A sequential optimization algorithm (SOA) for resource allocation in a cyclicprefixed singlecarrier cognitive relay system is proposed in this study. Both subcarrier pairing (SP) and power allocation are performed subject to a primary user interference constraint to minimize the mean squared error of frequencydomain equalization at the secondary destination receiver. Under uniform power allocation at the secondary source and optimal power allocation at the secondary relay, the ordered SP is proven to be asymptotically optimal in maximizing the matched filter bound on the signaltointerferenceplusnoise ratio. SOA implements the ordered SP before power allocation optimization by decoupling the ordered SP from the power allocation. Simulation results show that SOA can optimize resource allocation efficiently by significantly reducing complexity.
1. Introduction
B
eing combined with frequency domain equalization, cyclicprefixed singlecarrier (CPSC) transmission exhibits performance similar to that of orthogonal frequencydivision multiplex (OFDM) with essentially the same overall complexity
[1]
. In CPSCbased systems, a cyclic prefix (CP) is prepended to each transmission symbol block to prevent interblock symbol interference (IBSI) such that the convolutional channel becomes a right circulant matrix in the time domain after the removal of the signal part related to CP. Moreover, CP prepending allows CPSCbased systems to achieve multipath diversity gain in the practical signaltonoise ratio (SNR) region
[2
,
3]
. Owing to its low peaktoaverage power ratio and insensitivity to Doppler shift and carrier frequency offsets, CPSC transmission has become a choice to implement many wireless systems, including future cooperative technology
[2

6]
.
Resource allocation for CPSC relay systems has recently elicited some attention although these systems are still in their infancy. In
[4]
, an optimal power allocation (OPA) scheme across subcarriers for a dual hop CPSC relay system was developed.
[5]
presented several power allocation schemes by assuming a dual hop CPSCbased system with multiple relays and cooperative beamforming. Meanwhile, the relay that receives a message from a particular subcarrier in the first hop has an opportunity to forward the processed message to a different subcarrier in the second hop because of the independent fading in each subcarrier in each hop
[7
,
8]
. Thus, subcarrier pairing (SP) has become a simple but effective method to enhance the transmission performance in broadband relay systems
[7

9]
. Although beamforming and equalization can be performed in the frequencydomain (FD) of a relay, SP has not been applied in CPSC relay systems so far.
As an effective method to enhance the utilization of existing radio spectra, cognitive radio (CR) has elicited much attention from researchers
[2
,
3]
[6

8]
[10

12]
. Particularly, the scarcity of the spectrum can be alleviated by allowing the secondary user (SU) to reuse the radio spectrum licensed to the primary user (PU). In underlay CR systems, SU is allowed to access the spectrum of PU only when the peak interference power constraint at PU is satisfied
[2
,
3]
. One drawback of this approach is that the constrained transmission power of SU typically results in unstable transmission and restricted coverage. Cognitive relay was proposed as a powerful solution to extend communication coverage of the SU system and reduce interference at the PU system
[2
,
3]
[6

8]
. Recent studies have shown that CPSC transmission achieves good performance in cognitive relay systems
[2
,
3
,
6]
. Given that the SU system has to limit the generated interference toward the PU system in CPSC cognitive relay systems, resource allocation becomes more challenging than that in noncognitive relay systems.
A sequential optimization algorithm (SOA) for SP and power allocation in a dual hop CPSC cognitive relay system is proposed in this study. The SU system operates in the underlay CR model
[10
,
11]
, and the secondary relay (SR) employs the amplifyandforward protocol
[6
,
7]
. Equalization or beamforming is not assumed at SR to maintain a simple operation. Furthermore, the system is designed such that no channel state information (CSI) of the sourcetorelay link is fed back to the secondary source (SS); thus, uniform power allocation (UPA) is employed at SS. SR is assumed to contain the CSI of the sourcetorelay and relaytodestination links in this study
[6
,
7]
. Therefore, both SP and OPA are adopted in SR to minimize the mean squared error (MSE) of the receiver at the secondary destination (SD). For the primary channel, this study assumes perfect CSI of the SStoPU and SRtoPU links, which can be obtained through direct feedback from PU or indirect feedback from a third party
[12]
. FD linear equalization (FDLE), FD decision feedback equalization (FDDFE), and an idealized matchedfilter (MF) receiver are considered at SD, and the corresponding objective functions are specified with resource allocation subject to a prespecified interference threshold at PU.
