Enhanced multiple-bit differential detection of DOQPSK

In this paper, we consider multiple-bit differential detection (MBDD) of differential offset quadrature phase-shift keying (DOQPSK) with conventional bit-wise differential encoding (DE). We propose 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 first scheme uses the full available detection window spanning N-1 bit intervals, and is referred to as F-MBDD. A careful bit-error rate (BER) analysis shows that a significant performance improvement can be realized by reducing the detection window size to N-3 bit intervals. The resulting improved MBDD (I-MBDD) of DOQPSK with bit-wise DE achieves a similar performance as Phoel's MBDD of DOQPSK with more complex symbol-wise DE. For both F-MBDD and I-MBDD, tight upper bounds and accurate BER approximations are derived. In addition, since the complexity per bit decision of brute-force decoding of MBDD of DOQPSK grows exponentially with N, we develop optimum and suboptimum fast decoding algorithms with complexities per bit decision of orders log(N+1) and N, respectively.