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The impact of High Resolution Spectral Analysis methods on the performance and design of millimetre wave FMCW radars D. Bonacci1 , C. Mailhes1 , M. Chabert1 , F. Castanié1 1: ENSEEIHT/TéSA, National Polytechnic Institute, 2 Rue Camichel, BP 7122, 31071 Toulouse Cedex 7, France, phone: +33 5 61 58 80 10, fax: +33 5 61 58 80 14, email: david.bonacci, corinne.mailhes, marie.chabert, francis.castanie@tesa.prd.fr Abstract: This paper addresses the problem of joint estimation and consequently range and velocity measures of range and velocity of moving targets using estimation. These procedures come from recent signal millimetre wave FMCW radar (in the 77 Ghz range) processing investigations and include parametric within the field of automotive applications. The proposed modeling [1] (as Autoregressive predictive methods) and solution is to determine range and velocity using spectral subband decomposition [2-3]. In section 2, FFT-based and estimation of downconverted signals, theoretically High-Resolution (HR) methods are discussed. Section 3 is composed of multiple sine functions embedded in noise. devoted to subband decomposition and its interesting As a consequence, their accuracy is closely related to the properties, especially for parametric spectral estimation. accuracy of frequency estimation. In this paper, High In section 4, simulation results are presented and Resolution spectral analysis methods (such as Auto- commented. The last section gives conclusions. Regressive or Prony modeling) are shown to strongly impact the technological design constraints of the radars. 2. Frequency estimation methods More precisely, for a given sampling frequency of the Downconverted FMCW signals can be written as a sum of downconverted signal, these methods show their ability sinusoids with given amplitudes, phases and frequencies either to significantly reduce the bandwidth of the linear embedded in some additive noise. For range and velocity frequency modulated radar sweeps although keeping estimation, the main concern is the estimation of constant the frequency resolution, or, for a given frequencies. technological design, increase the same figure of merit. Moreover, adequate pre-processing of the signal is 2.1 FFT-based methods described, yielding correction of some 'nasty' non-linear The main interest of classical periodogram-based methods effects (VCO, mixers, …) as well as denoising received is their low computational cost, since they use FFT (Fast signals. Theoretical study of the performances is given Fourier Transform) algorithms. But these methods suffer and illustrated on simulated and real signals (provided by from two important problems referred in [4] as short- the RadarNet project of the 5th Framework Program). range and long-range spectral leakage. Keywords : High Resolution Spectral Analysis, millimetre The first problem is the bias induced by the computation wave radars, automotive applications. of FFT in a grid of discrete frequencies. Zero-padding is a way to mitigate this problem but it can be computationally expensive if high accuracy is needed. More adapted 1. Introduction methods dealing with the granularity of the FFT have been developed, like the Interpolated FFT (IFTT) in [5-6], Within the field of an European project or the Weighted Phase Averager (WPA) method [7-8]. In (http://www.radarnet.org/), automotive vehicules are these methods, a first coarse estimate of the frequency is equipped with FMCW (Frequency Modulated Continuous corrected using phase information of the periodogram. Wave) in order to prevent from collisions. The FMCW WPA methods achieve, in general, better results than signals obtained after demodulation are linear IFFT methods. combinations of sinusoids, the number of which is linked to the number of reflecting targets. Frequencies of these The second problem is long-range leakage. It denotes sinusoids carry both information of range and Doppler interference between sinusoidal components. It occurs shift. Thus, accuracy and resolution on speed and range

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