Cognitive Beamforming for Multiple Secondary Data Streams With Individual SNR Constraints

TL;DR

This paper develops cognitive beamforming techniques for multiple secondary data streams with individual SNR constraints, optimizing power usage while respecting primary user interference limits.

Contribution

It introduces a novel optimization framework on the Stiefel manifold for cognitive beamforming with individual SNR constraints, providing closed-form and duality-based solutions.

Findings

Closed-form solution for zero forcing beamforming

Strong duality holds for nonzero forcing beamforming

Numerical results demonstrate effective power minimization

Abstract

In this paper, we consider cognitive beamforming for multiple secondary data streams subject to individual signal-to-noise ratio (SNR) requirements for each secondary data stream. In such a cognitive radio system, the secondary user is permitted to use the spectrum allocated to the primary user as long as the caused interference at the primary receiver is tolerable. With both secondary SNR constraint and primary interference power constraint, we aim to minimize the secondary transmit power consumption. By exploiting the individual SNR requirements, we formulate this cognitive beamforming problem as an optimization problem on the Stiefel manifold. Both zero forcing beamforming (ZFB) and nonzero forcing beamforming (NFB) are considered. For the ZFB case, we derive a closed form beamforming solution. For the NFB case, we prove that the strong duality holds for the nonconvex primal problem and thus the optimal solution can be easily obtained by solving the dual problem. Finally, numerical results are presented to illustrate the performance of the proposed cognitive beamforming solutions.