The Effect of Weighting upon Signal-to-Noise Ratio in Pulse Bursts

The Doppler sidelobes of a received pulse burst may be partially controlled by varying the amplitudes of the pulses in the burst or sequence upon transmission and/or reception. When there is a peak power limitation, weighting the amplitudes produces a loss in signal-to-noise ratio. A general expression is derived for the loss factor under the peak power limitation, and loss factor formulas are given for the following cases: Case A: Full nominal weights upon reception. Uniform weights on transmission. Case B: Square roots of the nominal weights on both transmission and reception. Case C: Full nominal weights on both transmission and reception. These cases are listed in order of increasing loss. Numerical results are tabulated for regular spacings and for the following nominal weights: 1) Dolph-Tchebycheff, 2) Taylor, 3) Hamming, and 4) Hann.