The equivalent Lagrange dual problem is decomposed into two subproblems to solve the resource allocation optimization problem. One of the subproblems is for power allocation, and the other one is for SP, which requires a joint iteration to optimize power allocation and SP. With UPA at SS and OPA at SR, the ordered SP is proven to be asymptotically optimal in maximizing the MF bound (MFB) on signaltointerferenceplusnoise ratio (SINR), which enables the ordered SP to be decoupled from the power allocation such that the ordered SP and power allocation can be solved in a sequential manner. Then, SOA is proposed with the ordered SP determined before power allocation optimization, which greatly improves the error performances of all considered receivers with low complexity.
Notation
: The superscripts (⋅)
^{T}
and (⋅)
^{H}
denote transpose and conjugate transpose, respectively.
0
_{N}
denotes a zero vector with
N
elements, [
A
]
_{l,k}
is the (
l,k
)th entry of matrix
A
,
I
_{N}
is an
N
×
N
identity matrix,
F
is the
N
×
N
Fourier transformation matrix, and Tr(
A
) is the trace of matrix
A
.
CN
(
x, y
) denotes the complex Gaussian distribution with mean
x
and variance
y
.
E
{⋅} is the expectation.
2. System Model
We consider a dual hop CPSC cognitive relay system with one SS, one amplifyandforward SR, one SD, and a PU as shown in
Fig. 1
. In the SU system, SS and SR are assumed to transmit in the same primary licensed frequency band subject to interference constraints imposed by PU. It is assumed that SR operates in halfduplex mode and that no direct link exists between SS and SD because of the deep fading between them. With the help of SR, one period of relaying is accomplished within two hops: the first hop from SS to SR and the second hop from SR to SD. Similar to the model employed in
[2
,
3]
and
[7
,
8]
, PU is assumed to be located far from the SU system; as such, interference from PU is negligible. Assuming that the number of subcarriers of CPSC transmission is
N
, the channels of the two hops of the secondary system can be expressed by the
N
×
N
right circulant matrices
H
and
G
, respectively, with their first columns provided by
h
= [
h
_{0}
,
h
_{1}
, ...,
h_{Nf}
_{1}
,
0
^{T}_{NNf}
]
^{T}
and
g
= [
g
_{0}
,
g
_{1}
,...,
g_{Nf}
_{1}
,
0
^{T}_{NNf}
]
^{T}
, respectively. The power delay profiles of the channels satisfy
E
{
x_{n}

^{2}
} =
ce^{n}
with
n
= 0,...,
N_{f}
1, where
x_{n}
∈ {
h_{n}
,
g_{n}
} and the constant
c
is selected such that
. According to the properties of a right circulant matrix, channel matrices can be decomposed into
H
=
F
^{H}
ΛF
and
G
=
F
^{H}
ΦF
, where
Λ
= diag(
λ
_{1}
,...,
λ_{N}
) and
Φ
= diag(
Φ
_{1}
,...,
Φ_{N}
) are diagonal matrices
[5
,
6]
. The SStoPU and SRtoPU channels are denoted by
respectively, which are similarly defined as
H
and
G
, respectively. Timedomain (TD) UPA is adopted at SS because we assume that SS has no CSI of the SStoSR channel. The transmit symbol block at SS is denoted by
, where
s
is an
N
× 1 vector that satisfies
E
{
ss
^{H}
} =
I
_{N}
and
p
_{0}
is the UPA factor at SS. UPA factor
p
_{0}
satisfies
Np
_{0}
≤
P
_{0}
, where
P
_{0}
is the total power budget of each symbol block at SS. Furthermore,
p
_{0}
is limited such that the interference introduced by SS at PU is under the prespecified interference threshold. After appending a CP of
N_{g}
symbols in its front, the symbol block
is transmitted from SS. To prevent IBSI, the length of CP is assumed to comprise the maximum path delay, namely,
N_{f}
<
N_{g}
.
CPSC cognitive relay system.
After removing the CPrelated part, the received signal at SR is provided by
where
n
_{1}
∈
CN
(0
_{N}
,
σ
_{1}
^{2}
I
_{N}
) is the additive noise at SR. By using FFT,
r
is transformed to the FD as
where
S
=
Fs
and
N
_{1}
=
Fn
_{1}
.
