# Accession Number:

## AD0411222

# Title:

## PERFORMANCE OF THE BIASED SQUARE-LAW SEQUENTIAL DETECTOR IN THE ABSENCE OF SIGNAL,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Personal Author(s):

# Report Date:

## 1963-07-01

# Pagination or Media Count:

## 25.0

# Abstract:

G. E. Alberts general sequential test for making one of r distinct decisions about a distribution function F x sub i given x sub i-1 by observ ing a sequence of x sub is is presented, and his results, which give the performance of this test as the solutions of integral equations, are stated. These equations are then used to treat the incoherent detection of a sinewave in Gaussian noise by a biased square-law detector. This detector uses samples y sub j of the envelope of the received waveform to calculate the sums x sub i k times the summation between i and j 1 of y sub j squared-bias, i 1, 2, ..., and sequentially compares the x sub i tohres holds until an x sub i less than the lower thres hold B or greater than the upper threshold A is found. Then if x sub i less than or equal to B it is decided that the signal is not present dismissal, and if A less than or equal to x sub i it is decided that the signal is present alarm. For y sub j having the Rayleigh proba bility distribution fy y exp minus y squared divided by 2, i.e., for the received waveform consisting of Gaussian noise alone, exact solu tions are obtained for the probability of false alarm and for the average test duration. These solutions are unique in that they involve no approximations. Curves of the probability of false alarm versus the upper threshold A, and of the average test duration versus the expected input signal-to-noise ratio are presented. Author