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Hindawi Publishing Corporation
International Journal of Antennas and Propagation
Volume 2012, Article ID 929018, 8pages
doi:10.1155/2012/929018
Research Article
On the Performance of the Time Reversal SM-MIMO-UWB
System on Correlated Channels
Hieu Nguyen,1Va n D uc N gu y en ,2Trung Kien Nguyen,1Kiattisak Maichalernnukul,1
Feng Zheng,3and Thomas Kaiser3
1Institute of Communications Technology, Leibniz University of Hannover, 30167 Hannover, Germany
2School of Electronics and Telecommunications, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi 10000, Vietnam
3Institute of Digital Signal Processing, Faculty of Engineering, University of Duisburg-Essen, 47057 Duisburg, Germany
Correspondence should be addressed to Hieu Nguyen, hieunth@gmail.com
Received 3 January 2012; Revised 9 March 2012; Accepted 9 March 2012
Academic Editor: David A. Sanchez-Hernandez
Copyright © 2012 Hieu Nguyen et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The impact of spatial correlation on the multi-input multi-output ultrawide band (MIMO-UWB) system using the time reversal
(TR) technique is investigated. Thanks to TR, several data streams can be transmitted by using only one antenna in a system
named virtual MIMO-TRUWB. Since the virtual MIMO-TR-UWB system is not affected by the transmit correlation, under the
condition of the high spatial correlation, it outperforms the true MIMO-UWB system with multiple transmit antennas. The
channel measurements are performed in short-range indoor environment, both line-of-sight and non-line-of-sight to verify the
adoptedcorrelatedchannelmodel.
1. Introduction
An ultrawide band (UWB) communication system, whose
relative bandwidth is usually defined as greater than twenty-
five percents, has become a promising candidate for high
data rate and short-range communication systems, which
have attracted great interests from both academic and
industrial aspects recently [1,2]. Impulse radio UWB is
however designed with low complexity and low power
consumption applications such as in many application such
as wireless sensor networks, sensing and positioning systems,
interchip communication, contact less wireless, biological or
biomedical networks, imaging systems, health monitoring,
and body-area networks [3]. However, due to the wide
bandwidth property, UWB systems suffer from a very long
delay spread by multipath effect [4–6]. One has to deploy
RAKE receivers to combat the intersymbol interference (ISI).
The time reversal (TR) technique, which is originated
from under-water acoustics and ultrasonic [7,8], now has
been used in many applications such as localization, imaging
and green wireless communications [9–14]. TR also has
shown its potential in dealing with the ISI problems in UWB
[15,16]. In a TR system, the time-reversed channel impulse
response (CIR) is implemented as a filter at the transmitter
side. This process leads to a very narrow focus of power at the
receiver at one specific time instant, and one specific space
position if the CIRs between any two communication pairs
at different locations are de-correlated. In other words, a TR-
UWB prefiltering system has a unique feature of space-time
domain focusing.
The space-time focusing feature is also beneficial in a
MIMO spatial multiplexing scheme [17,18]. Several studies
have applied the TR technique to multiple antennas beam-
forming systems. In [19–21], the same stream of data is
beamformed by a TR filter and transmitted over transmit
antennas. In [22,23], a joint ZF and TR preequalizer is
designed to minimize the ISI and maximize the received
power at the intended receiver. This proposal only deals with
the ISI problem for beamforming schemes. The potential of
a MIMO UWB system using spatial multiplexing scheme is
considered in [24], where the matching filter plays the role
of a passive time reversal filter and the maximum likelihood
(ML) detector is used to deal with the multistream interfer-
ence (MSI) but ignores the ISI. The SM-MIMO-UWB system
using TR is introduced in [25] with the capability of transmit
2 International Journal of Antennas and Propagation
antenna selection. The TR technique and preequalizer are
proposed in [26] for the so-called virtual MIMO UWB
system.
