Accuracy Estimation of Window-Based Nonlinear Frequency-Modulated Waveforms

We present a generalized framework for designing rectangular envelope (RE) window-based nonlinear frequency-modulated (NLFM) radar waveforms and derive a closed-form expression of the Cramér–Rao lower bound (CRLB) for their range-Doppler accuracy. This provides a means for creating accurate measurement covariance matrices needed in Kalman filter applications when using said waveform and may be utilized for waveform agile radar systems. First, the proposed approach shapes the waveforms power spectral density with a generalized cosine-sum window. Then, we construct the time domain representation using the principle of stationary phase (PoSP) and a Fourier series approximation. Next, the sidelobe behavior of the resulting waveform is analyzed and a method for masking mitigation by placing nulls as desired in the autocorrelation response is presented. Finally, we derive a closed-form expression for its CRLB and simplify it further for cases where only a reduced set of spectral shaping parameters is needed. Numerical simulations confirm that the theoretical findings match with Monte Carlo evaluations. The proposed waveform is more accurate than traditional ones based on Gaussian amplitude modulation (AM) when jointly estimating range and Doppler.