Characterization of UWB Transmit-Receive Antenna

Characterization of UWB Transmit-Receive Antenna
Characterization of UWB Transmit-Receive Antenna System
Alireza H. Mohammadian†, Amol Rajkotia, and Samir S. Soliman
QUALCOMM Incorporated, 5775 Morehouse Drive, San Diego, CA 92130
†E-mail: [email protected]
Abstract – An ultra-wide-band (UWB), stripline-fed Vivaldi
antenna is characterized both numerically and experimentally.
Three-dimensional far-field measurements are conducted and
accurate antenna gain and efficiency as well as gain variation
versus frequency in the boresight direction are measured. Using
two Vivaldi antennas, a free-space communication link is set up.
The impulse response of the cascaded antenna system is obtained
using full-wave numerical electromagnetic time-domain
simulations. These results are compared with frequency-domain
measurements using a network analyzer. Full-wave numerical
simulation of the free-space channel is performed using a two step
process to circumvent the computationally intense simulation
problem. Vector transfer function concept is used to obtain the
overall system transfer function and the impulse response.
I. INTRODUCTION
U
nlike narrowband systems, the antenna plays an
integral role in an UWB system. UWB systems
transmit extremely narrow pulses on the order of 1ns or
less resulting in bandwidths in excess of 1 GHz. From a
system design perspective, the impulse response of the
antenna is of particular interest because it has the ability
to alter or shape the transmitted or received pulses. If
one were to design a matched filter receiver, a clear
understanding of the shape of the pulse at the receiving
antenna terminals is needed. Hence, the cascaded
response of the transmitting (TX) and receiving (RX)
antennas play a key role in shaping the pulse.
In several papers on UWB, it has been claimed that the
voltage received at the RX antenna terminals is the
second derivative of the excitation voltage at the TX
antenna terminals. For example, a Gaussian pulse
exciting a TX antenna would be transformed to its
second derivative when observed at the RX antenna
terminals. In fact, this assumption has been used in
most papers to design the template waveform for a
correlator- (matched-filter-) based receiver.
The relationship between the input voltage/current of a
TX antenna and the field it generates is a function of
several parameters including the antenna geometry,
material, current mode, and the transmitter impedance.
In general, this relationship does not hold a fixed form
(derivative, double derivative, etc.) and is dependent on
these parameters. The same is true for the relationship
between the incident field and the received
voltage/current for an RX antenna. That is also true for
the terminal voltages (or currents) of a TX-RX antenna
system. To claim that for an UWB system, the received
voltage is always the first or second derivative of
transmitted voltage is incorrect. The myth may have
been stemmed from an extrapolation of some early
research works on the transient behavior of linear
antennas. For example, it may be shown [1] that if a
pulse excites a dipole much shorter than the wavelength
of the highest frequency in that pulse, the radiated field
is proportional to the first or second derivative of the
pulse depending on whether the current distribution is
assumed traveling or standing. It is not an inherent
property of the UWB signals or system that the output is
always the first or second derivative of the input. We
will address this issue in a future correspondence.
Ideal antennas used in an UWB TX-RX system should
faithfully replicate the transmitted pulse at the receiving
end. In practice, attempt must be made to limit the
amplitude and group delay distortion below certain
threshold that will ensure reliable system performance.
The purpose of the current study is to establish a fullwave numerical simulation approach for the
characterization of an UWB TX-RX antenna system in
an attempt to design better receivers. The predicted
impulse response and transfer function of the system is
compared to the measured results to prove the validity
of the numerical approach. The Vivaldi antenna chosen
here merely serves as an example to show the
characterization methodology. This antenna, while
providing an adequate bandwidth for the UWB
spectrum, may not necessarily be the optimum choice
for every UWB system. In Section II, we discuss the
numerical approach used to characterize an individual
antenna, followed by a post-processing stage to create a
model for a free-space link with two antennas. The
transfer function and impulse response of this link is
then derived. In Section III, our measurement method
will be explained leading to an experimental evaluation
of the transfer function and impulse response of our
free-space link. Finally, in Section IV, the numerical
and experimental results are compared and some
conclusions are derived.
II. FULL-WAVE NUMERICAL APPROACH
Electromagnetic (EM) simulation provides useful
insight into the performance of the individual
components of an UWB link, in particular the TX and
the RX antenna. It also makes it more time and cost
effective to investigate the effects of the antenna type
and orientation on the UWB system performance
through parametric studies. Traditionally, most EM
simulations of antennas are limited to characterization
of the antenna input impedance and far field gain
patterns over a narrow band of frequencies. As such, an
EM simulation tool in the frequency domain is often
adequate and preferred. In our study of UWB antennas
and UWB communication links, we characterize the
antennas and the channel using system level concepts
such as transfer functions and impulse responses.
