MATLAB Code Implementation of Cross-Correlation Ambiguity Function

The cross-correlation ambiguity function serves as a crucial tool in signal processing, primarily used to analyze similarity between two signals. Implementing this function in MATLAB enables rapid assessment of signal matching quality, with applications spanning radar systems, sonar technology, communication engineering, and multiple other domains. The core mechanism of the cross-correlation ambiguity function involves evaluating signal matching degree through computed cross-correlation values. While MATLAB's built-in `xcorr` function can calculate basic cross-correlation, custom implementation becomes necessary for handling advanced scenarios involving time delays or Doppler frequency shifts. The function signature typically follows: `ambiguity_func = custom_xcorr_amb(signal1, signal2, delay_range, doppler_range)`. A standard MATLAB implementation approach involves: First, defining input signals as time-series data or sampled sequences using vectors like `sig1 = [s1, s2, ..., sn]`. Second, establishing parameter grids for time delays and frequency shifts through `meshgrid` or linear spacing functions. Third, computing cross-correlation values under various conditions using convolution operations, where FFT-based circular convolution (`ifft(fft(sig1).*conj(fft(sig2)))`) significantly reduces computational complexity from O(n²) to O(n log n). The analysis results are typically visualized through 3D plots such as contour maps or surface plots, where the x-axis represents time delay, y-axis denotes frequency offset, and color intensity reflects correlation magnitude. MATLAB's visualization commands like `contourf(delay, doppler, amb_matrix)` or `surf(delay, doppler, amb_matrix)` facilitate intuitive identification of optimal signal matching conditions. For implementation optimization, adjusting sampling rates (`fs`) and signal lengths involves trade-offs between computational accuracy and efficiency. Incorporating window functions (e.g., Hamming window via `hamming(N)`) mitigates spectral leakage and enhances ambiguity function resolution. Memory management techniques like pre-allocation (`amb_matrix = zeros(length(delay), length(doppler))`) prevent performance degradation during matrix operations. Custom MATLAB script development for cross-correlation ambiguity functions provides adaptability to diverse application requirements while deepening understanding of signal matching principles and time-frequency analysis methodologies. Key algorithmic considerations include proper normalization of output values and handling edge cases through zero-padding techniques (`padarray` function).