Optimization of Non-convex Multiband Joint Detection Using Branch Reduce and Bound Algorithm with Convex Relaxation

In Multiband Joint Detection (MJD) of wideband sensing, the most challenge is to set the optimal decision thresholds due to the non-convex nature of the problem. This paper proposes the Branch Reduce and Bound algorithm with Convex Relaxation (BRBCR) technique to optimize the problem which can be transformed into a Monotonic Optimization Problem (MOP). The performance of the proposed method is analyzed through computer simulations. Experiment results show that this method can significantly improve the system performance as compared with the conventional convex optimization method. The convergence speed of the proposed method is two orders of magnitude faster than the Polyblock Algorithm (PA) or the conventional Branch Reduce and Bound (BRB) algorithm. Even though the number of channels is 16 and the convergence precision is 10-6, this method can converge within 16 s. In addition, the proposed algorithm can also provide an important benchmark for evaluating the performance of other heuristic algorithms targeting with the same problem.