A Short Range FMCW Radar System with Low Computational ... · (Frequency Modulated Continuous...

A Short Range FMCW Radar System with Low

Computational Complexity

Hyeokjin Lim and Seongjoo Lee Department of Electrical Engineering, Sejong University, Seoul, Korea

Email: [email protected], [email protected]

Abstract—In this paper, a short range FMCW (Frequency

Modulated Continuous Wave) radar system with low

computation complexity is proposed. In order to improve

the frequency linearity, the proposed FMCW radar system

adopts the digital frequency modulation with the counter

and look-up tables for sine and cosine waves in an FPGA

(Field Programmable Gate Array). In order to reduce the

complexity of hardware, it utilizes the arc cosine rom in

time domain for calculating the distance instead of FFT. The

total RMSE of the distance is less than one meter. The

suggested FMCW radar is applicable to unmanned vehicle,

train, ship, exploration robot, military tank and obstacle

sensor.

Index Terms—radar, fast fourier transform, frequency

modulated continuous wave

I. INTRODUCTION

Radar is a device which sends out electromagnetic

wave energy and can measure the distance between the

transmission antenna and the target object with a value

which calculates the arrival time of the reflected wave

after being reflected from the target object [1]. Radar

systems are not only used as a navigation device in

airplanes and ships but also used in diverse fields such as,

calculating large scale tank in the heavy chemical

industry, climate observation, marine safety facility and

vehicle collision prevention [2]-[6]. Especially, the

demands of unmanned vehicle radar technology have

increased [7]-[8]. While normal anti-air radar is used for

detecting objects which are hundreds of kilometers away,

the radar used for unmanned vehicle needs to detect

objects within 200m. The unmanned vehicle radar

systems have many methods, including FMCW

(Frequency Modulated Continuous Wave), pulse, CW

(Continuous Wave) and spread spectrum method. FMCW

method is the most widely used methods due to

economical reason. The analog FMCW method radar

with VCO (Voltage Controlled Oscillator) needs to have

increased in the number of kHz per nanosecond to find

the distance delay. However, it is hard to induce the

frequency increase in VCO and high quality VCO is

expensive and complicated actuation circuit.

In this paper, the proposed FMCW radar system with

low computation complexity suggested using counter in

an FPGA (Field Programmable Gate Array), rather than

Manuscript received June 18, 2015; revised November 17, 2015.

VCO, to generate the FMCW wave. Furthermore, the

proposed one does not use the FFT (Fast Fourier

Transform) for distance measurement algorithm with

FMCW radar systems and also reduced the complicated

hardware by using arc cosine ROM (Read only Memory)

table.

In Section 2, the basic theory of FMCW radar and the

calculation of distance are described. In the 3rd section,

the proposed FMCW radar system is analyzed and

designed. In Section 4, the results of distance calculation

are shown. Finally, the conclusions are reached in Section

5.

II. BASIC THEORY OF FMCW RADAR AND

CALCULATION OF DISTANCE AND SPEED

Radars are divided into pulse and continuous wave

depending on the modulation method. A pulse radar

system transmits pulses with small width and measures

the distance by using the delay time of the signal wave,

reflected from the object. It is called the amplitude

modulation method. CW radar systems are a method

which calculates the difference of the frequency signal

while signals are transmitted and reflected. It measures

the distance with the modulated amount of the

transmitted frequency by modulating the transmitting

frequency per time. A conventional FMCW radar system

is composed as shown in Fig. 1.

VCO

AMPPowerdivider

Tx

LNAMixer

LPFADCDSP(FFT)

Cos fc

Cos fc

RxRF mixer

IF mixer

Figure 1. A conventional FMCW radar system block diagram.

The system is consisted of transmission, receipt and

antenna part. Except the part where the transmission part

transmits the signal by modulating the frequency, there is

not much structural difference with the normal

continuous wave radar system, but as the FMCW radar

system’s capability is determined by the linearity which

modulates the frequency, there is a big difference in

structuring the transmission part.

International Journal of Electronics and Electrical Engineering Vol. 4, No. 4, August 2016

©2016 Int. J. Electron. Electr. Eng. 370doi: 10.18178/ijeee.4.4.370-373

The conventional FMCW radar uses VCO in order to

modulate the frequency of the transmission signal. VCO

modulates the frequency according to the input voltage.

But the output frequency is not linear for the input

voltage. PLL (Phase Locked Loop) is utilized in order to

convert the frequency linearly. The transmission signal

that comes out by modulating the frequency is released

through one antenna after amplification. The reflected

signal from the object is received by the same antenna

and it comes back to the mixer, after going through the

circulator. Although the sum and the difference of

transmission and receipt signals are output on the mixer,

the summed frequency is removed through the LPF (Low

Pass Filter) and the difference is only input as ADC

(Analog Digital Converter). The input signal is shown as

the frequency domain with the FFT. The extracted

difference frequency is converted into the distance

information from the frequency spectrum. The FMCW

radar systems have the advantages of having smaller

transmission power, size, and simple structure for the

pulse radar. But there are disadvantages such as, isolation

between the transmission and receipt, phase noise and

linearity according to the broadband frequency

modulation. It needs reinforcements for problems.

