On the Performance of Practical Pulse-Shaped OTFS with Analog Receivers

We study the impacts of practical pulse-shaping on the performance of orthogonal time frequency space (OTFS) systems with a matched filter based analog receiver. Unlike most existing OTFS works that use a sampling and DFT-based digital receiver, we investigate the OTFS waveform in a precise manner by strictly following the continuous-time Heisenberg and Wigner transforms as in the original OTFS architecture. Closed-form expressions of the cross-ambiguity functions of several practical pulses are developed to facilitate the modeling and analysis of the analog architecture. In particular, we derive a matrix representation of the input-output relationship of the OTFS system with the help of an equivalent discrete delay-Doppler channel spread function, which incorporates the combined effects of the physical propagation channel, the bandwidth and duration restrictions imposed on the OTFS signals, and the transmit and receive pulses. Numerical results demonstrated that under the analog OTFS architecture, practical rectangular pulse-shaping waveforms can achieve similar performance as the ideal bi-orthogonal robust waveforms in high mobility scenarios.