21-05-2012, 03:55 PM
Linear Precoding for Orthogonal Space-Time Block Coded MIMO-OFDM Cognitive Radio
[attachment=22601]
Abstract
The paper presents design of a linear precoder
for orthogonal space-time block coded orthogonal frequency
division multiplexing (OFDM)-based multiple-input multipleoutput
(MIMO) antenna cognitive radio (CR) when operating
in correlated Rayleigh fading channels. Unlike previous studies
on precoder design for CR, this proposed linear precoder is
capable of handling both transmit and receive correlation in a
multi-carrier based CR system. The linear precoder is designed
to minimize an upper bound on the average pairwise error
probability, constrained to a set of per subcarrier transmit power
constraints at the CR transmitter and a set of interference power
thresholds at primary user receivers. The CR transmitter exploits
the knowledge of transmit and receive correlation matrices while
designing the precoder. It is shown that the linear precoder design
problem is convex with these constraints, and convex optimization
techniques are exploited to derive an efficient algorithm to
obtain the optimal precoder matrices. Computer simulations are
performed to investigate the performance of the proposed linear
precoder in a CR system.
Index Terms—Cognitive radio, convex optimization, orthogonal
space-time block coding, multiple-input multiple-output
antennas, orthogonal frequency division multiplexing.
I. INTRODUCTION
THE electromagnetic radio spectrum is a precious resource
available for wireless communications, which demands
efficient usage. However, it has become increasingly scarce
due to a wide deployment of wireless services. According to
the Federal Communications Commission’s spectrum policy
task report [1], the usage of allocated spectrum varies from
fifteen to eighty-five percent at specific time and geographical
location. This low spectrum utilization coupled with spectrum
scarcity motivates the development of novel spectrum-sharing
technologies with the aim of improving spectrum utilization.
Cognitive radio (CR) has emerged as a promising technology
to improve spectrum utilization, while accommodating the
growing amount of services and applications in wireless
communications [2]. CR is capable of dynamically sensing
and identifying unoccupied spectrum bands that are initially
allocated to licensed (primary) users (PUs), and allowing
unlicensed (secondary) users (SUs) to communicate through
Paper approved by I. Lee, the Editor for Wireless Communication Theory of
the IEEE Communications Society. Manuscript received September 8, 2009;
revised June 2, 2010 and August 16, 2010.
A. Punchihewa and V. K. Bhargava are with the Department of Electrical
and Computer Engineering, University of British Columbia, Vancouver, BC,
Canada (e-mail: anjana[at]ece.ubc.ca, vijayb[at]ece.ubc.ca).
C. Despins is with the Université du Québec, Montréal, QC, Canada (email:
cdespins[at]promptinc.org).
Digital Object Identifier 10.1109/TCOMM.2011.011811.090548
these available spectrum segments without causing harmful
interference to PUs, thus having the potential to efficiently
improve spectrum utilization. Since CR operates with opportunistic
spectrum sharing in dynamically changing environments,
managing the quality of services (QoS) offered by a CR
system while maintaining the QoS of the PUs, is challenging.
Hence, proper design of a transmission scheme for CR to
facilitate high data rate access and better performance along
with high spectral efficiency is very important. To achieve
this objective, it is crucial to integrate recent physical layer
technical advances into the CR systems.
Multiple-input multiple-output (MIMO) antenna systems
and space-time block coding (STBC) in wireless communications
have attached considerable attention due to their
ability to increase capacity and improve system performance
over hostile wireless channels [3]-[5]. Orthogonal frequency
division multiplexing (OFDM) is a promising transmission
technique in CR systems due to its several advantages such
as scalability, robustness against multipath fading, multiple
access mechanisms, simplicity in channel equalization and
coding [6]. Therefore, with these valuable features, incorporating
MIMO, STBC and OFDM into CR would promise
enhanced performance in terms of spectral efficiency, capacity
and bit error rate over hostile wireless channels.
It is shown in previous studies that the performance of
conventional MIMO systems is degraded in spatially correlated
channels based on the available channel state information
(CSI) at the transmitter [7], [8]. However, efficient precoding
techniques in combination with STBC can be used to further
improve the system performance in such channel conditions,
when the knowledge of CSI is available at the transmitter
[9]-[12]. Therefore, linear precoding is a vital technique to
combat the correlation effect of MIMO channels. In practice
a perfect CSI is seldom available and is difficult to obtain at
the transmitter. Thus, a common practice is to assume partial
channel knowledge at the transmitter, for example, in terms
of transmit or both transmit and receive correlation matrices
[9]-[12]. In conventional MIMO systems [9]-[12], the linear
precoder is designed with the knowledge of transmit or both
transmit and receive correlation matrices at the transmitter by
minimizing a metric related to average error probability and
constrained only to total transmit power.
