n such an adaptive system, information on the desired null direction is obtained from the measured covariance matrix. This contains the mean values of the cross-products of the Chapter 9 Antennas signals received by the array elements. For a two-element system, the covariance matrix M is given by equation 9.46, where S*S is a complex conjugate and <> denotes a time-averaged value. (9.46) For two isotropic elements and a single interferer at angle 0, equation 9.47 is obtained, where J is the jammer or interferer power, R is the receiver noise at each element (assumed uncorrected), and Q = (2nd sin 0) / 2. Jexp(jo) (9.47) The direction of the interferer can be derived using the relation of equation 9.48. exp(2j9)=M21 (9.48) In principle, the N x N covariance matrix of an element array can be used to find the directions of up to N-1 - interferers. For the commonly used maximum signal-to-noise adap- tive algorithm, this step can be avoided because the optimum element excitations (weights) are found by inversion of the covariance matrix (Rudge et al., 1986). The preceding theory has assumed that the wanted signal is absent when the adaptive weights are calculated. Wanted signal discriminations are an important topic in adaptive systems and take a number of forms. Possible discriminates include timing, spatial filtering, and coding. Reflective Antenna Types Reflective antennas are commonly used in terrestrial microwave and satellite applications. In this section, a simple parabolic reflector is first described, followed by "dual-symmetric" and "offset" antenna designs that are able to give improved performace. The properties of various forms of horn feeder, which are used with reflective antennas, are also described. Prime-Focus Symmetric Reflector Antennas The axisymmetric parabolic reflector with a feed at the focus of the paraboloid is the simplest type of reflector antenna. The geometry is shown in Figure 9.10. The paraboloid has the property that energy from the feed at F goes to the point P on the surface, where 