Divergence and minimum mean-square error in continuous-time additive white Gaussian noise channels

New relations between the divergence of a process measure in the function space relative to the measure of the Gaussian process with the same covariance, and both the causal minimum mean-square error (CMMSE) and the noncausal minimum mean-square error (MMSE), are proved. As an example-a special type of signal which is composed of a sum of independent narrow-band waves, the divergence and its derivative relative to the signal energy to the white Gaussian noise (WGN) energy ratio, is calculated. The results are used to evaluate the CMMSE and the MMSE of the signal optimum estimation. Since the divergence takes also a significant role in the derivation of the capacity of the additive non-Gaussian channel, we use the calculation that was made for the divergence in the example to evaluate the capacity of an additive noise channel, where the noise is composed of the sum of WGN and narrow-band interferes