One-Bit Direct Localization in Wireless Sensor Networks Over Rayleigh Fading Channels

Classic direct localization techniques have been shown to offer better localization performance and robustness in low signal-to-noise ratio (SNR) conditions. However, they require the transmission of complete baseband signals to the fusion center (FC), resulting in significant data transmission and storage burdens. To address the high data communication load in direct localization within wireless sensor networks, we propose a one-bit direct localization method. In particular, we account for the potential realistic channel effects between sensors and the FC, modeling them as Rayleigh fading channels incorporated into the position inference process. Subsequently, at the FC, we propose two one-bit direct localization methods corresponding to coherent and noncoherent reception decoding strategies. Since the localization process involves non-convex optimization of high-dimensional coupled parameters, we present an efficient solution based on the Majorization-Minimization (MM) method, which transforms the position estimation problem into a low-dimensional iterative search. We derive the Cramér-Rao lower bound (CRLB) for the proposed methods under both decoding strategies and provide a quantizer design aimed at optimizing the system's localization performance. Due to the fading channel's impact, the constructed quantization threshold optimization problem is a combination of highly nonlinear and non-convex functions, making it difficult to solve directly. We further provide a computationally feasible solution based on the modified Barzilai-Borwein-based gradient descent (MBB-GD) method, which is a polynomial time algorithm. Numerical simulations validate the effectiveness of the proposed method in reducing the network communication load, mitigating the impact of fading channels, and ensuring the localization performance.