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 non-clustered). 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 is 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 idealistic assumption of full-duplex relays and a clustered network, this virtual multi-input multi-output (MIMO) system can never fully mimic a real MIMO DMT. For cooperative systems with multiple sources and multiple destinations the same limitation remains to be in effect.
When multiple single antenna relays are present, the papers @cite_12 @cite_9 @cite_49 @cite_27 @cite_32 @cite_22 @cite_30 show that diversity gains similar to multi-input single-output ( ) or single-input multi-output ( ) systems are achievable for Rayleigh fading channels. Similarly, @cite_3 @cite_48 @cite_18 @cite_29 upper bound the system behavior by or if all links have Rayleigh fading. In other words, relay systems behave similar to either transmit or receive antenna arrays. is first analyzed in @cite_2 in terms of achievable rates only, where the authors compare a two-source two-destination cooperative system with a @math and show that the former is multiplexing gain limited by 1, whereas the latter has maximum multiplexing gain of 2.
@cite_30 @cite_18 @cite_22 @cite_48 @cite_9 @cite_29 @cite_32 @cite_3 @cite_27 @cite_49 @cite_2 @cite_12
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We consider a dense fading multi-user network with multiple active multi-antenna source-destination pair terminals communicating simultaneously through a large common set of K multi-antenna relay terminals in the full spatial multiplexing mode. We use Shannon-theoretic tools to analyze the tradeoff between energy efficiency and spectral efficiency (known as the power-bandwidth tradeoff) in meaningful asymptotic regimes of signal-to-noise ratio (SNR) and network size. We design linear distributed multi-antenna relay beamforming (LDMRB) schemes that exploit the spatial signature of multi-user interference and characterize their power-bandwidth tradeoff under a system-wide power constraint on source and relay transmissions. The impact of multiple users, multiple relays and multiple antennas on the key performance measures of the high and low SNR regimes is investigated in order to shed new light on the possible reduction in power and bandwidth requirements through the usage of such practical relay cooperation techniques. Our results indicate that point-to-point coded multi-user networks supported by distributed relay beamforming techniques yield enhanced energy efficiency and spectral efficiency, and with appropriate signaling and sufficient antenna degrees of freedom, can achieve asymptotically optimal power-bandwidth tradeoff with the best possible (i.e., as in the cutset bound) energy scaling of K-1 and the best possible spectral efficiency slope at any SNR for large number of relay terminals. Furthermore, our results help to identify the role of interference cancellation capability at the relay terminals on realizing the optimal power- bandwidth tradeoff; and show how relaying schemes that do not attempt to mitigate multi-user interference, despite their optimal capacity scaling performance, could yield a poor power- bandwidth tradeoff. We consider the use of spatial diversity to improve the performance of analog joint source-channel coding in wireless fading channels. The communication system analyzed in this paper consists of discrete-time all-analog-processing joint source-channel coding where Maximum Likelihood (ML) and Minimum Mean Square Error (MMSE) detection are employed. By assuming a fast-fading Rayleigh channel, we show that MMSE performs much better than ML at high Channel Signal-to-Noise Ratios (CSNR) in single-antenna wireless systems. However, such performance gap can be significantly reduced by using multiple receive antennas, thus making low complexity ML decoding very attractive in the case of receive diversity. Moreover, we show that the analog scheme can be considerably robust to imperfect channel estimation. In addition, as an alternative to multiple antennas, we also consider spatial diversity through cooperative communications, and show that the application of the Amplify-and-Forward (AF) protocol with single antenna nodes leads to similar results than when two antennas are available at the receiver and Maximal Ratio Combining (MRC) is applied. Finally, we show that the MMSE implementation of the analog scheme performs very close to the unconstrained capacity of digital schemes using scalar quantization, while its complexity is much lower than that of capacity-approaching digital systems. We study the capacity of multiple-input multiple- output (MIMO) relay channels. We first consider the Gaussian MIMO relay channel with fixed channel conditions, and derive upper bounds and lower bounds that can be obtained numerically by convex programming. We present algorithms to compute the bounds. Next, we generalize the study to the Rayleigh fading case. We find an upper bound and a lower bound on the ergodic capacity. It is somewhat surprising that the upper bound can meet the lower bound under certain regularity conditions (not necessarily degradedness), and therefore the capacity can be characterized exactly; previously this has been proven only for the degraded Gaussian relay channel. We investigate sufficient conditions for achieving the ergodic capacity; and in particular, for the case where all nodes have the same number of antennas, the capacity can be achieved under certain signal-to-noise ratio (SNR) conditions. Numerical results are also provided to illustrate the bounds on the ergodic capacity of the MIMO relay channel over Rayleigh fading. Finally, we present a potential application of the MIMO relay channel for cooperative communications in ad hoc networks. This paper extends Khatri (1964, 1969) distribution of the largest eigenvalue of central complex Wishart matrices to the noncentral case. It then applies the resulting new statistical results to obtain closed-form expressions for the outage probability of multiple-input-multiple-output (MIMO) systems employing maximal ratio combining (known also as "beamforming" systems) and operating over Rician-fading channels. When applicable these expressions are compared with special cases previously reported in the literature dealing with the performance of (1) MIMO systems over Rayleigh-fading channels and (2) single-input-multiple-output (SIMO) systems over Rician-fading channels. As a double check these analytical results are validated by Monte Carlo simulations and as an illustration of the mathematical formalism some numerical examples for particular cases of interest are plotted and discussed. These results show that, given a fixed number of total antenna elements and under the same scattering condition (1) SIMO systems are equivalent to multiple-input-single-output systems and (2) it is preferable to distribute the number of antenna elements evenly between the transmitter and the receiver for a minimum outage probability performance.