Mathematical analysis of main-to-sidelobe ratio after pulse compression in pseudorandom code phase modulation CW radar

The relation between main-to-sidelobe ratio and Doppler frequency after pulse compression in pseudorandom code (m-sequence) phase modulation CW radar is studied, and the deduction of its mathematical expression is presented. Since the pulse compression with the non-target range gate in m-sequence phase modulation CW radar is a “wide-band input, narrow-band output process”, the sidelobe’s real part and imaginary part after pulse compression approximately obey Normal distribution, respectively. Thus, the peak sidelobe’s real part and imaginary part can be calculated. Then the mathematical expression of the main-to-sidelobe ratio after pulse compression is also gained. Simulation study indicates that the data calculated by the mathematical expression of the main-to-sidelobe ratio is close to the data attained by simulation, when the period length of m-sequence p≥31.