A joint optimization algorithm using adaptive minimum coset number based discrete multi-coset sampling

Abstract

We address the problem of sparse multi-band signal reconstruction in the case of unknown band position through the discrete multi-coset sampling (DMCS). In this article, the signal has complex frequency components, and the minimum coset number is determined on the assumption that there is only one frequency component with same characteristics. According to the frequency characteristics, we analyze the influence of the parameterized compressed matrix on the two reconstruction algorithms, and get that a single algorithm does not have universal adaptability to different frequency components. In order to solve this problem, under the discrete multi-coset sampling model, a joint optimization algorithm with discriminant factor (DF-JOA) is proposed to identify the different characteristics and automatically select an appropriate algorithm for signal reconstruction, numerical simulation experiments show the effectiveness of the algorithm. We also simulate the reconstruction success ratio of amplitude and the total coset number under different compressed matrices, determine the influence law, and confirm the improvement of signal reconstruction probability by joint optimization algorithm. Our method ensures the spectrum reconstruction of the multi-band signal. This article can guide how to better select the coset parameters under the condition that the channels of the discrete multi-coset sampling system are limited but the minimum coset number can be guaranteed. It will have a great significance to the sub-Nyquist sampling technique.