The pdf and cdf for the sum of N filtered outputs of an analog cross correlator with bandpass inputs (Corresp.)

Several expressions are derived for the probability density and cumulative distribution functions associated with the sum of sampled outputs of an analog cross correlator. The correlator inputs consist of deterministic signals having the same frequency with additive correlated stationary narrow-band Gaussian noise processes. Spectral symmetry of the noises is not assumed, and the noise components in each input channel have distinct variances. Wherever possible, comparisons of our results with previous work are discussed. The results derived are more general than previous work and, for the most part, functionally less complicated.