Study on performance behavior of compressive sensing measurements for multiple sensor system

In this paper, we will analyze the performance limit for a multiple sensor system (MSS) based on compressive sensing. In our MSS, all of the sensors measure signals from a common source. There exists the redundancy in the measured signal because the measured signal comes from the common source. To reduce communication costs, this redundancy must be removed. For this purpose, we use compressive sensing at each sensor to obtain compressed measurements. After all of the sensors obtain compressed measurements, they transmit them to a central unit. A decoder at the central unit receives all of the transmitted signals and attempts to jointly estimate the correct support set, which is the set of indices corresponding to the locations of the non-zero coefficients of the measured signals. In order to analyze our MSS, we present a jointly typical decoder inspired by recent work [4]. We first obtain the upper bound probability that the jointly typical decoder fails to estimate the correct support set. Next, we prove that as the number of sensors increases, the compressed measurements per sensor (per-sensor measurements) can be reduced to sparsity, which is the number of non-zero coefficients in the measured signal. We present the sufficient number of sensors required with the increase in the noise variance.