The impact of impedance matching on channel estimation in compact MIMO receivers

Accurate channel estimates are essential to realize the high capacity of multiple-input, multiple-output (MIMO) communication channels. In compact receivers, prior work has shown that mutual coupling among antennas can significantly degrade the performance of channel estimation algorithms. However, this work did not consider the impact of coupling on observation noise, or the possible benefits of antenna impedance matching, which can profoundly alter the characteristics of observation noise. In this paper, we revisit the channel estimation problem for compact MIMO receivers. We consider a MIMO front-end that consists of coupled antennas, impedance matching and amplifiers, and includes physical models of antenna and amplifier noise. Using this model, we derive the error covariance of mimimum-mean-squared-error (MMSE) channel estimation and explore how it varies with front-end impedance and noise characteristics. We show the MMSE error covariance is always minimized by one kind of impedance matching, called minimum-noise-factor (MNF) matching. We present numerical results that compare the estimation error achievable with optimal matching to conventional antenna self-matching. These results suggest that, when conventional self-matching is used, estimation error is highly sensitive to amplifier noise in the presence of strong coupling. However, optimal MNF matching completely eliminates this sensitivity and significantly outperforms self-matching when amplifier noise is not negligible.