As shown in [26], with the help of the TR prefilter
and a properly designed preequalizer, the system with only
one transmit antenna can deliver several independent data
streams at the same time. However, the spatial correlation
among the transmit and receive antennas has not been inves-
tigated. We have taken the spatial correlation into account in
[27], where a constant spatial correlation model for MIMO
UWB with linear array structure has been applied. In this
paper, the performance of system over both correlated line-
of-sight (LOS) and non-line-of-sight (NLOS) channels is
investigated with the same correlation model. In order to
verify the adopted correlation model, the correlated channels
are measured in both scenarios NLOS and LOS in indoor
environment. These scenarios are referred to as channel
models CM1 and CM2, respectively, in the IEEE 802.15.3a
standard [28]. The BER results on the adopted correlated
channel model with an appropriate value of correlation
coefficient are shown closely matching with those on the
measured indoor channel.
It is well known that the MIMO-TR-UWB system can
achieve transmit diversity [26], but it suffers from penalty
caused by both transmit and receive antenna correla-
tions. Meanwhile, the single-input multiple-output TR-
UWB (SIMO-TR-UWB) or virtual MIMO-TR-UWB does
not face the transmit antenna correlation because it has only
one transmit antenna. It will be shown that, under some
conditions, the virtual MIMO outperforms the true MIMO
system in term of the BER performance.
The remainder of the paper is organized as follows: in
Section 2, the correlated MIMO channel model is shown,
and then the virtual MIMO-UWB-TR system is presented
in Section 3; UWB channel measurement is described in
Section 4; in Sections 5and 6, numerical simulation results
and conclusions are presented, respectively.
2. Correlated MIMO Channel Model
In order to achieve the high data rate without expanding the
bandwidth, the spatial multiplexing scheme with multiple
transmit antennas is introduced. In the spatial multiplexing
(SM) system, several streams of data are transmitted over
several transmit antennas at the same time. The channel ca-
pacity can be increased proportionally to the number of
antennas. Let us consider an SM-MIMO UWB system with
Mtransmit and Nreceive antennas as shown in Figure 1,
where the preequalizer and prefilter blocks will be discussed
in the next section. We assume that the maximum length
of each channel realization is L. The CIR between transmit
antenna jand receive antenna iis
hi,j(t)=
L
l=1
αi,j
lδt−τi,j
l,i=1, ...,N,j=1, ...,M.
(1)
X1
X
N
Pre-equalizer
TR pre-filter
hN,M
hN,1
h,1
11
1
h1,M
.
.
.
.
.
.
.
.
..
.
.
.
.
.
∫
∫
MN
Figure 1: Block diagram of an SM-MIMO UWB system.
We can arrange these channels in a matrix form as follows:
H(t)=
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
h1,1(t)h1,2 (t)··· h1,M(t)
h2,1(t)h2,2 (t)··· h2,M(t)
.
.
..
.
.....
.
.
hN,1(t)hN,2 (t)··· hN,M(t)
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
.(2)
Generally, the entries of the MIMO channel matrix Hare
assumed to be independent of each other. In the real world,
however, the spatial correlation among antennas (transmit
or receive antennas) exists. In other words, the individual
channels of Hare correlated [29,30]. The correlation is
caused by a variety of reasons such as inadequate antenna
spacing.
The correlation can be included into the MIMO UWB
channel model by introducing fixed transmit and receive
correlation matrices following the well-known Kronecker
model. The transmit and receive correlation can be repre-
sented by an M×Mmatrix RTx and an N×Nmatrix RRx ,
respectively [31]. The correlated channel is represented by
equation
H=R1/2
Rx HwR1/2
Tx ,(3)
where Hwis the channel matrix of independent channel
realization.
For the fixed correlation matrix in the Kronecker model,
there are some variations in terms of whether or not the
impact of interelement distance is considered [32,33]. In
this paper, the exponential decay model for the correlation
is deployed [30,32]. The transmit and receive correlation
matrices are
RTx =
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
1ρTx ρ2
Tx ··· ρM−1
Tx
ρTx 1ρTx ··· ρM−2
Tx
.
.
..
.
..
.
.....
.
.
ρM−1
Tx ρM−2
Tx ρM−3
Tx ··· 1
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
,
RRx =
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
1ρRx ρ2
Rx ··· ρN−1
Rx
ρRx 1ρRx ··· ρN−2
Rx
.
.
..
