Windowed Dictionary Design for Delay-Aware OMP Channel Estimation under Fractional Doppler

Delay-Doppler (DD) signal processing has emerged as a powerful tool for analyzing multipath and time-varying channel effects. Due to the inherent sparsity of the wireless channel in the DD domain, compressed sensing (CS) based techniques, such as orthogonal matching pursuit (OMP), are commonly used for channel estimation. However, many of these methods assume integer Doppler shifts, which can lead to performance degradation in the presence of fractional Doppler. In this paper, we propose a windowed dictionary design technique while we develop a delay-aware orthogonal matching pursuit (DA-OMP) algorithm that mitigates the impact of fractional Doppler shifts on DD domain channel estimation. First, we apply receiver windowing to reduce the correlation between the columns of our proposed dictionary matrix. Second, we introduce a delay-aware interference block to quantify the interference caused by fractional Doppler. This approach removes the need for a pre-determined stopping criterion, which is typically based on the number of propagation paths, in conventional OMP algorithm. Our simulation results confirm the effective performance of our proposed DA-OMP algorithm using the proposed windowed dictionary in terms of normalized mean square error (NMSE) of the channel estimate. In particular, our proposed DA-OMP algorithm demonstrates substantial gains compared to standard OMP algorithm in terms of channel estimation NMSE with and without windowed dictionary.