Advanced Channel Decomposition Techniques in OTFS: A GSVD Approach for Multi-User Downlink

In this paper, we propose a multi-user downlink system for two users based on the orthogonal time frequency space (OTFS) modulation scheme. The design leverages the generalized singular value decomposition (GSVD) of the channels between the base station and the two users, applying precoding and detection matrices based on the right and left singular vectors, respectively. We derive the analytical expressions for three scenarios and present the corresponding simulation results. These results demonstrate that, in terms of bit error rate (BER), the proposed system outperforms the conventional multi-user OTFS system in two scenarios when using minimum mean square error (MMSE) equalizers or precoder, both for perfect channel state information and for a scenario with channel estimation errors. In the third scenario, the design is equivalent to zero-forcing (ZF) precoding at the transmitter.