Power Allocation and User Satisfaction-Based Switching Method in ...

Power Allocation and User Satisfaction-Based
Switching Method in Cognitive Radio MIMO System
Jaebum Cho, Sungjeen Jang, Wonsik Jung, Jaemoung Kim
INHA-WiTLAB, INHA University
253 Yonghyun-dong, Nam-gu, Incheon, Korea
{jaebum.cho, sungjeen.jang, wonsik}@witlab.kr, jaekim@inha.ac.kr
Abstract—Secondary users (SUs) should have power constraints
because primary users (PUs) should not be interfered by SUs in
cognitive radio (CR) network. Therefore it is important for SUs
to maximize throughput and ensure quality of service (QoS) on
the premise of generating no interference to PUs. In this paper,
SUs are equipped with multiple antennas. Multiple-input
multiple-output (MIMO) wireless communication systems can
offer high data rate or reliability through spatial multiplexing or
diversity. Therefore we present a method which user satisfactionbased
on switching between spatial multiplexing and transmit
diversity to maximize total user satisfaction. When we use spatial
multiplexing, user satisfaction is formulated as a function with
data rate and power consumed. In case we use transmit diversity,
user satisfaction is formulated as a function with reliability and
power consumed. For estimating reliability, we provide a novel
bit error rate (BER) equation. And we use different power
allocation method in each case. We apply capped water-filling
method for spatial multiplexing and Lagrangian method for
transmit diversity. Simulation results show that proposed
switching scheme increase user satisfaction. And we study the
effect of interference of PU on the performance
Keywords: cognitive radio, MIMO, power allocation, switching
I. INTRODUCTION
In recently years, with the rapid development of various
wireless systems, the demand of radio spectrum has increased.
But this demand is not satisfied because resource of radio
spectrum is limited. To ensure future growth of wireless
system, it is necessary to increase the spectrum efficiency. For
this, CR system is proposed as a new technique [1], [2]. CR
system is designed to improve spectrum efficiency by
allowing opportunistic spectrum access to SUs, on the premise
of generating no interference to PUs while taking advantage of
the available spectrum resources. As the PUs have higher
priority in using the spectrum and should not be interfered by
SUs, SUs are subject to constraints. So it is hard for SUs to
maximize the throughput or to ensure the QoS with power
constraint.
One of the techniques which improve throughput or QoS
This work was supported by the National Research Foundation of Korea
(NRF) grant funded by the Korea government Ministry of Education, Science
and Technology (MEST) (No. 2010-0008000). And this research was also
supported by the Ministry of Knowledge Economy (MKE), Korea, under the
Information Technology Research Center (ITRC) support program supervised
by the National IT Industry Promotion Agency (NIPA), (NIPA-2010-C1090-
111-0007).
of SUs is to employ multiple antennas at transmitter and
receiver. So we can improve quality, capacity and reliability of
SUs by employing MIMO technique. In recent years, there are
some works to improve performance of SUs with a single
antenna or multiple antennas. For instance, weighted sum rate
maximization problem for the SUs MIMO broadcast channel
(BC) has been studied under the multi-constraint [3]. In [4],
the ergodic capacity of a single SU link was considered under
the instantaneous or average power constraint. Other works for
power loading and joint beamforming can be founded [5], [6].
In this paper, switching between spatial multiplexing and
transmit diversity is proposed because it is clear that there is a
tradeoff between multiplexing and diversity in MIMO system.
