Spectrally Efficient Time-Frequency Space Modulation: A Delay-Doppler Domain FTN Waveform for ISAC Systems

This paper introduces the spectrally efficient time-frequency space (SETFS) modulation, a two-dimensional (2D) modulation extending the concepts of spectrally efficient frequency division multiplexing (SEFDM) and orthogonal time–frequency space (OTFS) modulation by increasing the spectral overlap at two levels, i.e., in both frequency and Doppler domains. This double compression improves the use of the available spectrum. Moreover, in SETFS, the periodicity in both time and frequency is maintained through the use of a double cyclic prefix (DCP) in order to simplify channel equalization and avoid 2D inter-symbol interference (ISI). However, the presence of a spectral overlap unavoidably induces 2D inter-carrier interference (ICI), that makes symbol detection more complicated. To mitigate channel estimation errors and also support high-resolution sensing, a novel channel estimator, dubbed Newton-based estimation and spectral cancellation algorithm (NESCA), is proposed. Numerical results show that SETFS achieves up to a 24% gain in the achievable communication rate with respect to OTFS at the cost of higher receiver complexity. Combined with NESCA, SETFS provides near optimal delay and Doppler estimation, outperforming other three algorithms available in the technical literature. In terms of communication performance, SETFS employing the NESCA, followed by a minimum mean square error equalizer and iterative detector with soft symbol mapping, reaches quasi optimal capacity, while throughput saturation occurs with an SNR gap of about 10 dB in favor of OTFS-DCP and increasing with less advanced estimators. Nevertheless, SETFS combined with NESCA achieves a better communication-sensing tradeoff, improving spectral efficiency up to 25% with respect to OTFS at the price of a higher detection complexity. Overall, SETFS offers a relevant tradeoff between spectral efficiency, complexity and sensing accuracy, making it a promising candidate for future wireless systems.