Optimum receiver filter for a noise-based frequency-offset modulation system

A frequency-offset transmit-reference (TR) system using a noise carrier is considered in additive white Gaussian noise. The system is studied for any given spectrum of the noise carrier, and the expression for the transfer function of an optimal receiver front-end filter is derived. The maximum achievable performance with respect to spectral shape is evaluated and discussed. The results indicate that the optimal filter in this system, unlike in traditional wireless systems, needs dynamic adaptation to the received signal and noise levels. A convenient but suboptimal choice of the filter is also suggested, and the achievable performance is compared with that of an optimal filter and a performance upper bound. For a certain spectral shape, the suboptimal filter is shown to be an overall good compromise. To meet the performance upper bound, a system using the suboptimal filter, and a noise carrier shaped by a Butterworth filter of order 1, faces a power penalty of 1.89 dB.