A Correlation-Aware Sliding-Window MMSE Equalization with Optimal Multi-Observation Combining for Block Transmission

In practical communication systems, signals suffer from attenuation during transmission over channels, particularly in multipath environments where inter-symbol interference (ISI), fading, and noise further degrade signal quality. To mitigate channel-induced distortion, receivers typically employ equalization techniques. Common channel equalization methods include linear equalizers, adaptive equalizers, and decision feedback equalizers (DFEs). Single-carrier frequency-domain equalization (SC-FDE) systems can effectively combat frequency-selective interference. Compared with time-domain equalization, frequency-domain equalization not only improves compensation performance but also significantly reduces computational complexity. This paper proposes a correlation-aware multi-observation SC-FDE receiver for frequency-selective multipath channels. The proposed receiver employs sliding windows to obtain multiple equalized observations of the same target symbol, thereby exploiting the observation diversity associated with different symbol positions and channel conditions. These observations are subsequently combined using an MVDR-based combiner, which suppresses position-dependent residual ISI while preserving the desired signal under a distortionless constraint. Through simulation tests, the proposed MVDR-based sliding-window scheme achieves favorable equalization performance under various channel models.