Optimal Symbol-Length Filter Design for Sidelobe Suppression in Filter Bank Based Orthogonal Time Frequency Space (FB-OTFS) Systems

In this paper, we propose symbol-length transceive filter optimization methods for sidelobe suppression in filter bank based orthogonal time frequency space (FB-OTFS) systems. Specifically, we firstly establish the FB-OTFS system model with fast implementation for transceive filters. Then, we analyze the impact of the transceive filters on the orthogonal transmission and derive the constraints for symbol-length transceive filters to achieve the orthogonal transmission. Moreover, the complexity analysis is provided. With the derived orthogonal conditions as constraints, we formulate a transceive filter optimization problem to minimize the stopband energy (a commonly used sidelobe suppression criterion), and derive the theoretically optimal solutions. To further achieve flexible suppression of the spectral sidelobes within specific frequency intervals, we formulate a transceive filter optimization to minimize the weighted stopband energy by designing adjustable frequency domain weights, and also obtain the optimal solutions. Numerical results demonstrate that: 1) The proposed transceive filters have the lowest spectral sidelobes compared with the commonly used rectangular pulse and the Gaussian filter; 2) The sidelobe suppression effects within specific frequency intervals are successfully controlled by designing the frequency domain weights; 3) All proposed transceive filters are verified to satisfy the orthogonal conditions.