Parameter Determination in Basis Pursuit Denoising via Stein’s Unbiased Risk Estimate for Underwater Acoustic Communication With Orthogonal Signal Division Multiplexing

This paper proposes a novel method for determining parameters in underwater acoustic (UWA) communication using orthogonal signal division multiplexing (OSDM) combined with basis pursuit denoising (BPDN). Recent studies revealed that BPDN can improve channel estimation accuracy and communication quality in OSDM by deriving the channel impulse response from the received signal along with the regularization parameter value. The existing method determines the regularization parameter value through a linear relationship between the noise standard deviation and the optimal parameter value. This linear relationship is tuned by a UWA communication simulation based on the Monte Carlo method, which entails a high computational cost. To avoid the linear tuning procedure, ideally, the regularization parameter should be determined by minimizing the channel estimation error. However, given that the original channel impulse response is unknown for both the transmitter and receiver, we are unable to compute the actual estimation error. Therefore, we introduce the parameter determination method rooted in Stein’s unbiased risk estimate and propose a novel approximate soft thresholding function for computing an unbiased estimate of the channel estimation error. Our simulation results revealed that the unbiased estimate calculated using the proposed method could approximate the channel estimation error even in circumstances where the original channel impulse response is unknown. In addition, our sea trial demonstrated that the proposed parameter determination method achieved almost the same demodulation performance as the existing system.