Equivalence of Linear Communication Systems with Swapping of Transmit and Receive Filters

The signal-to-noise ratio at the receiver output of a linear communication system is shown to be equal to that of a linear communication system which uses the receive and the transmit filters of the former system as its transmit and receive filters, respectively, kprovided that the average signal power at the transmitter output is constrained to a fixed level and that the power spectrum of the random data input equals that of the additive noise power spectrum within a multiplicative constant.