This is the accepted version of the journal article: Verdú Tirado, Jordi; Guerrero, Eloi; Parrón Granados, Josep; [et al.]. «Star- shaped wheel for mechanical micro-Doppler modulation». IEEE antennas and wireless propagation letters, Vol. 20, Issue 12 (December 2021), p. 2452-2456. DOI 10.1109/LAWP.2021.3114440 This version is available at https://ddd.uab.cat/record/274029 under the terms of the license 1 Star-Shaped Wheel for Mechanical Micro-Doppler Modulation Jordi Verdú, Senior, IEEE, Eloi Guerrero, Student Member, IEEE, Josep Parrón, Antonio Lázaro, Senior, IEEE and Pedro de Paco, Senior, IEEE Abstract—This paper investigates the possibility of using star-shaped rotating wheels with deliberated geometries which provides unique micro-Doppler signature. Beyond the signature g provided by the rotation rate of the target, additional information a related with a particular target can be obtained taking advantage of specific and unique modulation waveforms. This feature d can be very useful to increase detectability and classification and the approach can be used to generate warning signals in applications such automotive radars. Different star-shaped wheels with particular geometries have been designed demonstrating different reflection characteristics and modulation waveforms. The signature of these rotating star-shaped wheels has been measured in an anechoic chamber using a general purpose 24 GHz FMCW radar platform. As a detection method, an algorithm based on the derivative of the cross-correlation is proposed which validates the proposed approach. Index Terms—Frequency-Modulated Continuous Wave, Micro- Doppler, Radar Fig. 1. 3D manufactured 5, 10, 20 and 30 tip star-shaped wheels prior to covering with copper layer. I. I NTRODUCTION OMPARED with other radar configurations, Frequency- C Modulated Continous Wave (FMCW) radars allow micro-dynamics (vibrations, rotations) identification due to describing a rotation around a reference axis as it is the case of rotating blades [11], [12]. Beyond the dynamic analysis of previous works, in this their capability in micro-Doppler detection beyond range and contribution we analyze, simulate and validate how the shape relative velocity. The working principle of a FMCW radar of the rotating target determines the time-dependent radar is based on the transmission of a continuous frequency- cross section (RCS) which takes the role of the modulation modulated microwave signal that will be later mixed with the waveform. The spectrum of the IF signal is not only deter- signal reflected from the target. Phase variations in consecutive mined by the frequency allocation of side lobes, given by the chirp ramps provide precise information about a specific rotation rate, but also by the amplitude which is directly related target reaching sub-λ resolution [1]. FMCW radars have been to the time-dependent RCS. This particular feature can be of successfully used in human target detection and classification interest in some applications, such as automotive radars, where applications related to autonomous vehicle [2], [3], medical unique micro-Doppler signatures can be generated to identify monitoring [4], [5], or retrieval of audio signals by measuring objects on the road and/or to avoid spoofing attacks. micro-vibrations [6] among others. Micro-Doppler phenomena is related to a frequency modu- In previous works [13], [14], it has been demonstrated lation in the reflected signal when the target is under certain that rotating elements can be used as warning signals (traffic mechanical vibration or rotation. This feature has been very control, road works signalling, etc...). In this work, instead useful in order to classify or recognize the nature of different of using 90 degrees rotating dihedral reflection corners, the objects since the micro-Doppler signature can be related to influence of star-shaped geometries is investigated to obtain specific geometric or dynamic characteristics [7]–[10]. The additional information from the target and thus improve the de- rotation-induced micro-Doppler modulation occurs when a tectability. Taking advantage on the additive 3D manufacturing certain target moves from a given position to a new one technologies, different star-shaped wheels in Fig. 1 have been designed with the objective to provide particular and specific J. Verdú, E. Guerrero, J. Parrón and P. de Paco are with the Department modulation micro-Doppler signals by means of the particular of Telecommunications and Systems Engineering, Universitat Autònoma de Barcelona. 