Optimum Linear Systems for Power Constrained Transmission

This paper studies transmission of sources over noisy channels by a communication system subject to a power constraint at the transmitter. We consider the transmission of continuous- or discrete-time Gaussian sources and assume that the processing on the signals are within the family of linear operations. For stationary signals, a constraint on the power at the output of the transmission filter results in bandpass transmit and receive filters whose bandpass region include the frequencies at which the source spectra is above some threshold. This result shows similarities between the rate distortion arguments and the minimum mean square error (MSE) attainable by the optimum linear systems. Examples for frequently encountered source statistics are also studied and it is shown that linear processing both at the transmitter and at the receiver reduces the estimation errors significantly compared to the standard Wiener filtering approach. It is shown that for communication of a bandlimited source with arbitrary spectrum over a bandlimited channel with the same bandwidth as the source, using proposed linear processing approach attains the same distortion exponent as the theoretically optimum system does