EE Seminar: Optimal Sampling of a Noisy Multiple Output Channel
Speaker: Gaston Solodky
M.Sc. student under the supervision of Prof. Meir Feder
Monday, January 21th, 2019 at 15:00
Room 011, Kitot Bldg., Faculty of Engineering
Optimal Sampling of a Noisy Multiple Output Channel
Abstract
This thesis deals with an extension of Papoulis’ generalized sampling expansion (GSE) to a case where noise is added before sampling and the total sampling rate may be higher than the Nyquist rate. We look for the best sampling scheme that maximizes the capacity or minimizes the mean-square error (MSE) of the sampled channel between the input signal and the 
sampled outputs signals, where the channels are composed of all-pass linear time-invariant (LTI) systems with additive Gaussian white noise. For the case where the total rate is between 
and M times the Nyquist rate, the optimal scheme samples 
outputs at Nyquist rate and the last output at the remaining rate. When 
the optimal performance can also be attained by an equally sampled scheme under some condition on the LTI systems. Surprisingly, equal sampling is suboptimal in general. Nevertheless, for some total sampling rates where there is an integer relation between the number of channels and the total normalized rate, equal sampling achieves the optimal performance. When the total rate is between 
to times the Nyquist rate and the number of channels is greater than 
, we conjecture that the best scheme samples outputs at Nyquist rate, one output at the remaining rate, and the last output is not sampled at all, similar to the best scheme when the total sampling rate is larger than times the Nyquist rate. Finally, we proposed a reconstruction scheme and discuss the relation between maximizing the capacity and minimizing the MSE.
