This article considers regularized Weighted Decision Feedback Differential Coherent (WDFDC) receivers for selective Detect-and-Forward multi-relaying systems, operating over fast fading channels. Non-regularized WDFDC receivers have been employed in such One-Way Relay Network (OWRN) with DQPSK modulation, and shown to provide significant performance gains over Conventional Differential Detection (CDD). This paper demonstrates, however, that such non-regularized WDFDC receivers are plagued by a

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... ER increase phenomenon in the high SNR range due to decision feedback error propagation and intermittent transmissions from relays. Because of this effect, the non-regularized WDFDC receivers are unable to provide very low error rates, making them unsuitable for ultra-reliable communication systems. To address this problem, our paper introduces a novel WDFDC receiver based on a regularized linear predictor (RLP) for relay to destination channels. We show that such regularized WDFDC receivers yield significant performance gains over their non-regularized counterparts in the high SNR range, without noticeable degradation at low SNR. Regularized WDFDC receivers on relay to destination links enable OWRN systems to provide very low error rates, making them suitable for ultra-reliable communication over fast fading channels.