Digital troposcatter transmission and modulation theory

In tropospheric scatter transmission beyond the horizon, the amplitude, phase and frequency of a received sine wave exhibit random fluctuations owing to variable multipath transmission and noise. The probability of errors in digital transmission over such random multipath media has been dealt with in the literature on the proemise of flat Rayleigh fading over the band occupied by the spectrum of transmitted pulses. This is a legitimate approximation at low transmission rates, such that the pulse spectrum is adequately narrow, but not at high digital transmission rates. The probability of errors is determined here also for high transmission rates, such that selective fading over the pulse spectrum band must be considered. Such selective fading gives rise to pulse distortion and resultant intersymbol interference that may cause errors even in the absence of noise. Troposcatter transmission can be approximated by an idealized multipath model in which the amplitudes of signal wave components received over different paths vary at random and in which there is a linear variation in transmission delay with a maximum departure ±Δ from the mean delay. Various statistical transmission parameters are determined on this premise, among them the probability distribution of amplitude and phase fluctuations and of derivatives thereof with respect to time and with respect to frequency. The probability of errors in the absence of noise owing to such fluctuations is determined together with the probability of errors owing to noise, for digital transmission by binary PM and FM. Charts are presented, from which can be determined the combined probability of errors from various sources, as related to the transmission rate and certain basic parameters of troposcatter links.