Design of Sum and Difference Patterns With Common Nulls and Low SLLs Simultaneously in the Presence of Array Errors

Sum ( $\Sigma$ ) and difference ( $\Delta$ ) beampatterns are commonly utilized to estimate the bearings of targets in the radar system. However, the nulls of $\Delta $ -pattern are not always aligned with those of $\Sigma $ -pattern, and this phenomenon would become more severe in practical scenario since the array errors exist. Meanwhile, the sidelobe level (SLL) of the array would also increase due to the unavoidable errors. The above-described factors would dramatically decrease the performance of radar in the adaptive suppression of interference. To increase the output signal-to-interference-plus-noise ratio of a radar system, this paper presents an approach to design the low SLL $\Sigma \Delta $ -patterns where the nulls of the $\Delta $ -pattern, excluding the central null, are always aligned with those of the $\Sigma $ -pattern in the presence of errors. Two schemes are addressed to obtain the covariance matrix for null-alignment constraint, which is exploited to force nulling in desired angles accordingly. In the sequel, the matrix tapering method is adopted to broaden the nulls and enhance the robustness for the possible errors. With the proposed approach, the low SLL and nulls alignment can be achieved simultaneously. Numerical examples are provided and discussed to demonstrate the effectiveness of the proposed solution, including the results based on a linearly spaced microstrip array antenna.