A Special Class of Fractional QCQP and Its Applications on Cognitive Collaborative Beamforming

In this paper, we investigate a special class of the fractional quadratically constrained quadratic problem (QCQP) with more than two quadratic constraints. We propose to effectively solve this special fractional QCQP by one or two convex semidefinite programmings (SDPs). For the two SDPs, one is equivalent to the original fractional QCQP with rank-one relaxation from the Charnes-Cooper transformation and the other, exploiting the optimal value of the former SDP, always has rank-one solution, which is optimal to the former SDP. Theoretical analysis shows that our proposed non-iterative SDP-based algorithm achieves the global optimal solution to the special fractional QCQP. In specific scenarios, our proposed non-iterative SDP-based algorithm has lower computational complexity compared to the second-order cone programming (SOCP)-based and constrained concave convex procedure (CCCP)-based iterative algorithms. We apply the proposed non-iterative SDP-based algorithm on two collaborative beamforming problems in cognitive relay networks, specifically, one is the achievable rate region for two-way non-regenerative cognitive relay networks and the other is the achievable secrecy rate for one-way regenerative cognitive relay networks. Simulation results have shown that our proposed non-iterative SDP-based algorithm achieves the same performance as the SOCP-based iterative algorithm. Our proposed algorithm achieves the better performance than the CCCP-based iterative algorithm.