Low Complexity Lookup Table Aided Soft Output Semidefinite Relaxation based Faster-than-Nyquist Signaling Detector

Spectrum scarcity necessitates innovative, spectral-efficient strategies to meet the ever-growing demand for high data rates. Faster-than-Nyquist (FTN) signaling emerges as a compelling spectral-efficient transmission method that pushes transmit data symbols beyond the Nyquist limit, offering enhanced spectral efficiency (SE). While FTN signaling maintains SE with the same energy and bandwidth as the Nyquist signaling, it introduces increased complexity, particularly at higher modulation levels. This complexity predominantly arises from the detection process, which seeks to mitigate the intentional intersymbol interference generated by FTN signaling. Another challenge involves the generation of reliable log-likelihood ratios (LLRs) vital for soft channel decoders. In this study, we introduce a lookup table (LUT) aided soft output semidefinite relaxation (soSDR) based sub-optimal FTN detector, which can be extended to higher modulation levels. This detector possesses polynomial computational complexity, given the negligible complexity associated with soft value generation. Our study assesses the performance of this soft output detector against that of the optimal FTN detector, Bahl, Cocke, Jelinek and Raviv (BCJR) algorithm as the benchmark. The likelihood values produced by our LUT aided semidefinite relaxation (SDR) based FTN signaling detector show promising viability in coded scenario.