To combat the impact of fading on the error rate, diversity or
transmit diversity techniques are employed. The principle of
diversity is to transmit same information over multiple
antennas, and then the received signals on all antennas are
combined to increase the signal quality [7]. On the other hand,
to increase transmission rate or capacity of the communication
system, spatial multiplexing is employed. The principle of
multiplexing is to divide data stream into multiple antennas,
and each substream is transmitted and received over a
different antenna to increase the capacity [8]. The scheme
proposed in [10] uses the minimum Euclidean distance, which
can be used to estimate the BER, to switch between
multiplexing and diversity in MIMO system and the scheme
proposed in [11] uses received signal-to-interference-plusnoise
ratio (SINR), which can be used to estimate the
throughput, to switch between multiplexing and diversity in
MIMO system. Similarly, conventional switching schemes
consider just one term as criterion. We consider combination
with power consumption. Thus we have to use different
switching criterion. We propose a user satisfaction-based
switching scheme. It is expected that the proposed user
satisfaction-based switching scheme can increase user
satisfaction than a scheme with spatial multiplexing or
transmit diversity that is solely employed.
New metric of user satisfaction is in the form of numerical
value which represents combination of power consumption
and achievable data rate, reliability. For example, if users
prefer high data rate, power efficiency is lower, whereas if
users prefer high power efficiency, data rate is lower. Previous
user satisfaction has two terms, data rate satisfaction and
power consumption satisfaction [9]. However the influence of
channel fading and interference from PUs in CR networks

don’t guarantee reliability of SUs link. Therefore, we consider
reliability as well as data rate and power consumption. In other
words, we consider target data rate and target BER related to
reliability satisfaction. In case we use transmit diversity, we
provide a new BER equation of Space-Time Block Coding
(STBC), and then estimate BER for reliability.
We apply two difference power allocation methods to
maximize user satisfaction in each case, data rate and
reliability satisfaction. For data rate, allocated power is set by
water-filling method and optimal power level of water-filling
is updated by an iterative algorithm. For reliability,
Lagrangian function and Karush-Kuhn-Tucker (KKT)
conditions are applied.
The remainder of paper is organized as follows. CR system
model and formulate optimization problem with power
constraint and channel allocated power constraint are
presented in Section II. In Section III, we consider data rate
problem, BER equation expression in STBC-MIMO system
and power allocation algorithm for orthogonal transmission.
Simulation results of proposed system are given in Section IV.
Conclusions are given in the last section.
A. System Model
II. SYSTEM MODEL
Consider a CR-MIMO system where K SUs coexist with L
PUs. And we assume the availability of a set of N channels.
SUs can receive and transmit over multiple channels. SUs are
equipped with Nr receive antennas and Nt transmit antennas.
The transmit-receive signal model from the SU to another SU
can be represented as:
y=Hx+H x +z (1)
where y denotes received signal vector. H = [h11, …, hij]
denotes the channel matrix with hij being the channel response
from SUi to the SUj. x is the transmit signal vector. The
channel gain is represented by hij=aijbij/(1+dij 2 ). dij denote the
distance between SUi’s transmitter and SUj’s receiver. aij 2
follows the lognormal distribution with mean 1 and bij follows
the complex Gaussian distribution with zero mean and unit
variance. H =[h 1, …, h L] denotes channel matrix where h L is
the channel response from PUs’s transmitter to the SU, x is
transmit signal vector from PUs. Channel gain is h l=(d ij/d l) 2 α l,
dl denotes the distance between PU’s transmitter and SU’s
receiver. And we assume that all SUs are at the same distance
dl. α l is modeled as circularly symmetric complex Gaussian
(CSCG) random variables (RVs) with mean zero and variance
1. z is the Gaussian noise vector whose entries are assumed to
be independent Gaussian RVs with mean zero and variance σ 2 .
Similar to [9], K SUs are randomly deployed in a unit
area and are trying to access the vacant channels. Each user
has a power constraint P k max , k = 1, …, K. There is also a
constraint on the amount of power that can be allocated in
each channel, P n mask , n = 1, …, N.
We consider the case with a single PU. And we assume
block fading channel model, i.e., channel matrix H, H are
fixed during each transmission block and change
independently from one block to another according to ergodic
random process.
