Adaptive transmit nulling using waveform embedded dithers

This paper describes a novel concept for performing adaptive transmit nulling in radars. Typically, the average depth of open-loop transmit nulls is limited by the Error Sidelobe Level (ESL) of an array. The ESL is determined by random errors in the array manifold, such as the residual calibration errors. Theoretically, it is possible to null below the ESL by using the backscatter from a target to create a null adaptively. The objective function to be minimized in this case is the power of the received backscatter in the direction of the target, which is assumed to be the same as the desired null direction. A potential drawback to this nulling approach would be long radar dwell times on the target to estimate the gradient of the objective function. To accelerate the convergence of a closed-loop transmit nulling algorithm, this paper proposes a theoretical technique for estimating the gradient of the array beamformer output in near real time by embedding narrowband sinusoidal dithers in the transmitted waveform. Dithers are externally applied disturbances that have been used in control system and signal processing applications to mitigate the effects of nonlinearity, hysteresis, and quantization [1, 2]. Typically the dithers applied are wideband random signals, essentially additive noise. The dithers described in this paper are different however in that they are narrowband sinusoids. The proposed dithering technique has been successfully applied to optical communication links to achieve adaptation speeds on the order of microseconds, [3] [7]. The simulated results in this paper are intended to demonstrate the feasibility of using narrowband dithers to perform adaptive transmit nulling in near real time on radars.