## Decoding algorithms for continuous phase modulation

Master Thesis

2002

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University of Cape Town

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Continuous Phase Modulation (CPM) possesses characteristics that make it very attractive for many applications. Efficient non-linear power amplifiers can be used in the transmitters of constant envelope CPM schemes. CPM also allows for the use of simple limiters in the demodulator rather than linear receivers with gain control. These characteristics not only increases the life of the power source, but it improves circuit reliability since less heat is generated. In some applications, such as satellite transmitters, where power and circuit failure is very expensive, CPM is the most attractive choice. Bandwidth efficiency, also, is very attractive, and improves as the order of the scheme increases (together with reduction in modulation index). Still further improvement is obtained through pulse shaping which normally result in partial response schemes as opposed to full-response (CPFSK) schemes. The inherent memory or coding gain of CPM increases the minimum distance, which is a figure of merit for a scheme's error performance. The length of the inherent memory is the constraint length of the scheme. Successful extraction of this inherent memory result in improved power efficiency. By periodic variation of the modulation index as in multi-h CPFSK, a sub class of CPM, coding gain or inherent memory can be significantly improved. CPM demodulation is also less sensitive to fading channels than some other comparable systems. Well-known schemes such as GSM digital mobile systems, DECT and Iridium all use some form of CPM to transport their information. These implementations are normally pulse-shaped FSK or MSK and are used for the reasons above, except that their receivers do not always exploit the inherent memory. Unfortunately, though, when one wants to exploit the inherent memory of higher level CPM schemes, all these attractive characteristics are offset by the complexity of the receiver structures which increases exponentially in complexity as the order or constraint length is increased. Optimum receivers for binary CPFSK were first described by Osborne and Luntz [19] in 1974 and their research was later extended by Schonhoff [26] to include M-ary CPFSK. These receivers evaluate likelihood functions after observing the received signal for a certain number of symbol intervals, say N, then calculate a set of likelihood parameters on which a likelihood ratio test regarding the first symbol is based. These receivers are complex and impractical but does provide valuable insight. This is called maximum likelihood sequence estimation (MLSE). Another way to do MLSE would be to correlate all possible transmitted sequences (reference signals at the demodulator) over a period of N symbol intervals with the received sequence. The first symbol of the reference sequence with which the received sequence has the largest correlation, is decoded as the most likely symbol. The number of reference sequences required at the receiver grow very fast as the observation period increases. Up to now, only the lowest order CPM schemes have feasible optimal receiver structures. The only practical solution thus far for the MLSE of higher order schemes is the use of software implementations of which the Viterbi algorithm is the most popular. Through recursive or sequential processing of data per interval, the number of matched filters required can be reduced. However, for schemes beyond a certain order and constraint length, the Viterbi algorithm's consumption of computational resources reduces its feasibility. Research into CPM is focused mainly on the quest for simpler demodulators and decoders or lower order schemes with better coding gain. In order to gain further insight into CPM, research is approached from different angles.

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Includes bibliographical references.

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Kleyn, W. 2002. Decoding algorithms for continuous phase modulation. University of Cape Town.