This paper considers the so-called partial decode-and-forward (DF) strategy for the Gaussian multiple-input multiple-output (MIMO) relay channel. Unlike for the DF strategy or point-to-point (P2P) transmission from source to destination, for which Gaussian channel inputs are known to maximize the achievable rates, the input distribution that attains the maximum achievable partial DF rate for the Gaussian MIMO relay channel has remained unknown so far. For some special cases, e.g., for relay channels where the partial DF strategy reduces to the DF or P2P transmission, it could be deduced that Gaussian inputs maximize the rate that can be achieved with the partial DF strategy. For the general case, however, the problem has remained open until now. In this paper, we solve this problem by proving that the maximum achievable partial DF rate for the Gaussian MIMO relay channel is always attained by Gaussian channel inputs. Our proof relies on the channel enhancement technique, which was originally introduced by Weingarten et al. to derive the (private message) capacity region of the Gaussian MIMO broadcast channel. By combining this technique with a primal decomposition approach, we first establish that jointly Gaussian source and relay inputs maximize the achievable partial DF rate for the aligned Gaussian MIMO relay channel. Subsequently, we use a limiting argument to extend this result from the aligned to the general Gaussian MIMO relay channel.

In this paper, we consider achievable rates for the Gaussian multiple-input multiple-output (MIMO) relay channel that can be obtained with the relay using the partial decode-and-forward scheme. The partial decode-and-forward strategy allows to optimize the amount of information the relay has to decode and can hence be seen as a generalization of the decode-and-forward strategy, where the relay must decode the entire source message. Since we cannot determine the maximal achievable partial decode-and-forward rate, we propose a suboptimal approach that is based on zero-forcing the interference the relay would suffer from the part of the source signal that it is not required to decode. For this purpose, a zero-forcing receive filter is introduced at the relay. We then show that, if the receive filter is fixed, standard convex optimization techniques can be used to evaluate the best rate our suboptimal partial decode-and-forward scheme can achieve. Simulation results demonstrate that the coding scheme we propose significantly outperforms the decode-and-forward scheme and/or approximates the cut-set bound for different network scenarios.

This paper addresses utility maximization problems in the half-duplex two-way multiple-input multiple-output (MIMO) relay channel, where the relay uses the decode-and-forward strategy. Perfect channel information at all nodes and a time division duplex communication protocol with per node peak power constraints for every protocol phase are assumed. For this scenario, we show how solutions to the considered class of problems can efficiently be determined by means of a dual decomposition approach.

We consider uni- and bidirectional communication in the half-duplex multiple-input multiple-output (MIMO) relay channel. Assuming perfect channel state information at all nodes and the use of time division duplex communication protocols with a peak power constraint for every protocol phase, we propose a dual decomposition approach to efficiently determine the cut-set bound and the maximum achievable decode-and-forward rate for the Gaussian MIMO relay channel. A general outer bound on the rate regions that can be achieved in the restricted two-way MIMO relay channel is established, and we present an achievable rate region based on the decode-and-forward scheme which is a superset of several previously derived achievable rate regions. Finally, it is shown how the stated outer bound and achievable rate region can also be evaluated by means of the proposed dual decomposition approach, and we discuss how our work may be used for designing optimal protocols.

This paper addresses the optimization of upper and lower bounds on the capacity of the multiple-input multiple-output (MIMO) relay channel. In particular, we show that evaluating the cut-set bound and the maximal achievable decode-and-forward rate is equivalent to solving convex optimization problems, where we assume that perfect channel state information is available at all nodes. Our optimized bounds thus improve on previously published results while they can be efficiently determined using convex programming techniques at the same time.

We study the minimum cut between one source and one terminal in a dynamically changing random wireless ad hoc network that is modeled as a random geometric graph. The nature of ad hoc networks is accounted for by letting nodes join and leave. Given the values of all cuts that can be formed in the original network and assuming information about the nodes that join or leave, expressions for the expected value and variance of any particular cut that may arise are derived. However, it is not possible to obtain a closed form expression for the minimum expected cut value in our framework. Nevertheless, we give a simple and reasonable upper bound for the minimum expected cut value which is also extendable to multicast transmissions.