B. Problem Formulation
In this paper, we consider the problem of switching
between multiplexing and diversity. So we define two user
satisfactions equations.
tar
max
S f ( R , R ) ( 1
) g(
P , P )
k,
mul k mul k k
k k k
tar
max
S f ( B , B ) ( 1
) g(
P , P )
k,
div k div k k
k k k
In [9], it considers data rate and power consumption terms,
i.e. (2). However the phenomena of channel fading and
interference from PUs in CR networks don’t guarantee
reliability of SUs link. Therefore, we consider reliability as
well as data rate and power consumption. (2) is applied when
multiplexing is selected, (3) is applied when diversity is
selected.
We assume kth SU has an expected target data rate, Rk tar ,
expected target BER, Bk tar . Where γ k is a weighted factor for
control between power consumption satisfaction and other two
satisfactions. Small γ k implies that users focus on saving its
battery energy while accepting a lower data rate or reliability.
On other hand, large γ k means that users focus on enhancing
its data rate or reliability with a short high battery life. Data
rate satisfaction fmul(Rk, Rk tar ), BER satisfaction fdiv(Bk, Bk tar )
and power consumption satisfaction g(Pk, Pk max ) are defined
as:
f
f
mul
div
tar
1
Rk
Rk
tar
( Rk
, Rk
) R
k
tar
0 Rk
R
tar
k
R
k
( B , B
k
tar
k
1
) log( Bk
)
tar
log(
Bk
)
B
k
B
B
tar
k
tar
k
B
k
1
max P
max
k
g( Pk
, Pk
) 1
0 P
max
k P
k
P
k
First term of user satisfaction (2), (3) can be conventional
data rate satisfaction (

Fig. 1. Switching between sprtial multiplexing and transmit diversity
based on user satisfaction
s.
t.
max S(
P)
K
k 1
N
P
n1
P
P
kn
kn
P
P
mask
n
max
k
We consider orthogonal transmission, one channel can be
occupied by only one user, to allocate channel. Next section,
we show appropriated power allocation method for data rate
and reliability.
III. TRANSMIT POWER ALLOCATION
In this section, we consider power allocation methods for
data rate problem and reliability problem to improve total user
satisfaction. Power allocation method for data rate is similar to
[9]. In case reliability problem, STBC for transmit diversity is
applied and we estimate BER related to reliability by
formulating a new equation.
A. Data rate Problem
Data rate problem is explained in detail in [9]. So we
simply explain this part. First, the achievable data rate of SUk
with multiple antennas is
R
k
N
mk
kn
n1
t1
2
t Pknt
log
1
2
A={α kn} is channel allocation matrix. P knt= 0 if α kn= 0.
After we apply singular value decomposition (SVD) on Hkn,
i.e, Hkn=U V, then take power allocation on mt = min(Nt, Nr)
parallel subchannels. The channel gains are the diagonal
elements of , λ t, t=1,…,mk.
Performance of SUs can be affected by interference from
PUs. Thus, we additionally consider interference from PUs to
ensure QoS of SUs. Applying the QR decomposition to the
channel matrix H of SUs, and we can write H=QR, where Q =
[q1, …, qM] has orthogonal columns, and define M as the rank
2 2 L H H of H. ςi =ς + l=1 p lqi (h lh l )qi is the interference-plus
noise power [6].
We use capped water-filling method to allocate power each
users. Allocated power is Pknt=min max Lk- ς2 2 mask λt ,0 ,Pnt .
If SUs are equipped with two transmit-receive antennas,
power constraint for first antenna is same as the case of single
antenna. However power constraint for second antenna is
Pn mask minus allocated power at first antenna.
Optimal power level Lk satisfying all constraints is
Lk=min([Lk P ,Lk R ,Lk o ]).
1) Lk o : if the condition holds that when Pk max is used, the
achievable data rate Rk Rk tar .
Total user satisfaction
2) Lk P : when allocating all power Pk max
3) Lk R : achieves Rk tar
We propose a channel-by-channel optimization (CBCO)
method [12]. We outline the algorithm to maximize total user
satisfaction. First, set l = 0 and we choose an initial channel
allocation matrix Al, and then power allocation matrix Pl is
found to maximize each user satisfaction based on the optimal
power level Lk. the achieved total user satisfaction is denote
by Sl. The process repeats until the algorithm converges Sl −
Sl−1

equipped with 2 2 antennas. PU’s transmit power is p l=10dB
and distance ratio is dij/dl=0.5. We can also know performance
degradation by effect of PU interference. If a channel is
allocated to the user with the smallest noise floor, then largest
contribution can be obtained towards total user satisfaction.
