Carrier-to-Noise Statistics for Various Carrier and Interference Characteristics

Techniques are presented for the calculation of the statistical properties of the resultant carrier-to-noise ratios of systems subject to both additive and multiplicative noise. The cases considered are those in which the desired signal is either steady or exhibits Rayleigh fading while the interference consists of receiver noise plus an interfering signal which may be steady, Rayleigh fading, Gaussian fading, or Rayleigh fast fading with slow Gaussian fading of the median of the Rayleigh distribution. The results of the indicated calculations are presented graphically. A simple process is outlined for converting the data presented for use with any other signal strength. The utility of the data is demonstrated by a sample calculation the results of which are presented graphically. This calculation derives threshold data for the system as a function of desired signal power with the percentage of time that it operates in one of its two possible modes (fading or nonfading) as a parameter. Attention is called to the technique demonstrated in the Appendix. This result appears quite useful in many joint or combination probability problems, especially those requiring numerical solutions. Although this paper stemmed from work on line-of-sight microwave links, the results may be useful in other applications in the hf, vhf, and uhf regions.