Movement Detection Using a Modified FMCW Waveform and GNU Radio

Transcription

1 Movement Detetion Using a Modified FMCW Waveform and GNU Radio Ali Bazzi, Majd Ghareeb, Mohammad Raad and Samih Abdul-Nabi Shool of Engineering, Computer and Communiation Department Lebanese International University (LIU) Beirut, Lebanon Abstrat In this paper results of previous researhes and modifiations to the Frequeny Modulated Continuous Wave (FMCW) are applied on GNU Radio. GNU Radio is an open soure software for Software Defined Radio (SDR). The standard FMCW has frequeny hanging linearly with time. The frequeny hanges take the form of a triangle. Here, the triangular waveform is modified to obtain two triangles instead of one where the seond triangle has a different form. The system is implemented using GNU Radio. We obtained a good estimation of the distane and the speed of different targets. Moreover, the Doppler frequeny is estimated with a high preision. Keywords FMCW; Detetion; Estimation; GnuRadio; Radar I. INTRODUCTION The RADAR (RAdio Detetion And Ranging) is based on the propagation of Radio Frequeny (RF) eletromagneti waves. In the late of the 19 th entury, the experiments of Heinrih Heirtz showed that the eletromagneti waves are refleted by metalli objets. The Radar priniple was found in 1911 by the Amerian Hugo Gernsbak. In 1934, the Frenhman Pierre David suessfully did the first experiments to detet the presene of airraft. The first range alulations were applied on Iebergs with waves of 16 m wavelength. Then the radar had an important usage in military appliations. The radar uses the refletion properties of an eletromagneti wave on a target. The simplest and the first used waveform onsists on a series of pulses [1]. By measuring the delay τ between emission and reeption, it is possible to alulate the distane d between the radar and the target by the following equation: d = τ / 2 (1) where is the speed of the light (3x10 8 m/s). A pulse must have a short duration, A pulse width of 1 nm is needed to detet objets faing the radar with distane less than 1m. Moreover, another problem of Pulse Radar is that we annot detet nor alulate the speed of moving targets. This problem was solved by the Pulse-Doppler radar [2] where the pulses are modulated on a sine wave. But this system need huge power to work as expeted. A monohromati radar uses the Doppler effet and gives no information on the distane of the target [3]. A monohromati ontinuous wave radar system onsists of an RF transmitter and a reeiver that mixes the transmitted and the reeived signals to obtain the beat frequeny. The beat frequeny f b is defined as the differene between the frequenies of the reeived (f r) and the transmitted signals (f t): f b = f r f t. It is proportional to the relative speed (v) of the target: f b = 2f 0v where f 0 is the frequeny of the osillator. The problem of the monohromati radar is that it does not provide any information about the distane. FSK (Frequeny Shift Keying) radar [4] transmits a frequeny modulated waveform. This modulation uses at least two slightly different frequenies, i.e. f 0 and f 1 = f 0 + Δf whih are transmitted periodially every T seonds. The spetral analysis of the reeived information makes it possible to extrat the distane and speed. The reeived signals have equal amplitudes (proportional to the amplitude of the transmitted signal), the same frequeny (equal to the Doppler frequeny of the target) and a differential phase shift proportional to the distane to be measured. The speed is alulated by performing a time-disrete Fourier transform of the reeived signals. The targets are then deteted by a previously defined amplitude threshold. Given the small variation Δf of the frequeny of a target between two repetition periods, a target will give the same Doppler frequeny in the two adjaent intervals assoiated with f 0 and f 1. But the reeived signals have a phase differene Δφ = φ 0 - φ 1. From this phase differene, alulated by mixing the transmitted and reeived signals, the distane d of the target is obtained using the equation: d = φ 4π f This waveform is simple to produe but it an t detet unmoving targets. After looking to the different waveform tehniques, the FMCW is the best hoie to detet a moving or unmoving targets. II. FMCW THEORY In the ase of the FMCW radar [5], the transmitted frequeny varies ontinuously as a funtion of time, typially in a linear manner (figure 1). To detet a target plaed at a distane d, we mix the transmitted and the reeived signals to produe a beat frequeny f b. In the absene of Doppler (fixed target) this frequeny is only related to the distane of the target. (2) (3) (This work is liensed under a Creative Commons Attribution 4.0 International Liense.) 601

