Finding the approximate angular probability density function of wave arrival by using a directional antenna

The first-order approximate angular probability density function of wave arrival can be obtained by plotting the mean-square value of signal level versus the pointing angle of a mobile radio directional antenna during an entire test run. The accuracy of this first-order approximation is dependent on the beamwidth of the antenna. As the beamwidth of the antenna becomes narrower, the approximate density function becomes more accurate. There are also higher order approximations for obtaining a more accurate angular probability density function without narrowing the directional antenna beamwidth. These higher order approximations are related to the moments of the signal strength received by the same directional antenna used in obtaining the first-order approximation. All of these are theoretical predictions. An experimental verification using a first-order approximate angular probability density function in finding theoretical level crossing rates of a mobile radio signal is given. The theoretical level crossing rates are in fairly good agreement with the experimental ones as long as the angular probability density function is not far from a uniform distribution.