Frequency-domain equalizers with zero restoration for zero-padded block transmission with high SNR

This paper focuses on the equalization of block transmissions with zero pad (ZP). If the channel impulse response length does not exceed the ZP length, it is possible to construct zero-forcing equalizers (ZFEs). Improved performance may be achieved using a minimum mean squared error (MMSE) equalizer. However, these equalizers are computationally intensive when a time-domain implementation is used. While the frequency-domain implementation of a ZFE has a lower complexity, it is prone to—potentially infinite—noise enhancement in the presence of spectral zeros. The MMSE equalizer in the frequency domain performs better by limiting the noise enhancement but still loses all information stored at the spectral zeros. This paper presents a method to exploit the redundancy of the padding to recover this lost information, leading to two new frequency-domain equalizers, a ZFE and an MMSE-like equalizer. These two equalizers are evaluated through simulations. They have a performance close to the time-domain equalizers, while maintaining the low complexity of the original frequency-domain equalizers. The equalizers are especially useful for scenarios with a high signal-to-noise ratio (SNR), where the performance is not limited by the presence of noise, but by the absence of the information stored in the spectral zeros. In practice, this means an SNR >30 dB. With minor modifications, the equalizers can also be applied if the ZP is replaced by a unique word (UW).