Analysis of a cross correlator with a clipper in one channel (Corresp.)

General expressions are derived for the characteristic function and probability density function of the output of a cross crrelator utilizing a hard clipper in one input channel. The inputs are assumed to be
A_{1} \cos(\omega_{o}t)+n_{l}(t)
and
A_{2} \cos(\omega_{o}t+\phi)+n_{2}(t)
, where
n_{1}
and
n_{2}
are independent narrowband Gaussian noises. From the characteristic function, which is expressed in the form of a Fourier series in the relative phase angle
\phi
, a double series involving cosines of multiples of
\phi
and Hermite polynomials of all orders is obtained as the probability density function of the output. Both the characteristic function and the density function pertain to the output at only a single instant of time. The first and second moments of the output are also calculated from the characteristic function, and lead to a closed-form expression for the output signal-to-noise ratio as a function of the input signal-to-noise ratios. Limiting cases of the output signal-to-noise ratio are computed and compared with similar cases involving the more conventional analog correlator without clippers and with the polarity-coincidence correlator.