Multiple Bit Differential Detection of SOQPSK with Diversity Reception

In this paper, we consider multiple bit differential detection (MBDD) of differentially encoded shapedoffset quadrature phase-shift keying (SOQPSK) over slow fading channels, especially Rayleigh fading channels. SOQPSK is a highly bandwidth efficient and popular form of constant envelope continuous phase modulation (CPM). We present two versions of the MBDD algorithm: the full-size version (FMBDD) which uses a detection window that spans the entire N -bit observation window, and an improved version (I-MBDD) which maintains the original N -bit observation window but detects only N − 2 bits within the window. The complexity of both algorithms is shown to increase linearly with the order of diversity reception, L, and exponentially with the size of the observation window, N ; the I-MBDD achieves the best performance for given values of L and N . As expected, the performance in the case of diversity reception shows a marked improvement over the single channel case. INTRODUCTION SOQPSK is a highly bandwidth efficient modulation scheme which is able to achieve higher bandwidth efficiency compared to other modulation schemes as it involves continuous phase transitions (shaped) rather than instantaneous phase shifts. It is similar to offset QPSK (OQPSK) in that data transmission on in phase and quadrature channels can be viewed as being delayed by half a symbol time relative to each other. In this paper we concentrate on “MIL-STD” SOQPSK, which is the most popular form of SOQPSK and is incorporated in military satellite communication standards [1], although our approach is general and can be applied to other versions of SOQPSK, e.g. [2]. We focus on the problem of multiple-bit differential detection of differentially encoded SOQPSK over fading channels. This type of detection was considered recently in [3] for additive white Gaussian noise (AWGN) channels, but has yet to receive any attention for more realistic wireless fading channels. Due to the relationship between this problem and others, our approach is similar to [3] (MBDD of SOQPSK over AWGN channels) and [4] (multi-symbol differential detection of linear phase modulations over fading channels). As with these previous results, we show that performance improves significantly as the length of the multiple-bit observation interval, N , increases. We also show that the performance is greatly improved as the number of receive channels, L, increases. The primary contribution of this paper is to develop these MBDD diversity detection schemes and quantify their performance. The algorithms are based on a recent continuous phase modulation (CPM) based receiver model for SOQPSK [5]. Using the CPM-based approach, we develop two versions of the basic MBDD algorithm.