Generation of Time-Domain Waveforms for Weibull-Distributed Clutter

Weibull-distributed clutter modeling is a widely used environmental simulation technique in radar and communication systems. The core principle involves adjusting shape and scale parameters to simulate non-Gaussian random processes with different characteristics.

Time-domain waveform generation typically follows three steps: First, determine the Weibull distribution's shape parameter β (controlling tail characteristics) and scale parameter η (determining distribution range). Then generate random sequences conforming to this distribution using inverse transform methods or product methods. Finally, apply linear filtering for correlation control. In code implementation, this often involves using wblrnd() function in MATLAB or implementing inverse CDF transformation with random number generators. The amplitude spectrum can be directly obtained through discrete Fourier transform, where the spectral envelope trend shows strong correlation with parameter β - smaller β values result in more pronounced spectral tailing phenomena.

Spectral analysis requires special attention to phase randomization. While preserving amplitude spectrum characteristics, phase should be constrained with uniform distribution to ensure time-domain signal stationarity. Engineering implementations often combine IIR filters for coloring processing, enabling output clutter power spectra to meet specific scenario requirements (such as sea clutter's 1/f characteristic). In practice, this can be implemented using filtfilt() for zero-phase filtering or designing Butterworth filters for specific spectral shapes.

This model holds significant value in radar target detection and electronic warfare applications. By adjusting β, it can flexibly simulate various electromagnetic environments ranging from Rayleigh distribution (β=2) to impulse noise (β<1). The flexibility makes it particularly useful for testing detection algorithms under different clutter conditions.