Implementation of HighResolution Angle Estimator for an Unmanned Ground Vehicle
 Author: Cha SeungHun, Yeom DongJin, Kim EunHee
 Publish: Journal of electromagnetic engineering and science Volume 15, Issue1, p37~43, 00 Jan 2015

ABSTRACT
We implemented a realtime radar system for an unmanned ground vehicle designed to run on unpaved or bumpy roads. The system must be able to detect slow targets in a cluttered environment and cover wide angular sections with high resolution at the same time. The system consists of array antennas, preprocessors for digital beam forming, and digital signal processors for the detection process which uses sawtooth waveforms and highresolution estimation, and is called forward/backward spatial smoothing beamspace multiple signal classification (FBSS BSMUSIC). We show that the sawtooth waveforms enhance the angular estimation capability of FBSS BSMUSIC in addition to their wellknown advantages of removing the ambiguity of targets and detecting slow targets with improved velocity resolution.

KEYWORD
Angle Estimation , Beam Space MUSIC , FMCW Radar , Spatial Smoothing

I. INTRODUCTION
Radar has been developed in automotive sensor systems since the 1970s because of its long range, accuracy, and adaptability in allweather conditions. Initially, the key idea of the automotive radar system was collision avoidance; however, many different applications of the vehicle radar system are now under development [1]. For example, convenience equipment, such as adaptive cruise control (ACC), has already been commercialized. Applications of the safety system for autonomous driving are the major topics of current radar research [1,2].
One of the requirements for radar of an autonomous driving system is a highresolution capability, which is very difficult for the smallsized automotive radar because angular resolution directly depends on the antenna aperture size. However, parameter estimation methods by an array antenna can overcome this limitation of size. Multiple signal classification (MUSIC) is a wellknown array processing method for highresolution angular estimation [35], and its applications are being extended to various areas [69]. In this method, angle resolution is independent of the aperture size with ideal assumptions, such as uncorrelated signals, high signaltonoise ratio (SNR), and large samples [10,11].
Unfortunately in practice, as in automotive radar systems, these assumptions cannot be satisfied because of the highly correlated signals, low SNR, and small number of snapshots. Research efforts have attempted to overcome these limitations; most of these are decorrelation methods based on preprocessing schemes, such as forward/backward (FB) averaging or spatial smoothing (SS) [12]. In another approach, beamspace MUSIC (BSMUSIC) has been studied to improve radar performance in low SNR conditions. Several studies have reported that BSMUSIC has advantages of low sensitivity to system errors, reduced resolution threshold, and improved performance in environments with spatially colored noise [1317].
In this paper, we focus on increasing the number of snapshots by applying sawtooth waveforms. We show that this waveform enhances the angular estimation capability of MUSIC in addition to its wellknown advantages of removing the ambiguity of the targets and improving velocity resolution. Despite these advantages, sawtooth waveforms have not often been used because of their high computational power. However, due to advances in digital technology, such as the digital signal processor (DSP) and FPGA, we can now implement signal processing units, including sawtooth waveforms and FBSS BSMUSIC, which is one of the highresolution angle estimators.
In cooperation with the Korea Agency for Defense Development, we developed a 77GHz FMCW radar sensor as part of the sensor system for the defense unmanned ground vehicle (UGV) or robot, which is designed to run on unpaved or bumpy terrain, such as mountain roads. Fig. 1 shows the operational concept of the radar in a UGV.
Compared with commercial automotive radar, UGV radar must be capable of detecting slower targets in a harsh cluttered environment, covering wide angular sections in an azimuth up to 120°, and resolving targets with high angular resolution at the same time. In order to meet these requirements, we applied sawtooth waveforms in our process and designed the system using array antennas, an FPGAbased preprocessor for digital beam forming (DBF), and DSP for complex signal processing and highresolution angle estimation.
This paper is organized as follows: Section II describes our FMCW radar sensor and the signal processing method, including waveform design and highresolution angle estimation. Section III shows the experimental results with simulated data as well as measured data. Conclusions are presented in Section IV.
II. SYSTEM DESCRIPTION
The radar system consists of antenna devices, transmitter/receiver, and the signal processing unit, as shown in Fig. 2. The transmitter/receiver has a homodyne structure. One broad illuminating transmitting beam and eight receiving beams overlap in the azimuth to yield a total azimuthal coverage of 60°. DBF was developed by using these eight received signals. The 3dB beamwidth after DBF is about 15°. Some specifications of the transmitter/receiver are listed in Table 1.
1. Signal Processing Unit
Due to the impairments of the radio frequency (RF) frontend, the signal vector is distorted and degrades the resolution. Thus, the first process after converting the input to a digital signal is channel alignment by a premeasured calibration matrix. Each data signal is transferred to the frequency domain through first FFT for extracting the range information according to the FMCW principle. Then, the corrected signals are transferred to the beam space via DBF. Because of the sawtooth waveform, a second FFT is necessary to extract velocity information; this will be explained in the next section. The resulting data from the second FFT, which is called the rangeDoppler map, are used to detect the targets via the constant false alarm rate (CFAR) method. After this main detection process, MUSIC is performed with some information in advance. The whole block diagram is shown in Fig. 3(a).
Since various computations of DBF, FFT, and MUSIC are included in signal processing chains, we designed our board using Virtex5 FPGA (XC5VLX330; Xilinx Inc., San Jose, CA, USA) and DSP (TMS320C6455; Texas Instruments, Dallas, TX, USA) in order to make a realtime system. The preprocessing part including channel correction and DBF is implemented in FPGA, and the detection and FBSS BSMUSIC are implemented in DSP. Fig. 3(b) shows our signal processing board.
2. Design of the Waveform
