the signal distortion in baseband digital domain. For the first time, at no extra hardware cost, an ac-coupled interferometric radar can be used to measure slow ...
A Digital Post-Distortion Technique for Noncontact Accurate Movement Measurement Using Interferometric Radar 2 l Changzhan Gu , and Changzhi Li 1 Marvell 2Department
Technology Group Ltd., Santa Clara, CA 95054, USA
of Electrical and Computer Engineering, Texas Tech University, Lubbock, TX 79409, USA
Abstract - Signal distortion may happen in conventional ac coupled
interferometric
radar
when
measuring
slow
target
movements. Existing solutions to preserve signal integrity add to hardware complexity and are at extra cost. In this paper, a digi tal post-distortion (DPD) technique is proposed to compensate the signal distortion in baseband digital domain. For the first time, at no extra hardware cost, an ac-coupled interferometric radar can be used to measure slow movements without losing any signal information-even those with stationary moment. The DPD technique is realized by applying a compensation function, which is the inverse of the baseband system response and ob tained in hardware calibration, to the digitized baseband IIQ
R
F
D(n )
Fig. I. A simplified block diagram of the homodyne quadrature radar receiver. Baseband is ac-coupled to remove dc offset.
signals. Both simulation and experimental results show that the proposed technique is robust to recover distorted signals.
IH(z) I
Index Terms - Interferometric radar, signal integrity, distor
IH'(z)I
tion, compensation, post-distortion.
I.
INTRODUCTION
Interferometric radar finds wide applications in noncontact measurement of mechanical vibrations [1] and physiological activities [2]. Among all interferometric radar receiver archi tectures, quadrature direct-conversion is probably the most popular one, due to its less complexity, lower hardware cost, and higher level of chip integration [3]. The mixer output is usually coupled via a capacitor to the baseband circuitry, in order to deal with dc offset that is inevitable in direct conversion receiver. However, the high-pass characteristics of ac coupling may result in significant distortion in measuring low frequency movements [4]. Researchers have proposed various techniques to avoid sig nal distortion and preserve signal integrity. For example, sev eral dc-coupled receiver architectures have been proposed to calibrate dc offset while preserving dc information [3-4]. The dc-coupled receiver is an all-pass structure that avoids the distortion to low frequency or stationary movements. Howev er, dc tuning requires extra effort and also adds to hardware complexity. Digital intermediate frequency (IF) sampling is another candidate to avoid dc offset at baseband [5-6]. How ever, it requires high-speed digitizer which increases the hardware cost. In this paper, a novel DPD technique is proposed to com pensate the signal distortion due to ac-coupling in interferometric radar sensing. As to the best knowledge of the authors, it is the first time that the conventional ac-coupled radar can be used to measure low frequency movements with out losing any signal information. The signal distortion is due
�
hi
h2
h3
h4
Nonlinear
modulation
h5
Frequency
Fig. 2. The proposed DPD technique: a system response of H(z) is employed in digital domain to compensate the signal distortion due to the baseband high-pass response H(z).
to the high pass characteristics of the ac-coupled receiver [7]. In the proposed DPD technique, a compensation function is employed in baseband digital domain to recover the signal information that is lost in ac-coupled receiver. Without requir ing any hardware modification, the conventional ac-coupled radar architecture can preserve the complete signal integrity, which is important for applications such as tumor tracking in motion-adaptive radar radiotherapy [7]. II.
THEORY
Figure 1 shows the simplified block diagram of a homodyne quadrature radar receiver. The mixer output llQ signals are: 1(t)=A-cos(4ITX(t)/ 4+�e(t))+DCJ
(1)
Q(t)= A-sin ( 47rx(t)/ 4+�e(t))+DCQ
(2)
where A is the amplitude, DC/DCQ are dc offsets, �6\'t) is the residual phase, and x(t) is the target movement. The baseband forms a first-order high-pass filter with cut-off frequency of wc=l/(R-C). However, it can also be designed as higher order filters with different gain configurations for different applica-
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OF----�--..�----�----�--�----� - original ----- distorted .... recovered
Iii' s
(a)
h2
�
g -20
o Qi
§
(a)
E (;
Ol .s:::: U
z
0.5
unit circle
0
Distorted -0.5 -1
o
(b)
0.1
o Qi
0.2
0.5
0.3 0.4 Frequency (Hz)
0.5
0.6
-1
-- distorted --
c c Ol .s:::: U
--
--
o
al O 99 al O 97 al O 96 =
.