On the other hand, if channel is allocated to the user with the
largest noise floor, then smallest contribution can be obtained
towards total user satisfaction.
B. Reliability Problem
For MPSK digital demodulation, we assume that
wireless channel is flat Rayleigh fading environment. The
conditional probability density function (pdf) of STBC-
MIMO system is presented as [13] :
m n
STBC 2
(
n,
R | X ) Q 2C
n R K M b
x
c
,
k
j1
i1
Pe c
where k=log2M, KM=ksin 2 ( π
M ), X={x1,1,…,xn,m}, xij=αi,j and αij is path gain from independent complex Gaussian
random variables. Specially, for x≥0, we approximate Qfunction
as [14].
Q proposed
approx
i,
j
1
2 1
2
( x,
1, 2 ) : exp( 1x
) exp(
2 x )
12
4
In STBC-MIMO system, estimated BER can be expressed
through substituting (9) into (10).
2
B ( 1
2 )
k
k
where Φ1= 1
12 exp -2ρ1Cn,Rc K Pk 2 2
M
ς
2 λ1+λ2 ,
i
Φ2= 1
4 exp -2ρ2Cn,Rc K Pk 2 2
M
ς
2 (λ1+λ2) .
i
We also define the interference-plus noise power,
2 2 L H H ςi =ς + l=1 p lqi h lh l qi [6]. We substitute (11) into (3),
and then into (7). The Lagrangian function of the equation is
given by.
k
L(
P,
,
v)
log( B
tar
(
P
2
log (
)
k
max
1
P ) v(
P
k
2
)
mask
P )
k
2
Where and v are Lagrangian coefficients. The KKT
conditions are listed as:
1
3 3
3 exp
) 6k
1
3exp
v 0
( 2 1Pk
3)
( P )
k
tar
log( B 2 1 k 3
( ) 0
max
P P
Total user satisfaction
3.8
3.6
3.4
3.2
3
2.8
2.6
2.4
k
mask
Pk
v( P ) 0
where Φ3 = −2Cn ,R c KM (λ
2
1+λ2 2
)
ς
2 .
i
We rearrange Eq. (13) for Pk. allocated power to each SUs
is given by (16). Each antenna can be allocated same power
Pk/2.
P k
Y
ln
3{
(
2 1)
3
Y}
where Y= λ+v+ (1-γ k)
Pmax log(Btar )
γk 2x2 diversity no PU interference
2x2 diversity with PU interference
2.2
-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0
Noise power[dB]
2
1
2(
)
+ ρ1Φ3
6k .
2
1
3
The parameter λ and v can be obtained through
substituting (16) into (14) and (15). Without loss of generality,
we can assume v=0. Please note the denoting difference
between Lagrangian multiplier (λ) and channel gain λ 1, λ 2 .
Calculated λ is given by
( 2
1)
3
1 3 1
k
max
3exp
( ) 6k
k 3exp
tar
log( B ) (
2
1)
3
2 1 3 P
Fig. 3. show total user satisfaction by using Lagrangian
method with diversity for reliability satisfaction. SUs are
equipped with 2 2 antennas. PU’s transmit power is p l=
10dB and distance ratio is dij/dl = 0.5. We can also know
performance degradation by effect of PU interference. Two
cases between data rate and reliability have similar graph
pattern. However User satisfaction curve for reliability is
gentler than data rate case.