The difference frequency between the transmitted

signal and the reflected signal, from the FMCW radar

changes according to the distance. Normally, the

frequency modulation of the transmission signal uses

linearly chopping form or sawtooth wave. In the case of

calculating the distance, it uses sawtooth wave most of

the time, but as the sawtooth wave is not continuous in

modulation and in order to extract the distance. It needs

to create modulation wave with different slopes. It uses

chopping wave. Fig. 2 shows the diagram of linearly

chopping wave modulation.

τ

fc

fc +Δf

fb

Ts

Freq.

Time

Transmitted signalReceived signal

Figure 2. A triangular pulse and difference frequency of FMCW radar of the fixed target.

The slope (fm) that modulates into chopping form is the

value that divided modulation broadband (Δf) by

modulation period (TS) and the frequency difference of

the transmission and receipt signal of after the delay of τ

can be expressed as the below (1).

2b

S S

f f Rf

T T c

(1)

The chopping form modulation creates a point where

the difference frequency is 0 when it switches to decrease

frequency modulation after linearly increase frequency

modulation during the modulation period, it is ignored as

it is regarded as a very small section. The extracted

difference frequency can be converted into distance

information by using (1), and the organization is as

follows:

2

S bT f c

Rf

(2)

For the fixed object, the difference in the frequency

between the increase and decrease modulation section is

the same, but the difference frequency for the moving

object creates a Doppler frequency succession. It presents

the difference of the Doppler frequency per modulation

section. The Fig. 3 shows the transmission and receipt

frequency and difference frequency of the moving object.

τ

fc

fc +Δf

fb

Ts

Freq.

Time

Transmitted signalReceived signal

Figure 3. A triangular pulse and difference frequency of FMCW radar of the moving target.

Each section indicates the speed information according

to the Doppler frequency succession and the distance

information according to the time delay and it can extract

both information through simultaneous equation of

increase (fup) and decrease (fdown) sections as follows:

up r df f f (3)

down r df f f (4)

2

up down

r

f ff

(5)

2

down up

d

f ff

(6)

2

S rT f c

Rf

(7)

III. PROPOSED FMCW RADAR SYSTEM

The proposed FMCW radar system is divided into the

transmission, receipt and antenna part as shows in Fig. 4.

The antenna part is not different from the conventional

FMCW radar system. The transmission part generates the

FMCW wave by using the counter in an FPGA rather

than VCO. Because it consumes about 6.6ns for the


©2016 Int. J. Electron. Electr. Eng. 371

absolute delay of 1m depending on the (8), it is

oversampled to 150MHz corresponding 6.6 ns per 1 step.

2d

RT

c (8)

Td is absolute delay, R is distance and c means the speed

of light (299792458 m/s). The transmission signal is as

1 2cos(2 ( ( )) )Tx f f t t (9)

Transmission signal is transmitted through DAC

(Digital Analog Converter). The delayed receipt signal is

1 2cos(2 ( ( )) ( ))Rx f f t t (10)

Receiving signal multiplies the transmitted signal’s (9)

and the receiving signal’s (10) to calculate the frequency

difference. The cosine signal is received through ADC.

With the low pass filter, it filters the high frequency

signals and finds the difference frequency of lower

frequency. In the case of a conventional FMCW radar

system, the signal frequency is calculated with FFT. But

the proposed FMCW radar system utilizes arc cosine

ROM table in order to reduce the complexity of the

hardware. The distance is calculated with the frequency

signal which gained from the arc cosine table and (7).

Figure 4. The proposed FMCW radar system.

The performance of distance sensor is measured with

respect to the RMSE (Root Mean Square Error). If the

transmission SNR is 35 and 40 dB, the result is shown in

Table I-Table IV and Table V-Table VIII, respectively.

The total RMSE of the distance is less than one for the

area, Doppler, transmission SNR and distance.

