Resource Allocation for OFDMA-based Cognitive Radio Systems with Primary User Activity

Consideration

Li Li, Changqing Xu, and Jian He Department of Electronic Engineering

Shanghai JiaoTong University Shanghai, China

wsll320@gmail.com, cqxu@sjtu.edu.cn, sword2144@yahoo.com.cn

AbstractIn OFDMA-based Cognitive Radio (CR) systems, how to deal with the time-varying nature of avaliliable spectrum resources has become a hotspot and challenging problem in resource allocation. Traditional resource allocation algorithms can not guarantee proportional rates among non-real-time CR users (CRU) because the number of available subchannels is smaller than that of CRUs in some OFDM symbol durations. In this paper, taking the maximizing of the sum-rate of all CRUs as the optimization objective, we propose a resource allocation algorithm in OFDMA-based CR systems using dual methods which can maintain statistical proportional rates among CRUs while keeping the interference introduced to Primary users (PU) under specified thresholds. In contrast to traditional resource allocation algorithms, the proposed algorithm can achieve higher transmission rate and guarantee non-real-time services of CRUs.

Keywords-Cognitive Radio; OFDMA; resource allocation; proportional rate; Primary User activity; dual methods

I. INTRODUCTION Cognitive Radio (CR) is an efficient technology for

improving the utilization of scarce radio spectrum resources by allowing CR users (CRU) to access frequency bands not being occupied by Primary users (PU) [1]-[2]. Orthogonal frequency division multiple access (OFDMA), also known as multiuser orthogonal frequency division multiplexing (OFDM), is a potential candidate for CR systems due to its flexibility in allocating resource among CRUs [3].

In contrast to traditional OFDMA systems, resource allocation in CR systems has two challenges: firstly, mutual interference between PU and CRU has to be considered especially in systems where PUs do not use OFDM and the interference introduced to PUs must be limited under specified thresholds [4]; secondly, the time-varying nature of available spectrum resources due to PU activity also needs to be considered. Many resource allocation algorithms have been proposed in interference-limited CR systems and resource allocation algorithm with PU activity consideration is a new hotspot in CR systems. When a PU is active, the corresponding subchannels in this PUs frequency band are not available to CRUs, so how to deal with the time-varying nature of available spectrum resource is a difficult problem. In traditional OFDMA systems, a suboptimal resource allocation algorithm

has been proposed to guarantee proportional rates among non-real-time users during each OFDM symbol duration in [5], and it is implicitly assumed that the number of available subchannels is sufficiently large in this OFDM symbol duration. However, in CR systems, the number of available subchannels is sometimes smaller than the number of CRUs in some OFDM symbol durations, so the algorithm in [5] can not guarantee proportional rates among CRUs. In fact, non-real-time services are delay-tolerant and it is unnecessary to guarantee proportional rates among CRUs in each OFDM symbol duration, thus non-real-time services can be guaranteed even in CR systems. In [6], a novel resource allocation algorithm with consideration of the time-varying nature of available spectrum resource has been proposed to provide statistical proportional rates among CRUs. However, interference between PUs and CRUs is not taken into consideration in this paper.

In this paper, we extend the scenario in [6] to general case, taking into account both interference and PU activity in OFDMA-based CR systems. We will see that, for a given subchannel assignment, the optimal power allocation follows water-filling approach with different water levels for different subchannels. Basing on this property, we propose a resource allocation algorithm to guarantee statistical proportional rates among CRUs using dual methods.

