SUMMARY AND DISCUSSION OF SIGNAL-TO-NOISE RATIO IMPROVEMENT FORMULAE FOR FM and FM/FM LINKS

Frequently, a need exists to compute the postdetection (recovered data) signal-to-noise ratios (SNR) in a given frequency modulated (FM) or double frequency modulated (FM/FM) transmission link; alternately certain postdetection SNR requirements are established, and the link’s parameters must be correspondingly specified. In either case, relationships that clearly relate postdetection SNR to link parameters, for either FM (or FM/PM) or FM/FM links, are useful to the telemetr system designer. Although such relationships have been stated 2), 3), 5) in varying degrees of applicability, and rigor of derivation, it has been the author’s experience that the sources are scattered, and often not sufficiently explicit. Further, the deviations from the mathematically ideal situation are often overlooked. It is the purpose of this paper to present useful SNR improvement formulae for the general FM and FM/FM case (both for IRIG and non-IRlG multiplexes), and also present data that takes nonideal postdetection filtering into account. PRELIMINARY SYSTEM DESCRIPTION The elements of a typical FM or FM/FM transmission link, as analyzed, are shown in Figure 1. An FM link would begin at the modulator input, and terminate at the carrier demodulator output (after postdetection filtering). The modulating data signals considered will be assumed periodic; however, this is not a limitation, since the postdetection SNR derived can be considered to apply to aperiodic signals during their time of occurrence. The FM/FM link in its most general sense will employ i subcarriers, of different center frequencies and deviations, each frequency modulating the carrier. In addition, a more specialized analysis to two basic subcarrier modulation schemes, described by IRIG standards, will be carried out. These are the proportional and constant bandwidth channels; both will be discussed. TABULATION OF SNR IMPROVEMENT FORMULAE The glossary of terms is given at the conclusion of this paper. Sinusoidal signal modulation is presumed throughout the discussion. Single FM (same as second detection in FM/FM link) (1) For ideal link elements, *, the degradation factor, is set at – 1.0. Otherwise, a value of * can be selected from the appropriate Figures 2 through 4 (d). A more general form of Equation (1), which can be used below threshold (defined as the departure from linearity on the SNR transfer characteristic) is given below) (2) For SNRif >> 1, i.e., the above-threshold case, Equation 2 simplifies to Equation 1. Subcarrier Predetection SNR Relative to Carrier SNR, in FM/FM Link