Condition Number Analysis for MIMO-OTFS Communication Systems

Orthogonal Time-Frequency Space (OTFS) modulation is an innovative modulation technique that operates in the two-dimensional delay-Doppler (DD) domain. It is specifically designed for high Doppler scenarios, where the channel can be transformed into an almost non-fading channel for DD domain symbol transmission. In multiple-input multiple-output (MIMO) OTFS systems, the DD domain input-output relation has considerable complexity, especially under fractional delays and Dopplers. The condition number is a key indicator of channel matrix quality as it reflects the sensitivity to noise and disturbance. In this paper, a novel Zak-OTFS modulation in the DD domain has been proposed as a competitive alternative to the conventional multi-carrier (MC) OTFS scheme, where MC-OTFS is implemented in two steps in the time-frequency (TF) domain. We focus on both MIMO-Zak-OTFS and MIMO-MC-OTFS schemes and study the condition numbers for the residual error covariance matrix and the channel matrix. We investigate the condition number under various system parameters, and the results indicate that OTFS outperforms MIMO-orthogonal frequency division multiplexing (MIMO-OFDM) in terms of condition number distributions. Meanwhile, the condition numbers of MIMO-Zak-OTFS matrices also outperform those of MIMO-MC-OTFS, while MIMO-Zak-OTFS shows a better BER performance compared to MIMO-MC-OTFS and MIMO-OFDM using both LMMSE and sphere decoders in the experimental results.