Rectangular Pulse-Shaped OTFS with Fractional Delay and Doppler Shift for MU-MIMO Systems

We consider the uplink of an orthogonal time frequency space (OTFS)-based multiuser multiple-input multiple-output (MU-MIMO) system. For this setup, we consider, for the first time ever, the more practical rectangular pulse-shaped functions along with the fractional delay and Doppler shift. We first provide the exact OTFS-based input-output relationship. Subsequently, the orthogonal frequency division multiplexing (OFDM)-based OTFS input-output approximation is derived by reconstructing the continuous time domain signal via a sinc-function. Based on these two results, an important performance metric, namely, the pairwise error probability (PEP) with maximum-likelihood (ML) and nearest-neighbor (NN) decoding rules, is analyzed. A series of interesting insights are obtained from the analysis: i) for our system setting, the effective channel matrix is not doubly-block circulant or sparse structured any-more, while the OFDM-based approximation result consists of a block-Toeplitz with Toeplitz block (BTTB) structured matrix; ii) the practical rectangular pulses suffer from a significant perfomance degradation.