BER Analysis for OTFS Zero Forcing Receiver

We derive closed form bit error rate (BER) expression for orthogonal time frequency space (OTFS) zero-forcing (ZF) receiver with perfect and imperfect receive channel information. Depending on the delay-Doppler locations of the propagation paths of the OTFS channel H, the expression $\mathrm {H}^{H}\mathrm {H}$ is shown to have either distinct or repetitive eigenvalues. When $\mathrm {H}^{H}\mathrm {H}$ has two or less distinct eigenvalues and the remaining ones are repetitive, we derive the probability distribution function (pdf) of the signal-to-noise-plus-interference-ratio (SINR) of the ZF receiver. A closed form BER expression is then derived by averaging the conditional BER over the SINR pdf. When $\mathrm {H}^{H}\mathrm {H}$ has $n$ distinct eigenvalues, we use numerical integration to derive a generalized expression for the SINR pdf. We show that this pdf can be tightly approximated by the Gamma pdf, and then use it to derive the BER expression. The derived OTFS ZF BER expression therefore, unlike the existing ones in the literature, does not require averaging over multiple channel realizations. We show, for different modulation schemes and OTFS system parameters, that the BER calculated using the derived expressions closely matches the one calculated numerically.