A belief propagation-based framework for soft multiple-symbol differential detection

Abstract

Soft noncoherent detection, which relies on calculating the a posteriori probabilities (APPs) of the bits transmitted with no channel estimation, is imperative for achieving excellent detection performance in high-dimensional wireless communications. In this paper, a high-performance belief propagation (BP) based soft multiple-symbol differential detection (MSDD) framework, dubbed BP-MSDD, is proposed with its illustrative application in the differential space-time block-code (DSTBC) aided ultra-wideband impulse radio (UWB-IR) systems. Firstly, we revisit the signal sampling with the aid of a trellis structure and decompose the trellis into multiple subtrellises. Furthermore, we derive an APP calculation approach, in which the forward-and-backward message passing mechanism of BP operates on the subtrellises. The proposed BP-MSDD is capable of significantly outperforming the conventional hard-decision MSDDs. However, the computational complexity of the BP-MSDD increases exponentially with the number of MSDD trellis states. To circumvent this excessive complexity for practical implementations, we reformulate the BP-MSDD, and additionally propose a Viterbi algorithm (VA) based hard-decision MSDD (VA-HMSDD) and a VA based soft-decision MSDD (VA-SMSDD). Moreover, both the proposed BP-MSDD and VA-SMSDD can be exploited in conjunction with soft channel decoding to obtain powerful iterative detection and decoding based receivers. Simulation results demonstrate the effectiveness of the proposed approaches in the DSTBC aided UWB-IR systems.

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