2 If we denote by f t(t)=f 0 + αt the transmitted frequeny. At the reeiver, we obtain the frequeny f r = f 0 + α (t-2d/). A mixer is used to provide the beat frequeny: f b = f r f t = 2αd Where α is the slope of the frequeny. Fig. 1. FMCW waveform But we have two ramps (up and down). So, for a nonmoving target, we obtain two beat frequenies: f b down = f b up = 2αd If the target is moving the beat frequenies are: and, f b up = f d 2αd f down b = f d + 2αd (7) Using equations (6) and (7) and beause the slope α is equal to the bandwidth B divided by the time of the slope (T/2), by a simple alulation, we an obtain the distane and the Doppler frequeny of the targets using: and, d = T 8B (f b down f b up ) f d = 1 2 (f b down + f b up ) Using equations (2) and (9) we an obtain the speed: v = (f down 4f b + f up b ) 0 (4) (5) (6) (8) (9) (10) As the distane is inversely proportional to the Bandwidth, we should use a large bandwidth to detet near objets. Conerning the speed, we need to use an osillator with a large frequeny. III. THE MODIFIED FMCW When we have multiple targets, it is hard to assoiate the f up and f down for eah target when using the FMCW waveform. Miyahra introdued in [6] a new waveform with two (or more) suessive ramps with slightly different slopes. In this waveform, the order in whih the beat frequenies are observed on the first ramp is idential to the order observed on the seond ramp. Thus, the assoiation between the beat frequenies on the ramps is easy, and the problem of FMCW is solved. The simplified assoiation between the beat frequenies, is a great advantage of this waveform. By ombining the idea of ramps of near slopes and that of ramps of opposite slopes, a new waveform, alled double FMCW, omposed of two suessive triangles with slightly different slopes between the first and Seond triangle was proposed. The order of the beat frequenies of the targets is thus preserved between the two rising ramps, as well as between the two desending ramps. The assoiation of beat frequenies remains simple and the variane of the estimate of the speed remains low, by onsidering, in a seond step, the ramps of opposite slopes. The struture of this waveform is summarized in Figure 2. It an be haraterized by four parameters: - The arrier frequeny (f 0) - The bandwidth (B) - Total duration (T) - The duration of the first triangle (θ) Fig. 2. The modified FMCW waveform By some alulations like the equations (4-10) we an obtain two estimates of the distane and the Doppler frequeny: d 1 = θ 8B (f b down1 f b up1 ) f d1 = 1 2 (f b down1 + f b up1 ) And on the seond one: d 2 = (T θ) (f down2 8B b f up2 b ) f d2 = 1 2 (f b down2 + f b up2 ) (11) (12) (13) (14) (This work is liensed under a Creative Commons Attribution 4.0 International Liense.) 602

3 A final estimate is done by taking the averages of the equations (11-14) to obtain: d = 16B [θ(f b down1 f up1 b ) + (T θ)(f down2 b f up2 b )] (15) f d = 1 4 (f b down1 + f b up1 + f b down2 + f b up2 ) (16) The obtained beat frequenies are: f up2 = 2.155MHz f up1 = 1.030MHz f down1 = 1.218MHz f down2 = 2.343MHz IV. GNU RADIO IMPLEMENTATION The FMCW was implemented using GNU Radio in many publiations [7-11]. Here, the first hange is the use of a file soure instead of signal soure. The values of the modified triangles (Figure 3) are alulated using Matlab, then were written in a binary file. In the file soure blok the repeat option is set. Fig. 4. Beat frequenies when we have a fixed target. Using equation (15) we obtain the same distane d= Km. And using equation (16), the estimated Doppler frequeny f d=94khz. Fig. 3. Beat frequenies when we have a moving target. In the simulation, we have hosen the following parameters: Bandwidth (B) Carrier frequeny Period of the two triangles Time of the first triangle 15MHz 500MHz 4ms ms In the first simulation, we supposed that we have 1 fixed target. We supposed that the delay of the eho is 100 s (distane of 15 Km). The Fourier transform of the omplex mixed signal is illustrated in Figure 4. We see that we have 4 beating frequenies: f up2 = 2.248MHz f up1 = 1.124MHz f down1 = 1.124MHz f down2 = 2.248MHz We see that, in the absene of Doppler, the equation (5) is verified. By applying the equation (15) we obtain d = Km. So, the distane is orretly estimated. And using the equation (16) the Doppler frequeny f d is equal to zero. In the seond senario (figure 7), we suppose we have a target at the same distane of the first senario. But in addition, we have a Doppler shift of 94.2 KHz. After the mixer, we obtain the spetrum of figure 5. Fig. 5. Beat frequenies when we have a moving target. In a third senario, we supposed that we have two moving targets. The system is illustrated in figure 8. The beat frequenies obtained after the mixer are shown in Figure 5. We see that we have 8 beat frequenies. We an alloate to eah target its beat frequenies by searhing the mathing four peaks in frequenies. The first target, simulated as in the seond senario provides the same beating frequenies obtained before. The seond target is simulated with a delay 400 (orresponds to s or 10Km) and a Doppler frequeny equal to 150 KHz. The beat frequenies are always in the same order: f up2, f up1, f down1 then f down2 So, the beat frequenies of the seond target are: f up2 = 1350KHz f up1 = 600KHz f down1 = 899.4KHz f down2 = 1649KHz Again, using equations (15) and (16) we obtain an estimated distane equal to 9.99Km and an estimated Doppler frequeny equal to 149.6KHz. (This work is liensed under a Creative Commons Attribution 4.0 International Liense.) 603

