On the transmission of an analog wideband signal through a narrowband channel

The problem of transmitting a wideband signal through a narrowband channel is considered. A new solution to this problem is proposed in which the wideband signal is divided into two parts: a first part which occupies exactly the spectrum that the channel can carry and a second-the rest of the signal. It is proposed to transmit the fast part without any coding (in analog form) while the second part is sampled and quantized and the resulting data stream is transmitted simultaneously with the first part via the same channel. An alternative approach, based on the separation theorem, is to optimally quantize the whole signal using an optimal source encoder at the rate equal to the channel capacity and then to transmit the signal (digitally) using an optimal channel encoder. Such double optimality yields the best achievable MSE performance. It is shown that if the double optimality assumptions are applied to the second part of the signal, in the proposed case, than the MSE performance equals that which follows from the separation theorem. If, however at least one of these optimal encoders can not be achieved, the proposed method has a better MSE performance than that based on the separation theorem when applied to the whole signal.