.
..
.
.....
.
.
ρN−1
Rx ρN−2
Rx ρN−3
Rx ··· 1
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
,
(4)
where ρTx and ρRx are the correlation coefficients of transmit
and receive antennas, respectively.
International Journal of Antennas and Propagation 3
3. Virtual MIMO-UWB-TR System
In this paper, a TR prefilter combined with a zero forcing
(ZF) preequalizer, which has been proposed in [26,27], is
adopted to combat the ISI and the MSI in the SM-MIMO
UWB system.
The TR prefilter matrix of the MIMO system is given by
[27]
H(t)=⎛
⎜
⎜
⎜
⎜
⎜
⎝
h1,1(−t)h2,1 (−t)··· hN,1(−t)
h1,2(−t)h2,2 (−t)··· hN,2(−t)
.
.
..
.
.....
.
.
h1,M(−t)h2,M(−t)··· hN,M(−t)
⎞
⎟
⎟
⎟
⎟
⎟
⎠
,(5)
which is based on the original CIR matrix reversed in time
and transposed in space. The CIR matrix of the equivalent
channel is
H(t)=
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
h1,1(t)
h1,2(t)···
h1,N(t)
h2,1(t)
h2,2(t)···
h2,N(t)
.
.
..
.
.....
.
.
hN,1(t)
hN,2(t)···
hN,N(t)
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
,(6)
where each component of the equivalent composite channel
(which we will call equivalent channel in the sequel for
simplicity) is calculated by
hi,j(t)=
M
k=1
hi,k(t)⊗hj,k(−t),i,j=1, ...,N. (7)
Some remarks can be drawn from the matrix of the
equivalent channel. Firstly, the maximum number of inde-
pendent data streams the system can achieve is N,whichis
the number of receive instead of transmit antennas. Secondly,
the matrix of the equivalent channel is a square matrix with
the entries in the main diagonal being the summation of
the autocorrelation of the original CIRs and other entries
being the summation of the cross-correlation of the original
CIRs between the transmit and receive antennas. Third, the
TR technique in MIMO-UWB can exploit Morder transmit
diversity, and the diversity gain depends on the number of
transmit antennas.
Let us consider the special case of MIMO-TR-UWB
system, where the data is transmitted over only one antenna,
that is, M=1.Thechannelmatrixisthusonlyacolumn
vector H(t)=[h1(t), h2(t), ...,hN(t)]Tand the TR filter
matrix is a row vector H(t)=[h1(−t), h2(−t), ...,hN(−t)].
The equivalent channel, however, is still a square N×N
matrix as presented in (6). Each entry of equivalent matrix
is
hi,j(t)=hi(t)⊗hj(−t),i,j=1, ...,N. (8)
In this case, Ndata stream are multiplexed to be transmitted
over one antenna. In other words, the data are seen to be
transmitted over Nvirtual antennas. Hence, the system is
named virtual MIMO-TR-UWB.
In the true MIMO-TR-UWB system, when the separation
distance between antenna elements is small, the spatial
correlation appears at both transmit and receive sides. These
correlation will doubly degrade the performance of the
system. Meanwhile, in the virtual MIMO-TR-UWB system,
the correlation appears only at the receiver side and the
degradation is caused only by receiver correlation. The
virtual MIMO-TR-UWB system can mitigate the impact
of the transmit correlation. However, it cannot achieve the
transmit diversity gain as the true one does.
The CIR can also be reused by the preequalizer design
at the transmitter side for further multistream interference
(MSI) mitigation. Here, we assume that a ZF preequalizer
is deployed. A simple TR filter focuses the energy into a
short-time duration in the equivalent CIR, so we can use
the shortened equivalent channels to design the preequalizer.
Suppose that the maximum length of the equivalent channel
is Le. As shown in [27], we can choose Ls(LsLe) capturing
most of the energy to compute the linear preequalizer.
We assume that the channels do not change when a block
of K+Ls−1 data symbols is transmitted. The new equivalent
channel matrix can be represented by a block Toeplitz matrix
Hs=
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
H[Ls−1]···
H[0]0··· 0
0
H[Ls−1]···
H[0]··· 0
.
