Joint Optimization of Cooperative Beamforming and Relay Assignment in Multi-User Wireless Relay Networks

Abstract

This paper considers joint optimization of cooperative beamforming and relay assignment for multi-user multirelay wireless networks to maximize the minimum of the received signal-to-interference-plus-noise ratios (SINR). Separated continuous optimization of beamforming and binary optimization of relay assignment already pose very challenging programs. Certainly, their joint optimization, which involves nonconvex objectives and coupled constraints in continuous and binary variables, is among the most challenging optimization problems. Even the conventional relaxation of binary constraints by continuous box constraints is still computationally intractable because the relaxed program is still highly nonconvex. However, it is shown in this paper that the joint programs fit well in the d.c (difference of two convex functions/sets) optimization framework. Efficient optimization algorithms are then developed for both cases of orthogonal and nonorthogonal transmission by multiple users. Simulation results show that the jointly optimized beamforming and relay assignment not only save transmission bandwidth but can also maintain well the network SINRs. Index Terms-Cooperativebeamforming, power allocation, relay selection, relay assignment, wireless relay networks, d.c. programming. 1536-1276 (c) , IEEE Transactions on Wireless Communications 2 straints. Although these d.c. programs are still very hard, they motivate exploring hidden convex structures of the problem at hand in order to obtain the constructive solutions [36], [37]. It has been recognized for a long time [36] that the d.c. structure of binary constraints has yet to be explored as the binary constraints seem to be more suitable in a d.m. (difference of two monotonic functions/sets) setting [38], [39]. Moreover, different from a binary quadratic problem [40], which has been successfully solved by d.c. optimization, the constructive d.c.representations of the mixed-binary programs considered in the present paper are not available. Through elegant variable changes and effective approximations, our contribution is to reformulate these problems as tractable d.c. programs, which become solvable by d.c. iterations of polynomial complexity and also re-optimization processes. Simulation results show that the proposed computational procedures are capable of locating approximation solutions that are very close to the global optimal solutions. This is evidenced by the fact that the approximation solutions achieve SINR performances that are very close to their upper bounds.The paper is structured as follows. Section II provides a fundamental background on a class of mixed binary optimization and d.c. programming for finding its solution. Its application to the joint program of beamforming and relay assignment for the case of orthogonal transmission of the users is presented in Section III. Section IV is devoted to the problem of jointly optimized beamforming and relay assignment in nonorthogonal transmission of the users. Simulations are presented in Section V. Section VI ...

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