Multichannel equalization lower bound: a function of channel noise and disparity

Studies have shown that in the presence of spatial or temporal diversity, blind identification/equalization is perfectly achievable under some conditions on the channel transfer function and amount of data considered. However, in the presence of channel noise, equalization can no longer be achieved perfectly. We study the best achievable linear equalizer performance in terms of the input/output minimum mean square error (MMSE), defining the channel equalizability as a function of the multichannel transfer function roots and the signal to noise ratio (SNR). We show that a channel disparity lower bound can be deduced as a function of the SNR in order to achieve a given MMSE