The Effective Number of Pulses Per Beamwidth for a Scanning Radar

The effective number of pulses received when a radar scans past a target is analyzed in terms of the integration of a train of pulses of amplitudes determined by the antenna beam pattern. It has been customary to take for this number the pulses occurring in the half-power beamwidth, ß, and to assume that these pulses were all of full (mid-beam) amplitude (this assumption roughly compensating for the discard of pulses outside the half-power points). The present analysis is based on the existence of an optimum integration angle, which gives a greater improvement of signal-to-noise ratio than integration over greater or lesser arcs. This optimum is found to be 0.84ß for a Gaussian-shaped beam. Integration over this angle gives the same signal-to-noise improvement as integration over a rectangular-shaped beam of width 0.47ß. Thus the equivalent number of full-amplitude pulses is 0.47 times the number usually assumed, representing a reduction in calculated radar system sensitivity of 1.6 db.