The Probability Distribution of the Sum of N Sampled Baseband Outputs of a Product Detector Whose Inputs are Equal Power Coherent Narrow-Band Signals in a Gaussian Channel

General expressions for the probability distribution and density of the sum of
N
low-pass filtered outputs of a multiplier whose inputs are coherent, equal power noisy narrowband signals are derived in a finite series form. Graphs of the density for several values of
N
and two signal-noise ratios are presented and discussed.