6.6 Sum Beam Equalization

To steer a broadband sum beam, we need only to replace the simple phase shift at the carrier frequency corresponding to the relative delay that is to be compensated, which is applied to the output of each element in the narrowband case, with the delay itself. In fact, it is not easy in practice to provide flexible delays at RF, as would be required for a beam to be steered freely in various directions, but for arrays with digital processing, we can provide a very close approximation to the required delays using the methods discussed here, which can be implemented rapidly. In fact, as the processing is carried out at baseband, after downconversion and digitization, the delay is implemented at baseband. The phase shift on the carrier is still required and can be applied at the RF stage, as for the narrowband application, or digitally after downconversion, but is independent of the equalization process. For the sum beam, considered here, the channel equalization is a simple delay, which can be approximated by the methods of Chapter 5, so this application of equalization requires essentially no new ideas. However, we show the benefit of this equalization in the example of a simple array, and in the next section we consider the equalization for the difference beam, which is more complex and uses the results of Sections 6.2 and 6.3, and we illustrate this using the same array.

The system we model is a 16-element linear array of...