The practical use of any equalization scheme that relies on pilot-based channel estimates is often hindered by high computational requirements, especially in cases where a precise estimation criterion is crucial. The goal of this paper is to show that any pilot based scheme that is able to induce a Toeplitz structure in the channel correlation matrix, can make use of an existing class of so-called superfast algorithms for Toeplitz inverses which are specially suitable to pilot-based estimators. The key point behind such observation is that the required Toeplitz inverse inherent to common minimum mean-square error (MMSE) or least-squares (LS) criteria can not only be performed offline, but efficiently implemented via efficient FFT techniques. The most significant consequence of this fact is that, given a structure for the vector of pilots and an upper bound for the channel delay spread, say N, it is only necessary to store 2N coefficients per pilot structure in order to recover the entire channel. This is particularly useful in turbo equalization scenarios and DVB applications, especially for sparse channels. We shall illustrate the idea via a zero-padded (ZP) and standard cyclic prefix based block transmission schemes.
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