ORing loss for quantizers followed by an ORing device and an accumulator

A mathematical model is developed to compute the ORing loss for quantizers followed by an ORing device and an accumulator. A three-bit (eight-level) quantizer is selected as an example. The ORing loss is then computed using Gaussian input statistics for a detection probability of 0.5 and false alarm probabilities of 10^-2, 10^-3, 10^-4, and 10^-6. The ORing loss is computed as a function of the number of channels ORed and the number of samples in the accumulator. It is concluded that there will be a large signal-to-noise ratio loss if integration is done following ORing