.
..............
.
.
0··· 0
H[Ls−1]···
H[0]
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
,
(9)
where each block matrix is
H[k]=
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
h1,1[k]
h1,2[k]···
h1,N[k]
h2,1[k]
h2,2[k]···
h2,N[k]
.
.
..
.
.....
.
.
hN,1[k]
hN,2[k]···
hN,N[k]
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
.(10)
The preequalizer matrix GZF is the inverse of the
shortened equivalent channels matrix, given by [27,34]
GZF =α
H†
s=α
HH
s
Hs−1
HH
s, (11)
where †denotes the Moore-Penrose pseudoinverse of a
matrix. The coefficient α, which can be found from [34], is
introduced for the power constraint of the transmit signal.
4. UWB Channel Measurement
We generate the channel realizations for comparison using
both the adopted correlated channel model and those
obtained from our indoor measurements. The indoor UWB
channels are measured in time domain within a 4.7 m ×
6.3 m room with a table, a chair, a wooden rack, and different
kinds of smaller scattering objects as shown in Figure 2(a).
The floor and walls of this room are constructed from
concrete materials. The ceiling (3.2m above the floor) is
composed of iron sheets and metallic beams.
4 International Journal of Antennas and Propagation
4700 mm
6300 mm
1000 mm
1000 mm
Rack
Table
Rx ant.1 Rx ant.2
Tx ant.1 Tx ant.2
(a) Floor plan and measurement configuration
Synchronization
AWG7102 DPO71604
BPF
LNA
RF
Hub
Visa interface
Real channel
(b) A sketch of system
Figure 2: Setup of UWB channel measurement.
Thesketchofthewholesystemisillustratedin
Figure 2(b). The major components used in the measure-
ments are a Tektronix AWG7102 arbitrary waveform gen-
erator (AWG) and a Tektronix DPO71604 digital phosphor
oscilloscope (DPO) which are synchronized by the reference
clock signal and connected to the processing computer via
Ethernet. The AWG supports two channels with sampling
rates of up to 10 GSamples/s (GS/s) and 3.5 GHz bandwidth
or one channel with sampling rates of up to 20 GS/s and
5.8 GHz analog bandwidth using interleaving. The DPO
provides four channels with sampling rates of up to 50 GS/s
and 16 GHz frequency span. The small-size omnidirectional
UWB patch antennas are used. On the receiver side, each
antenna is connected to the DPO through a bank of
bandpass filters (1.5 GHz bandwidth) and +55 dB low-noise
amplifiers for reliable signal acquisition under harsh SNR
conditions. The transmit and receive antennas are placed at
the same height of 1.1 m. The probe UWB pulse used in all
measurements is a second-order derivative Gaussian pulse
with the symbol duration T=250 ns.
The common scenario for applications of UWB systems
is in a small office or home environment. Therefore, we
focus on the short-range indoor environment, both NLOS
and LOS. These scenarios are referred to as CM1 (for LOS)
0 50 100 150 200 250 300
−0.1
−0.05
0
0.05
0.15
0.1
Time (ns)
Amplitude (V)
Received signal
(a)
−0.1
0 50 100 150 200 250 300
0
Time (ns)
Amplitude (V)
CIR extracted by using clean Alg.
0.3
0.2
0.1
(b)
Figure 3: An example of the received signal and the extracted CIR.
and CM2 (for NLOS) in the IEEE 802.15.3a UWB channel
models [28]. In our measurement, the blockage for the NLOS
scenario is created by vertically placing a large iron sheet in
the direct propagation path.
The temporal stationarity of the environment is ensured
by the absence of mobile objects/persons, thus allowing us
to assume that the channels for the links are quasistatic over
the duration of data transmissions. For the MIMO channels,
the spatial antenna arrays at both transmitter and receiver
are synthesized by sequential measurements exploiting such
temporal stationarity. Due to this array synthesis, our
measurement results do not include the effects of antenna
coupling. A (2 ×2) virtual MIMO channel, corresponding
to 4 SISO channels (49 realizations for each), are measured
in our campaign. The adjacent antennas are separated by
0.2 m, and the mean separation between transmit and receive
antennasiskeptat4m.
