Conference Paper

New Optimized Solution Method for Beamforming in Cognitive Multicast Transmission

Sch. of Electr. Eng. & Telecommun., Univ. of New South Wales, Sydney, NSW, Australia
DOI: 10.1109/VETECF.2010.5594325 Conference: Vehicular Technology Conference Fall (VTC 2010-Fall), 2010 IEEE 72nd
Source: IEEE Xplore


The optimal beamforming for cognitive multicast transmission is a 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 propose a simple and efficient alternative method, which offers much better solutions. Several numerical simulation examples are provided to illustrate the effectiveness of our method.

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    • "–[11]) is to recast the formulated problems to relaxed semi-definite programs and generate feasible solutions from the pool of possible candidates by means of randomization. While our earlier numerical results in [15] have revealed the numerical inconsistency of such approach, we will discuss the capacity of this conventional method in the following. Let us begin with (1). "
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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.
    Full-text · Article · Jun 2012 · IEEE Transactions on Signal Processing
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    • "[1]) is to relax (4) by dropping only nonconvex rank-one constraint (4d) and then employ randomization to generated feasible solutions from the optimal solution of the relaxed programm. Some analysis on this conventional approach have been made in [5], [6], which particularly show that as far the optimal solution of the relaxed program is not rank-one, such randomization is too narrow and hardly bring the optimal solution of the original rank-one constrained optimization. A novel approach for locating the global optimal solution of (3) is proposed in the next section. "
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    ABSTRACT: The paper is concerned with a multiuser commu- nication network, which is assisted by multiple relays. It has been observed through our previous related works that the conventional simultaneous beamforming at parallel amply-and- forward (AF) relays is not quite effective and often infeasible to target practically desirable signal-to-interference-and-noise ratio (SINR) at the destinations. To overcome this shortage, we propose the time-division for multiple-user transmission to the relays so the later can perform beamforming on signals received from the individuals and then parallelly forward its combinations at once to the destinations. The optimal beamforming problem is a non- convex quadratically constrained optimization, which is globally solved by our tailored algorithm of nonsmooth optimization. Its found global optimal solutions are shown very effective and over- perform other possible multi-user relay beamformings.
    Full-text · Conference Paper · Jan 2011
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    • "This is a modification of the alternating projection approach [7] to directly tackle the original indefinite quadratic program. Nevertheless, our simulation [8] was able not only to show its much better performance than that of the conventional one but particularly revealed that the latter often yields solutions that are very far from the optimal ones. "
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    ABSTRACT: It is well-known that the optimal beamforming problems for cognitive multicast transmission are indefinite quadratic (nonconvex) optimization programs. The conventional approach is to reformulate them as convex semi-definite programs (SDPs) with additional rank-one (nonconvex and discontinuous) constraints. The rank-one constraints are then dropped for relaxed solutions, and randomization techniques are employed for solution search. In many practical cases, this approach fails to deliver satisfactory solutions, i.e., its found solutions are very far from the optimal ones. In contrast, in this paper we cast the optimal beamforming problems as SDPs with the additional reverse convex (but continuous) constraints. An efficient algo-rithm of nonsmooth optimization is then proposed for seeking the optimal solution. Our simulation results show that the proposed approach yields almost global optimal solutions with much less computational load than the mentioned conventional one.
    Preview · Conference Paper · Jan 2010
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