II. SYSTEM MODEL We consider resource allocation problem on the downlink

of an OFDMA-based CR system in which a CR Base Station (BS) serves M CRUs and PU BS transmits signals to N PUs. The total bandwidth is W, which is divided into K subchannels and each subchannel has a bandwidth of f. The bandwidth of frequency band occupied by each PU is Wp, which contains K/N subchannels. It is assumed that the transmission is time-slotted with a slot duration equals to the OFDM symbol duration Ts. Let htm,k and gtk,n denote the time-varying channel power gain of the mth CRU and the nth PU of the kth subchannel in time slot t respectively. The probability density function (PDF) and cumulative distribution function (CDF) of the mth CRU are fm(hm) and Fm(hm) respectively. The noise power density spectrum (PSD) is N0. We assume that a subchannel can not be shared by more than one CRU and define tm,k as a

This work was supported in part by the National High Technology Research and Development Program (863) of China under Grant No. 2007AA01Z224 and the National Natural Science Foundation of China under Grant No. 61071079.

978-1-61284-231-8/11/$26.00 2011 IEEE

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings

subchannel allocation indicator which could only be either 1 or 0, indicating whether the kth subchannel is allocated to the mth CRU or not in time slot t.

Without loss of generality, we assume that all PUs have the same probability pa of staying in active mode. During the time slot t, if the nth PU is active, the subchannels in this PUs frequency band are not available to CRUs and there exists interference between this PU and available subchannels which are occupied by CRUs.

In this paper, we consider proportional rates among CRUs in T time slots first and define {rm, m=1M} as a set of predetermined values which satisfy

1 2 1 2: : ... : : : ... :M MR R R r r r= (1)

By introducing the service share d for each CRU [6], the constraint above can be rewritten as

1 1 2 2/ / ... /M MR r R r R r d= = = = (2)

where Rm is the transmission rate of the mth CRU during T time slots.

The PSD of the kth subchannel is

, ,1

sin( ) ( )M

t t sk m k m k s

m s

fTf p TfT

=

= (3) where ptm,k is the power allocated to the mth CRU on the kth subchannel in time slot t. Thus, the interference introduced by the kth subchannel to the nth PU in time slot t can be written as

,

,

/2

, , , , ,/21

( )k n pk n p

Md Wt t t t tk n k n k m k m k k nd W

mI f df P U +

=

= = g (4) where dk,n is the spectrum distance between the kth subchannel and the nth PUs frequency band and Utk,n denote the interference factor of the kth subchannel to the nth PUs frequency band.

The interference introduced by the nth PU signal to the kth subchannel of the mth CRU in time slot t can be written as

( ),,

/2

, , ,/2

k n

k n

d ft t jn m k m k RRd f

J h e d +

= (5) where RR(ej) is the PSD of PU signal.

Mathematically, we formulate the resource allocation problem as maximizing the sum-rate of all CRUs subject to the constraints of interference thresholds, total transmit power and proportional rates among CRUs. The optimization problem can be formulated as

OP1: { }, , , ,, 1 1

max t t

tm k m k

T Mt tm k m k

R t m k A

R

= =

(6) subject to

, ,1 t

Tt tm k m k m

t k A

R dr=

= , 1,...,m M= (7)

,1

1M

tm k

m

=

= , 1,...,tk A t T = (8)

( ), / ,,1 ,

2 1tm k

t

tMR f k nt

m k ntmk A m k

U

=

1,...,tn S t T = (9)

( ), /,1 1 ,

12 1tm k

t

T MR ft

m k totaltt mk A m k

TP

= =

(10) where Rtm,k and ( ), , 0 , ,/ tt t tm k m k n m kn Sh N f J = + are the transmission rate and the channel-to-interference and noise ratio of the mth CRU in the kth subchannel respectively . tA is the set of the available subchannels and tS is the set of the active PUs during time slot t. In (9), n denotes the interference threshold level of the nth PU and the total interference introduced by all CRUs to the nth PU, the left side of (9), must be limited under this level. In (10), Ptotal is the total transmit power per time slot.

