We consider the optimization of coded continuous phase modulation (CPM) systems operating at the spectral efficiencies 0.5bps/Hz, 1.0bps/Hz, 1.5bps/Hz and 2.0bps/Hz. Due to the difficulty of defining an analytic fitness function and the discreteness of the CPM parameters, we opt for an evolutionary optimization, which easily deals with such limitations. We apply a bi-objective instance of the non-dominated sorting genetic algorithm II (NSGA-II) where the mutual information between the transmit bits and soft bits at the output of the CPM detector as well as the complexity are taken as objective functions. This enables us to quantify the trade-off between complexity and performance. The results show that for all considered spectral efficiencies, the best schemes are usually quaternary or octal with a frequency pulse length not exceeding 2 symbol durations and a code rate ranging between 0.7−0.8.

The benefits of continuous phase modulation (CPM), namely high power and spectral efficiencies, are often overshadowed by the high complexity that comes along with the nonlinearity of the modulation format. We tackle the problem of detection of a quaternary CPM signal in a frequency-selective fast fading channel. In particular, we derive a joint detector-equalizer using the Laurent principal pulse approximation. To handle time-selectivity, we adopt the well-known turbo-estimation approach. However, it turns out that classical turbo-estimation cannot be directly applied, but has to be modified beforehand. With the help of Monte Carlo bit error rate (BER) simulations, we show that using the modified turbo-estimation approach, the receiver is able to track channel variations within a transmit burst under fast fading conditions. This allows for a larger payload-to-overhead ratio. Since joint detection-equalization is practically feasible only for channels with short memory, we also consider a suboptimal approach which decouples detection from equalization.

We consider the detection of short continuous phase modulation (CPM) bursts in a frequency-selective fading channel. The conventional solution comprises training-aided channel estimation followed by coherent detection. However, the performance of the coherent detector is optimal only when the channel is perfectly known, which is practically never the case. In practice, the performance is limited by the quality of the channel estimate. This poses a problem for short bursts, where the number of training symbols must be kept low. When the channel is unknown, the optimal receiver uses available a priori stochastic information to marginalize the channel out of the likelihood function and determine the transmit sequence that maximizes it. Due to the lack of a priori information and the high complexity associated with marginalizing out a multi-tap channel, we derive a suboptimal detector, which replaces the unknown channel by the conditional maximum likelihood (ML) estimate for each hypothesis transmit sequence. From that, we derive a noncoherent soft-input soft-output (SISO) symbol-by-symbol detector. Using Monte-Carlo simulations to estimate the bit error rate (BER), we show the superiority of the proposed approach over the conventional one, especially for extremely short bursts in a time-variant environment.