Time Domain, Frequency Domain, and Ambiguity Function Analysis of Chirp-Barker Hybrid Radar Signals

This article explores the time domain characteristics, frequency domain properties, and ambiguity function visualization of hybrid radar signals combining linear frequency modulation (LFM) with Barker codes. We begin by examining LFM signals, which demonstrate linearly varying frequency over time, typically implemented using phase accumulation algorithms with quadratic phase modulation. The mathematical representation involves generating a signal with instantaneous frequency f(t) = f0 + k·t, where k represents the chirp rate, achievable through code like numpy.linspace() in Python or linspace() in MATLAB for time vector creation followed by complex exponential generation.

Next, we investigate Barker code signals - specialized binary sequences known for optimal autocorrelation properties that minimize sidelobes in pulse compression systems. These codes are generated using predefined sequences (e.g., 13-bit Barker code: [+1 +1 +1 +1 +1 -1 -1 +1 +1 -1 +1 -1 +1]) and implemented via digital modulation techniques, where each bit corresponds to a phase shift in BPSK modulation. The code implementation typically involves array initialization with bipolar values and convolution operations for matched filtering.

Finally, we analyze the hybrid signal's spectral characteristics through Fast Fourier Transform (FFT) algorithms and demonstrate the ambiguity function's implementation using 2D correlation techniques. The ambiguity function, computed through double integration or FFT-based methods, reveals the signal's resolution capabilities in range and Doppler domains. Practical MATLAB/Python implementations would involve meshgrid() for coordinate generation and contour plotting functions for visualization, enabling applications in modern radar systems for improved target detection and parameter estimation.