Movement Detection Using a Modified FMCW Waveform and GNU Radio

Movement Detection Using a Modified FMCW Waveform and GNU Radio

Ali Bazzi, Majd Ghareeb, Mohammad Raad and Samih Abdul-Nabi School of Engineering, Computer and Communication Department Lebanese International University (LIU)

Beirut, Lebanon

Abstract In this paper results of previous researches and modifications to the Frequency Modulated Continuous Wave (FMCW) are applied on GNU Radio. GNU Radio is an open source software for Software Defined Radio (SDR). The standard FMCW has frequency changing linearly with time. The

frequency fb is defined as the difference between the frequencies of the received (fr) and the transmitted signals (ft): fb = fr ft. It is proportional to the relative speed (v) of the target:

frequency changes take the form of a triangle. Here, the triangular waveform is modified to obtain two triangles instead of one where the second triangle has a different form. The system

= 20

(2)

is implemented using GNU Radio. We obtained a good estimation of the distance and the speed of different targets. Moreover, the Doppler frequency is estimated with a high precision.

KeywordsFMCW; Detection; Estimation; GnuRadio; Radar

1. INTRODUCTION

   The RADAR (RAdio Detection And Ranging) is based on the propagation of Radio Frequency (RF) electromagnetic waves. In the late of the 19th century, the experiments of Heinrich Heirtz showed that the electromagnetic waves are reflected by metallic objects. The Radar principle was found in 1911 by the American Hugo Gernsback. In 1934, the Frenchman Pierre David successfully did the first experiments to detect the presence of aircraft. The first range calculations were applied on Icebergs with waves of 16 cm wavelength. Then the radar had an important usage in military applications.

   The radar uses the reflection properties of an electromagnetic wave on a target. The simplest and the first used waveform consists on a series of pulses [1]. By measuring the delay between emission and reception, it is possible to calculate the distance d between the radar and the target by the following equation:

   where f0 is the frequency of the oscillator.

   The problem of the monochromatic radar is that it does not provide any information about the distance.

   FSK (Frequency Shift Keying) radar [4] transmits a frequency modulated waveform. This modulation uses at least two slightly different frequencies, i.e. f0 and f1 = f0 + f which are transmitted periodically every T seconds. The spectral analysis of the received information makes it possible to extract the distance and speed. The received signals have equal amplitudes (proportional to the amplitude of the transmitted signal), the same frequency (equal to the Doppler frequency of the target) and a differential phase shift proportional to the distance to be measured.

   The speed is calculated by performing a time-discrete Fourier transform of the received signals. The targets are then detected by a previously defined amplitude threshold. Given the small variation f of the frequency of a target between two repetition periods, a target will give the same Doppler frequency in the two adjacent intervals associated with f0 and f1. But the received signals have a phase difference = |0 – 1|. From this phase difference, calculated by mixing the transmitted and received signals, the distance d of the target is obtained using the equation:

   = / 2 (1)

   8

   =

   4

   (3)

   where c is the speed of the light (3×10 m/s).

   A pulse must have a short duration, A pulse width of 1 nm is needed to detect objects facing the radar with distance less than 1m. Moreover, another problem of Pulse Radar is that we cannot detect nor calculate 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 expected.

   A monochromatic radar uses the Doppler effect and gives no information on the distance of the target [3]. A monochromatic continuous wave radar system consists of an RF transmitter and a receiver that mixes the transmitted and the received signals to obtain the beat frequency. The beat

   This waveform is simple to produce but it cant detect unmoving targets.

   After looking to the different waveform techniques, the FMCW is the best choice to detect a moving or unmoving targets.

2. FMCW THEORY

   In the case of the FMCW radar [5], the transmitted frequency varies continuously as a function of time, typically in a linear manner (figure 1). To detect a target placed at a distance d, we mix the transmitted and the received signals to produce a beat frequency fb. In the absence of Doppler (fixed target) this frequency is only related to the distance of the target.

   If we denote by ft(t)=f0 + t the transmitted frequency. At the receiver, we obtain the frequency fr = f0 + (t-2d/c). A mixer is used to provide the beat frequency:

3. THE MODIFIED FMCW

   When we have multiple targets, it is hard to associate the

   = =

   2

   (4)

   f up and f down for each target when using the FMCW waveform.

   Where is the slope of the frequency.

   Fig. 1. FMCW waveform

   But we have two ramps (up and down). So, for a non- moving target, we obtain two beat frequencies:

   Miyahra introduced in [6] a new waveform with two (or more) successive ramps with slightly different slopes. In this waveform, the order in which the beat frequencies are observed on the first ramp is identical to the order observed on the second ramp. Thus, the association between the beat frequencies on the ramps is easy, and the problem of FMCW is solved. The simplified association between the beat frequencies, is a great advantage of this waveform.

   By combining the idea of ramps of near slopes and that of ramps of opposite slopes, a new waveform, called double FMCW, composed of two successive triangles with slightly different slopes between the first and Second triangle was proposed. The order of the beat frequencies of the targets is thus preserved between the two rising ramps, as well as between the two descending ramps. The association of beat frequencies remains simple and the variance of the estimate of the speed remains low, by considering, in a second step, the ramps of opposite slopes.

   The structure of this waveform is summarized in Figure 2.

