Enhancing the performance of the CR blind channel estimation algorithm using the Karhunen-Loève expansion

This paper introduces a new formulation for the blind channel estimation problem. In particular, it is found that any possible realization of the discrete time channel impulse response can be expressed as a linear combination of a set of predetermined eigenvectors. These are obtained from a certain “universal” autocorrelation matrix that depends only on the pulse shaping filter and the maximum delay spread of the multi-path channel, and not on the specific characteristics of the power delay profile. This new formulation shows that an interrelation exists between the different sub-channel responses of the single-input multiple-output equivalent model of the over-sampled baseband signal. Thus, the number of free parameters equals the number of signal space eigenvectors and not the number of coefficients in the multi-channel model. Therefore the optimization associated with the CR algorithm [1] can be reformulated as a reduced dimensional minimization problem with a notoriously enhanced estimation performance.