# A Novel Method of Radar Modeling for Vehicle Intelligence.

I. INTRODUCTIONAs one of the ultimate solutions to traffic safety and vehicle performance, intelligent vehicle is gaining momentum. Radar detection system plays a key role on environmental perception for intelligent vehicles. Although field experiment has been traditionally dominating in vehicle development, it is not an efficient or even safe way in developing and testing radar-based ADAS for ACC, collision avoidance, and etc. It is hard or sometimes even impossible to set up such field environment that could cover large variations, great uncertainties and complexity of real driving scenarios. Besides high cost, long duration, lack of flexibility, and worse yet, lack of guaranteed safety, limited field experiment can hardly ensure system robustness and reliability. The steadier detection performance, that is, affected slightly by environment like atmosphere, and low cost compared with Light Detection And Ranging (LiDAR), the longer detection range up to 300 meters compared to ultrasonic radar, and the ability to detect the relevant velocity makes millimeter wave radar widely used in ADAS applications by now. So this paper intends to propose a millimeter wave radar modeling method of high fidelity with the abundant driving environment provided by PanoSim [1] aimed to maximum the meaning of virtual simulation experiment before field experiment in the minimum cost.

There are indeed lots of radar simulation solutions resulted in mature commercial products in different domains like ENDOCOM in medical domain, MultiPASS and OP2H in telecommunication, WinPROP, FERMAT and so on in environment perception [2]. The first two solutions are based on statistical modeling and hardly meet the requirements of complex dynamic situations. This paper focuses on automotive radar simulation solutions to be discussed in detail next.

The technologies in prior research on radar modeling for automotive applications are mainly through function-based approaches, physics-based approaches or both [3].

The function-based modeling approach mainly focuses on the functions of radar detection and measurement with little detail on its physical components and working mechanism. In this approach, the radio wave that radar fires is treated as a confined geometrical shape, such as a cone; the targets to be detected are modeled as a collection of polygons, bounding box or just scattering center for the sake of computational efficiency. Radar detection is abstracted as a solution of the intersection between the geometrical representation of radar beam and the targets. However the simulation result is ideal and often unrealistic.

There have been mainly two ways to model radar in a physics-based approach. One approach is to model radar components with electromagnetic and electronic circuits software and concurrently to simulate the propagation channels usually by means of "ray tracing". This approach can be very time-consuming and often real-time prohibitive [4]. The other approach is signal-based that synthesizes radar signal echoed from the targets and other objects in the driving environment with clutter and noise that affect radar detection with various physical factors [5][6].

Then this paper presents a novel radar modeling approach, of which the architecture is depicted in Section II. This novel approach primarily consists of two modules. The first one, geometric model is discussed in Section III and the second one, physical model is described in detail in Section IV. Section V shows the independent validation of physical model in Matlab/Simulink and the integrated validation of the whole model in Matlab/Simulink and PanoSim. Finally the paper concludes in Section VI.

II. DESCRIPTION OF MODEL ARCHITECTURE

The architecture of the proposed radar model is shown in figure 1 below. At first, it is necessary to clear the differences between the two conceptions, "Radar Model" and "Radar System Model". Radar, an acronym for radio detection and ranging, is an object detection system which fires electromagnetic wave into the surrounding environment, then receives and processes its echo signal reflected, so as to determine the range, range rate and angle of objects.

To abstract the function of radar, if treat the actual radar as a black box, then the input of this black box should be the surrounding environment information and the output should be the detected result. Thus the black box and its input and output composes the radar system. Accordingly in the virtual world depicted in figure 1, the red frame named radar model is equivalent to the actual radar or the black box. Note that the block of environment model refers in particular to infrastructure like buildings, ground, trees, bush and transport facilities, excluding the active transport participants like all kinds of vehicles and pedestrians, what the block of target model exactly means. The block of RCS estimation serves as the response of objects to the radar EM-wave which will be discussed more detailed later. These three blocks provide a complete input information to the radar model and the detection output which is not expressed in a block flows into the ACC controller as input. Hence all the blocks except ACC controller composes the radar system model as blue frame shows.

