Low-Complexity Channel Matrix Calculation for OTFS Systems with Fractional Delay and Doppler

Abstract

Orthogonal Time Frequency Space (OTFS) modulation has been introduced to manage channel induced high Doppler shifts in mobile communication networks. In an OTFS system, the information carrying symbols are placed in the data frames in the delay-Doppler (DD) domain before transformed into the time domain for transmission. Accordingly, the DD domain channel matrix can be estimated using the corresponding pilots in the DD domain. For OTFS systems with integer delay and Doppler values, the underlying channel matrix in the DD domain is sparse. However, the counterpart channel matrix is no longer sparse when the delay and Doppler values are fractional. In fact, even for the integer case calculating the sparse channel matrix is still time-consuming due to its large size. To significantly reduce the computational complexity, in this paper, we introduce a low complexity algorithm for calculating the channel matrix of OTFS systems with fractional delay and Doppler. The introduced algorithm leverages the circulant property of the underlying channel matrix in the DD domain and calculates a small portion of elements in one initial block. Through some simple operation, the elements in the initial block can be replicated into other parts of the channel matrix. Both theoretical complexity analysis and simulation results demonstrate that our method can significantly reduce the computation complexity when computing the channel matrix. Since DD domain channel matrix is crucial for OTFS receive processing, we believe this is an important step to bring OTFS towards practical communication systems.