Therefore, EM simulation in the time domain is more
appropriate. In the following analysis, the time-domain
EM simulation tool Micro-Stripes [2] was used.
Channel
RX
Fig. 1. Components of an UWB communication link.
The communication link is divided into two components
(Fig. 1), the TX antenna and the channel as one
segment, and the RX antenna as the other. The complete
link is reconstructed in the post-processing stage.
A. Characterization of an Individual Vivaldi Antenna
A Vivaldi antenna is designed and its performance is
optimized through full-wave numerical simulations.
Two prototypes of this design measuring 90 mm by 40
mm by 3.15 mm were built on a two-layer Roger 5870
substrate (εr = 2.33, tanδ = 0.0016), and their return loss
measured. (See Fig. 2.)
Fig. 3. Boresight gain versus frequency for the Vivaldi
antenna.
B. Simulation of TX/Channel Segment
In the TX / Channel portion, the TX antenna is excited
by an input pulse voltage and the time-domain fields are
computed at a distance R ( > 2D2/λ) from the antenna as
depicted in Fig. 4. A full-wave simulation of Maxwell’s
equations in the time domain is performed and the
observation point is extended to the far-field region.
D
TX
stripline feed and the counterpoise, while the mid-layer
metallization, serves as the poise and the strip. Fig. 3
shows predicted and measured boresight gains versus
frequency.
The agreement between the predicted and
measured gain values is very good over the entire UWB
spectrum (i.e. 3.1 GHz ~ 10.6 GHz).
vTX (t )
G
× e (t )
~
R
TX Antenna
Channel
Observation
point
Fig. 4. TX-Channel portion of the UWB communication link
D is the characteristic dimension of the antenna and λ is
the wavelength of the highest frequency in the pulse
spectrum with non-negligible power.
C. Post-Processing of the TX Antenna / Channel
Segment
The output and input signals are converted to the
frequency domain using Fourier transformation.
(c)
Fig. 2. (a) A picture of the UWB Vivaldi antenna prototypes.
(b) Simulation geometry showing the internal details of the
antenna. (c) Measured return loss for the two Vivaldi
antennas.
As Fig. 2(b) shows, the top- and bottom-layer
metallizations constitute the ground planes for the
A vector transfer function for the TX antenna/channel is
defined relating the input voltage at the terminals of the
TX antenna to the electric far field in the desired
direction:
G
G
E( f )
(1)
(f)=
.
H
TX / Ch
VTX ( f )
G
where E ( f ) and VTX ( f ) are the Fourier transform of the
G
electric field e (t ) and the input voltage vTX (t ) ,
respectively.
D. Simulation of the RX Antenna
A plane wave pulse with polarization ĉ is incident
upon the RX antenna from a direction parallel to the line
that connects the phase centers of the TX and RX
antennas as depicted in Fig. 5(a). In theory, an impulse
is used to find the impulse response of a system. In
numerical simulations, a pulse such as
g (t ) = 2 f c sinc(2πf c t )e
− (πf g t ) 2
(2)
may be used instead, provided the pulse amplitude in
the frequency domain over the frequency band of
interest remains nearly a constant. The parameters in
(2) are given as fc = 1.3 fop and fg = 0.2 fop where fop is
the highest output frequency. This plane wave pulse
generates a voltage across the terminals of the RX
antenna that may be computed via a full-wave
simulation of Maxwell’s equations in the time domain.
E. Post-processing of the RX Antenna Simulation
In general, the sampling rates for the simulations of the
TX and RX antenna are different. Therefore, it may
become necessary to use zero padding and interpolation
before calculating the transfer function in the postprocessing stage. Once the sampling rates are identical,
the Fast Fourier Transforms (FFTs) are utilized to find
the frequency spectrum of the input and output
quantities and derive a transfer function. The details are
shown in Fig. 5(b) where tilde indicates original quantities. A vector transfer function for the RX antenna is
now defined through the following vector expression:
G
G
V RX ( f ) = E ( f ) ⋅ H RX ( f ).
~G
e (t ) = g (t )cˆ
(3)
~G
 e (t ) 
~

v
 RX (t ) 
~
RX Antenna
G
e (t )
v RX (t )
G
 e (t ) 
v (t )
 RX 
Inte rpolations
0
FFT
G
E( f )
VRX ( f )
(a)
(b)
Fig. 5. (a) A plane-wave pulse incident on the RX antenna.
(b) Post-processing of the RX antenna input and output.
F. Transfer Function and Impulse Response of the
Overall System
G
E ( f ) is substituted from (1) into (3) to establish a
relationship between the excitation voltage at the TX
antenna and the received voltage at the RX antenna.
The transfer function between the TX and RX antenna
may then be given by
G
G
(4)
H Link ( f ) = VRX / VTX = H TX / Ch ( f ) ⋅ H RX ( f ).
