Blind channel estimation using the second-order statistics: asymptotic performance and limitations

We consider the asymptotic performance and fundamental limitations of the class of blind estimators that use second-order statistics. An achievable lower bound of the asymptotic normalized mean-square error (ANMSE) is derived. It is shown that the achievable ANMSE is lower bounded by the condition number of the Jacobian matrix of the correlation function with respect to the channel parameters. It is shown next that the Jacobian matrix is singular if and only if the subchannels share common conjugate reciprocal zeros. This condition is different from the existing channel identification conditions. Asymptotic performance of some existing eigenstructure-based algorithms is analyzed. Closed-form expressions of ANMSE and their lower bounds are derived for the least-squares (LS) and the subspace (SS) blind channel estimators when there are two subchannels. Asymptotic efficiency of LS/SS algorithms is also evaluated, showing that significant performance improvement is possible when the information of the source correlation is exploited.