New models for random channels

Two new models of random channels are developed. In one, input signals are expanded in a complete orthonormal basis, but channel outputs are formed of linear combinations of random vectors. In the second model, output signals are expanded in an orthonormal set that is complete over the space of all possible output signals from all channels in the ensemble. Input signals are represented in a frame of random vectors that is correlated to the channel. This bases is over-complete in that there are more vectors in the frame than the dimensionality of the input and output spaces for any channel in the ensemble.