Asymptotic Loss of the "Sum-of-Magnitudes" Approximation to a Square-Law Detector

Approximations to a square-law detector in digital signal processor implementations using quadrature channels result in a loss of detectability. Previous studies to determine this loss in several cases of practical interest are supplemented by an asymptotic analysis which applies when a large number of pulses are integrated. The results obtained show that the asymptotic loss due to the "sum-of magnitudes" detector, as compared to a square-law detector, is O.29 dB. Similarly, the asymptotic loss in a system which sums the magnitudes in a single channel (video MTI canceller) is 1.79 dB. For both of these results, it should be recalled, however, that even a perfect envelope detector is subject to an asymptotic loss of O.19 dB, as compared to the square-law detector.