Cross-Domain OTFS Detection via Delay-Doppler Decoupling: Reduced-Complexity Design and Performance Analysis

In this paper, a reduced-complexity cross-domain iterative detection for orthogonal time frequency space (OTFS) modulation is proposed that exploits channel properties in both time and delay-Doppler domains. Specifically, we first show that in the time-domain effective channel, the path delay only introduces interference among samples in adjacent time slots, while the Doppler becomes a phase term that does not affect the channel sparsity. This investigation indicates that the effects of delay and Doppler can be decoupled and treated separately. This "band-limited" matrix structure further motivates us to apply a reduced-size linear minimum mean square error (LMMSE) filter to eliminate the effect of delay in the time domain, while exploiting the cross-domain iteration for minimizing the effect of Doppler by noticing that the time and Doppler are a Fourier dual pair. Furthermore, we apply eigenvalue decomposition to the reduced-size LMMSE estimator, which makes the computational complexity independent of the number of cross-domain iterations, thus significantly reducing the computational complexity. The bias evolution and variance evolution are derived to evaluate the average MSE performance of the proposed scheme, which shows that the proposed estimators suffer from only negligible estimation bias in both time and DD domains. Particularly, the state (MSE) evolution is compared with bounds to verify the effectiveness of the proposed scheme. Simulation results demonstrate that the proposed scheme achieves almost the same error performance as the optimal detection, but only requires a reduced complexity.