Impulse Noise Performance Bounds for Binary Correlation Receivers

A general performance equation is derived for digital receivers in the presence of impulse noise. Two bounding techniques are employed to simplify the results. First, the Schwarz inequality removes the dependence on both the impulse noise waveforms and the signal-set basis functions. Second, the Chebyshev inequality is applied to the Schwarz results to additionally eliminate the statistical dependence on the probability density function of the noise waveform weighting factor. The bound curves are compared to specific theoretical results where the noise waveforms and probability density functions have been assumed. The tightness of the bound curves is a function of the signal-energy-to-noise-weighting-factor variance ratio and converges for the Schwarz bound as the ratio increases. Considerably looser bounds are obtained by the Chebyshev technique, but rough estimates of system performance can be obtained when the signalenergy-to-signal-energy-to-noise-variance ratio is the only known parameter.