Jointly Optimal Source Power Control and Relay Matrix Design in Multipoint-to-Multipoint Cooperative Communication Networks

A cooperative communication network is considered wherein
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sources aim to transmit to their designated destinations through the use of a multiple-antenna relay. All sources transmit to the relay in a shared channel in the first transmission phase. Then, the relay linearly processes its received signal vector using
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relaying matrices and retransmits the resultant signals towards the destinations in dedicated channels in the second transmission phase. The goal is to jointly optimize the sources' transmit powers and the relaying matrices such that the worst normalized signal-to-interference-plus-noise ratio (SINR) among all
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destinations is maximized while the relays' transmit powers in the dedicated channels as well as the sources' individual and total transmit powers do not exceed predetermined thresholds. It is shown that the jointly optimal sources' transmit powers and the relaying matrices are the solutions to an optimization problem with a nonconvex objective function and multiple nonconvex constraints. To solve this problem, it is first proved that all normalized SINRs are equal at the optimal point of the objective function. Then, the optimization problem is transformed through multiple stages into an equivalent problem that is amenable to an iterative solution. Finally, an efficient iterative algorithm is developed that offers the jointly optimal sources' transmit powers and the relaying matrices. An extension to the above problem is then studied in the case when the cooperative communication network acts as a cognitive system that is expected to operate such that its interfering effect on the primary users is below some admissibility thresholds. In such a case, the sources' and relay's transmit powers should further satisfy some additional constraints that compel a new technique to tackle the problem of the joint optimization of the sources' transmit powers and the relaying matrices. An iterative solution to the latter problem is also proposed and the efficiency and the high rate of convergence of the proposed iterative algorithms in both the original and the cognitive cases are verified by simulation examples.