08193 Cerdanyola del Vallès, Spain: (Jordi.Verdu@uab.cat). time-dependent RCS. The wheels have been covered by an A. Lázaro is with the Electronics, Electrical and Automatics Engineering adhesive cooper layer to increase the reflectivity of the targets. Department, Universitat Rovira i Virgili. 43007 Tarragona, Spain. Since the modulation signal is mechanically generated, it This work has been supported by the Spanish Secretarı́a de Estado de Investigación, Desarrollo e Innovación under Grant RTI2018-096019-B-C33. is independent from operating frequency which may hinder electronic designs at high frequencies, for example in the 77 2 GHz band. Since the objective is to use these targets as a warning signals, the received IF signal will be known a priori, therefore, similarly to [15], a method based on the derivative of the cross-correlation between the reference (simulated) and the received (measured) has been implemented. This contribution is organized as follows, the theoretical analysis of the received IF signal is carried out considering the time-dependence of the RCS is found in Section II. In Section III it is compared the previous simulation results with the measurements of rotating star-shaped wheels on an anechoic chamber with a 24 GHz FMCW radar. In Section IV (a) (b) an algorithm is proposed to carry out the signal detection based on the cross-correlation. Finally, the conclusions are presented in section V. II. M ECHANICAL M ODULATION BY MEANS OF T IME - DEPENDENT RCS The basic mode of operation of the FMCW radar consists in the transmission of L chirps of duration Tc which will be later translated to intermediate frequency (IF). The chirp signal is defined by an amplitude A, the carrier frequency fc and the (c) (d) chirp sweeping slope µ = B/Tc , being B the bandwidth. The Fig. 2. Normalised polar representation of the monostatic RCS for the (a) 5 received signal will be delayed with an amplitude proportional tip, (b) 10 tip, (c) 20 tip and (d) 30 tip star-shaped wheels respectively. to the radar cross-section σ of the target. For a simplified rotating target modelled using N backscatters, the IF signal can be obtained by the contribution of each one as [13], p Y  t  −j2πfc τ − µτ 2  Taking into account the size of the target, d = 5.6 cm, as well xIF (t) = A σ(t) e 2 e−j2πµτ t (1) as the operating frequency 24 GHz, far-field conditions can Tc be assumed so the monostatic RCS in Fig. 3 is used to model In the case of the 90 degrees rotating dihedral reflection the received IF signal. Otherwise, in a near-field scenario, the corners, the modulation waveform is very similar to an on- RCS should be computed as the integration of the electric off keying (OOK) ASK modulation which is modelled by the field in the radiation pattern of the antenna. The resulting RCS term e−jβ sin(Ωr t+θ0 ) as developed in [13], where β = 4πd/λ has been normalized with respect its maximum value with the is the modulation index in FM signals (being d the radius of aim to compare the behaviour among the different wheels. the wheel), and Ωr is the rotation rate. However, our star- The RCS is periodic for all the wheels. Depending on the shaped wheel cannot be modelled in the same way because angle between adjacent walls the number of RCS peaks can the walls reflect the incident electric field in a particular be N (N = 10 and 30) or 2N (N = 5 and 20). Of course, direction, or generate internal reflections between adjacent different geometries would lead different RCS behavior. This walls, triggering destructive or constructive interferences in is an interesting feature to improve recognition. the LOS of the radar. Therefore, the geometry of the target Without loss of generality, the 20 tips star-shaped wheel has will have an influence on the modulation waveform. Due to been simulated using different rotation rates Ωr = 300, 800 the time-dependence of the RCS the theoretical approach in and 1400 RPM. As shown in Fig. 4, and using the obtained (1) is not precise enough to properly model the received IF RCS in Fig. 3 as modulation waveform, first side lobes are signal. found at 100Hz, 266 Hz and 466 Hz respectively, being the To analyze the impact of the RCS on the received IF signal, consecutive second and third side lobes separated by N Ωr four different star-shaped wheels with 5, 10, 20 and 30 tips, which is in agreement with results in [17]. It is also important shown in Fig. 1, have been designed with radius d = 5.6 cm to highlight that the amplitude of side lobes does not depend and tip angle α = 24◦ in all of