Fig. 3. Comparison of total user satisfaction with diversity

IV. SIMULATION RESULTS OF SWITCHING
In this section, we test the performance of switching
between multiplexing and diversity to improve performance of
SUs communication link. We use prior user satisfaction value
as switching criterion. To evaluate the efficiency of proposed
method, we simulate K=4 SUs randomly deployed in unit area
and N = 7, L = 1, Pn mask = 0.5, Pk max = 2, Rk tar = 8, Bk tar = 0.001,
γ k= 0.5, Nt = Nr = 2. When diversity is selected by switching
with BPSK modulation, ρ 1,ρ 2 =(0.48, 0.79) [14]. Lower
bound is achievable when no power is allocated. Since γ k=
0.5, lower bound is 0.5 and upper bound is 1 for each users.
We obtained all results using Monte Carlo simulations.
The performance improvements of the proposed switching
system are provided in Fig. 4. Fig. 5. First, we consider the
case which ignores the interference from the PU to the SUs.
Fig. 4. shows three curves indicating multiplexing, diversity
and switching results. The spatial multiplexing and transmit
diversity curves cross at approximately noise power = -13dB.
Spatial multiplexing is preferred for noise power < -13dB
while transmit diversity is preferred for noise power > -13dB.
And proposed switching scheme performs following better
one or better than two cases around cross point.
We next evaluate the effect of the interference from the PU
on the switching scheme. Fig. 5. shows also three curves.
Again we consider p l = 10dB and dij/dl = 1/2. As expected,
the overall performance is degraded. The spatial multiplexing
and transmit diversity curves cross at approximately noise
power = -15dB. The multiplexing curve performs better one at
noise power is smaller than cross point. However diversity
curve is better at high noise power. Performance of Switching
is similar to Fig. 4.
In fact, if two approaches in the MIMO channel have same
transmit power, spatial multiplexing performance is better than
transmit diversity one in high noise power, since spatial
multiplexing has diversity gain on the order of the number of
receive antenna, in this case second order, while transmit
diversity has diversity gain on the order of the product of the
number of transmit and receive antennas, in this case forth
order. But we consider combination with power consumption.
So these results are achievable.
We also have to consider interference plus noise power to
PU since PU have higher priority in CR system. Fig. 6. Show
interference plus noise power to PU in each case. We can see
all of cases have same value in high noise power and little
different value in low noise power. But in generally, it is
indicated similar value in overall noise power. So we can
improve performance of SUs without increasing interference
to PU.
V. CONCLUSTION
In this paper, we consider K SUs who have two
constraints to minimize or no interference to PU in an ad hoc
manner, trying to access N available channel. We propose
power allocation methods and a user satisfaction-based
switching between spatial multiplexing and transmit diversity
in CR-MIMO system.
If the multiplexing is selected by switching, we formulate
Total user satisfaction
Total user satisfaction
4
3.8
3.6
3.4
3.2
3
2.8
2.6
2.4
2.2
2x2 multiplexing no pu interference
2x2 diversity with no interference
2x2 switching with no interference
2
-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0
Noise power[dB]
Fig. 4. Switching result of multiplexing and diversity with no PU
interference
3.8
3.6
3.4
3.2
3
2.8
2.6
2.4
2.2
2x2 multiplexing with pu interference
2x2 diversity with with interference
2x2 switching with with interference
2
-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0
Noise power[dB]
Fig. 5. Switching result of multiplexing and diversity with PU
interference
interference plus noise power to PU
15
10
5
multiplexing
diversity
proposed switching method
0
-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0
Noise power[dB]
Fig. 6. Interference plus noise power to PU

user satisfaction in both data rate and power consumption. The
otherwise, diversity is selected; we formulate user satisfaction
in both reliability and power consumption. Then since tradeoff
between diversity and multiplexing, switching scheme should
be an effective approach to enhance the systems.
As power allocation methods, we use capped water-filling
method and CBCO algorithm for data rate satisfaction. On the
other hand, for reliability satisfaction, Lagrangian method and
KKT conditions are applied. For reliability representation, we
estimate BER by using Q-function in STBC-MIMO system.
The performance improvement of proposed switching scheme
and performance comparisons are demonstrated through
simulations.
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