NLFM

NLFM stands for Non-Linear Frequency Modulation, a class of frequency-modulated waveforms in which the instantaneous frequency varies according to a nonlinear function of time, unlike linear FM (LFM) chirps where frequency changes linearly during the pulse.

The primary motivation for NLFM is to shape the waveform’s spectrum and autocorrelation function to achieve lower sidelobe levels, improving target detection and range resolution in radar and sonar systems, especially in noisy environments. By choosing a nonlinear time-to-frequency mapping, designers can suppress range sidelobes more effectively than with standard LFM.

Design methods for NLFM typically involve determining a nonlinear frequency history f(t) that yields a desired spectral envelope or autocorrelation shape. Approaches include solving integral relations that link the frequency function to the target sidelobe spectrum, or applying window-design ideas (for example, Chebyshev or Kaiser-type envelopes) to guide the frequency progression. The resulting waveform often features curved frequency trajectories (quadratic, exponential, or higher-order polynomials) rather than a straight line.

Practical considerations include increased design and processing complexity, and potential sensitivity to Doppler shifts and range-Doppler coupling. The benefits—reduced peak sidelobes and more controlled off-peak response—must be weighed against these costs.

NLFM is used in radar and, to a lesser extent, sonar and experimental communications contexts where suppressing range sidelobes is advantageous and the added complexity can be justified.