III. GEOMETRIC MODELING APPROACH

This paper firstly adopts a geometric modeling approach to establish the link between the object information and the radar without concerning about any details of physics factor. In this approach, the object to be detected is abstracted as a set of pre-defined Points of Shape Characteristics (PSC)illustrated in figure 2, the EM-wave radar fires is represented as a closed geometry created by an elliptic cone and a plane, and then the radar detection process is transformed into a problem to find out the PSC illuminated by the EM-wave, or radar beam. These illuminated PSC should meet the following two conditions: a) located inside of the radar beam geometry; b) not blocked by other objects, that is, there exists no objects, not PSC, on the line from the radar beam firing point to the illuminated PSC. Then among these PSC, find out the closest point to the radar of each object and transmit them to the physical model.

Geometric Representation of Objects

The object in general refers to any moving or stationary things that may fall into radar RVV and generate echo signals physically. To discretize a complex object in terms of its shape, a set of points are pre-defined that capture the major characteristics of the object shape (PSC), such as vertices, center, edge, etc, as illustrated in Figure 2.

Geometric Representation of Radar Beam

As figure 3 shows, the radar beam is assumed to be a close geometry named Radar View Volume(RVV) created by an elliptic cone and a plane and have the three property parameters: range R, azimuth angle [alpha], elevation angle [beta]. The RVV geometric representation is defined in the equation (1) where [x, y, z] denotes the coordinates of a 3D point.

[x.sup.2]/[(ytan [alpha]/2).sup.2]+[z.sup.2]/[(ytan [beta/2]).sup.2] [less than or equal to]1y[less than or equal to]R (1)

Geometric Representation of Detection Process

In order to determine which sets of PSC are falling into RVV and not blocked simultaneously, the premise of detection process is to unify the coordinate systems. Then find the special PSC that meet the demands quickly with a series of steps taken.

A. Unify the Coordinate Systems

Considering that RVV has accurate and succinct mathematical expression and the point coordinate is easy to be converted, so transform the coordinates of PSC from world frame to vehicle frame and actually to radar frame, as shown in figure 2.

First, to transform the coordinates of a point [P.sub.w] [[x.sub.w], [y.sub.w], [z.sub.w]] given under world frame to vehicle frame, denote the position of vehicle or the origin of vehicle coordinate system under world frame by [T.sub.V] [[X.sub.V], [Y.sub.V], [Z.sub.V]], and orientation of vehicle (in yaw-pitch-roll sequence) or the Euler angles (Gillespie, 1992) by [[psi], [theta], [phi]], then the coordinate of the point under vehicle frame can be expressed as follows

[mathematical expression not reproducible] (2)

Where the rotation matrix is given by [mathematical expression not reproducible]:

[mathematical expression not reproducible]

[mathematical expression not reproducible]

[mathematical expression not reproducible]

To obtain a homogeneous transformation matrix defined as [mathematical expression not reproducible] considering both rotation and translation for the sake of format conciseness, add a dimensionality to the point coordinate, thus equation 1 is turned as follows:

[mathematical expression not reproducible]

[mathematical expression not reproducible]

Similarly, the transformation from the vehicle frame to the radar frame can be represented by the homogeneous matrix [mathematical expression not reproducible]:

[mathematical expression not reproducible]

Thus the total transformation formula of a point from world frame to sensor frame can be defined as

[mathematical expression not reproducible] (3)

where [mathematical expression not reproducible]

B. Detailed Detection Process

The key problem to the radar detection process of the virtual world is how to screen PSC to get those special ones which are "visible" to the radar beams quickly. Consequently this paper adopts the approach of Axis Aligned Bounding Box (AABB) among others to achieve this goal. As illustrated in figure 4, AABB is defined as the minimum hexahedron that encloses object and of which each edge is parallel to the coordinate axis. The coordinate of AABB vertices can be easily calculated through the maximum and minimum values of the mesh point coordinate of objects.