4 Fig. 6. Beat frequenies when we have two moving targets. V. CONCLUSION A modifiation on the FMCW was implemented using GNU Radio to detet stationary and moving targets. We showed that the obtained results are orret and orresponds to the theoretial values. Using a modified FMCW waveform, the targets an be deteted and their distane and veloity an be estimated in a simple way. If we have different targets, the beat frequenies are ordered, and by mathing its amplitudes we an assoiate to eah target the orresponding beat frequenies. The system will be modified in the future to implement a real-time Radar using USRPs and Log-periodi diretive antennas. REFERENCES [1] M. G. M. Hussain and M. J. Yedlin. Ative-array beamforming for ultrawideband impulse radar. In Radar Conferene, The Reord of the IEEE 2000 International, pages , 2000 [2] M.I Skolnik. Introdution to radar systems. TM Graw-Hill, book Company In, 1962.J. Clerk Maxwell, A Treatise on Eletriity and Magnetism, 3rd ed., vol. 2. Oxford: Clarendon, 1892, pp [3] M. Petit Didier G. Sol, P. Larzabal and H. Clergeot. A new approah for wind profiling with doppler radar. In International journal of Radio sienes, vo- lume 32, pages , July-August [4] Kemkemians J. P. Artis. The radar in the automotive domain. In Annales des te le ommuniations, volume 60, pages , Marh/April [5] G. Piel. Contribution a la Mise en oeuvre d une Platforme De Simulation D un Syste me Radar : Appliation A Un Radar Automobile D aide a La Conduite. PhD thesis, Teleom Bretagne, [6] S. Miyahara. New algorithm for multiple objet detetion in the fmw radar. In SAE Tehnial Paper Series, [7] Saputera, Yussi Perdana, et al. "Linear frequeny modulated ontinuous wave radar using GNU radio and USRP." Wireless and Telematis (ICWT), st International Conferene on. IEEE, [8] Sundaresan, S., et al. "Real time implementation of FMCW radar for target detetion using GNU radio and USRP." Communiations and Signal Proessing (ICCSP), 2015 International Conferene on. IEEE, [9] Prabaswara, Aditya, Ahmad Munir, and Andriyan Bayu Suksmono. "GNU Radio based software-defined FMCW radar for weather surveillane appliation." Teleommuniation Systems, Servies, and Appliations (TSSA), th International Conferene on. IEEE, [10] Amin, Ershad Junus, Andriyan Bayu Suksmono, and Ahmad Munir. "Auray analysis of FM hirp in GNU radio-based FMCW radar for multiple target detetion." Computer, Control, Informatis and Its Appliations (IC3INA), 2014 International Conferene on. IEEE, [11] Aulia, Siska, Andriyan Bayu Suksmono, and Ahmad Munir. "Stationary and moving targets detetion on FMCW radar using GNU radio-based software defined radio." Intelligent Signal Proessing and Communiation Systems (ISPACS), 2015 International Symposium on. IEEE, (This work is liensed under a Creative Commons Attribution 4.0 International Liense.) 604

5 Fig 7. GNU Radio bloks to simulate one moving target (This work is liensed under a Creative Commons Attribution 4.0 International Liense.) 605

6 Fig 8. GNU Radio bloks to simulate one moving target (This work is liensed under a Creative Commons Attribution 4.0 International Liense.) 606