Communication at Low Data Rates - Oscillator Models and Corresponding Optimal Receivers

For virtually any model of an unstable oscillator, at low signal-to-noise ratios, the maximum-likelihood ratio receiver is asymptotically quadratic. A quadratic receiver roughly corresponds to a weighted spectral analysis of the received signal. Two major models of unstable oscillators which seem reasonable for low data rate communication using orthogonal signals are considered. The first assumes that the signal is a stationary narrow-band Gaussian process. The second assumes that the oscillator phase is a random process. Optimal receivers are obtained for the first model and several examples of the second. These receivers are all noted for their inordinate degree of nonlinearity and complexity.