Pulse Compression Sidelobe Reduction by Minimization of Lp-Norms

Most modern radar systems make extensive use of pulse compression techniques. This paper presents a technique for the design of mismatched receive finite impulse response (FIR) filters based on the minimization of L_p -norms of the sidelobes. The goal of the minimization process is to reduce the range sidelobe levels of the convolution of the transmit pulse and the receive filter. A closed-form solution is derived for the least-squares case (which is equivalent to the L₂-norm) and an expression for the optimization of the higher order norms is developed. The solutions for the higher order norms have to be obtained by means of iterative numerical methods. The effect of using receive filters which are longer than the transmit pulses is also investigated. Results are presented for linear FM transmit waveforms having time-bandwidth products ranging from 10 to 100 in combination with selected values of the norm order ranging from 2 to 200. Receive filter lengths up to three times the transmit pulse lengths are investigated. Results are presented which highlight the tradeoffs between sidelobe level, mismatch loss and mainlobe width. The effect of Doppler shift on the sidelobe response of these receive filters is also investigated.