Compressive blind source recovery with Random Demodulation

Distributed Compressive Sensing (DCS) theory effectively reduces the number of measurements of each signal, by exploiting both intra- and inter-signal correlation structures, which saves on the costs of sampling devices as well as of communication and data processing. In many fields, only the mixtures of source signals are available for compressive sampling, without prior information on both the source signals and the mixing process. However, people are still interested in the source signal rather than the mixing signals. There is a basic solution which reconstructs the mixing signals from the compressive measurements first and then separates the source signals by estimating mixing matrix. However, the reconstruction process takes considerable time and also introduces error into the estimation step. A novel method is proposed in this paper, which directly separates the mixing compressive measurements by estimating the mixing matrix first and then reconstruct the interesting source signals. At the same time, in most situations, the source signals are analog signals. In this paper, Random Demodulation (RD) system is introduced to compressively sample the analog signal. We also verify the independence and non-Gaussian property of the compressive measurement. The experimental results proves that the proposed method is feasible and compared to the basic method, the estimation accuracy is improved.