An original expectation propagation (EP) based message passing framework is introduced, wherein transmitted symbols are considered to belong to the multivariate white Gaussian distribution family. This approach allows deriving a novel class of single-tap frequency domain (FD) receivers with a quasi-linear computational complexity in block length, thanks to Fast-Fourier transform (FFT) based implementation. This framework is exposed in detail, through the design of a novel double-loop single-carrier frequency domain equalizer (SC-FDE), where self-iterations of the equalizer with the demapper, and turbo iterations with the decoder, provide numerous combinations for the performance and complexity trade-off. Furthermore, the flexibility of this framework is illustrated with the derivation of an overlap FDE, used for time-varying channel equalization, among others, and with the design of a FD multiple-input multiple-output (MIMO) detector, used for spatial multiplexing. Through these different receiver design problems, this framework is shown to improve the mitigation of inter-symbol, inter-block and multi-antenna interferences, compared to alternative single-tap FD structures of previous works. Thanks to finite-length and asymptotic analysis, supported by numerical results, the improvement brought by the proposed structures is assessed, and then completed by also accounting for computational costs.
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