Shaped-Offset QPSK with Multiple-Bit Differential Detection

We consider multiple-bit differential detection (MBDD) of differentially encoded shaped-offset quadrature phase-shift keying (SOQPSK), a highly bandwidth-efficient and popular constant-envelope modulation. We propose two MBDD schemes that are based on a recent continuous phase modulation (CPM) interpretation of SOQPSK. We show that the performance of these MBDD schemes approaches that of coherent detection as the multiple-bit observation window N increases. The first scheme uses a detection window that spans the full N-bit observation window (F-MBDD) and is shown to require very large values of N to approach the performance of coherent detection. This presents a practical problem since the complexity of MBDD grows exponentially with N. The second scheme is an improved version (I-MBDD) with a detection window that is shortened to N - 2 bit intervals and requires more modest values of N for high performance. These performance characteristics are identified via a detailed performance analysis, which provides asymptotic formulas for the probability of bit error that are confirmed with computer simulations.