Iterative Equalization of CPM With Unitary Approximate Message Passing

Continuous phase modulation (CPM) has extensive applications in wireless communications due to its high spectral and power efficiency. However, its nonlinear characteristics pose significant challenges for detection in frequency selective fading channels. This paper proposes an iterative receiver tailored for the detection of CPM signals over frequency selective fading channels. This design leverages the factor graph framework to integrate equalization, demodulation, and decoding functions. The equalizer employs the unitary approximate message passing (UAMP) algorithm, while the unitary transformation is implemented using the fast Fourier transform (FFT) with the aid of a cyclic prefix (CP), thereby achieving low computational complexity while with high performance. For CPM demodulation and channel decoding, with belief propagation (BP), we design a message passing-based maximum a posteriori (MAP) algorithm, and the message exchange between the demodulator, decoder and equalizer is elaborated. With proper message passing schedules, the receiver can achieve fast convergence. Simulation results show that compared with existing turbo receivers, the proposed receiver delivers significant performance enhancement with low computational complexity.