Design of Optimum Weighting Functions for LFM Signals

Abstract

Linear frequency-modulated (LFM) pulse signals are probably the most common type of pulse compression waveforms for various radar systems (Barton, 2005; CookB Curlander & McDonough, 1991; Levanon & Mozeson, 2004; Richards, 2005; Skolnik, 2008). LFM signals are also often the waveform of choice for wideband systems, where the required bandwidth may be hundreds of megahertz. The ambiguity function of the LFM signal suffers from significant sidelobes, both in delay (range) and in Doppler. It is known, for example, that the first range sidelobe is approximately 13 dB below the main peak of the ambiguity function. Such sidelobes may be unacceptable in many applications due to system performance degradation caused by high sidelobes (Cook & Bernfeld, 1967; Levanon & Mozeson, 2004; Richards, 2005). To suppress the sidelobes some form of weighting can be applied to the matched filter response. The main drawbacks associated with conventional weighting functions (e.g., Hamming, Kaiser windows) are the broadening of the main lobe of the ambiguity function cut along the time axis and an inevitable attenuation in the peak response which decreases the signal-to-noise ratio. The chapter provides theoretical justification for a new approach, which is being applied to the design of discrete weighting function, or in other words, digital mismatched receiving filters. This approach considers the design of weighting functions as a problem of finding such a digital mismatched filter that will maximize the proportion of the total response power that is concentrated in the specified time-frequency region. Two applications of the proposed approach are theoretically addressed in sections 2 and 3. First, in section 2, we apply it to the problem of the optimum Doppler-tolerant pair signalfilter design when a given signal is specified to be an LFM signal. Section 3 addresses the specification of weighting functions in interferometric synthetic aperture radars with the purpose of improving the height measurement accuracy. Both of these sections are supplimented with numerical results, which demonstrate benefits that one can derive from using the proposed optimum weigthing functions as compared to conventional weighting functions. Conclusions are given in section 4.