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原文摘要

The performance of Zak-OTFS modulation depends critically on the delay-Doppler (DD) domain pulse shaping filter, which must support both accurate channel estimation and reliable data detection. Filters reported in the Zak-OTFS literature fall short in bit error rate (BER) performance for higher-order modulation due to sensitivity to model-free channel estimation errors and pilot-data interference. Motivated by this, in this paper, we introduce a separable two-dimensional Mirabbasi-Martin (MM) filter for Zak-OTFS and propose a filter coefficient optimization framework that minimizes the aggregate sidelobe energy while preserving the compact structure of the MM prototype. By trading exact Nyquist nulls for high localization, the optimized MM filter exhibits no sidelobes with the narrowest $-40$ dB DD domain pulsewidth compared to sinc, Gaussian, and GS pulses. This compactness of the optimized filter tightly confines the pilot energy within the pilot region of the embedded frame, ensuring that the full response is captured for model-free channel estimation while significantly reducing pilot-data interference. This yields both an improved estimation performance and a significantly improved BER performance for higher-order QAM. For the proposed filter, we derive closed-form expressions for the effective DD domain channel and the covariance of the receive-filtered noise, which drastically reduce simulation run times. Our simulation results demonstrate that the optimized MM filter achieves significantly better uncoded/coded BER performance for higher-order QAM compared to that of sinc, Gaussian, and GS filters. For example, for 64-QAM with M=32, N=48, rate-1/2 convolutional code, and TDL-A channel model with fractional DDs, the optimized MM filter achieves a coded BER of 3x10^{-4} at an E_b/N_0 of 40 dB, while the sinc, Gaussian, and GS filters exhibit error floors above 10^{-2}.