A model of the probability distribution of the signal–to–noise ratio estimated from BER measurements

For additive white Gaussian noise (AWGN) channels, first we show that the conditional probability distribution of the symbol error ratio (BER), in n transmitted symbols, can be modeled as lognormal in BPSK, QPSK and QAM transmission schemes, for a given average probability of symbol error p, and then we show that the channel signal-to-noise ratio (SNR), conditioned to p, can be modeled as a Gaussian random variable, as long as p >> 1, n >> 1, np >= 1000. The theoretical results could be useful in assessing bounds to the estimated SNR in terrestrial, satellite or deep-space AWGN channels. Moreover, from the estimated SNR, it should be possible to estimate the fading due to slow tropospheric phenomena, such as rain, water vapor, oxygen attenuation.