In the FMCW principle, targets are detected using the difference in frequency between transmitted and received signals, as shown in Fig. 4(a). This difference is due to the range and the velocity of targets. Each frequency difference by range (Δ
f_{r} ) and by velocity (Δf_{v} ) can be represented bywhere
F_{BW} is the frequency bandwidth,T is the duration of one ramp,c is the speed of light,R andv are the range and velocity of each target, respectively, andf_{c} is the carrier frequency, which is 77 GHz in this case. In general,F_{BW} is only a few hundred MHz andT is a few milliseconds. This radar uses three or four ramps with different slopes to resolve signals from multiple targets and to calculate each range and velocity. However, inherently, measuring the sum or subtraction of frequencies can give the same value for several targets with a different range and velocity, including false targets.As the slope increases, usually by decreasing
T , only the frequency difference by range (Δf_{r} ) increases in Eq. (1). Fig. 4(b) shows this waveform. If Δf_{v} is less than 1/T , the frequency resolution Δf_{r} becomes the major component within one ramp and Δf_{v} appears in phase difference between ramps, the same as in stretch processing [18]. Therefore, Δf_{v} can be detected using a burst of ramps through a second FFT. In this paper, this burst of ramps is called sawtooth waveforms.Although the sawtooth waveforms might require more elaborate design work and much more computational power, it improves performance of detection for multiple targets with more velocity resolution, which is necessary for slowmovingtarget detection in a cluttered environment. Moreover, this burst of ramps improves the performance of highresolution estimation, a main interest in this paper, by giving more snapshots. The computational power is no longer challenging, considering the advances of FPGA and DSP technology.
The parameters used in this paper are
T = 33 seconds andF_{BW} = 200 MHz, which give Δf_{v} = 14.25 kHz and Δf_{r} = 6.06 MHz for a target moving at 100 km/h in a 150 m range. The number of ramps in a burst is 108, which is the maximum number of snapshots.3. HighResolution Estimation Algorithm: FBSS BSMUSIC
Consider a uniform linear array consisting of M identical sensors and
K receiving signals that arrive at the linear array from directionsθ _{1},θ _{2}, …,θ_{k} . The signal model is given bywhere s(
t ) is theK × 1 array replica vector, x(t ) is theM × 1 array output vector, and n(t ) is theM × 1 noise signal vector generated through the antenna and transmitter/receiver [12]. A represents anM ×K direction matrix (M >K ) with rankK and is given bywith
a (θ_{k} ) the direction vector associated with the arrival angleθ_{k} , i.e.,If the beamforming matrix is
W^{H} , such asthen the covariance matrix is
where
U_{s} is the signal subspace consisting ofK dominant eigenvectors andU_{n} is the noise subspace consisting of the remaining (M –K ) eigenvectors. The BSMUSIC algorithm shows that each peak in the angular spectrum isand that it corresponds to a target direction of angle (DOA).
We apply the FBSS method in [12] as the configuration of Fig. 5. The covariance matrix of the
l ^{th} forward beamsR_{l}^{f} and that of thel ^{th} backward beamsR_{l}^{b} are given bywhere
Y_{l}^{f}(t) stands for the output of thel ^{th} beam andY_{l}^{b}(t) for the complex conjugate of the output ofl ^{th} backward ignal forl = 1, 2,…,L , whereL denotes the total number of forward beams.R^{f} andR^{b} in Eq. (10) represent the FB spatially smoothed covariance matrix as the mean of the FB beam covariance matrices.The FB smoothed covariance matrix
R' is the mean ofR^{f} andR^{b} ; i.e.,Replacing
R withR' in (6), the angular spectrum in (7) changes intowhere
U'_{n} is the noise subspace ofR' consisting of the (L –K ) eigenvectors, as in Eq. (6).If
L ,M , and the number of beams are appropriately chosen satisfying thatL =M –M _{0} + 1 ≥K , the dimension of the signal subspaceK is determined by the target numbers. Each value chosen in our system isM = 8,M _{0} = 6, andK = 2.III. RESULTS AND DISCUSSION
1. Simulated Signals
In order to see the effect of the number of snapshots, i.e., sawtooth waveforms, a set of received signals on arrays from two targets at 14° and 18.5° was simulated with random noise. Shown in Eq. (4), the signals were simulated based on the equal and omnidirectional element pattern. Although we verified the effect with white Gaussian noise, we used the colored noise in this simulation because it shows the effect clearly and is more realistic. The colored noises are generated by random noises passed through a filter. Based on the SNR, they were amplified and added to the signals.
The normalized angular spectrums with different SNRs are shown in Fig. 6. As the number of snapshots increases, two peaks from the targets sharpen so that the two targets can be more easily resolved. In addition, the estimated angles approach the true values.
The sharpness can be represented by the depth, which is defined as the value of the second peak from the valley between two peaks. The depth increases as the number of snapshots increases if the SNR is ≥5 dB, as shown in Fig. 7.
In addition, the number of snapshots improves the error performance. Fig. 8 shows the angle errors with respect to the number of snapshots for different SNRs.
As the number of snapshots increases up to 20 in this case, the estimated errors decrease and converge to a single value for each SNR. This bias error decreases as SNR increases. Moreover, the variance of errors is reduced continuously as the number of the snapshots increases for all SNRs.
2. Real Signals
In the experiment to verify the method, we used two corner reflectors, as shown in Fig. 9. The reflectors were located at 2.4° and 11.5°, respectively, from the bore sight of the radar. The angle difference was about 60% of the beamwidth.
First, using a premeasured calibration matrix, each channel data record were aligned, as shown in Fig. 10.
The resulting depth and errors are shown in Figs. 11 and 12, respectively, with respect to the number of snapshots. The estimated errors are reduced to less than 0.5° in bias and 0.1° in variance by using more snapshots.
IV. CONCLUSIONS
We implemented a realtime radar system of the highresolution angle estimation for a UGV. We designed sawtooth waveforms and applied them with DBF and FBSS BSMUSIC in signal processing units using FPGA and DSPs. The experimental results showed that two targets apart in less than 60 % of the beamwidth are resolved in realtime processing. We also showed that more snapshots from sawtooth waveforms improve the accuracy and the robustness for the highresolution angle estimation