The figure 5 shows the flowchart of the detailed detection procedure of which the function is accomplished primarily by four steps of judgement highlighted by four yellow diamonds. Firstly, in view of the fact that the 3D scene is far greater than the radar beam and there generally exists plenty of objects which are definitely can not be detected by radar, this paper adopts quadtree to establish and query the 3D scene. A quadtree is a tree data structure in which each internal node has exactly four children. Only those AABB located in the same node as radar beam, namely, the so-called minimum visible zone, go on with the next judgement and other AABB with the sets of PSC enclosed are excluded. Secondly, according to the different position relationship of AABB and RVV (figure 3 shows one situation that AABB lies partly in RVV), choose different measures. Then the following two procedures deal with PSC instead of AABB. Eventually the detection information (relevant range, range rate, angle) the radar geometric model outputs can be easily calculated based on geometric relationships. Note that among all the visible PSC of one object detected, only the closest PSC to the radar should be converted as detection information.

IV. PHYSICAL MODELING APPROACH

This paper adopts the echo signal based physical modeling approach to take the non-ideal factors such as signal attenuation and noise resulted from the stochastic nature of the physics components, channel propagation of radio wave with absorption and scattering due to atmosphere, ground and object reflectivity, etc. The sense of physical model lies in refining the detection result of geometric model further to improve the whole model's fidelity.

Detection Principle of FMCW Radar

Figure 6 shows the FMCW radar block diagram. The CW signal with constant amplitude generated by Voltage Controlled Oscillator (VCO) is modulated in frequency to produce a linear chirp which is radiated toward targets through transceiver. The return radiation collected by transceiver is mixed with Local Oscillator (LO) reference signal and fed into the low-pass filter. The yielded beat signal is digitized by the Analogue to Digital Circuit (ADC) and processed to compute the sensing attributes.

Signal Processing

The proposed physical model is based on a classic radar signal processing method, i.e., Range and Doppler Processing Method [7] [8]. As figure 7 shows, the basic idea of FMCW is to generate a linear frequency ramp (chirp) periodically. Conventionally one period data is often taken as a unit to process, so the instantaneous transmission frequency for one ramp can be written as:

[f.sub.r](t) = [f.sub.c]+B/T t

where [f.sub.c] is the carrier frequency, B is bandwidth and T is sweep duration. After integration, the instantaneous phase becomes

[mathematical expression not reproducible]

Where [[phi].sub.0] is the initial phase. If is the time delay between the transmitted and received signal of the same target is [tau], then the instantaneous phase of received signal is

([[phi].sub.R])(t) = [[phi].sub.T](t-[tau])

[tau] = 2(R + vt)/c (4)

where c is the light speed in vacuum, R and v is respectively the distance and velocity of target at the moment when radar fires EM-wave. And the instantaneous phase of the down-converted signal (beat signal) from the mixed signal is

[[phi].sub.B](t) = [[phi].sub.[tau]](t) - [[phi].sub.R](t) = 2[pi]([f.sub.c][tau] + B/T t[tau] - 1B/2T [[tau].sup.2]) (5)

Giving t is relatively small sufficiently, neglect the high order term and plug equation (4) into equation (5), which then becomes

[[phi].sub.B](t) = 2[pi][2[f.sub.c]R/c] + ([2[f.sub.c]v/c + 2BR/Tc)t] (6)

Thus the instantaneous frequency of the beat signal is

[f.sub.B] = d[[phi].sub.B](t)/2[pi]dt = 2[f.sub.c]v/c + 2BR/Tc (7)

From equation (7), it can be easily seen that both R and v contribute to the frequency of beat signal. In figure 7, the black solid line denotes the transmitted signal of L periods and the black dashed line denotes the received signal reflected by a stationary target at a certain distance R from radar with the time delay [tau] (black) and the beat frequency [f.sub.B] (black). Then if the stationary target is located at a greater distance corresponding to the longer time delay [tau] (blue), the received signal (blue) will move right along the time axis and lead to a bigger beat frequency. If the target is located in the same position with a certain speed v away from radar, the received signal (red) will results in a smaller beat frequency.

However equation (7) is ambiguous since the target's range R and range rate v cannot be determined simultaneously with one frequency ramp and multiple ramps are needed to resolve the range-Doppler ambiguity. Considering that computer can only deal with digital signal, discretize the instantaneous phase of beat signal by taking N ramps and sampling M points in every ramp (denote the sample time interval by [t.sub.s] = T/M).

[[phi].sub.(n,m)] = [2[f.sub.c](R + nTv/c + 2BR/Tc)m[t.sub.s]]

= 2[pi][2[f.sub.c]R/c + 2[f.sub.c]v/c nT + (2[f.sub.c]v/c + 2BR/Tc)m[t.sub.s]] (8)

where n = 0,1...N - 1, m = 0,1...M - 1.

