On Binary Data Transmission Error Rates Due to Combinations of Gaussian and Impulse Noise

Abstract

Error rates are computed for a binary data transmission system subject to both Gaussian and impulse noise. The rates are displayed as a function of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lambdaT</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> is the signal duration and λ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> is the average time between noise pulses. Poisson-distributed impulse noise and periodically recurring noise pulse clusters are considered. Error rates are computed for cases in which 2 per cent, 5 per cent, 10 per cent, 30 per cent, 50 per cent and 100 per cent of the total noise power is impulse noise power, and for signal-to-noise ratios that would give error rates of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10^{-4}, 10^{-5}, 10^{-6}</tex> and 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup> if the noise were 100 per cent Gaussian. A linear receiver and correlator are assumed and the assumption about the distribution of the correlator output caused by impulse noise is varied to illustrate how this assumption affects the error rate. Stretch transformations are used to modify the error rate curves presented according to system and noise pulse-width parameters. Simple graphical techniques are described for the construction of approximate error rate curves. The computed error rates illustrate, for data transmission systems subject to impulsive interference, the reduction in error rate that can be realized by increasing the signal duration. The simultaneous transmission of orthogonal signals is discussed. This makes it possible to use signals having a long duration without reducing the data rate or causing intersignal interference; this can be done without requiring additional bandwidth.