We consider a general multiple-antenna network with multiple sources, multiple destinations, and multiple relays in terms of the diversity-multiplexing tradeoff (DMT). We examine several subcases of this most general problem taking into account the processing capability of the relays (half-duplex or full-duplex), and the network geometry (clustered or nonclustered). We first study the multiple-antenna relay channel with a full-duplex relay to understand the effect of increased degrees of freedom in the direct link. We find DMT upper bounds and investigate the achievable performance of decode-and-forward (DF), and compress-and-forward (CF) protocols. Our results suggest that while DF is DMT optimal when all terminals have one antenna each, it may not maintain its good performance when the degrees of freedom in the direct link are increased, whereas CF continues to perform optimally. We also study the multiple-antenna relay channel with a half-duplex relay. We show that the half-duplex DMT behavior can significantly be different from the full-duplex case. We find that CF is DMT optimal for half-duplex relaying as well, and is the first protocol known to achieve the half-duplex relay DMT. We next study the multiple-access relay channel (MARC) DMT. Finally, we investigate a system with a single source-destination pair and multiple relays, each node with a single antenna, and show that even under the ideal assumption of full-duplex relays and a clustered network, this virtual multiple-input multiple-output (MIMO) system can never fully mimic a real MIMO DMT. For cooperative systems with multiple sources and multiple destinations the same limitation remains in effect.

Multiple-Antenna Cooperative Wireless Systems: A Diversity–Multiplexing Tradeoff Perspective

Understand the fundamentals of wireless and MIMO communication with this accessible and comprehensive text. Viewing the subject through an information theory lens, but also drawing on other perspectives, it provides a sound treatment of the key concepts underpinning contemporary wireless communication and MIMO, all the way to massive MIMO. Authoritative and insightful, it includes over 330 worked examples and 450 homework problems, with solutions and MATLAB code and data available online. Altogether, this is an excellent resource for instructors and graduate students, as well as an outstanding reference for researchers and practicing engineers.

Foundations of MIMO Communication

This paper identifies the first general, explicit, and nonrandom MIMO encoder-decoder structures that guarantee optimality with respect to the diversity-multiplexing tradeoff (DMT), without employing a computationally expensive maximum-likelihood (ML) receiver. Specifically, the work establishes the DMT optimality of a class of regularized lattice decoders, and more importantly the DMT optimality of their lattice-reduction (LR)-aided linear counterparts. The results hold for all channel statistics, for all channel dimensions, and most interestingly, irrespective of the particular lattice-code applied. As a special case, it is established that the LLL-based LR-aided linear implementation of the MMSE-GDFE lattice decoder facilitates DMT optimal decoding of any lattice code at a worst-case complexity that grows at most linearly in the data rate. This represents a fundamental reduction in the decoding complexity when compared to ML decoding whose complexity is generally exponential in the rate. The results' generality lends them applicable to a plethora of pertinent communication scenarios such as quasi-static MIMO, MIMO-OFDM, ISI, cooperative-relaying, and MIMO-ARQ channels, in all of which the DMT optimality of the LR-aided linear decoder is guaranteed. The adopted approach yields insight, and motivates further study, into joint transceiver designs with an improved SNR gap to ML decoding.

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DMT Optimality of LR-Aided Linear Decoders for a General Class of Channels, Lattice Designs, and System Models

The optimal tradeoff between diversity gain and multiplexing gain for multiple-inputmultiple-output (MIMO) channels has been studied recently under the independent and identically distributed (i.i.d.) Rayleigh-fading assumption. In this correspondence, this result is extended and the optimal tradeoff performance is derived for generalized fading channel conditions, including different fading types, nonidentical fading distributions, spatial correlation, and nonzero channel means. Our results include many known models as special cases and shed light on the effects of different channel parameters on the optimal tradeoff performance

