In this paper, a low-complexity symbol-spaced turbo frequency domain equalization (FDE) algorithm based on Laurent decomposition is proposed for precoded binary continuous phase modulation (CPM) with modulation index h=1/2. At the transmitter, a precoder is utilized to eliminate the inherent memory of the CPM signal. At the receiver, a matched filter based on Laurent decomposition is utilized to make the detection symbol-spaced. As a result, the symbol-spaced iteration can be taken between the equalizer and the decoder directly without a CPM demodulator, and we derive a symbol-spaced soft interference cancellation frequency domain equalization (SSIC-FDE) algorithm for binary CPM with h=1/2. A new data block structure for FDE of partial response CPM is also presented. The computational complexity analysis and simulations show that this approach provides a complexity reduction and an impressive performance improvement over previously proposed turbo FDE algorithm for binary CPM with h=1/2 in multi-path fading channels.

This letter develops an efficient CPM demodulator which provides soft outputs for use in coded CPM. The proposed algorithm offers reduced-complexity soft output detection in which the number of matched filters and trellis states is appreciably reduced. The complexity reduction is achieved by approximating the CPM signal using the Laurent representation. A simulation study of iterative decoding of serially concatenated CPM with an outer code was performed. The performance degradation of the proposed algorithm relative to optimal full complexity generation of soft outputs was found to be small.