Approximate determination of the extreme threshold position in frequency modulation (Abstr.)

This study is devoted to approximately determine the reception threshold position in large lncex frequency modulation, as reached by the use of a hypothetical (yet unknown) optimum demodulator. First, an interpretation of threshold phenomenon is given, in the case of a continuous modulation system with modulation gain (i.e., which trades minimum necessary power against bandwidth). After SHANNON, demodulation is then represented as a non-topological mapping in high-dimensional signal spaces. For a continuous modulation system, however, it is locally topological (in a neighbourhood of the signal point). One may thus share the noise after demodulation into ,"neighbourhood" and "error" noise, whether the signal plus noise point remains or not in the locally topological neighbourhood of the signal point. The former is predominant above threshold, the latter below; threshold is defined by the equality of their powers. In the FM case, neighbourhood noise is already known, according to the conventional large signal theory. Error noise may be approximately computed after replacing the actual continuous modulating signal by a discontinuous one, in such a way that: a) the performance, as far as error noise is concerned, remains essentially unchanged; b) but the optimum demodulator is then explicitely known (optimum in the sense of maximum likelihood, in the presence of stationary white gaussian noise), and allows thus for the explicit computation of the extreme threshold position. For this purpose, the modulating signal is a) quantized (this is justified by the discontinuous nature of the error noise); b) sampled at the NYQUIST rate, each of the samples being held till the following occurs (this is justified with the help of basic principles of statistical communication theory). The modulated signal thus obtained with aL-levels quantization is (for large index, and a somewhat rough choice ofL) a (quasi-)orthogonalL-ary signal, for which explicit calculation of error noise is easy. Its results show that a large improvement beyond the threshold of limiter-discriminator type demodulators is possible, though not as large as sometimes written about frequencyfeedback demodulators. A physical interpretation of these results is them attempted, by the use of the concept of "short term" spectrum. Finally, a critical review of the frequency feedback type demodulators is given, and a novel type of demodulator is proposed, which is believed to more closely approach the theoretical limit than does the frequencyfeedback type.