基于单调优化框架的凸松弛分支定界算法求解非凸多信道联合感知问题

摘要

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.%多信道联合感知问题由于具有非凸性使得求解困难，该文首次尝试用确定性全局优化方法对该问题进行求解。该问题首先被转化为单调优化问题，进而提出一种基于单调优化框架的凸松弛分支定界(BRBCR)算法。仿真实验表明，所提算法较传统的凸优化方法可大幅度提升系统性能，收敛速度较PA(Polyblock Algorithm)以及传统的BRB算法提高了2个数量级，即使信道数目多达16，收敛精度为610-，该文算法16 s内即可收敛。此外，该算法还可为其它算法提供基准，对这些算法性能进行评估。