A BER formula of OTFS modulation with message-passing receiver

The orthogonal time frequency space (OTFS) modulation is a promising multicarrier waveform which can have good performance in high-mobility scenarios. Among various receivers designed for the OTFS modulation, the message-passing (MP) receiver has received much attention which can achieve a good bit error rate (BER) performance. However, the BER performance of MP receiver is usually obtained through simulations due to the lack of corresponding BER formula in the literature. This work studies the BER formula of OTFS modulation with MP receiver over doubly selective fading channel. Specifically, equivalent signal models of the MP receiver are first defined and the expression of the corresponding signal-noise-ratio (SNR) is derived, then the probability distribution function of the SNR is estimated by assuming the distribution of SNR as a lognormal distribution, then the methods to estimate the parameters of the distribution function are proposed, and finally the formula for calculating the BER of the OTFS modulation with MP receiver is obtained. Simulation results verify that the proposed BER formula is accurate.