TABLE I. THE RMSE RESULT OF AREA AND DOPPLER FOR

TRANSMISSION SNR 35DB AND DISTANCE 1M

Area/Doppler 0 Hz 300 Hz 450 Hz 600 Hz

1.0 m2 0.009 0.008 0.009 0.009

1.5 m2 0.008 0.008 0.008 0.008

2.0 m2 0.008 0.008 0.007 0.007

TABLE II. THE RMSE RESULT OF AREA AND DOPPLER FOR



1.0 m2 0.044 0.046 0.042 0.042

1.5 m2 0.039 0.037 0.037 0.040

2.0 m2 0.038 0.034 0.036 0.037

TABLE III. THE RMSE RESULT OF AREA AND DOPPLER FOR



1.0 m2 0.088 0.084 0.081 0.082

1.5 m2 0.073 0.069 0.066 0.070

2.0 m2 0.061 0.063 0.059 0.061

TABLE IV. THE RMSE RESULT OF AREA AND DOPPLER FOR



1.0 m2 0.112 0.121 0.114 0.110

1.5 m2 0.100 0.085 0.089 0.088

2.0 m2 0.087 0.089 0.083 0.087

TABLE V. THE RMSE RESULT OF AREA AND DOPPLER FOR



1.0 m2 0.007 0.007 0.006 0.007

1.5 m2 0.007 0.006 0.007 0.007

2.0 m2 0.007 0.006 0.006 0.007

TABLE VI. THE RMSE RESULT OF AREA AND DOPPLER FOR



1.0 m2 0.034 0.033 0.034 0.032

1.5 m2 0.032 0.031 0.030 0.034

2.0 m2 0.032 0.031 0.030 0.033

TABLE VII. THE RMSE RESULT OF AREA AND DOPPLER FOR



1.0 m2 0.060 0.056 0.060 0.057

1.5 m2 0.054 0.057 0.054 0.055

2.0 m2 0.056 0.056 0.054 0.055



follows in

expressed as

(9) from the measurement time t.

(10) for delay time τ.

IV. THE MESUREMNT RESULT OF THE DISTANCE

TABLE VIII. THE RMSE RESULT OF AREA AND DOPPLER FOR



1.0 m2 0.077 0.075 0.073 0.074

1.5 m2 0.069 0.070 0.073 0.070

2.0 m2 0.067 0.064 0.065 0.062

V. CONCLUSIONS

In this paper, the short range FMCW radar system with

low computational complexity is proposed. Because the

VCO’s linearity affects directly the accuracy of

measurement distance in FMCW radar, the VCO’s

frequency linearity is very important to measure distance.

In this research, in order to improve the frequency

linearity, the proposed FMCW radar system used the

FMCW wave which increases by 6.6kHz per 1 step with

the counter in an FPGA. In order to reduce the

complexity of the hardware, it utilized the arc cosine

ROM for the distance. The suggested FMCW radar is

applicable to unmanned vehicle, train, ship, exploration

robot, military tank and obstacle sensor.

ACKNOWLEDGMENT

This work was supported by the National Research

Foundation of Korea (NRF) grant funded by the Korea

government (MOE) (No.2013R1A1A2064733) and also

by R&D program funded by IITP & MSIP

(B01261510760001002, “Development of non-powered

technology combined with ambient RF energy harvesting

and Backscatter data transfer”), and CAD tools are

supported by IDEC in Korea.

REFERENCES

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anticollision (MIRANDA),” Trans. on M.T.A.T., vol. 47, no. 9, pp. 1891-1900, September 1999.

[3] J. H. Zhang, G. S. Liu, H. Gu, and W. M. Su, “Coding step FM continuous wave signal’s apply in vehicles collision avoidance

radar system,” ACTA Electronica Sinica, vol. 29, no. 7, pp. 943-

946, July 2001. [4] J. H. Jeong, et al., “A study on the development of the active radar

reflector with enhanced function,” Journal of the Korea Industrial Information System Society, vol. 83, pp. 38-43, 2000.

[5] L. Giubbolini, “A multistatic microwave radar sensor for short

range anticollision warning,” IEEE Transactions on Vehicular Technology, vol. 49, pp. 2270-2275, 2000.

[6] C. H. Bae, “The study on vehicle radar technology trends,” Korea: Electronic Communications Trends Analysis, vol. 21, no. 4, 2006.

[7] Wang, Shuiying, et al., “Shader-Based sensor simulation for

autonomous car testing,” in Proc. 15th International IEEE Conference on Intelligent Transportation Systems, 2012.

[8] T. Wang, X. Jingmin, and Z. Nanning, “A method integrating human visual attention and consciousness of radar and vision

fusion for autonomous vehicle navigation,” in Proc. IEEE Fourth

International Conference on Space Mission Challenges for Information Technology, 2011.

Hyeokjin Lim was born in Mokpo, Korea in

1988. He received his B.S and M.S degrees in Electrical Engineering from Sejong University,

Seoul, Korea, in 2012 and 2014, respectively. He is working for a PhD degree at Sejong

University. His current research interests

include SoC design for digital spectrum analyzer and touch screen devices.

Seongjoo Lee received his BS, MS, and PhD

degrees in Electrical and Electronic Engineering from Yonsei University, Seoul,

Korea, in 1993, 1998, and 2002, respectively. From 2002 to 2003, he was a senior research

engineer at the IT SoC Research Center and

the ASIC Research Center, Yonsei University, Seoul, Korea. From 2003 to 2005, he was a

senior engineer in the Core Tech Sector, Visual-Display Division, Samsung Electronics

Co. Ltd., Suwon, Korea. He was a research professor at the IT Center

and the IT SoC Research Center, Yonsei University, Seoul, Korea from 2005 and to 2006. He is currently an Associate Professor in the

Department of Electrical Engineering at Sejong University, Seoul, Korea. His current research interests include SoC design for high-speed

wireless communication systems and image processing systems.



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