Performance Analysis of OTFS Modulation with Transmit Antenna Selection

In this paper, we consider transmit antenna selection (TAS) in orthogonal time frequency space (OTFS) modulation and analyze its performance. We assume that the channel is quasi-static in the delay-Doppler (DD) domain and there is limited feedback from the receiver to the transmitter. The diversity performance of TAS is analyzed in a multiple-input multiple-output OTFS (MIMO-OTFS) system. Antenna selection is done based on the maximum channel Frobenius norm in the DD domain, where n
s
antennas are selected out of n
t
transmit antennas. Our analysis for one resolvable path in the DD channel (i.e., P = 1) shows that i) when n
s
= 1, full spatial diversity of n
r
n
t
(i.e., full receive diversity of n
r
and full transmit diversity of n
t
) is achieved since the underlying symbol difference matrix is full rank, and ii) when n
s
> 1, only n
r
th order receive diversity is achieved because of rank deficiency. Simulation results are shown to validate the analytically predicted diversity performance. For P > 1, diversity orders are predicted through rank of the difference matrices, validated through computation of pairwise error probability (PEP) bounds and simulations.