It is interesting to note that while the transfer functions
of the TX antenna/Channel and the RX antenna are
vector quantities, the transfer function of the link being
the inner product of these two vectors is scalar since the
input and output quantities are scalars.
The impulse response may be obtained by computing
the inverse Fourier transform of the transfer function
1 +∞
(5)
hLink (t ) =
H Link ( f )e i 2πtf df .
2π
∫
−∞
III. MEASUREMENT METHOD
There are two different approaches for the impulse
response measurements. The first is the direct timedomain approach using an extremely fast sampling
oscilloscope. The second approach is to make the
measurement in the frequency domain using a network
analyzer. In the first method, the transmitting antenna is
excited with an extremely narrow pulse and the received
waveform is captured using an oscilloscope. If the
exciting pulse bandwidth is much larger than the
antenna system bandwidth, then the measured signal is a
good approximation of the system impulse response.
However, if the exciting pulse bandwidth is comparable
to that of the antennas, then, a de-convolution process is
required.
The second approach is to make the measurements in
the frequency domain. Here, a network analyzer is used
to measure the cascaded frequency response of the
RX/TX antennas. The analyzer is swept from close to
DC to about 12 GHz and the complex response of the
system measured. This frequency data is then converted
to the bandpass equivalent by taking the complex
conjugate data and zero padding it where needed. The
impulse response is then computed by taking the IFFT.
The reason for choosing 12 GHz as the upper limit is
because (a) the antennas are designed to operate below
10 GHz and (b) even if the antennas have high
frequency gain, the rest of the receiver will most likely
have a front-end interference rejection filter with a cutoff of 12 GHz or less. Detailed procedure for making
this measurement is explained below and a block
diagram of this approach is shown in Fig. 6.
Mathematically, the cascaded impulse response can be
computed as shown below.
H ( f ) = H TX ( f ) H CH ( f ) H RX ( f ) =
Y( f )
= S 21
X(f )
(6)
h[ n] = Re{IFFT [ H ( f )]}
where h[n] is the impulse response computed using
IFFTs. Due to the lack of a fast sampling oscilloscope,
we chose the second approach in making the measureH (f),h (t)
X (f)
xt
H te
C H (f)
H T X (f)
Y (f)
H R X (f)
utilizing exactly the same size FIR filter, all samples
between 2ns and 6ns were chosen as the FIR
coefficients. This 4ns window contained more than
99% of the power.
C. Group Delay
P o rt 1
N e tw o rk
A n a lyz e r P o r t 2
Fig. 6. Frequency Domain Measurement
ments. This is also the approach that has been taken by
several researchers to model RF channels. [3, 4]
A. Impulse Response
The RX and TX antennas were placed in an anechoic
chamber with sufficient horizontal separation to be in
the far field of each other as shown in Fig. 7. The two
antennas were oriented to boresight. The network
analyzer frequency was swept in the desired range and
the magnitude and phase of the RX/TX cascaded
response were stored. This provided the complex
scattering parameter S21. Next, a conjugate reflected
frequency response S*21 was formed and with
appropriately zero padding the data, arrived at the final
frequency response vector, which is called H(f). The
impulse response h[n] was obtained by taking the real
part of the IFFT of H(f). The above procedure was
repeated for various orientations of the RX antenna.
Z
-X
RX
TX
X
Ez
Z
RX
Hy
X
TX
(
θ=
,φ
90
=
0)
18
Y
(a)
(b)
Fig 7. (a) Free-space UWB link inside an anechoic chamber.
(b) TX and RX antenna and the direction of propagation.
B. Antenna FIR model from impulse response
We took the impulse response samples that contain
more than 97% of the power. This is given by the
following expression:
n2
100 *
N
∑ h [n] / ∑ h [n] ≥ 97
2
n = n1
2
(7)
n =1
where N is total number of points in the impulse
response, and n1,n2 are sample indices of window that
contains 97% of the power. The samples from n1 to n2
are chosen as the coefficients of the FIR filter used to
model the cascaded RX/TX antenna.
When different antenna orientations are used, the above
method may sometimes give different number of
coefficients. Thus, to be consistent in the simulation by
A good measure of the performance of a filter is its
group delay, defined as the negative derivative of the
filter phase with respect to frequency. When a signal
passes through a filter, it experiences both amplitude
and phase distortion. The amount of distortion depends
on the characteristics of the filter. A waveform incident
at the input of a filter may have several frequency
components. The group delay gives an indication of the
average time delay the input signal suffers at each
frequency. Stated differently, this parameter gives an
indication of the dispersive nature of the filter.
Mathematically, the filter response and group delay are
given by:
dθ (ω )
(8)
H ( f ) = A(ω )e jθ (ω ) ;
τg = −
.
dω
If the filter has a non-linear phase response, the group
delay will vary with frequency causing the input signal
to experience different delays at different frequencies.