Although this topic has been extensively studied for conventional
MIMO systems, less attention is given in previous
studies for design of a linear precoder for MIMO-based CR,
where additional constraints need to be incorporated in pre-
0090-6778/11$25.00 ⃝c 2011 IEEE
768 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 59, NO. 3, MARCH 2011
coder design. The linear precoder designed in [13] for CR with
the intention of improving the error rate performance assumes
only the SU transmit antenna correlation, single antenna at
the PU receiver and considers the single carrier transmission
scheme. However, this paper extend the linear precoder design
for CR in several ways. The theoretical analysis of the linear
precoder design is based on a comprehensive signal model that
takes into account of multiple antennas at both SU and PUs,
multi-carrier transmission scheme and the correlation effects
of SU’s both transmit and receive antennas. A linear precoder
is designed for orthogonal space-time block coded (OSTBC)
MIMO-OFDM based CR, when operating in frequency-flat
correlated Rayleigh fading channels. The linear precoder is
designed to minimize an upper bound on the average pairwise
error probability (PEP) when the SU transmitter has the
knowledge of transmit and receive correlation matrices, while
imposing a set of interference power constraints at the PUs
and a set of per subcarrier transmit power constraints at the
SU transmitter. It is shown that the precoder design problem
for CR is convex with these constraints. Furthermore, an
efficient algorithm based on the Lagrange dual-decomposition
is proposed to obtain the linear precoder. The individual
effects of the SU transmit and receive antenna correlation
on the linear precoder design for CR is also addressed in
this paper. A closed-form solutions for power loading in each
OFDM subcarrier for simplified correlation scenarios are also
presented.
The rest of the paper is organized as follows. The system
model and OSTBC MIMO-OFDM transmission scheme are
introduced in Section II. The optimal linear precoder design
problem is formulated in Section III. The linear precoder
design with SU’s different correlation scenarios are investigated
in Section IV, and the Lagrangian dual-decompositionbased
efficient algorithm is proposed to obtain the linear
precoder. Simulation results are provided in Section V. Finally,
conclusions are drawn in Section VI. Proofs of the theorems
are given in the Appendix.
The following notations are used throughout the paper.
Vectors are denoted by boldfaced lowercase letters, e.g., a,
b, and matrices are denoted by boldface uppercase letters,
e.g., A, B. The superscripts (⋅)−1, (⋅)
[attachment=22601]
Abstract
The paper presents design of a linear precoder
for orthogonal space-time block coded orthogonal frequency
division multiplexing (OFDM)-based multiple-input multipleoutput
(MIMO) antenna cognitive radio (CR) when operating
in correlated Rayleigh fading channels. Unlike previous studies
on precoder design for CR, this proposed linear precoder is
capable of handling both transmit and receive correlation in a
multi-carrier based CR system. The linear precoder is designed
to minimize an upper bound on the average pairwise error
probability, constrained to a set of per subcarrier transmit power
constraints at the CR transmitter and a set of interference power
thresholds at primary user receivers. The CR transmitter exploits
the knowledge of transmit and receive correlation matrices while
designing the precoder. It is shown that the linear precoder design
problem is convex with these constraints, and convex optimization
techniques are exploited to derive an efficient algorithm to
obtain the optimal precoder matrices. Computer simulations are
performed to investigate the performance of the proposed linear
precoder in a CR system.
Index Terms—Cognitive radio, convex optimization, orthogonal
space-time block coding, multiple-input multiple-output
antennas, orthogonal frequency division multiplexing.
I. INTRODUCTION
THE electromagnetic radio spectrum is a precious resource
available for wireless communications, which demands
efficient usage. However, it has become increasingly scarce
due to a wide deployment of wireless services. According to
the Federal Communications Commission’s spectrum policy
task report [1], the usage of allocated spectrum varies from
fifteen to eighty-five percent at specific time and geographical
location. This low spectrum utilization coupled with spectrum
scarcity motivates the development of novel spectrum-sharing
technologies with the aim of improving spectrum utilization.
Cognitive radio (CR) has emerged as a promising technology
to improve spectrum utilization, while accommodating the
growing amount of services and applications in wireless
communications [2]. CR is capable of dynamically sensing
and identifying unoccupied spectrum bands that are initially
allocated to licensed (primary) users (PUs), and allowing
unlicensed (secondary) users (SUs) to communicate through
Paper approved by I. Lee, the Editor for Wireless Communication Theory of
the IEEE Communications Society. Manuscript received September 8, 2009;
revised June 2, 2010 and August 16, 2010.
