Frequency-domain equalization for continuous phase modulation
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Continuous phase modulation~(CPM) is a non-linear, constant-envelope modulation scheme with memory, known for its bandwidth and power efficiency. Multi-h CPM uses multiple modulation indices in successive symbol intervals to improve the error performance as compared to single-h CPM~(basic CPM that utilizes only a single modulation index). One of the major applications of multi-h CPM is in aeronautical telemetry systems. Modern aeronautical devices host an increasing number of sensors, which can transmit flight testing data to the ground station. However, this excess data transfer increases the intersymbol interference, and thus channel equalization is required at the receiver. The objective of our research is to propose low-complexity frqeuency-domain equalization~(FDE) techniques for multi-h CPM waveforms. For a modulation scheme with memory, such as CPM, the cyclic constraint on the FDE block necessitates the use of an extra segment of symbols, called intrafix or tail segment. We have used very simple geometric arguments to derive upper and lower bounds on the length of the intrafix in terms of the parameters of the modulation scheme and the Frobenius number. It is concluded that the length of the intrafix for multi-h CPM schemes is typically shorter than those required for single-h modulation schemes. We propose two receiver architectures; one uses a matched filter front end, while the other utilizes a fractional sampling front end. Various simplifications are proposed for each architecture, and the trade-off between receiver complexity and performance is analyzed and verified through detailed simulation studies.