A Distributed 1-bit Compressed Sensing Algorithm for Nonlinear Sensors With a Cramer–Rao Bound

Abstract

A distributed 1-bit compressed sensing (CS) algorithm in a wireless sensor network with nonlinear sensors is proposed. In the context of 1-bit CS, the diffusion cooperation scheme is used with distributed implementation. Toward that end, a traditional steepest-descent solution is considered to minimize the appropriate global and local convex cost functions. Hence, a common parameter vector is optimally and cooperatively estimated solely from the sign of nonlinear measurements. A diffusion cooperation scheme is suggested for distributive learning of the vector in two scenarios. The first is the non-blind case, where the nonlinearity is known in advance. The second is the blind case, where the nonlinearity of sensors are unknown in advance. In addition, for the linear case, a Cramer-Rao bound for distributed 1-bit CS is derived and compared with the experimental results. Considering the nonlinear case, the proposed algorithm for the non-blind and blind cases is compared with the linear case. Simulation results show the efficacy of the proposed distributed algorithm and its robustness against nonlinearity of the sensors.