limit practical application to TDD or low-mobility settings. To circumvent this problem and reduce feedback load, combining MU-MIMO with opportunistic scheduling seems a promising direction. The success for this type of scheduler is strongly traffic and QoS-dependent, however.

Shifting the MIMO Paradigm

We consider the downlink of a wireless system with an M-antenna base station and K single-antenna users. A limited feedback-based scheduling and precoding scenario is considered that builds on the multiuser random beamforming (RBF). Such a scheme was shown to yield the same capacity scaling, in terms of multiplexing and multiuser diversity gain, as the optimal full CSIT-based (channel state information at transmitter) precoding scheme, in the large number of users K regime. Unfortunately, for more practically relevant (low to moderate) K values, RBF yields degraded performance. In this work, we investigate solutions to this problem. We introduce a two-stage framework that decouples the scheduling and beamforming problems. In our scenario, RBF is exploited to identify good, spatially separable, users in a first stage. In the second stage, the initial random beams are refined based on the available feedback to offer improved performance toward the selected users. Specifically, we propose beam power control techniques that do not change the direction of the second-stage beams, offering feedback reduction and performance tradeoffs. The common feature of these schemes is to restore robustness of RBF with respect to sparse network settings (low K), at the cost of moderate complexity increase.

Enhanced multiuser random beamforming: dealing with the not so large number of users case

We consider a downlink channel where a base station equipped with M transmit antennas communicates with K ≥ M single-antenna receivers and has partial channel knowledge obtained via a limited rate feedback channel. We propose scalar feedback metrics that provide an estimate of the received signal-to-noise plus interference ratio (SINR), which are combined with efficient user selection algorithms and zero-forcing beamforming. The asymptotic system sum rate for large K is analyzed and numerical results are provided, showing the performance of each metric in different scenarios.

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Efficient Metrics for Scheduling in MIMO Broadcast Channels with Limited Feedback

We consider joint scheduling and beamforming in a broadcast channel with multiple antennas at the transmitter and a single antenna at the mobile receiver Perfect channel knowledge is assumed to be available at the receiver while the transmitter is provided with partial channel state information (CSIT) through a limited rate feedback channel Each user feeds back quantized information regarding the channel vector direction (from a codebook) and a quantized (scalar) channel quality indicator We identify the tradeoff between multiuser diversity and spatial multiplexing gain given a limited amount of feedback bits Scaling laws of the above parameters are derived in order to achieve a target rate performance Our results reveal useful design guidelines for the split of feedback bits for channel quantization and channel quality

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Multiuser Diversity - Multiplexing Tradeoff in MIMO Broadcast Channels with Limited Feedback

The problem of joint scheduling and beam-forming for a multiple antenna broadcast channel with partial channel state information at the transmitter (CSIT) is considered. We show how long-term statistical channel knowledge can be efficiently combined with instantaneous low-rate feedback for user selection and linear beamforming. A low complexity algorithm based on an estimate (bound) of the multiuser interference is proposed. Our scheme is shown to exhibit significant throughput gain over opportunistic techniques, approaching the sum rate of full CSIT for small angle spreads.

Thomas Salzer

Papers

Shifting the MIMO Paradigm

Enhanced multiuser random beamforming: dealing with the not so large number of users case

Efficient Metrics for Scheduling in MIMO Broadcast Channels with Limited Feedback

Multiuser Diversity - Multiplexing Tradeoff in MIMO Broadcast Channels with Limited Feedback

Low Complexity Scheduling and Beamforming for Multiuser MIMO Systems