, where the authors illustrated the resilience of OTFS against a high amount of frequency dispersion due to oscillator phase noise and Doppler effect and its superior performance to that of OFDM. In [14], a matrix-form discrete-time formulation of a single-antenna OTFS transceiver with rectan- gular windows at both transmitter and receiver was presented. The authors in [15] derived a more accurate matrix formulation for OTFS where separable receive window functions were considered. This brought deep insights into understanding of OTFS and the channel impact on the transmitted data symbols in delay-Doppler domain in light of the derived matrix formulation. It is worth mentioning that most of the mathematical derivations that are presented in this chapter are based on the results of [15] with more generalizations on the channel impact and the choice of transmit and receive windows. In [16], an end-to-end formulation for OTFS in multiple-input multiple-output (MIMO) channels was presented, which led to derivation of ergodic capacity for OTFS and its comparison with that of OFDM. In [17], an in-depth diversity analysis of OTFS for both SISO and MIMO OTFS systems is presented. Based on their analysis, the authors in [17] propose a phase rotation method for OTFS that achieves the full diversity gain in delay-Doppler domain in both cases of SISO and MIMO channels. More recently, effective diversity for OTFS is analyzed in [18], which provides a more in-depth and accurate diversity analysis than [17]. The authors in [6] presented a discrete-time formulation of OTFS by sampling the continuous-time channel for rectangular transmit and receive window functions. They also proposed a detection technique based on message passing algorithm. In a more recent work [19], the authors leverage the vectorized formulation for OTFS and propose a detection method based on Markov chain Monte Carlo (MCMC) sampling technique. Moreover, a channel estimation method by deploying a pseudo-random noise (PN) sequence in delay-Doppler domain was 