Total error in signal processing due to linear detector approximation errors

Several linear approximations to square root of the sum of the squares operation are well known and have been designed for implementation by digital hardware. Various papers have been written which calculate the peak, average, and mean square errors of the approximations as compared to an exact linear detector. In many radar signal processors, in-phase and quadrature moving-target-indicator residues are combined by a linear approximation circuit and integrated to improve signal-to-noise ratio. For radar signal processors, it is shown that the total error contribution due to the linear approximation circuit is a function of: (1) approximation error curve, (2) input signal doppler frequency, and (3) number of residues integrated. Simulations and analytical results were used to illustrate this phenomenon.