An Analysis of the Bias-Property of the Sample Auto-Correlation Matrices of Doubly Selective Fading Channels for OFDM Systems

In this paper, by assuming equiprobable centrosymmetric constellation adopted for modulation, the mathematic expectation of the sample auto-correlation matrix obtained through the least-squared channel estimation is derived under a rigorous model of the doubly selective fading channel for orthogonal frequency division multiplexing (OFDM) systems. Based on the derived expectation, the bias-property of the sample auto-correlation matrix is analyzed with respect to the total squared error (TSE) and the eigen-structure. And according to the analyses, when the sample auto-correlation matrix is used to estimate the signal and noise subspaces, BPSK may not be a good choice for modulation of pilot tones, which contradicts with the experience of most current OFDM systems. Numerical results demonstrate this bias-property and the analyses on it.