Chirp Signal Matched Filter Simulation with Phase Error Analysis

Linear Frequency Modulated (LFM) signals, commonly known as chirp signals, are widely employed in communications, radar systems, and various other applications. In signal processing, matched filtering serves as a fundamental technique for pulse compression, which enhances range resolution by compressing wideband signals into narrow pulses. Pulse compression processing typically involves correlating the received signal with a time-reversed conjugated version of the transmitted waveform using convolution operations. However, during signal transmission and processing, various phase distortions may occur including first-order (linear), second-order (quadratic), third-order, fourth-order polynomial phase errors, and random phase fluctuations. These errors can significantly degrade pulse compression performance by causing mainlobe broadening, sidelobe elevation, and target positioning inaccuracies. Implementation typically requires phase error modeling using polynomial functions (e.g., polyval in MATLAB) and compensation through complex conjugate multiplication in the frequency domain. Signal quality assessment involves evaluating metrics like peak sidelobe ratio (PSLR) and integrated sidelobe ratio (ISLR) before and after error correction. Thus, comprehensive phase error analysis and compensation strategies are essential for maintaining signal reliability and measurement accuracy in practical systems.