R
is then normalized by an
N
×
N
diagonal matrix
B
= diag(
B
_{1}
,
B
_{2}
,...,
B_{N}
) with
B_{k}
= (
p
_{0}
λ_{k}
^{2}
+
σ
_{1}
^{2}
)
^{1/2}
. Aside from basic amplifyandforward processing
[5
–
7]
, SP and power allocation are also employed in SR. The powernormalized signal,
BR
, is multiplied with an
N
×
N
row permutation matrix,
M
, followed by an
N
×
N
diagonal power allocation matrix,
The power constraints at SR is denoted by
, where
P
_{1}
is the total power budget of each symbol block at SR. Moreover, the transmission power of SR is limited such that the interference introduced by SR at PU is under the prespecified interference threshold.With the help of the row permutation matrix, the signal received on the
k
th subcarrier in the first hop will be transmitted on the
l
th subcarrier in the second hop, namely, SPaided relaying through the subcarrier pair (
k, l
). The corresponding signal after SP and power allocation can be expressed by
which will be transformed back to TD as
t
=
FT
. After appending a CP of
N_{g}
symbols in its front,
t
is transmitted from SR to SD. At the end of the second hop transmission, the received signal at SD (after removing the CPrelated signal) is
where
is the equivalent channel and
n
_{t}
=
F
^{H}
ΦPMBFn
_{1}
+
n
_{2}
is the equivalent noise, with
n
_{2}
~
CN
(0
_{N}
,
σ
_{2}
^{2}
I
_{N}
) being the additive noise at SD.
3. Receiver Processing at SD
We consider three different receivers at SD, namely FDLE, FDDFE, and idealized MF receiver, to detect the transmitted signal. At SD, the received TD signal is transformed to FD. Then, the received FD signal is filtered by
N
×
N
feedforward filtering matrix
W
. For FDLE,
is utilized to obtain the estimation of the transmitted signal. For FDDFE,
is fed into a symbolbysymbol decision feedback module, which is described by
N
×
N
right circulant matrix
D
. The first column of
D
is provided by the
N
× 1 vector
where
N_{d}
is the number of taps of the feedback filter. Assuming that the decision feedback processing is errorfree, the output of the feedback filter is
When
N_{d}
= 1,
D
becomes an identity matrix and FDDFE degenerates into FDLE. The error vector between the filtered received signal and the transmitted signal of both FDLE and FDDFE can be expressed by
In Eq. (5), the property
D
=
F
^{H}
ΓF
is applied, where
Γ
= diag{
γ
_{1}
,
γ
_{2}
,...,
γ_{N}
} with
Then, the error covariance matrix can be written as
With the error covariance matrix, the MSE at SD is provided by Tr{
E
}. By differentiating Tr{
E
} with respect to
W
and setting the result to zero, the optimal feedforward filter is obtained by
where
By substituting Eq. (7) into Eq. (6) and using the matrix inversion lemma, the error covariance matrix can be rewritten as
where
Ψ
=
I
_{N}
+
H
_{f}^{H}
C
^{1}
H
_{f}
is an
N
×
N
diagonal matrix. Eq. (8) indicates that
E
has a circulant form with the all diagonal elements being identical. Given that the
k
th diagonal element of
E
stands for the MSE of the
k
th transmitted symbol, the circulant form of
E
indicates that the MSEs of all transmitted symbols in each symbol block are identical; this case is different from the case of OFDMbased transmission, where the MSEs of all the symbols are different
[5]
.
For FDLE, by substituting
Γ
=
I
_{N}
into Eq. (7), the optimal equalizer is provided by
W
=
H
_{f}^{H}
(
H
_{f}
H
_{f}^{H}
+
C
)
^{1}
. The MSE of FDLE can be expressed by
where
Ψ_{l}
is the
l
th diagonal element of
Ψ
, which is provided by
with
α_{k}
=
λ_{k}
^{2}
/
σ
_{1}
^{2}
and
β_{l}
=
Φ_{l}
^{2}
/
σ
_{2}
^{2}
.
Ψ_{l}
corresponds to the SPaided relaying transmission on the subcarrier pair (
k, l
).
Similarly, the MSE of FDDFE can be expressed by
The first tap of the feedback filter is set to
d
_{1}
= 1 to ensure the causal cancellation of intersymbol interference (ISI). The optimal feedback filter is provided by
[13]
where
η
= [1,
0
_{Nd}
_{1}
]
^{T}
and A is an
N_{d}
×
N_{d}
Hermitian matrix, with its (
m, n
)th entry being
To obtain a tractable objective function for FDDFE, the following asymptotic MSE expression is adopted for FDDFE
[5
,
13]
.