As a result, the output waveform is likely to be
distorted. For a filter to be linear phase (have constant
group delay), its phase response must satisfy one of the
following relationships:
(9)
θ (ω ) = −αω ;
θ (ω ) = β − αω .
It can be shown that in order to satisfy either one of the
above conditions of linear phase, the impulse response
of an FIR filter must have positive or negative
symmetry [5]. The simulation results of the previous
section shows that the antenna does not possess this
symmetry.
The UWB antenna can be viewed as a filter with some
magnitude and phase response. By representing the
Rx/Tx antenna system as a filter, we can determine its
phase linearity within the frequency band of interest by
looking at its group delay. The phase response and
group delay are related to the antenna magnitude (gain)
response. For example, if there is a null in the
magnitude, it implies a nonlinear phase, and therefore, a
non-constant group delay. Unless there are large
variations in the magnitude, it is difficult to determine
the phase linearity by simply looking at the phase plots.
The group delay plot is able to clearly show any nonlinearity that may be present in the phase. The pulse
input to the antenna system has an extremely large
bandwidth and hence, any variation in group delay
across the pass band of the transmitted pulse is likely to
distort the pulse. To characterize the antenna, the peakto-peak variations of the gain and group delay within
the 10dB bandwidth of the input pulse is determined.
IV. RESULTS
The UWB antenna was characterized for different
orientations of the receiving antenna. The RX antenna
was positioned at elevations of α = -135, -90, -45, 0, 45,
90, 135 degrees for each of the azimuths of β = 0, 90,
and 135 degrees to give a total of 21 orientations. The
elevation angles correspond to the rotation of the RX
antenna pedestal in the horizontal plane, while the
is relatively small, ranging from about 7 to 17 samples
for different α. The gain variation within the same
bandwidth is found to be about 3 dB to 11.6 dB. In
contrast, a large variation is seen when β = 90 degrees,
where the group delay varies from 19 to 42 samples and
the gain varies from 5 dB to 17 dB. Thus, the 90-degree
azimuth case will distort the incident signal the most.
Table 1. Antenna group delay and gain variation
Gain Variation (dB)
τg Variation (samples)
0°
90°
135°
0°
90°
135°
α↓,β→
UWB Vivaldi Antenna (variations within 4.32 to 5.68 GHz.)
-135°
16.8
42
27.7
11.6
17.2
4.9
-90°
7.6
20.5
20.3
5.5
11.6
9.3
-45°
13.9
28.3
18.2
3.4
9.1
7.2
0°
7.6
18.8
16.8
4.4
7.7
5
45°
11.3
19
15.3
3.3
10.1
6.6
90°
12.6
22.5
15.8
6.6
12.6
9.4
135°
16.4
38.9
15.8
7.4
5.2
7.3
(a)
(b)
Fig. 8. (a) Impulse response and (b) transfer function
corresponding to the case α = 0°, and β = 0° in Table 1.
(a)
(b)
Fig. 9. (a) Impulse response and (b) transfer function
corresponding to the case α = 90°, and β = 0° in Table 1.
(a)
(b)
Fig. 10. (a) Impulse response and (b) transfer function
corresponding to the case α = 135°, and β = 0° in Table 1.
V. CONCLUSIONS
A time-domain simulation method of characterizing
UWB TX-RX antenna systems was presented in this
paper. The measured antenna transfer function was
found to be close to the simulated one indicating that we
can use a software-based approach to determine an
antenna model for most orientations.
From the
cascaded impulse response, the received waveform can
easily be determined for any arbitrary incident pulse.
Since the incident signal bandwidth is in excess of 1
GHz, the group delay and gain variation across the
entire bandwidth has to remain relatively flat to prevent
signal distortion. Further measurement on an omnidirectional antenna need to be performed to validate the
effect of gain and group delay on the receiver
performance. In general, obtaining an antenna with flat
gain and group delay variation across multi-gigahertz
and across different angles is non-trivial and the
received waveform will be very sensitive to antenna
motion.
REFERENCES
azimuth angles correspond to the orientation of the TX
antenna on a fixed stand. The convention used for the
numerical simulations indicated on the figures (i.e., θ,
φ) is based on the direction of the waves propagating
from the TX antenna toward the RX antenna, which is
always fixed at its position as indicated in Fig. 7(b).
Some typical results are shown in Fig. 8 to Fig. 10. It
should be noted that the system noise floor for these
measurements was less than –75 dB.
Table 1 indicates that for β = 0 degrees, the peak to
peak group delay variation measured in 4.32 GHz to
5.68 GHz (10dB incident pulse bandwidth of 1.36 GHz)
[1]
[2]
[3]
[4]
[5]
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