Wide-band adaptive antenna nulling using tapped delay lines

For some applications it is desirable to have an antenna which can adaptively form antenna pattern "nulls" in the directions of a collection of interference sources. These nulls are generally required to be below some specified level of directive gain over the entire system bandwidth. Typically the nulls are formed by adaptively weighting each output of an N -port antenna, such as an N -element array. For large arrays operating over wide percentage bandwidths, some sort of frequency compensation is required at each output port to accomplish broad-band nulling. One technique commonly used is to employ a "tapped" delay line at each element output, with controllable weights (frequency independent) at the output of each tap. The objective of this paper is to develop some insight into the way in which delay-line compensation leads to improved performance, to develop some quantitative estimates of how performance varies with antenna and delay-line parameters, and to develop some tools useful in the performance evaluation of frequency-dependent weighting. Practical considerations dictate that only a minimum number of taps/ element be utilized. A primary consideration is to minimize the number of taps required for a specific system performance. With this objective in mind, we develop an analytic solution characterizing the two-element array, employing a two-tap delay line with each element. This provides valuable insight into the mechanism of delay-line compensation. Results for this simple case will then be extended to the N -element planar array using N_{t} taps/element. Tap spacing which optimizes the array performance from the viewpoint of providing wide-band nulls on sources incident on the array from locations arbitrarily specified over the antenna field of view is developed and applied to numerous types of array configurations. The composite performance of nine specific array configurations is used to estimate the number of taps and tap spacing which would be required for an arbitrary array configuration, as a function of the array and delay-line parameters \Delta_{\gamma m} = (2_{\pi}D/\lambda) \sin \theta_{m} , FBW, \phi_{0} , and N_{t} where FBW is the fractional bandwidth (100\ast FWB = percentage nulling bandwidth), \theta_{m} is the maximum scan angle off broadside, \phi_{0} is the tap spacing (in degrees, relative to the center-band frequency), D is the maximum aperture dimension, and N_{t} is the number of taps. The implications of using an Applebaum-Howells type of adaptive processor to determine the delay-line output weighting, and the algorithm effects on performance, are also developed.