14. Yang Y., Wan C., Sun C., Wang Q. 2003 "DOA estimation for coherent sources in beamspace using spatial smoothing," [in Proceedings of the 2003 Joint Conference of the 4th International Conference on Information, Communications and Signal Processing and 4th Pacific Rim Conference on Multimedia] P.10281032

[Fig. 1.] Operational concept of the unmanned ground vehicle.

[Fig. 2.] System description.

[Table 1.] Specifications of the transmitter/receiver

[Fig. 3.] Configuration of the signal processing unit. (a) Block diagram of the signal processing unit. (b) Processing board.

[]

[Fig. 4.] Shapes of waveforms. (a) Two up/down ramp. (b) Sawtooth with steep slope.

[]

[]

[]

[]

[]

[]

[]

[]

[]

[]

[Fig. 5.] The forward/backward spatial smoothing scheme.

[]

[]

[]

[Fig. 6.] Normalized angular spectrum with a different number of snapshots. (a) SNR = 0 dB, (b) SNR = 5 dB, and (c) SNR = 10 dB.

[Fig. 7.] Sharpness as the number of snapshots increases.

[Fig. 8.] Angle estimation performance of estimated errors and variance of the errors.

[Fig. 9.] Photograph of the radar and the corner reflectors.

[Fig. 10.] Date before and after the channel. (a) Raw data of arrays. (b) Aligned data.

[Fig. 11.] Normalized angular spectrum and depth with respect to the number of snapshots.

[Fig. 12.] Angular error according to the number of snapshots.