Closed Form BER For ZF OTFS Receivers

Recently-proposed orthogonal time frequency space (OTFS) waveform establishes reliable communication between high-speed moving devices by transforming a time and frequency selective channel into an almost-flat delay-Doppler domain channel. This work derives closed form bit error rate (BER) expression for zero-forcing (ZF) OTFS receiver by exploiting the doubly-circulant channel matrix structure. To achieve this aim, we first derive probability distribution function (pdf) for the signal-to-noise-plus-interference-ratio (SINR) of the ZF receiver. We then average the BER, which is conditioned on the SINR, over the SINR pdf. The derived OTFS ZF BER expression therefore, unlike the existing ones in the literature, does not require averaging over multiple channel realization to accurately calculate the BER. We show that the BER calculated using this expression perfectly matches with the calculated numerically.