Noise tolerance of diversity reception in frequency-adaptive digital transmission systems

This study investigates the influence of inaccurate estimation of the signal-to-noise ratio on the mean error probability in a frequency-adaptive digital transmission system employing space-diversity reception. The system operates by combining M spatially-separated signals and analyzing the equivalent signal-to-noise ratio for each of the N frequencies allocated for communications. The best frequency (in terms of the maximum signal-to-noise ratio at the output of the combining device) is sent back to the transmitter over the feedback channel, so that the signal can be emitted at the optimum frequency. The analysis assumes that signal feeding in the diversity branches is statistically homogeneous and mutually independent; additive interferences are approximated by normal white noise. It is found that the mean error probability is a strong function of the accuracy with which the signal-to-noise ratio is estimated (sample size n); for n = (5 - 6)N this probability is the same as that of a hypothetical system in which the average signal-to-noise ratio in any of M statistically homogeneous diversity branches is assumed to be known.