In Eq. (13), asymptotic optimality is achieved when both
N
and
N_{d}
approach infinity
[13]
.
For an idealized MF receiver, we assume that perfect CSI is available at the receiver and that the receiver is ideally synchronized to the received signal
[5
,
14]
. The socalled MFB achieved by the idealized MF receiver describes the performance of uncoded and ISIfree signaling over additive white Gaussian noise
[14]
. In general, MFB is a theoretical bound that cannot be achieved by practical equalizers because of several factors, such as ISI and the inaccuracies of channel estimation. Onetoone mapping exists between minimum MSE and maximum SINR
[15]
. The MFB on SINR is selected in this study as the goal of resource allocation optimization for the idealized MF receiver. Considering that the effective noise in Eq. (4) is colored, the prewhitened equivalent channel matrix required by idealized MF processing is provided by
Then, the MFB on SINR in the output of the idealized MF receiver can be expressed by
The goal of resource allocation is to minimize the MSE (or equivalently maximize the MFB on SINR) given that the performance of FD equalization is directly influenced by the MSE of the SD receiver. Considering the power allocation and SP and based on Eqs. (12), (13), and (14), the objective functions to be minimized can be compactly expressed by
In Eq. (15), the logarithm of the MSE is substituted in the objective function of FDDFE and has no effect on the optimal solution because of the monotonicity of the logarithm. Considering that the objective functions in Eq. (15) have the summation forms over all the subcarrier pairs, the minimization of Eq. (15) is equal to the sum of the minimization of the objective functions of all the subcarrier pairs. To this end, the objective functions over a given subcarrier pair (
k, l
) can be written as
Eq. (16) shows that the all objective functions over any given subcarrier pair are monotonically decreasing functions of
Ψ_{l}
. Therefore, for the all considered receivers, a unified framework of resource allocation optimization is implemented.
4. SP and Power Allocation
The problem of joint optimization of SP and power allocation is formulated in this section, and SOA is proposed to optimize SP and power allocation.
According to the principles of the underlay CR model
[10
,
11]
, the SU system must limit the generated interference toward PU to coexist with the PU system. Thus, the following interference constraints are considered.
where
S_{k}
is the
k
th element of
S
,
I
_{th}
is the prespecified interference threshold at PU, and
is the FD channel response on the
k
th (
l
th) subcarrier of
The optimization problem of interest can now be formulated to minimize the objective functions, with resource allocation optimization subject to individual power constraints and the prespecified interference threshold. The optimal transmit power at SS is obviously provided by
Considering that each and every subcarrier in the first hop can only be paired with a unique subcarrier in the second hop, the SP constraint with respect to permutation matrix
M
can be written as
We let
p
_{l}
_{}
_{k}
denote the value of
p_{l}
to be optimized with a given subcarrier pair (
k, l
). We introduce an
N
×
N
matrix
with its (
l, k
)th element being
p
_{l}
_{}
_{k}
. Then, with the obtained optimal solution
p
°
_{0}
, the optimizing problem can be reformulated as
where
The minimization in Eq. (19) with respect to
and
M
is a mixed integer programming problem.
N
! possible combinations of subcarrier pairs exist, a condition that makes Eq. (19) computationally prohibitive even for a small number of subcarriers. The solution to the dual problem is asymptotically optimal because the duality gap between the optimal solution of Eq. (19) and that of the corresponding dual problem approaches zero for sufficiently large
N
[16]
. The corresponding dual Lagrangian is provided by
where
η
_{1}
and
η
_{2}
are the dual variables associated with the power constraint and the interference constraint, respectively. By recomposing
L
(
η
_{1}
,
η
_{2}
,
M
,
)with respect to the SP constraint, the dual function can be written as
As can be seen in Eq. (21), the dual function can be decomposed into two subproblems: power allocation for any subcarrier pair (
k, l
) and SP for a known power allocation.