Note two things. First, the second R is not replaced by (R + nTv) because the movement during the measurement is short compared to the distance R in terms of physics, or the increment brought by nTvt is relatively small in terms of mathematics. Second, the ramp repetition interval denoted by [T.sub.RRI] is taken to equal to the sweep duration denoted by T. Thus the discretized beat signal is

[s.sub.B(n,m)] = A[e.sup.j[phi]B(n,m)] = Aexp{j[[phi].sub.B(n,m)]} = Aexp{j2[pi][2[f.sub.c]R/c + (2[f.sub.c]v/c + 2BR/Tc)m[t.sub.s]]} (9)

where A denotes the amplitude and can be calculated from the classic Radar Equation as follows:

[mathematical expression not reproducible] (10)

where the parameter definitions are shown in figure 8.

The 2D Fourier Fast Transformation (2D-FFT) for continuous temporal signal is

[mathematical expression not reproducible] (11)

Discretize the beat signal in both time and frequency domain by perform the 2D-FFT:

[mathematical expression not reproducible] (12)

where p = 0,1...N - 1, k = 0,1...M - 1.

The detailed analysis for equation (11) in respect of physics is presented as follows. Arrange the sample points of beat signal in N rows and M columns and perform 1D FFT to every M points row by row. As a result, the peak of each row appears in the same column and corresponds to the range frequency

[f.sub.R] = 2[f.sub.c]v/c + 2BR/Tc [approximately equal to] 2BR/Tc (13)

Then perform 1D FFT to every N computation results of the previous step column by column and consequently the peak of each column appears in the same row and corresponds to the Doppler frequency

[f.sub.D] = 2[f.sub.c]v/c (14)

At last, in the whole 2D area there appears one peak of which the position corresponds to the range and range rate of target.

According to the definition of Fourier transformation, the frequency resolution of first FFT and the range resolution are respectively:

[DELTA][f.sub.R] = 1/[t.sub.s]M = 1/T [DELTA]R = cT/2B [DELTA][f.sub.R] = c/2B

Then the frequency resolution of second FFT and the Doppler resolution are respectively:

[DELTA][f.sub.D] = 1/TN [DELTA]V = c/2[f.sub.c][DELTA][f.sub.[DELTA]] = c/2[f.sub.cTN]

In order to fulfill the Nyquist Sampling Theorem, the sample frequency should be greater than 2 times the maximum signal frequency as follows:

M/T > 2[f.sub.Rmax] = 4B/Tc [R.sub.max] 1/T > 2[f.sub.Dmax] = 4[f.sub.c]/c [v.sub.max]

FMCW Radar Model

Based on the signal processing method mentioned above, the block diagram of FMCW radar model presented is shown in figure 8 with detailed parameter inputs.

The geometric model described in Section IV outputs the detection information (range, range rate and angle) of the closest PSC to radar of each object detected. These sets of PSC are characterized by distance from radar (and thus a path loss associated with that distance), radial velocity, incident angle and the strength of reflection, i.e., Radar Cross Section (RCS). RCS is a measure of how detectable of an object is with radar. A larger RCS indicates the object is more easily detected. This paper doesn't focus on the estimation of RCS and takes it as known. The selected sets of PSC are fed to the physical model to be screened further by actual factors. The physical model is based on the signal processing method described in the last part. First, compute the beat signal in time domain and superpose an Additive Gaussian White Noise (AGWN) on it. Then perform 2D-FFT to convert the 2D input signal from time domain to frequency domain. A Constant False Alarm Rate (CFAR) threshold is applied to the yielded frequency spectrum and only those range Doppler bins whose Signal Noise Ratio (SNR) is larger than the threshold continue to the next step. Finally calculate the refined detection information (including range, range rate and azimuth angle) according to the position of peaks not submerged by the noise and output them as radar measurements to ACC controller.