In order to extract the CIR from received signals, we
use the well-known deconvolution technique, the so-called
Clean Algorithm [35]. A realization of the SISO channel
which is extracted from the received signal by using Clean
Algorithm is shown in Figure 3.
5. Numerical Results and Discussions
In our simulations, the binary data is modulated to the
binary phase-amplitude modulation format. The UWB
monocycle waveform is the 2nd derivative Gaussian pulse,
represented by
p(t)=1−4πt−tc
w2e−2π((t−tc)/w)2, (12)
where wis a parameter corresponding to pulse, width, tcis
a time shifting of the pulse and Tis the symbol duration. In
our simulations, w=1ns, tc=w/2, and T=2ns.
International Journal of Antennas and Propagation 5
Simulations results are based on the UWB channel model
in the IEEE 802.15.3a standard [28] and those obtained from
measurements. Results are followed by descriptions of the
channel models. The correlated MIMO channel model is
generated by modifying the channel models in the IEEE
802.15.3a standard, which is formulated for SISO UWB, then
included with the correlation matrices in (5). For the simu-
lation results based on the standard model, the correlation
of receive antennas affects in the same way on SIMO
and MIMO-TR-UWB systems and the receive correlation
coefficient is fixed at ρRx =0.2. For the fair comparison,
we shorten the equivalent channel when designing the ZF
preequalizer with the same ratio Ls/Le=0.2 for standard
channels and measured channels.
Figure 4 shows the BER performance of a 2 ×2MIMO
system operating in the modified CM1, CM2 channels with
the matched transmit correlation coefficient and in the
measured LOS and NLOS channels. The value of correlation
coefficient matched with the measurement result is found by
exhaustive search and is then rounded to one decimal place.
It can be seen that the average BERs based on realizations
of CM1 and CM2 with the selected value of ρTx =0.2are
closely matched with those based on the corresponsive
measured channels. It is noted that this correlation value is
specific to our measurement setting. Also observed from this
figure that the system performance in the LOS environment
is better than in the NLOS environment for standard chan-
nels as well as measured channels. Transmission through
walls and obstructions in NLOS environment leads to
additional delay before arriving at the receiver and significant
additional attenuation, which reduce the received strength
and lead to increased errors in estimation [36].
In Figures 5and 6, the effect of the transmit correlation
coefficient on the BER performance of the system is pre-
sented. In both figures, two data streams are transmitted over
M=1, 2, and 4 transmit antennas, respectively. The transmit
correlation coefficient ρTx varies from 0 (no correlation) to
0.95 (strong correlation), and the SNR =12 dB.
ItcanbeseenfromFigure 5, for the LOS environment,
that, when ρTx increases, the average BER of the SIMO or
virtual MIMO-TR-UWB system keeps unchanged while it
increases in the true MIMO case. This can be explained by
that the SIMO system is impacted by only the spatial corre-
lation between receive antennas, so the BER performance of
such system does not change with variation of the transmit
correlation. Meanwhile, the spatial correlation appears at
both transmit and receive sides in the MIMO system and
it will doubly degrade the performance of the system. The
BER performance of the MIMO system will be worse than the
SIMO system if the transmit correlation coefficient is greater
than a critical value. For example, the performance of the 2
×2 MIMO system is worse than the 1 ×2 SIMO system if
ρTx ≥0.7, and the performance of the 4 ×2MIMOsystem
is worse than the 1 ×2 SIMO system if ρTx ≥0.6.
At low transmit correlation regime, the more the trans-
mit antennas, the better the BER performance that the
system can achieve. This is the advantage of the transmit
diversity possessed by the MIMO-TR-UWB system [34].
