Joint Channel-Estimation and Equalization of Single-Carrier Systems via Bilinear AMP

We propose a novel soft-input soft-output equalizer for single-carrier transmissions over unknown frequency-selective block-fading channels. Our equalizer leverages the recently proposed parametric bilinear generalized approximate message passing algorithm for joint channel-estimation and symbol-detection, and exploits fast Fourier transform (FFT)-processing to achieve a per-symbol complexity that grows only logarithmically in the channel delay-spread. Furthermore, it supports the use of Gaussian mixture models to support the approximately sparse nature of wideband wireless channel responses. Numerical experiments, conducted using physically motivated Saleh-Valenzuela channel models, show that the proposed approach achieves channel normalized mean square error and bit error rate that are significant improved over existing turbo frequency-domain equalization approaches for unknown channels. Additional experiments show that the proposed scheme facilitates much higher spectral efficiencies than sparse deconvolution methods based on convex relaxation.