OPA for any given subcarrier pair (
k, l
) is first determined. With the subcarrier pair (
k, l
), the OPA solutions of
p
_{l}
_{}
_{k}
can be obtained from
Given that Eq. (22) is a standard convex problem, the KKT conditions provide OPA solutions for FDLE, FDDFE, and an idealized MF receiver as follows:
where [x]
^{+}
= max{0,
x
} and
The above solutions are not only determined by the power budget constraints but also by the maximum allowed interference to PU. By substituting UPA solution
p
°
_{0}
and the OPA solutions into Eq. (21), the dual function becomes
where
Once OPA is determined for each and every subcarrier pair, optimal SP can be obtained by solving the following:
The optimal permutation matrix,
M
°, can be obtained by the wellknown Hungarian algorithm because the minimization in Eq. (24) is a linear assignment problem
[17]
. However, the complexity of the Hungarian algorithm is
O
(
N
^{3}
), which is too large to be implemented in a realtime system. With the obtained OPA expressions, the complexity of resource allocation is mainly determined by computing the optimal SP. To reduce the complexity of resource allocation, we establish a simplified method of SP. Generally, two simple SP schemes exist, namely, ordered SP and inverse SP, which have both been applied in OFDMbased relay systems to maximize the sumrate and the minimum SNR, respectively (see
[9]
and the references therein). Unlike OFDMbased relay systems, the goal of resource allocation in the CPSC cognitive relay system is to minimize the MSE (or maximize the MFB on SINR). Moreover, SP should be optimized with this objective. The optimality of the ordered SP in maximizing the MFB on SINR for the CPSC cognitive relay system is provided as Theorem 1.
Theorem 1
: In a CPSC cognitive relay system that adopts UPA at SS and OPA at SR, the ordered SP is asymptotically optimal in maximizing the MFB on SINR for a sufficiently large
N
.
Proof
: See Appendix.
According to Theorem 1, regardless of the values of UPA at SS and OPA at SR, the MFB on SINR is asymptotically maximized with the ordered SP. Thus, the permutation matrix
M
° achieved by the ordered SP can be judged as asymptotical optimal beforehand to maximize the MFB on SINR with UPA at SS and OPA at SR.
Subgradient method is applied with the obtained
p
°
_{0}
,
M
° , and
to update the dual variables by
η_{i}
^{(t+1)}
=
η_{i}
^{(t)}

μ
^{(t)}
Δ
η_{i}
^{(t)}
for
i
= 1, 2, where the subgradients of
η
_{1}
and
η
_{2}
are provided by
respectively, and
μ
^{(t)}
is a diminishing step size at the
t
th iteration. With the diminishing step size rule, subgradient method is guaranteed to converge to the optimal value
[16]
. To avoid computing all the elements of
and to avoid executing the Hungarian algorithm per iteration, which is required by the joint optimization algorithm (JOA)
[7]
, SOA is proposed in
Algorithm 1
. In SOA, the ordered SP is decoupled from the power allocation. SOA determines the ordered SP before the power allocation given that implementing the ordered SP before and after the subgradient iterations requires
N
and
N
^{2}
computations of the OPA solution per iteration, respectively. Thus, a significant reduction in complexity is observed with the use of SOA as shown in
Table 1
.
Comparison of the Complexity of Different Algorithms
Comparison of the Complexity of Different Algorithms
5. Simulation Results
The performances of the proposed SOA are evaluated by simulations in this section. We assume that quadrature phase shift keying (QPSK) modulation is adopted at SS. The number of subcarriers of CPSC transmission is
N
= 64, and the channel length is
N_{f}
= 16. The number of the feedback filter taps is assumed to be
N_{d}
=
N_{f}
, and the first tap of the feedback filter is set to 1. The normalized transmit SINRs are defined by
and
for the first and second hops, respectively. The normalized transmission power budgets are set to
P
_{0}
/
N
= 1 and
P
_{1}
/
N
= 1, respectively. For simplicity,
σ
_{1}
^{2}
=
σ
_{2}
^{2}
is assumed such that SINR = SINR
_{1}
= SINR
_{2}
. In the all simulations, the optimal UPA is employed at SS, i.e.,
For the purpose of comparison, the following resource allocation schemes are considered at SR: (1) Only UPA, which employs UPA at SR without SP; (2) SP+UPA, which employs both the ordered SP and UPA at SR; (3) Only OPA, which employs OPA at SR without SP; (4) JOA of
[7]
, which optimizes SP and OPA at SR in an iterative manner; and (5) SOA, which is the proposed SOA adopted at SR to implement the ordered SP and OPA.