=
.
=
.
(b)
�
Ol .s:::: U
-0.5
0.5
0 Channell
0.5
unit circle
0 -0.5 -1
-1 -1
-0.5
0 Channell
-1
0.5
Fig. 3. Simulation results of distortion compensation using DPD: (a) harmonic amplitude,and (b) I1Q trajectories using different com pensation coefficients.
tions. It is known that, when measuring slow movement, sig nal distortion may happen if the harmonic ratios are changed when the target frequency and its harmonics are subject to different degrees of attenuation in the baseband high-pass fil ter [6]. Assume that C,n(t)=l(t)+j-Q(t) and the baseband system response is H(t), the baseband output before digitization is then the conjugate of c,n(t) and H(t): Coult)=lo(t)+j-Qo(t)= c,n(t)* H(t) ,
(3)
where lo(t)IQo(t) are IIQ signals before digitization. The baseband IIQ signals are digitized by the analog-to-digital converters. So the complex output signal in the z-domain is:
-0.5
o Channell
0.5
Fig. 4. llQ trajectories of (a) distorted signals of slow sinusoidal movement, and (b) recovered signals using DPD.
The system response of IH'(z)1 is shown in Fig. 2, which compensates the distortion by restoring the original harmonic ratios. The recovered signal is then: CD
( z) . H'(z) =Cin ( z) . H (z) . H'(z) = A ·Cin ( z) .
(7)
A
The baseband gain has no contribution to signal distortion because the radar measured movement is modulated in the signal phase. It is flat in frequency domain, as the movement speed is much smaller than the baseband amplifier bandwidth. It is calibrated out in arctangent demodulation [3]. The coeffi cients could be obtained in hardware calibration by char acterizing the baseband high-pass filter. The compensation model (6) is included in digital signal processing to ensure distortion-free measurement.
bJak
(4) where C,n(z) and H(z) are the z-transforms of c,n(t) and H(t), respectively. The system response can be expressed as:
H(Z)=A{(1-L�bkz-k)/(1-L�akz-k)J, (5) where A is the baseband gain. The coefficients bklak determine
the high-pass characteristics of the ac-coupled baseband, which may cause signal distortion. In the proposed DPD technique, the distortion is compensated by an mverse function of H(z) in baseband digital domain: H'(z)
= (1-L�akz-k)/(1-L�bkz-k) .
(6)
III.
SIMULATION
A radar-measured slow sinusoidal movement is simulated and distorted by the R-C low pass filter shown in Fig. and then compensated using the proposed DPD technique. The sinusoidal signal has a low frequency of 0. 7 Hz and a sam pling rate of 50 Hz. The capacitance for radar baseband ac coupling is C=10 ,llF and the following resistance is R=50 kD., as shown in Fig. The baseband is therefore a first order high-pass RC filter, of which the coefficients are al=0.961 and bl=l, and the transfer function is H(z)= · [(l-z-I)I(l-0.96 z-I)].
1,
1
1.
A
1
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m � � t>
(a)
Q) a.
(f) "0 Q)
--
distorted
----- recovered
-20
1:;1
ro
E
o z
-4
8 .1
0.15
0.2
0.25
0.3
Frequency (Hz)
0.35
0.4
4 �------��
E S (b)
2
C
- Ground Truth ----- Distorted -.-.-.- Recoverred
E 0 Q)
Q) u ro a.
is
-2
5
Time (second)
10
Fig. 5. (a) Spectra showing slow sinusoidal signals distorted and recovered using DPD; (b) time-domain comparison of the distorted and recovered signals with the ground truth.
