On trellis coded continuous phase frequency shift keying

Abstract

<p>This thesis reports my research work in the area of trellis coded continuous phase frequency shift keying (CPFSK). Previous approaches [1, 2, 3, 4, 5] applied binary convolutional codes to CPFSK to achieve power and bandwidth efficiency. However, the work in [6] and part of this thesis show that no single approach among previous approaches can be outperformed by the others if only binary convolutional codes are considered.</p> <p>A new coding scheme based on cnovolutional codes on the ring of integers modulo-P is shown to be a natural way to apply trellis coding to CPFSK [7]. Recent work has decomposed CPFSK into two parts; a linear encoder with memory, called the continuous phase encoder (CPE), and a memoryless modulator (MM), where the CPE often has a code structure defined over the ring of integers modulo-P. The combination of modulo-P convolutional channel encoder (CE) and the CPE, is a linear modulo-P encoder. Design examples are given for rate 1/2 coded quaternary CPFSK with modulation indices 1/2 and 1/4, and rate-2/3 coded octal CPFSK with modulation index 1/8. Combinations are optimized in the normalized minimum Euclidean distance sense for a given total number of states in the overall maximum likelihood sequence estimation (MLSE) receiver. Numerical results show that this new coding scheme consistently achieves better performance than previous schemes. [1, 2, 3, 4, 5].</p> <p>An upper bound on the bit error probability (BER) for ring convolutionally encoded CPFSK is derived. The bound shows that feedback-free CPFSK usually has a smaller error coefficient than CPFSK. The minimum Eucildean distance is a good parameter for estimating performance, and the ring convolutionally encoded CPFSK has a good BER for both moderate and practical signal to noise ratio.</p>