Statistical study of an acousto-optic correlator in terms of its bandwidth

An acousto-optic correlator (AOC) associated with pseudorandom sequences (PRS), as used in spread spectrum receivers, is considered. Simple expressions are derived for the output signal-to-noise ratio of an AOC in two cases: when the frequency response H(f) of the correlator is equal to rect(f/?f) or equal to sinc(?f/?f), where rect(x) is the rectangle function, sinc(x) = sinx/x and ?f is the correlator bandwidth. These simple expressions are given in terms of the ratio a of the code bit rate Fc of the PRS to the bandwidth Af of the AOC. It will be shown that when H(f) = rect(f/?f) and a is greater than 2, a loss results in the output signal-to-noise ratio approximately equal to 1/? with respect to an ideal (infinite bandwidth) AOC. When H(f) = sinc(?f/?f) the loss equals 1.5/?.