them. With this geometric on the Ωr . The amplitude for first, second and third side lobes definition, the angle between adjacent walls γ is different in all is coincident for all the rotation rates, and only depends on the wheels and so is the corresponding RCS. The monostatic the modulation waveform. For Ωr = 300 RPM, the amplitude RCS has been obtained for each wheel by means of 3D of the third side lobe is not perfectly aligned with the others simulation using FEKO software [16] as shown in Fig. 2. The as it occurs for higher rotation rates. This is due to the fact incident angle at which maximum reflection occurs is different that this side lobe is approximately allocated in the limit of in all of them, as well as the monostatic RCS periodicity which the modulation bandwidth which can be approximated as Bw is related to the number of tips N . Fig. 2 shows that all wheels ≈ 2(β + 1)Ωr /2π [13]. For Ωr = 300 RPM (5 Hz), the third generate strong echoes for that incident angles where one wall (k = 3) side lobe is allocated at kΩr N = 300 Hz, being Bw is perpendicular to the LOS of the radar. ≈ 580 Hz (with d = 5.7 cm and f0 = 24 GHz). 3 1 0.5 0 0 50 100 150 200 250 300 350 1 Modulation Waveform 0.5 0 0 50 100 150 200 250 300 350 1 0.5 Fig. 5. Characterization set-up inside the anechoic chamber. The distance 0 between the radar and the rotating wheel is R0 = 2.6 m. 0 50 100 150 200 250 300 350 1 0.50 0 Eq. (4) Monostatic -50 0 Bistatic 0 50 100 150 200 250 300 350 -50 -100 Incident angle -1500 -1000 -500 0 500 1000 1500 0 Normalized Level (dB) Fig. -100 3. Obtained RCS for the different wheels as a function of the incident -50 angle φ. From -1500 -2000 top to bottom -1000 5, -500 10, 20 and 0 30 tip star-shaped 500 1000 wheels. 1500 2000 -1500 -1000 -500 0 500 1000 1500 0 0 Normalized Level (dB) 1st side lobe 300 RPM 800 RPM -50 2nd side lobe 1400 RPM -50 3rd side lobe -100 -1500 -1000 -500 0 500 1000 1500 0 -50 -100 -2000 -1500 -1000 -500 0 500 1000 1500 2000 -100 -1500 -1000 -500 0 500 1000 1500 Doppler Frequency (Hz) Doppler Frequency (Hz) Fig. 4. Simulated received signal for 300 (solid black), 800 (dashed green) Fig. 6. Comparison between measurement (black) and simulation (yellow) and 1400 (solid yellow) RPMs in the 20 tip star-shaped wheel. received signal for the 5 (@1000RPM), 10 (@1100RPM), 20 (@1400RPM) and 30 (@1550RPM) tip star-shaped wheels (from top to bottom). From simulation results, it can be concluded that there is a trade-off between the rotation rate Ωr , the radius d of the The 5, 10, 20 and 30 tip star-shaped wheels have been mea- star-shaped wheel, and thus the modulation index β, for the sured at Ωr = 1000, 1100, 1400 and 1550 RPMs respectively. detection or recognition of side lobes. For low Ωr , it will be As shown in Fig. 6, there is a good agreement with theoretical interesting to use star-shaped wheels with large number of tips simulations. The allocation of the frequency lobes, given by N to increase separation between side lobes and facilitate the the product N Ωr , agrees with the theoretical prediction. The detection, and small N when the rotation rate is high. In case discrepancy in the amplitude of some lobes may come from of using large N at high rotation rates, it will be necessary vibrations in the elevation plane due to some vibration in the to use large values of d to increase the modulation bandwidth plane of rotation non considered in the theoretical model. For for detecting side lobes. sake of clarity in the comparison, the received signal level has been normalized in all cases. III. M EASUREMENTS AND C HARACTERIZATION OF IV. M ETHOD FOR D ETECTION OF ROTATING S TAR - SHAPED W HEELS S TAR - SHAPED W HEELS For the experimental set-up, each wheel with N = 5, 10, 20 The good agreement between simulation and measurement, and 30 tips, has been mounted on a generic current-controlled particularly in the allocation of the frequency lobes as well DC motor in order to characterize different rotating rates in an as the modulation bandwidth, allows to propose a detection anechoic chamber. The measurement set-up is shown in Fig. 5, method based on the derivative by finite differences of the where the distance between the radar and the rotating wheel is cross-correlation Rzx [n] in the discrete frequency domain R0 = 2.6 m. The measurements have been carried out using a between the reference (simulation) X[n] and the received general purpose 24 GHz FMCW DemoRad by Analog Devices (measurement) signal Z[n] as, and Inras. The operation bandwidth is 300 MHz leading to a ∞ velocity resolution of ∆v = 0.162 m/s, equivalently ∆fD = Rxz [n] = X[n] ? Z[n] , X X ∗ [m]Z[m + n] (2) 12.9 Hz for a Tc = 280 µs. m=−∞ 4 being ∗ the conjugate operator. N20 @1400 N10 @1250 N20 @1380 N30 @1810 Normalized Different experiments have been carried out in order to 0 Level (dB) validate the proposed detection method. First, a reference signal corresponding to a 20-tip star-shaped wheel has been -50 compared with the measurements for wheels with N = 10 -2000 -1500 -1000 -500 0 500 1000 1500 2000 Doppler Frequency (Hz) (green), N =20 (yellow) and N =30 (purple) tips in Fig. 7(a). 