In the simulation, a system response of H'(z)=(l-al·z-I)I(l-zI) is applied to the distorted signal to compensate the distor tion. The coefficient al is swept from 0.99 to 0.96. The simu lation results are shown in Fig. 3. It is seen that, the second harmonic of the distorted signal is higher than that of the orig inal. It is because it suffers from less attenuation than the fun damental in high-pass filtering. The change of fundamen tal!harmonic ratio results in signal distortion, which leads to a ribbon-like shape in llQ constellation as shown in Fig. 3(b). After applying the compensation with al=0.99 and al=0.97, the ribbon shape tends to better fit with the unit circle. When al=0.96, which is close to the actual coefficient 0.961 of the high-pass filter, the harmonic amplitude is restored to match with the original. The distorted signal is compensated and l!Q trajectory is recovered to fit well with the unit circle. It is also seen that the radian length of llQ trajectory changes as al ap proaches to the actual coefficient value. The radian of llQ tra jectory determines the displacement amplitude of the demodu lated signal [1]. Therefore, the proposed DPD technique is also beneficial for optimizing the trajectory radian in distor tion compensation for accurate displacement measurement. IV.
EXPERIMENT
Experiments were carried out in lab environment by using an ac-coupled interferometric radar to measure mechanical
movements of an actuator (Zaber T-NAOSA50). The actuator was placed about 0.5m away from the interferometric radar and programmed to produce a slow sinusoidal movement of 0. 16 Hz. The radar receiver has the same baseband structure as Fig. 1 with a cut-off frequency of 0. 32 Hz. It was calibrated as a first-order high-pass filter and the characterized coefficient is al=0.965. Therefore, in baseband signal processing, a sys l tem response of H'(z)=(l-0.965·z-1)/(l-z- ) is used to compen sate the distortions. The experimental results are shown in Figs. 4-5. As shown in Fig. 4, the slow sinusoidal movement was dis torted at ac-coupled baseband and is showing a ribbon-shape trajectory. However, the proposed DPD technique effectively restores harmonic ratio to offset the distortion and recover ideal trajectory that fits the unit circle, as shown in Figs. 5(a) and 4(b). Fig. 5(b) shows the demodulated displacement sig nals with and without DPD. It is seen that DPD recovered signal matches well with the ground truth while there is an offset for the distorted signal. This is because DPD helps to recover the correct trajectory radian for accurate phase de modulation. V.
CONCLUSION
A digital post-distortion technique is proposed to compen sate the signal distortion that happens in ac-coupled interferometric radar when measuring slow target movements. Both simulation and experiments show that, without hardware modification, the proposed DPD technique allows the conven tional ac-coupled interferometric radar to be able to keep the complete signal pattern in movement measurement. REFERENCES
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[4]
[5]
[6]
[7]
S. Kim and C. Nguyen, "A displacement measurement tech nique using millimeter-wave interferometry," iEEE Trans. Mi crowave Theory Tech., vol. 51,no. 6,pp. 1724 - 1728,2003. J. C. Lin, "Noninvasive microwave measurement of respira tion," Froc. iEEE, vol. 63,no. 10,pp. 1530-1530,Oct. 1975. B. K. Park, O. Boric-Lubecke, and V. M. Lubecke,"Arctangent demodulationwith DC offset compensation in quadrature Dop pler radar receiver systems," iEEE Trans. Microw. Theory Tech., vol. 55,no. 5,pp. 1073-1079,May 2007. C. Li, O. Boric-Lubecke, V. Lubecke, and J. Lin, "A review on recent advances in Doppler radar sensors for noncontact healthcare monitoring," iEEE Trans. Microw. Theory Tech., vol. 61,no. 5,pp. 2046-2060,May 2013. I. Mostafanezhad, O. Boric-Lubecke, and V. Lubecke, "A co herent low IF receiver architecture for Doppler radar motion de tector used in life signs monitoring," in iEEE Radio Wireless Symp., 2010,pp. 571-574. B. Jensen, S. Jonasson,T. Johansen,and T. Jensen,"Vital signs detection radar using low intermediate-frequency architecture and single-sideband transmission," European Radar Conference (EuRAD) 2012, c. Gu, R. Li, R. Fung, C. Torres, S. Jiang, and C. Li, "Accurate Respiration Measurement using DC-Coupled Continuous-Wave Radar Sensor for Motion-adaptive Cancer Radiotherapy", iEEE Trans. Biomed. Eng., vo1.59, no. 11,pp.3117-3123, Nov. 2012.
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