III. PROPOSED RESOURCE ALLOCATION ALGORITHM

By introducing a new variable l , , ,t t tm k m k m kR R= , OP1 can be

converted into a convex optimization problem and the Lagrangian is given by

l l

l( )l( )

,

,

1

, ,1 1 1 1

,1 1

,/,

1 1 ,

/,

1 1 ,

1

2 1

12 1

t t

t

tm k

t t

tm k

t

T M M Tt tm k m km m

t m m tk A k A

T Mt tk m k

t mk A

tT Mk nt t R f

n m k ntt mn S k A m k

T Mt R fm k totalt

t mk A m k

L

R dr R

U

TP

= = = =

= =

= =

= =

=

+

+

+

+

(11)

where m , tk , tn and are Lagrange multipliers for constraints (7), (8) (9) and (10) respectively. Let *,

tm k and l

*,

tm kR

denote the optimal values. Using the Karush-Kuhn-Tucker (KKT) conditions [7], the necessary and sufficient conditions for *,

tm k and l

*,

tm kR can be written as

l *,

10

t

T tm k m

t k A

R dr=

= , 1,...,m M= (12) *,

1

1 0M

tm k

m

=

= , 1,...,tk A t T = (13) l * *, ,/ , *

,1 ,

2 1 0t tm k m k

t

tMR f k nt t

n m k ntm k A m k

U

=

= ,

1,...,tn S t T = (14)

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings

l * *, ,/ *

,1 1 ,

12 1 0t tm k m k

t

T MR ft

m k totaltt mk A m k

TP

= =

= (15)

*, *1, *

, *,

0, 00, 0< 10, 1

tm ktm kt

m k tm k

L

> =

= (17)

Differentiating the Lagrangian with respect to *,tm k and

substituting the result into KKT conditions, we obtain the optimal subchannel assignment strategy in time slot t

* ,,

1, arg max0, otherwise

tt m km k

m H == (18)

and ( ) * * *, , , , ,,

1t t t t tm k m k m k m k m k t

m k

H L ln L L

++

= . Here,

( ) ( )max 0,x x+ . The optimal power allocated to the kth subchannel of the mth

CRU is

* *, ,

,

1t tm k m k t

m k

p L

+ =

(19)

Equation (19) shows that the optimal power allocation follows water-filling approach, and *,

tm kL is the optimal water

level. The expression of *,tm kL is given by

( ) *,

,

1

2t

tmt

m kt tn k n

n S

fL

U ln

+ =

+ (20)

We can see that, with a given subchannel assignment strategy, *,

tm kL varies with different subchannel k.

The conclusions above are the optimal values in time slot t, however proportional rates among CRUs need to be maintained during all T time slots and we can not predict the instantaneous values of the power gains of CRUs and PUs during the time slot after t. Therefore, we convert OP1 to OP2, in which statistics of power gains are considered and OP2 is the statistical form of OP1. In OP2, we drop superscript t in OP1 since we only consider statistical proportional rate. Furthermore, we assigne subchannels among CRUs using strategy (18) and next we will calculate the probability that the given subchannel is allocated to each CRU in this statistical problem.

OP2:{ }

( ) ( ),

,

, 2 , ,1 1 ( )

max

log

m k

m k

L

M K

m k m k m k n m m mm k L

Prob f L p f h dh

= =

(21)

subject to:

( ) ( ),

, 2 , ,1 ( )

logm k

K

m k m k m k n m m m mk L

Prob f L p f h dh dr

=

= 1,...,m M= (22)

( ),

, , ,1 1 ,( )

1

m k

M K

m k m k n k n m m m nm k m kL

Prob L p U f h dh

+

= =

1,...,n N= (23)

( ),

, ,1 1 ,( )

1

m k

M K

m k m k n m m m totalm k m kL

Prob L p f h dh P

+

= =

(24)

Here,

( ) ( ),,

0, /2

, /21

k n

k n

m k N d f jm k a RRd f

n

N fLL p e d

+

=

=

(25)

( )( )( )

, , ,

1, ,

( ) ( )

( )

m k j j k j m k mj m

j j j k m k mj m

Prob F H h H h

F h H H h

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