Fig. 2
shows MSE versus SINR for the different resource allocation schemes, with
I
_{th}
= 3dB. For FDLE and FDDFE, when the ordered SP and UPA are employed at SR (denoted by SP+UPA), the MSEs decrease compared with when only UPA is employed. However, for FDLE, the marginal gain achieved by the ordered SP is trivial because of the large MSE (approximately 10
^{−1}
). For FDLE and FDDFE, the only OPA scheme decreases the MSEs. For FDLE, the MSE achieved by SOA is almost similar to that of only OPA because of the trivial marginal gain achieved by the ordered SP; this result verifies that the MSE reduction by SOA is mainly achieved by power allocation. The proposed SOA achieves the lowest MSEs for the FDLE and FDDFE receivers. For FDDFE with the MSE of 10
^{−3}
, SOA achieves 2dB gain compared with only UPA. Furthermore, for FDDFE, the MSE achieved by SOA is almost coincident with that of JOA. This result indicates that SOA can achieve almost the same MSE performance as that of JOA. A similar situation is observed in the case of FDLE, which is not plotted in
Fig. 2
to conserve space.
MSE vs. SINR with I_{th} = –3 dB.
The simulation results of MSE versus SINR for FDDFE in the case of (
N
= 16,
N_{q}
=
N_{f}
= 4) are presented in
Fig. 3
. Compared with the scheme of only UPA, SOA achieves approximately 1.5 dB gain with the MSE of 10
^{−3}
. SOA achieves almost the same MSE as that of JOA, a result that verifies not only the effectiveness of SOA but also the effectiveness of the ordered SP in minimizing MSE even with a small
N
.
MSE vs. SINR with I_{th} = –3dB and N = 16.
Fig. 4
shows the average BER versus the interference threshold for the different schemes with SINR fixed at 20 dB. For FDDFE and MFB, the marginal gains achieved by the ordered SP and OPA are verified by the simulation results, respectively. Both SOA and JOA achieve the lowest average BER for FDDFE and the lowest MFB, respectively. Once
I
_{th}
reaches a large value ( > 4dB in this case), the average BER of all the schemes cannot decrease anymore. An error floor occurs, which corresponds to the scenario in which the allowed interference to PU is sufficiently large and the power budget must be allocated fully to minimize the MSE of the SD receiver.
Average BER vs. I_{th} with the SINR = 20 dB.
6. Conclusion
SOA was developed for the optimization of SP and power allocation in a dual hop CPSC cognitive relay system. Resource allocation optimization was transformed to its equivalent Lagrange dual problem to minimize the MSE of the SD receiver. The Lagrange dual problem was then decomposed into two subproblems of power allocation and SP. The ordered SP was proven to be asymptotically optimal in maximizing the MFB on SINR. The resource allocation problem was effectively addressed by SOA in a sequential optimizing manner with a significant reduction in complexity.
BIO
Hongwu Liu completed his Ph.D. degree in Southwest Jiaotong University in 2008, following the completion of his M.S. program in the same institution. From February 2010 to August 2011, he served as a postdoctoral fellow at the Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Science. He was a research fellow in the UWB Wireless Communications Research Center, Inha University, Korea, from September 2011 to August 2013. He is currently an associate professor at Shandong Jiaotong University. His research interests include resource allocation and transmission strategy in cooperative communications.
Jaijin Jung received his B.S. degree from Sungkyunkwan University, Seoul, Korea, in 1990, his M.S. degree from Yonsei University, Seoul, Korea, in 1996, and his Ph.D. degree from Sungkyunkwan University in 2003. Dr. Jung is a professor with the Department of Multimedia Engineering, Dankook University, Cheonan, Korea. His research interests include wireless transmission and mobile computing.
Kyung Sup Kwak received his B.S. degree from Inha University, Inchon, Korea, in 1977, his M.S. degree from the University of Southern California in 1981, and his Ph.D. degree from the University of California at San Diego in 1988 under Inha University and Korea Electric Association Scholarship grants. From 1988 to 1989, he was a member of the technical staff at Hughes Network Systems, San Diego, CA. He worked at IBM Network Analysis Center at Research Triangle Park, NC, from 1989 to 1990. Since then, he has been with Inha University, Korea, as a professor. His research interests include multiple access communication systems, mobile and satellite communication systems, data networks, and wireless multimedia. Dr. Kwak has been a member of the Board of Directors of the Korean Institute of Communication Sciences (KICS) since 1994 and a director of IEEE Seoul Section.
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