Joint ML Estimation of Channel and RF Chain Responses with Noisy Side Information

In this paper, a frequency-domain joint maximum- likelihood (ML) estimation of channel and radio frequency (RF) chain responses is considered when noisy side information is available. The channel includes only transmit and receive antennas and radio propagation medium, while the RF chain includes transmitter (Tx) and receiver (Rx) RF chains. A side information vector of the same length as an observation vector is obtained by directly connecting the Tx and the Rx RF chains after removing the antennas. Since the Rx RF chain is a part of the RF chain whose response is unknown, the problem appears ill-posed because the covariance matrices of Gaussian noise components in the observation and the side information vectors are unknown. However, it is shown, by using asymptotically equivalent sequences of matrices, that the simple entry-by-entry division of the discrete Fourier transform (DFT) of the observation vector by the DFT of the side information vector leads to the jointly optimal channel estimate if the length of the vectors is sufficiently large. A typical experimental result that is obtained using wideband channel sounders is also provided.