Bilinear approach to multiuser second-order statistics-based blind channel estimation

We present a bilinear approach to mutiple-input multiple-output (MIMO) blind channel estimation where products of channel parameters are first estimated from the covariance of the received data. The channel parameters are then obtained as the dominant eigenvectors of the outer-product estimate. Necessary and sufficient identifiability conditions are presented for a single channel and extended to the multichannel case. It is found that this technique can identify the channel to within a subspace ambiguity, as long as the basis functions for the channel satisfy certain constraints, regardless of the left invertability of the channel matrix. One important requirement for identifiability is that the number of channel parameters is small compared with the channel length; advantageously, this is exactly the situation in which this algorithm has significantly lower complexity than competing (parametric, multiuser) blind algorithms. Simulations show that the technique is applicable in situations where typical identifiability conditions fail: common nulls, a single symbol-spaced channel, and more users than channels. These simulations are for the “almost flat” faded situation when the propagation delay spread is a fraction of the transmission pulse duration (as might be found in current TDMA systems). Comparisons are made, when possible, to a subspace method incorporating knowledge of the basis functions. The bilinear approach requires significantly less computation but performs better than the subspace method at low SNR, especially for multiple users.