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.
relay channels are studied in terms of ergodic capacity in @cite_47 and in terms of in @cite_17 . The latter considers the protocol only, presents a lower bound on the performance and designs space-time block codes. This lower bound is not tight in general and is valid only if the number of relay antennas is less than or equal to the number of source antennas.
@cite_47 @cite_17
2106801259 2114973618 2152137554 1970578484
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. In this paper, we consider a three-terminal state-dependent relay channel (RC) with the channel state noncausally available at only the relay. Such a model may be useful for designing cooperative wireless networks with some terminals equipped with cognition capabilities, i.e., the relay in our setup. In the discrete memoryless (DM) case, we establish lower and upper bounds on channel capacity. The lower bound is obtained by a coding scheme at the relay that uses a combination of codeword splitting, Gel'fand-Pinsker binning, and decode-and-forward (DF) relaying. The upper bound improves upon that obtained by assuming that the channel state is available at the source, the relay, and the destination. For the Gaussian case, we also derive lower and upper bounds on the capacity. The lower bound is obtained by a coding scheme at the relay that uses a combination of codeword splitting, generalized dirty paper coding (DPC), and DF relaying; the upper bound is also better than that obtained by assuming that the channel state is available at the source, the relay, and the destination. In the case of degraded Gaussian channels, the lower bound meets with the upper bound for some special cases, and, so, the capacity is obtained for these cases. Furthermore, in the Gaussian case, we also extend the results to the case in which the relay operates in a half-duplex mode. In this paper, we consider a discrete memoryless state-dependent relay channel with non-causal Channel State Information (CSI). We investigate three different cases in which perfect channel states can be known non-causally: i) only to the source, ii) only to the relay or iii) both to the source and to the relay node. For these three cases we establish lower bounds on the channel capacity (achievable rates) based on using Gel'fand-Pinsker coding at the nodes where the CSI is available and using Compress-and-Forward (CF) strategy at the relay. Furthermore, for the general Gaussian relay channel with additive independent and identically distributed (i.i.d) states and noise, we obtain lower bounds on the capacity for the cases in which CSI is available at the source or at the relay. We also compare our derived bounds with the previously obtained results which were based on Decode-and-Forward (DF) strategy, and we show the cases in which our derived lower bounds outperform DF based bounds, and can achieve the rates close to the upper bound. We consider the problem of secure transmission in two-hop amplify-and-forward untrusted relay networks. We analyze the ergodic secrecy capacity (ESC) and present compact expressions for the ESC in the high signal-to-noise ratio regime. We also examine the impact of large scale antenna arrays at either the source or the destination. For large antenna arrays at the source, we confirm that the ESC is solely determined by the channel between the relay and the destination. For very large antenna arrays at the destination, we confirm that the ESC is solely determined by the channel between the source and the relay.