However, if the correlation is strong, more transmit antenna
0 5 10 15 20
SNR (dB)
Average BER
CM1
CM2
Measured, LOS
Measured, NLOS
100
10−1
10−2
10−3
10−4
10−5
Figure 4: BER performance comparison, for standard channels
with ρTx =0.2 and for measured indoor channels.
will greatly degrade the performance of MIMO systems
since the rank of the MIMO channel reduces, leading
to destroy the diversity. As shown in Figure 5, when the
transmit correlation coefficient ρTx is greater than 0.45, the
performance of the 2 ×2 MIMO system outperforms the
performance of the 4 ×2 MIMO system. It has been shown
in Figure 5 that, at high correlation, the BER increases from
0.002 to 0.0024. This trend is also observed in Figure 6 for
the NLOS environment. In CM1 channel, BER degradation
of MIMO system in comparison with SIMO system is about
0.0005, while, in CM2 channel, this value is 0.0015.
The BER performance of 1 ×2 SIMO and 2 ×2MIMO
systems operating in the CM1 and CM2 with some values
of ρTx is illustrated in Figures 7and 8.Ascanbeseenfrom
these figures, if there is no correlation, the MIMO-TR-UWB
system achieves very good BER performance. However, if the
correlation appears, the average BER will reach an error floor
at the high SNR. Particularly, the performance of the MIMO
system will be worse than the SIMO system if the transmit
correlation is too high (e.g., ρTx =0.9). In Figure 7,atBER=
10−3, the SNR of the MISO scheme 3 dB worse than the
MIMO scheme without correlation but 1 dB better than the
high correlation MIMO scheme. In Figure 8, these values are
5 dB and 3dB, respectively. This is also agreed with results in
Figures 5and 6.
6. Conclusion
We have investigated the impact of the spatial correlation on
the performance of the SM-MIMO UWB systems where the
TR prefilter and the ZF preequalizer are adopted to mitigate
the interferences. It is shown that the SIMO-TR-UWB system
canworkasavirtualMIMOsystemwhenseveraldata
streams are transmitted over only one transmit antenna.
The SIMO system suffers from only the receive correlation,
6 International Journal of Antennas and Propagation
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
0.5
1
1.5
2
2.5
Average BER
1×2 SIMO
2×2 MIMO
4×2 MIMO
ρTx
×10−3
Figure 5: BER performance versus transmit correlation coefficient,
for CM1 channels.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
1
2
3
4
5
6
Average BER
1×2 SIMO
2×2 MIMO
4×2 MIMO
ρTx
×10−3
Figure 6: BER performance versus transmit correlation coefficient,
for CM2 channels.
while both the transmit and receive correlation affect the
performance of the real MIMO system. The simulation
results show that, at the low transmit correlation regime,
the MIMO-TR-UWB systems outperform the SIMO-TR-
UWB systems in the BER performance. However, when the
transmit correlation becomes large, the performance of the
MIMO systems is worse than that of the SIMO systems.
0 5 10 15 20 25 30
SNR (dB)
Average BER
100
10−1
10−2
10−3
10−4
10−5
(2 ×2) MIMO, ρTx =0
(2 ×2) MIMO, ρTx =0.3
(2 ×2) MIMO, ρTx =0.9
(1 ×2) SIMO
Figure 7: BER performance of 2 ×2 MIMO and 1 ×2 SIMO
systems, for CM1 channels.
0 5 10 15 20 25 30
SNR (dB)
Average BER
100
10−1
10−2
10−3
10−4
(2 ×2) MIMO, ρTx =0
(2 ×2) MIMO, ρTx =0.3
(2 ×2) MIMO, ρTx =0.9
(1 ×2) SIMO
Figure 8: BER performance of 2 ×2 MIMO and 1 ×2 SIMO
systems, for CM2 channels.
The BER performance based on the fixed correlation
model generated from the standard UWB channel models
is compared with those based on the MIMO UWB channels
measured in indoor environment and the matched value of
the spatial correlation coefficient is found.
Additionally, we would like to point out that it is inter-
esting to combine the design of the TR prefilter and the
preequalizer into one-step design since both designs use the
same information. It is not clear yet whether or not the
integrate design can reduce the complexity in the system
International Journal of Antennas and Propagation 7
implementation. However, how to exploit the nice property
of the composite TR channel remains an issue in the integrate
design.
Acknowledgment
This paper is carried out under the framework of the Project
number 102.02.07.09 funded by the Vietnamese Nation-
al Foundation for Science and Technology Development
(NAFOSTED).
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