Determination of Sweep Linearity Requirements in FMCW Radar Systems Based on Simple Voltage-Controlled Oscillator Sources P. V. BRENNAN Y. HUANG M. ASH University College London K. CHETTY University College London Jill Dando Institute Linear frequency modulated (FM), or chirp, pulse compression is a widely used technique for improving the range resolution of radar systems, although it often places quite stringent demands on FM sweep linearity. This paper examines the impact of sweep nonlinearities on the performance of frequency modulated continuous wave (FMCW) radar systems, particularly those employing simple voltage-controlled oscillator (VCO) sources, using a new and straightforward approach based on the fractional slope variation (FSV). Modeled results are presented, assuming a square-law source nonlinearity representation, showing the effect of such nonlinearities on point-target response and range resolution. These results are then related to the standard definition of linearity. Measurements from a commercial VCO are finally used to convincingly validate the work, resulting in a simple and practical method to predict the impact of source nonlinearity, as defined by the FSV parameter, on the performance of an FMCW radar system. Manuscript received July 27, 2009; revised December 14, 2010; released for publication March 27, 2010. IEEE Log No. T-AES/47/3/941750. Refereeing of this contribution was handled by R. M. Narayanan. Authors’ addresses: P. V. Brennan, Y. Huang, and M. Ash, Dept. of Electronic & Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, UK; K. Chetty, Dept. of Security and Crime Science, University College London Jill Dando Institute, Brook House, 2-16 Torrington Place, London WC1E 7HN, UK, E-mail: (pbrennan@ee.ucl.ac.uk). 0018-9251/11/$26.00 c ° 2011 IEEE I. INTRODUCTION Frequency modulated (FM) radar is an important class of radar system [1, 2], overcoming the range versus resolution compromise that exists in simple pulsed radar. A common way of implementing frequency modulated continuous wave (FMCW) radar is to employ a transmitted linear FM signal (“chirp”) and a receiver that downconverts the radar echoes using a local oscillator signal at the same FM sweep rate. The signal used for this downconversion, or deramp, process may be derived from a sample of the transmitted pulse (FMCW radar) or from an FM sweep source that is triggered by a tracker processor. A simplified arrangement of an FMCW radar system is illustrated in Fig. 1. The chirp source in such a radar system may be generated in several ways, including the use of a swept voltage-controlled oscillator (VCO), a surface acoustic wave (SAW) dispersive delay line, or digital generation. As suggested in Fig. 1, the output beat frequency after the deramp process for a return from a given target at range R has a constant value [1] of f d = 2R c B T (1) where R is the range, B is the sweep bandwidth, and T is the sweep duration. The deramped signal may be fast Fourier transform processed to yield the Fig. 1. Simplified arrangement of FMCW radar system. range profile of the target scene. Such processing has a frequency resolution of approximately 1=T, from which the well-known range resolution expression may readily be deduced as ¢f d = 1 T = 2¢R c B T i.e., ¢R = c 2B : (2) In such radar systems, successful range processing critically depends on the FM sweep linearity. For radar systems based on matched filters (such as SAW dispersive delay lines), such linearity requirements vary inversely with the time-bandwidth product; however, for FMCW radar based on deramp processing, the relation is rather different in that the effect of these nonlinearities scales with range. 1594 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 3 JULY 2011