V. SIMULATION RESULTS

Figure 9 shows the information list of targets and the simulation results of the proposed FMCW model with the following key parameters: field of view is 30[degrees]; radar Radio Frequency (RF) [f.sub.c] = 24GHz;bandwidth B = 1GHz; sample parameter N = 256, M = 1024; transmit power [P.sub.t] = 10w; effective area of radar receive antenna [A.sub.eff] = 1[m.sup.2]; antenna gain is taken as constant 1. The designed sensing property is [-50,50]m/s for range rate and [0.1,150]m for range. The left bottom figure shows the beat signal contaminated by AGWN in time domain and the right bottom figure shows the same signal in frequency domain after performing 2D-FFT, where three peaks correspond to the three targets. It can be easily seen that none of the three targets is submerged in the noise, which leads to the detection of the three targets.

Figure 10 shows an ACC simulation scheme created under PanoSim and Matlab/Simulink environment. The upper section is the block diagram of the whole system model including driver model, radar model, vehicle dynamics model and ACC algorithm in Simulink. The lower right section is the 3D animation in PanoSim. The lower left and middle section are the detection information of range and range rate respectively and the lines in red circles means the target goes out of the radar detectable range.

VI. CONCLUSIONS

This paper presents a novel approach to simulate FMCW millimeter wave radar that combines both geometric and echo signal based modeling method to achieve good balance between model fidelity and computational efficiency. The mathematical derivation behind the described method is discussed in detail. The proposed model has been implemented and verified under various scenarios. Among others, a closed loop simulation with an ACC algorithm under a dynamic 3D virtual environment provided by PanoSim has been implemented and the result demonstrates the validity and effectiveness of the proposed modeling method. The proposed method further enables real-time simulation under a Hardware-Inthe-Loop (HIL) platform in the near future.

REFERENCES

(1.) http://www.panosim.com/

(2.) Steve PECHBERTI, Dominique GRUYER and Vincent VIGNERON, "Radar simulation in SiVIC platform for transportation issues. Antenna and propagation channel modelling", 15th international IEEE Conference on Intelligent Transportation Systems, Anchorage, Alaska, USA, September 16-19, 2012, pp.469-474.

(3.) Deng, W., Zeng, S., Zhao, Q. and Dai, J. "Modelling and simulation of sensor-guided autonomous driving", Int. J. Vehicle Design, Vol. 56, Nos. 1-4, 2011, pp.341-366.

(4.) Dudek Manuel, et. al., "Millimeter Wave FMCW Radar System Simulations including a 3D Ray Tracing Channel Simulator", Proc. of IEICE, 2010, pp.1665-1668.

(5.) Laet, T., Schutter, J. and Bruyninckx, H. (2008) "Rigorously Bayesian range finder sensor model for dynamic environment", Proceedings of 2008 IEEE International Conference on Robotics and Automation, 19-23 May, Pasadena, CA, USA, pp.2994-3001.

(6.) Schuler K., Becker D., and Wiesbeck W., "Extraction of vertical scattering centers of vehicles by ray-tracing simulations," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 11, November 2008, pp. 3543-3551.

(7.) Winkler, V., "Range Doppler detection for automotive FMCW Radar", Proceedings of the 4th IEEE European Radar Conference, pp. 166-169, Oct.. 2007.

(8.) Rohling, H., Moller, C., "Radar waveform for automotive radar systems and applications", Radar Conference 2008, pp. 1-4, May 2008

CONTACT INFORMATION

For questions or to contact the authors, please email to the corresponding author

Prof. Weiwen (Kevin) Deng State Key Lab of Automotive Simulation and Control Jilin University China 130025 kdeng@jlu.edu.cn

ACKNOWLEDGMENTS

The authors wish to acknowledge the support of China National Natural Science Foundation under grant U1564211 and National Key Research and Development Program under grant 2016YFB0100904.

Jiao Guo, Weiwen Deng, Sumin Zhang, and Shiqian Qi

Jilin University

Xin Li

Jilin Universisty; Aviation University of Air Force

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Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE International. The author is solely responsible for the content of the paper.

doi:10.4271/2016-01-1892

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Author: | Guo, Jiao; Deng, Weiwen; Zhang, Sumin; Qi, Shiqian; Li, Xin |
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Publication: | SAE International Journal of Passenger Cars - Electronic and Electrical Systems |

Article Type: | Technical report |

Date: | May 1, 2017 |

Words: | 3867 |

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