A. Punchihewa and V. K. Bhargava are with the Department of Electrical
and Computer Engineering, University of British Columbia, Vancouver, BC,
Canada (e-mail: anjana[at]ece.ubc.ca, vijayb[at]ece.ubc.ca).
C. Despins is with the Université du Québec, Montréal, QC, Canada (email:
cdespins[at]promptinc.org).
Digital Object Identifier 10.1109/TCOMM.2011.011811.090548
these available spectrum segments without causing harmful
interference to PUs, thus having the potential to efficiently
improve spectrum utilization. Since CR operates with opportunistic
spectrum sharing in dynamically changing environments,
managing the quality of services (QoS) offered by a CR
system while maintaining the QoS of the PUs, is challenging.
Hence, proper design of a transmission scheme for CR to
facilitate high data rate access and better performance along
with high spectral efficiency is very important. To achieve
this objective, it is crucial to integrate recent physical layer
technical advances into the CR systems.
Multiple-input multiple-output (MIMO) antenna systems
and space-time block coding (STBC) in wireless communications
have attached considerable attention due to their
ability to increase capacity and improve system performance
over hostile wireless channels [3]-[5]. Orthogonal frequency
division multiplexing (OFDM) is a promising transmission
technique in CR systems due to its several advantages such
as scalability, robustness against multipath fading, multiple
access mechanisms, simplicity in channel equalization and
coding [6]. Therefore, with these valuable features, incorporating
MIMO, STBC and OFDM into CR would promise
enhanced performance in terms of spectral efficiency, capacity
and bit error rate over hostile wireless channels.
It is shown in previous studies that the performance of
conventional MIMO systems is degraded in spatially correlated
channels based on the available channel state information
(CSI) at the transmitter [7], [8]. However, efficient precoding
techniques in combination with STBC can be used to further
improve the system performance in such channel conditions,
when the knowledge of CSI is available at the transmitter
[9]-[12]. Therefore, linear precoding is a vital technique to
combat the correlation effect of MIMO channels. In practice
a perfect CSI is seldom available and is difficult to obtain at
the transmitter. Thus, a common practice is to assume partial
channel knowledge at the transmitter, for example, in terms
of transmit or both transmit and receive correlation matrices
[9]-[12]. In conventional MIMO systems [9]-[12], the linear
precoder is designed with the knowledge of transmit or both
transmit and receive correlation matrices at the transmitter by
minimizing a metric related to average error probability and
constrained only to total transmit power.
Although this topic has been extensively studied for conventional
MIMO systems, less attention is given in previous
studies for design of a linear precoder for MIMO-based CR,
where additional constraints need to be incorporated in pre-
0090-6778/11$25.00 ⃝c 2011 IEEE
768 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 59, NO. 3, MARCH 2011
coder design. The linear precoder designed in [13] for CR with
the intention of improving the error rate performance assumes
only the SU transmit antenna correlation, single antenna at
the PU receiver and considers the single carrier transmission
scheme. However, this paper extend the linear precoder design
for CR in several ways. The theoretical analysis of the linear
precoder design is based on a comprehensive signal model that
takes into account of multiple antennas at both SU and PUs,
multi-carrier transmission scheme and the correlation effects
of SU’s both transmit and receive antennas. A linear precoder
is designed for orthogonal space-time block coded (OSTBC)
MIMO-OFDM based CR, when operating in frequency-flat
correlated Rayleigh fading channels. The linear precoder is
designed to minimize an upper bound on the average pairwise
error probability (PEP) when the SU transmitter has the
knowledge of transmit and receive correlation matrices, while
imposing a set of interference power constraints at the PUs
and a set of per subcarrier transmit power constraints at the
SU transmitter. It is shown that the precoder design problem
for CR is convex with these constraints. Furthermore, an
efficient algorithm based on the Lagrange dual-decomposition
is proposed to obtain the linear precoder. The individual
effects of the SU transmit and receive antenna correlation
on the linear precoder design for CR is also addressed in
this paper. A closed-form solutions for power loading in each
OFDM subcarrier for simplified correlation scenarios are also
presented.
The rest of the paper is organized as follows. The system
model and OSTBC MIMO-OFDM transmission scheme are
introduced in Section II. The optimal linear precoder design
problem is formulated in Section III. The linear precoder
design with SU’s different correlation scenarios are investigated
in Section IV, and the Lagrangian dual-decompositionbased
efficient algorithm is proposed to obtain the linear
precoder. Simulation results are provided in Section V. Finally,
conclusions are drawn in Section VI. Proofs of the theorems
are given in the Appendix.
The following notations are used throughout the paper.
Vectors are denoted by boldfaced lowercase letters, e.g., a,
b, and matrices are denoted by boldface uppercase letters,
e.g., A, B. The superscripts (⋅)−1, (⋅)