On the capacity of linear time-varying channels

Linear time-varying (LTV) channels are often encountered in mobile communications but, as opposed to the linear time-invariant (LTI) channels case, there is no a well established theory for computing the channel capacity, or providing simple bounds to the maximum information rate based only on the channel impulse response, or predicting the structure of the channel eigenfunctions. We provide: (i) a method for computing the mutual information between blocks of transmitted and received sequences, for any finite block length; (ii) the optimal precoding (decoding) strategy to achieve the maximum information rate; (iii) an upper bound for the channel capacity based only on the channel time-varying transfer function; and (iv) a time frequency representation of the channel eigenfunctions, revealing a rather intriguing, but nonetheless intuitively justifiable, bubble structure.