Multiple-Bit Differential Detection of Shaped-Offset QPSK

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 interpretation of SOQPSK. We show that the performance of these MBDD schemes approaches that of coherent detection (CD) as the multiple-bit observation N window increases. The first scheme uses a detection window that spans the full-bit observation window (F-MBDD), and is shown to require very large values of N to approach the performance of CD. 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. Although the complexity of I-MBDD also increases exponentially with N, it represents a significant improvement since only modest values of N are needed for high performance. These performance characteristics are identified via a detailed performance analysis, which provides asymptotic formulas for the bit error probability that are confirmed with computer simulations. The analysis is also used to find the symmetric frequency pulse shapes with the best and worst error performance. Finally, we develop a simplified and practical decision feedback differential detection algorithm that achieves near-optimal performance with complexity that grows only linearly with N.