New Optimized Solution Method for Beamforming in Cognitive Multicast Transmission
ABSTRACT The optimal beamforming for cognitive multicast transmission is nonconvex rank-one constrained optimization problem. For a solution, a popular method is the combination of relaxed convex semi-definite programming, where the rank-one constraint is dropped, and randomization. We show that in many cases, this method cannot give satisfactory solutions. As an initial step, we develop a simple alternative method, which gives much better solutions. Our simulation confirms this fact.
Conference Paper: D.C. iterations for SINR maximin multicasting in Cognitive radio[Show abstract] [Hide abstract]
ABSTRACT: The design of transmit beamforming vectors to maximize the threshold of the signal-to-interference-plus-noise ratios (SINR) at the secondary receivers in cognitive multicast transmission is maximin optimization of quadratic fractional functions. There is no efficient solver for this hard maximin program. In the present paper, we show that the program can be effectively represented by a canonical d.c. (difference of convex functions) program of the same size. Accordingly, d.c. iterations are derived to locate its optimized solution. Our thorough numerical examples verify that the proposed algorithms offer almost global optimality whilst requiring relatively low computational load.Signal Processing and Communication Systems (ICSPCS), 2012 6th International Conference on; 01/2012
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ABSTRACT: The cognitive beamforming problems are naturally formulated as indefinite quadratic (nonconvex) optimization programs. The typical methods for solving such optimization problems are to transform them into convex semi-definite programs (SDPs) with additional rank-one (nonconvex and discontinuous) constraints. The rank-one constraints are then dropped to obtain solvable SDP relaxed problems and randomization techniques are employed for seeking the feasible solutions to the original nonconvex optimization problems. In many practical cases, these approaches fail to deliver satisfactory solutions, i.e., their solutions are very far from the optimal ones. In contrast, in this paper the rank-one constraints are equivalently expressed as reverse convex constraints and are incorporated into the optimization problems. Then, we propose an efficient iterative algorithm for solving the nonsmooth reverse convex optimization problems. Our simulations show that our proposed approach yields nearly global optimal solutions with much less computational load as compared to the conventional one.Communications and Electronics (ICCE), 2010 Third International Conference on; 09/2010
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ABSTRACT: It is known that the design of optimal transmit beamforming vectors for cognitive radio multicast transmission can be formulated as indefinite quadratic optimization programs. Given the challenges of such nonconvex problems, the conventional approach in literature is to recast them as convex semidefinite programs (SDPs) together with rank-one constraints. Then, these nonconvex and discontinuous constraints are dropped allowing for the realization of a pool of relaxed candidate solutions, from which various randomization techniques are utilized with the hope to recover the optimal solutions. However, it has been shown that such approach fails to deliver satisfactory outcomes in many practical settings, wherein the determined solutions are found to be unacceptably far from the actual optimality. On the contrary, we in this contribution tackle the aforementioned optimal beamforming problems differently by representing them as SDPs with additional reverse convex (but continuous) constraints. Nonsmooth optimization algorithms are then proposed to locate the optimal solutions of such design problems in an efficient manner. Our thorough numerical examples verify that the proposed algorithms offer almost global optimality whilst requiring relatively low computational load.IEEE Transactions on Signal Processing 01/2012; 60(6):2941-2951. · 2.81 Impact Factor