Diversity and Multiplexing Tradeoff in General Fading Channels

In this paper, we analyze the diversity-multiplexing tradeoff (DMT), originally introduced by Zheng and Tse, and outage performance for Rician multiple-input-multiple-output (MIMO) channels. The DMT characteristics of Rayleigh and Rician channels are shown to be identical. In a high signal-to-noise ratio (SNR) regime, the log-log plot of outage probability versus SNR curve for a Rician channel is a shifted version of that for the corresponding Rayleigh channel. The SNR gap between the outage curves of the Rayleigh and Rician channels is derived. The DMT and outage performance are also analyzed for Rician multiple-input-single-output (MISO)/single-input-multiple-output (SIMO) channels over a finite SNR regime. A closed-form expression for the outage probability is derived and the finite SNR DMT characteristic is analyzed. It is observed that the maximum diversity gain can be achieved at some finite SNR-the maximum gain tends to increase linearly with the Rician factor. The finite SNR diversity gain is shown to be a linear function of the finite SNR multiplexing gain. The consistency between the DMTs for finite and infinite SNRs is also shown.

Diversity–Multiplexing Tradeoff and Outage Performance for Rician MIMO Channels

The optimal tradeoff between diversity gain and multiplexing gain for multiple-input multiple-output (MIMO) channels has been studied recently under the independently identically distributed (i.i.d) Rayleigh fading assumption. In this paper, we extend the results and derive the optimal tradeoff performance for a general fading channel setup with generic probability density functions for channel coefficients, which includes many known models as special cases. The effects of non-identical distribution, correlation and non-zero channel means are also treated.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=20071&context=rtd

The effect of spatial correlation on the performance of orthogonal space-time block codes (OSTBCs) over multiple-input-multiple-output (MIMO) Rician fading channels is studied. Asymptotic error-rate formulas for OSTBC with high average signal-to-noise ratios (ASNRs) over arbitrarily correlated Rician MIMO channels are derived in terms of the diversity and coding gains. Our results show that, in correlated fading, the phase vector phi of the channel line-of-sight (LOS) components affects the effective Rice K-factor at the OSTBC receiver output and, hence, may result in a coding gain that is significantly higher than that for independent Rician MIMO channels. Furthermore, when the channel covariance matrix is rank deficient and under some additional mild conditions, the error and outage probabilities of OSTBC achieve those in a nonfading additive-white-Gaussian-noise channel. For both cases of full-rank and rank-deficient channel covariance matrices, analytical expressions of optimal and worst case phase vectors phi, and exact upper and lower bounds of OSTBC performance are derived. These results provide new insights into the achievable performance of OSTBC over correlated Rician MIMO channels and, if incorporated into future multiple antenna systems design, will bring about significant performance enhancement

Achievable Performance of Orthogonal STBC Over Spatially Correlated Rician Channels

In this paper, we incorporate mmWave systems with relay techniques to propose a hybrid transceiver design approach. The existing researches of hybrid transceiver designs mostly rely on accurate channel state information acquisitions. However, it is hard to avoid estimation errors in practice, which motivates us to propose a robust design based on imperfect channel estimations. We first design the fully digital processors and then decompose them into hybrid ones. An alternating algorithm is proposed to solve the fully digital processors by utilizing the relationship between the maximization of the upper bound of the averaged mutual information and the weighted minimum mean squared error problem. A decomposition algorithm with closed-form solutions is also proposed to obtain hybrid processors with analog-digital-analog structure at the relay terminal. Compared with related works, the proposed decomposition algorithm outperforms existing decomposition methods under imperfect CSI condition and the proposed hybrid design sacrifices certain complexity to achieve obvious performance improvements, which are illustrated by numerical simulations. 

Lei Zhao

Papers

Diversity and Multiplexing Tradeoff in General Fading Channels

Diversity and Multiplexing Tradeoff in General Fading Channels

Achievable Performance of Orthogonal STBC Over Spatially Correlated Rician Channels

MmWave relay systems with robust hybrid transceiver designs under correlated channel estimation errors

Dual-spectrum resource allocation for coexisting LTE-advanced and Wi-Fi systems with imperfect channel state information