   = = 2

   If the target is moving the beat frequencies are:

   (5)

   It can be characterized by four parameters:

   • The carrier frequency (f0)

   • The bandwidth (B)

     =

     2

     (6)

   • Total duration (T)

   and,

   – The duration of the first triangle ()

   =

   + 2

   (7)

   Using equations (6) and (7) and because the slope is equal to the bandwidth B divided by the time of the slope (T/2), by a simple calculation, we can obtain the distance and the Doppler frequency of the targets using:

   = ( ) (8)

   and,

   8

   1

   (9)

   = 2 (

   + )

   Fig. 2. The modified FMCW waveform

   Using equations (2) and (9) we can obtain the speed:

   By some calculations like the equations (4-10) we can obtain two estimates of the distance and the Doppler frequency:

   =

   ( + ) (10)

   (11)

   40

   1 =

   (1 1)

   8

   1

   1

   1

   (12)

   <>As the distance is inversely proportional to the Bandwidth, we should use a large bandwidth to detect near objects. Concerning the speed, we need to use an oscillator with a large frequency.

   1 = 2 (

   And on the second one:

   + )

   = ( ) (2 2) (13)

   2 8

   1

   2

   2

   (14)

   2 = 2 (

   + )

   A final estimate is done by taking the averages of the equations (11-14) to obtain:

   = [( ) + ( )( )] (15)

   The obtained beat frequencies are:

   2 = 2.155

   1 = 1.030

   (16)

   1 = 1.218

   2 = 2.343

   = (

   +

   +

   + )

4. GNU RADIO IMPLEMENTATION

   The FMCW was implemented using GNU Radio in many publications [7-11].

   Here, the first change is the use of a file source instead of signal source. The values of the modified triangles (Figure 3) are calculated using Matlab, then were written in a binary file. In the file source block the repeat option is set.

   Fig. 3. Beat frequencies when we have a moving target.

   In the simulation, we have chosen the following parameters:

   Bandwidth (B)	15MHz
   Carrier frequency	500MHz
   Period of the two triangles	4ms
   Time of the first triangle	2.6666ms

   In the first simulation, we supposed that we have 1 fixed target. We supposed that the delay of the echo is 100s (distance of 15 Km). The Fourier transform of the complex mixed signal is illustrated in Figure 4.

   We see that we have 4 beating frequencies:

   2 = 2.248

   1 = 1.124

   1 = 1.124

   2 = 2.248

   We see that, in the absence of Doppler, the equation (5) is verified.

   By applying the equation (15) we obtain d = 14.985 Km. So, the distance is correctly estimated. And using the equation

   (16) the Doppler frequency fd is equal to zero.

   In the second scenario (figure 7), we suppose we have a target at the same distance of the first scenario. But in addition, we have a Doppler shift of 94.2 KHz. After the mixer, we obtain the spectrum of figure 5.

   Fig. 4. Beat frequencies when we have a fixed target.

   Using equation (15) we obtain the same distance d=14.985 Km. And using equation (16), the estimated Doppler frequency fd=94KHz.

   Fig. 5. Beat frequencies when we have a moving target.

   In a third scenario, we supposed that we have two moving targets. The system is illustrated in figure 8. The beat frequencies obtained after the mixer are shown in Figure 5. We see that we have 8 beat frequencies. We can allocate to each target its beat frequencies by searching the matching four peaks in frequencies.

   The first target, simulated as in the second scenario provides the same beating frequencies obtained before.

   The second target is simulated with a delay 400 (corresponds to 66.66667 s or 10Km) and a Doppler frequency equal to 150 KHz.

   The beat frequencies are always in the same order: fup2, fup1, fdown1 then fdown2

   So, the beat frequencies of the second target are:

   2 = 1350

   1 = 600

   1 = 899.4

   2 = 1649

   Again, using equations (15) and (16) we obtain an estimated distance equal to 9.99Km and an estimated Doppler frequency equal to 149.6KHz.

   Fig. 6. Beat frequencies when we have two moving targets.

5. CONCLUSION

A modification on the FMCW was implemented using GNU Radio to detect stationary and moving targets. We showed that the obtained results are correct and corresponds to the theoretical values. Using a modified FMCW waveform, the targets can be detected and their distance and velocity can be estimated in a simple way. If we have different targets, the beat frequencies are ordered, and by matching its amplitudes we can associate to each target the corresponding beat frequencies. The system will be modified in the future to implement a real-time Radar using USRPs and Log-periodic directive antennas.

REFERENCES

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2. M.I Skolnik. Introduction to radar systems. TMc Graw-Hill, book Company Inc, 1962.J. Clerk Maxwell, A Treatise on Electricity and Magnetism, 3rd ed., vol. 2. Oxford: Clarendon, 1892, pp.68-73.

3. M. Petit Didier G. Sol, P. Larzabal and H. Clergeot. A new approach for wind profiling with doppler radar. In International journal of Radio sciences, vo- lume 32, pages 13911408, July-August 1997.

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10. Amin, Ershad Junus, Andriyan Bayu Suksmono, and Achmad Munir. "Accuracy analysis of FM chirp in GNU radio-based FMCW radar for multiple target detection." Computer, Control, Informatics and Its Applications (IC3INA), 2014 International Conference on. IEEE, 2014.

11. Aulia, Siska, Andriyan Bayu Suksmono, and Achmad Munir. "Stationary and moving targets detection on FMCW radar using GNU radio-based software defined radio." Intelligent Signal Processing and Communication Systems (ISPACS), 2015 International Symposium on. IEEE, 2015.

Fig 7. GNU Radio blocks to simulate one moving target

Fig 8. GNU Radio blocks to simulate one moving target