0 R xz (dB) Since the wheels are different (different N ), for the same Ωr -2 the lobes are not coincident. Therefore, different Ωr has been -4 set in each wheel (1250, 1380 and 1810 RPM respectively) 0 100 200 300 400 500 in such a way some lobes are coincident with the lobes in Samples the reference signal which increases the complexity in the 1 (Rxz)' detection of the target. The result of the cross-correlation Rxz 0.5 shows that the highest value along the samples corresponds 0 to the one related with the N = 20 tips wheel as expected. 0 100 200 300 400 500 Samples Moreover, the most interesting issue is the presence of peaks separated a distance of N Ωr , that is, at those positions where (a) all the lobes are coincident. This only happens for the case @800 @1590 @1380 @1100 @1400 where the number of tips as well as the rotation rate is 0 Normalized Level (dB) coincident. Therefore, the derivative of the cross-correlation 0 Rxz can be used to determine the most-likely signal by the -50 inspection of the peaks with the highest level as shown in the -2000 -1500 -1000 -500 0 500 1000 1500 2000 bottom of Fig. 7(a). Doppler Frequency (Hz) A second experiment has been carried out using the wheel 0 with 20 tips with different rotation rates. The signal to be R xz (dB) -2 detected is the one provided by a wheel at 1380 RPM (yellow -4 trace). A reference signal with 1400 RPM has been used (grey 0 100 200 300 400 500 dot-dash line) which is slightly different from the signal to be Samples 1 detected to emulate some drift in the Ωr value. (Rxz)' The cross-correlation Rxz shows the presence of different 0.5 peaks as before. However, the measurements of wheels at 1100 0 and 800 RPM (green and blue respectively) result in a higher 0 100 200 300 400 500 level of cross-correlation which may be not suitable to carry Samples out a successful detection. However, as previously commented, (b) the derivative provides unambiguous detection because the Fig. 7. (Top) Comparison between the reference signal (grey dot-dash peaks only appear when the distance between lobes N Ωr is line) and measured received signals, (middle) Cross-correlation between coincident. This is shown in the bottom of Fig. 7(b) where the the reference signal and measurements, (bottom) derivative of the cross- peaks with the highest level corresponds to the yellow trace, correlation. (a) Results for star-shaped wheels with different number of tips N , (b) Results for a 20 tip wheel at different rotation rates. the one with the RPMs closer to the reference. Then, the peak detection can be easily associated to the expected signal to be received. has been proposed. The method has been successfully applied V. C ONCLUSION to scenarios where a reference signal is compared with the In this paper, it has been demonstrated that specific geomet- expected measured signal and other signals provided by star- ric shapes may lead to a particular modulation waveform in shaped wheels with different rotation rates or different number rotating targets. To this aim, star-shaped wheels with different of tips. In all cases the signal with the highest cross-correlation number of tips have been designed and tested. The allocation is the expected one which demonstrates the reliability of the of the frequency side lobes in the IF signal is directly related proposed approach. to the rotation rate, being the separation determined by the product between the number of tips and the rotation rate. ACKNOWLEDGMENT However, depending on the modulation waveform, given by a certain geometry, the amplitude of side lobes may be The authors would like to thank the OpenLabs at Universitat different and not dependent on the rotation rate. This particular Autònoma de Barcelona for the support in the manufacturing behaviour may improve classification and identification of of the star-shaped wheels allowing the use of the additive rotating targets. 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