A modified dispersed frequency and phase consensus algorithm based on differential evolution and credibility weighting matrix

In distributed antenna array systems, accurate synchronization of the frequency and phase of the transmission signals among subarrays is a premise for beamforming. To solve this problem, a modified dispersed frequency and phase consensus (MDFPC) algorithm, which is based on differential evolution (DE) and the credibility weighting matrix, is proposed in this paper. DE algorithm is adopted to optimize the mixing matrix of MDFPC algorithm, and the convergence speed of consensus algorithm can be improved. Moreover, Lanczos method is adopted to calculate the fitness of individuals during optimization, thus the computation amount of the eigenvalue decomposition of the large-scale, sparse and symmetric mixing matrix can be effectively reduced. In addition, the influence of the transmission distance between subarrays on the received Signal-to-Noise Ratio (SNR) is considered, and the credibility weighting matrix can be obtained. Then the contribution of low-credible frequency and phase messages to the iterative updated values can be decreased by the credibility weighting matrix, thus more accurate frequency and phase updated values can be obtained in each iteration. It is shown from simulation results that the proposed algorithm can further reduce the phase synchronization error by at least 8% and achieve at least 18% convergence speed improvement compared to dispersed frequency and phase consensus (DFPC) algorithm.