Power Allocation for Distributed Compressive Sensing with 1-Bit Quantization over Noisy Channels

Cost-efficient implementation with a low-complexity analog-to-digital converter is necessary for the sensor nodes in the internet of things. In the paper, we study the distributed compressive sensing (DCS) under the constraint of 1-bit quantization at each node. The entire transmission chain, composed of compressive sensing, 1-bit quantization, and joint source-channel coding (JSCC), is taken into consideration with joint signal reconstruction at the fusion center. A lower bound on the end-to-end mean square error distortion, which is a function of the measurement rate, distortion of 1-bit quantization, and that of JSCC, is derived under the assumption of the oracle reconstruction. The time-varying channel conditions have a major impact on the distortion of JSCC. Therefore, a suboptimal yet efficient power allocation scheme based on the successive convex approximation method is proposed to minimize the lower bound on the end-to-end distortion. Moreover, a practical coding and joint signal reconstruction scheme is provided to show its consistence with the derived theoretical limits.