Equalization Algorithms For Continuous Phase Modulation On Long Delay Spread Channels

In order to deal with the problem of the equalization of CPM signal transmitted over channels having long impulse responses, three novel equalization algorithms are proposed.For channels having long impulse responses, time-domain (TD) equalization algorithm is quite complex, but for sparse intersymbol interference (ISI) channels, based on the application of the sum - product (SP) algorithm to factor graphs (FGs) representing the joint a posteriori probability (APP) of the transmitted symbols, we propose new iterative soft-input soft-output (SISO) detection schemes for CPM on ISI channels. For sparse ISI channels, the proposed algorithm has advantages in terms of complexity over optimal detection schemes based on the Bahl - Cocke - Jelinek - Raviv (BCJR) algorithm. It also allows a parallel implementation of the receiver and the possibility of a more efficient complexity reduction.Because of high complexity, the time domain equalizer can not be applied to general channels having long channel impulse responses. To prevent channels having long channel impulse responses, based on single-carrier frequency-domain equalization (SCFDE) we propose a novel minimum mean-square error (MMSE) frequency-domain (FD) equalization algorithm for continuous phase frequency shift keying (CPFSK). The proposed algorithm also can be applied to linear CPM. However, it can not be applied to nonlinear CPM.For general continuous phase modulations (CPMs) with single modulation index, a novel equalization algorithm based on pulse amplitude modulation (PAM) representation is proposed. The main features of this algorithm are 1) its use for nonlinear modulations; 2) its overcoming the channels having long impulse responses; 3) its low complexity for CPMs. Simulation results show that our algorithm outperforms conventional frequency-domain equalization with a little computational cost and by simply discarding the smaller pulses we can reduce the computational complexity of equalizer and detector with negligible performance losses.