Multiple-bit differential detection of DOQPSK - revisited

In this paper, we revisit multiple-bit differential detection (MBDD) of differential offset quadrature phase-shift keying (DOQPSK) with conventional bit-wise differential encoding (DE). We introduce two novel MBDD schemes that outperform Simon´s MBDD and approach the performance of coherent detection (CD) as the observation window size N increases. The proposed full-size (F-MBDD) and improved (I-MBDD) MBDD schemes use the full available (N - 1 bit intervals) and a reduced (N - 3 bit intervals) detection window, respectively. For both MBDD schemes accurate BER approximations are derived. Our results show that I-MBDD of DOQPSK with bit-wise DE achieves a performance similar to that of Phoel´s MBDD of DOQPSK with more complex symbol-wise DE. Since the complexity per bit decision of brute force decoding of MBDD of DOQPSK grows exponentially with N, we develop a fast decoding algorithm with a complexity per bit decision of order log(N + 1).