Pilot-assisted channel estimation based on second-order statistics

A survey about linear channel estimation exploiting slowly varying channel properties is given for receivers with multiple antenna elements. The slowly varying channel properties are described by the channel's second-order statistics. First, a detailed comparison of classical linear pilot-based channel estimators, a novel matched filter, and reduced-rank (RR) approaches is made in a common framework with respect to the model they assume for the channel, their performance (MSE), and complexity. The matched filter channel estimator is introduced, which exploits second-order statistics with quadratic order of complexity. For flat correlated Rayleigh fading channels, an analytical performance comparison of all estimators in terms of the uncoded bit error probability is provided. It is a generalization of previous results and shows that the matched filter is a low complexity alternative with good performance at an interesting signal-to-noise ratio (SNR) range. The effects of these approaches on linear equalization are briefly discussed in the context of direct-sequence code division multiple access (DS-CDMA), where the focus is on a generalization of the rake receiver in space and time, which reduces the channel rank based on its second-order statistics, resulting in a complexity reduction of the equalizer. For this discussion, a new notation for the generalized rake is presented, which allows for its interpretation in the context of channel estimation and reveals alternatives for implementation. We conclude that exploiting second-order channel statistics results in significant performance gains, and RR channel estimation should only be used together with equalization in the reduced signal subspace.