Duration of radar false alarms in band-limited Gaussian noise

The duration of threshold crossings is investigated for the envelope of band-limited Gaussian noise. The results are applied to the estimation of false alarm times for radar detection and it is shown that the average duration of threshold crossings may be much less than the reciprocal of the noise bandwidth. The average shape of large excursions of the envelope of noise is given by the autocorrelation function, ACF, of the noise. It is shown how the ACF can be combined with the probability density function of the peak values of the noise to give an approximate expression for the average duration of threshold crossings. The accuracy of this expression has been investigated by Monte Carlo simulation and good agreement is achieved when the probability of exceeding a threshold (probability of false alarm) is less than about 10 ^-2