Optimum Angle Modulation

The problem of transmitting an analog message over a channel corrupted by additive Gaussian noise using angle modulation of a sinusoidal carrier is considered. The problem is formulated as a continuous estimation problem, where the desired output is a waveform that is the maximum a posteriori estimate of the transmitted message. The resulting structure is a nonrealizable, nonlinear system. We next find a demodulator structure that is realizable with delay, whose performance approximates the optimum system. Keeping the demodulator structure optimum, the transmitted signal is now optimized to obtain the best overall system. Two types of system constraints are considered. The demodulator is constrained to be above threshold, and the rms transmitted bandwidth is constrained. The modulator consists of a linear preemphasis network followed by a no-memory angle modulator. We find the linear network which causes the overall system to be optimum. Finally, we compare the optimum system to a phase modulation system using an optimum demodulator and properly chosen modulation index. For the class of message spectra, the difference is small.