Optimized multirate filter banks for radar pulse compression

Abstract

Many modern radar systems transmit broadband chirp waveforms of long duration, thereby realizing time-bandwidth products in the order of 10' to lo4. Thus matched filtering in a digital radar receiver requires FIR filters possessing up to several thousand taps. Fast convolution based on an FFT with blocksize B of at least twice the matched filter length L , has been known for quite some time. With increasing blocksize, the limited numerical accuracy of fixed point hardware and the growing latency in heavily pipelined F F T processors become serious problems. In this paper we propose a novel structure, consisting of a multirate filter bank with analysis and synthesis filters based on an F F T of a much smaller size B x a and B channel filters with very sparse coefficients, so that for high time-bandwidth products the computational complexity becomes even smaller than for the standard fast convolution method. Applying a least-squares optimization algorithm on the sparse set of channel filter coefficients minimizes the sidelobes of the matched filter output signal. Chirp WaveformsLet s ( t ) = a(t)ejw(t) be the complex-valued baseband representation of a continuous-time FM waveform s ( t ) of duration r. In radar applications the amplitude a ( t ) of the transmitted waveform is usually held constant. The simplest FM waveform is a linear chirp [I], the name coming from the fact that its instantaneous frequencyis linearly swept over a total bandwidth / 3 during the pulse duration r. In a digital radar receiver the complex baseband signal s ( t ) is sampled at a constant rate fc, which we set to unity, without loss of generality, and obtain the discrete-time sequencewith the integer index n marking the sampling instant. We have also introduced a real-valued random variable A, because the exact time of arrival of the radar return is not known. In order to avoid aliasing, the sampling rate fc must he sufficiently higher than the approximate bandwidth P of the chirp signal, which leads to the condition p < 1.The finite impulse response c[n] of the digital matched filter or pulse compression filter [ l ] , is defined as the complex conjugate of the time-reversed waveform s ( n ) , and therefore has a length L x T . Usually the matched filter impulse response is additionally weighted by a window sequence w [n], in order to keep down the time or range sidelobes occurring in addition to the main correlation peak at the filter output, so we get the response ~ [ n ] = w[n]s* (-n). All examples presented in this paper will be based on a linear chirp s ( t ) with bandwidth P = 0.7 and duration r = 1440.The primary design goal is to achieve a minimum sidelobe suppression of at least 50 dB. "Perfect Convolution" Filter BanksRecently it has been shown [2], how a multirate filter bank with an arbitrary subsampling factor N , can be used to implement a running convolution of an infinitely long input sequence z [ n ] with a finite filter impulse response c[n] of length L. The Figure 1: Multirate filter bank with B channels subsampled...