Rate Optimization for Digital Frequency Modulation

In this paper we optimize the information rate (subject to certain constraints) of a multilevel digital FM system. This problem of delivering the maximum information through an FM system has recently been formulated by J. R. Pierce.1 Specifically, he considered how one should choose the baseband signaling rate and the number of levels to get the most information through the channel, subject to fixed bandwidth, fixed RF signal-to-noise ratio, and fixed output error rate. This optimization has recently been carried out under the assumption that the conventional FM receiver can be linearized.2 Small-noise linear FM theory is satisfactory when analyzing analog systems, but has its well known pitfalls in digital applications. The purpose of this paper is to reexamine this problem more rigorously, paying particular attention to the anomalies (clicks) which can result from the nonlinear character of the receiver. In order to do this we must choose a particular mathematical model for digital 302 J