The probability density function for signal absent is obtained for a class of three channel receivers commonly used for direction finding. The receiver considered here is closely related to the multiplicative array processors first considered by Miller (1973). The false alarm probability and noise mean are derived. The statistics for signal present appear to be intractable, but the false alarm statistics presented here may be used to properly set the threshold for a Monte-Carlo study of detection performance. Detection probability is presented for an example case.