Quality of service aware admission control in cognitive device-to-device network

The Journal of China Universities of Posts and Telecommunications October 2011, 18(5): 22–29 www.sciencedirect.com/science/journal/10058885

http://jcupt.xsw.bupt.cn

Quality of service aware admission control in cognitive device-to-device network FU Zi-xi ( ), HU Chun-jing, PENG Tao, LU Qian-xi, WANG Wen-bo Wireless Signal Processing and Network Lab, Key Laboratory of Universal Wireless Communication Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China

Abstract

A hybrid system of cellular mode and device-to-device (D2D) mode is considered in this paper, where the cellular resource is reused by the D2D transmission. With the objective of capacity maximization, the power optimization of D2D sub-system is considered, taking into account quality of service (QoS) requirement. The power optimization problem is divided into two stages: The first stage is the admission control scheme design based on the QoS requirement of D2D users, and the second is power allocation to maximize aggregate throughput of admissible D2D users. For the D2D admission control problem, a heuristic sorting-based algorithm is proposed to index the admissible D2D links, where gain to Interference ratio (GIR) sorting criterion is used. Applying an approximate form of Shannon capacity, the power allocation problem can be solved by convex optimization and geometric programming tools efficiently. Based on the theoretical analysis, a practical algorithm is proposed. The precision can reach a trade-off between complexity and performance. Numerical simulation results confirm that combining with GIR sorting method, the proposed scheme can significantly improve the D2D system's capacity and fairness. Keywords cognitive radio, QoS, power control, geometric programming, sorting-based algorithm

1

Introduction 

With the development of wireless communication, the available spectrum resource becomes more and more insufficient with the current license-based spectrum policy. cognitive radio (CR) [1] is considered as an efficient technology to reuse the spectrum resource and improve the utility of spectrum. In Refs. [2–3], more detailed characteristics of cognitive radio network are presented. Cognitive radio makes the D2D communication possible, through reusing the licensed spectrum assigned to the primary wireless communication system. This type of network is usually named as CR based hybrid network which consists of two types of communication system. The one named as primary system uses the licensed spectrum, e.g. the traditional cellular network. The other one is called secondary system, which reuses the primary system’s frequency resource and communicates with each other under the authority of PU. The Received date: 21-01-2011 Corresponding author: FU Zi-xi, E-mail: [email protected] DOI: 10.1016/S1005-8885(10)60098-2

device-to-device network is a typical secondary system in the CR based hybrid network. With the cognitive radio, the D2D user can sense the interference environment and reuse the idle resource hole. In Ref. [4], three main cognitive radio network paradigms: underlay, overlay and interweave are summarized and explained. In this paper, the underlay paradigm is implemented in the cognitive hybrid network which means that the D2D user can operate if their interference to the primary user is lower than a threshold. It’s well known that the interference control in the hybrid network is a key issue that influences the performance of the hybrid system. In the underlay paradigm, the interference from D2D users to primary users should be under control. To achieve the maximum capacity of D2D network, the interference between D2D users should be considered as well. Therefore, the power optimization scheme of D2D networks is especially important, and is the main research item in this paper. The topic has attracted many interests, and numerous of power allocation schemes have been proposed. The optimization schemes proposed in Refs. [5–6] can improve the capacity of the whole secondary system significantly, with

Issue 5

FU Zi-xi, et al. / Quality of service aware admission control in cognitive device-to-device network

low interference to the primary user (PU). However, both of the models are based on the assumption of high SNR of the secondary user (SU), which requests well separation and fair resource allocation between different users (SU-SU, SU-PU). In the practical network, however, this key assumption cannot be always satisfied. Even if the optimal resource and power allocation for the whole network is achieved, some SUs cannot get high SNR. Another type of model proposed in Ref. [7] solves the problem based on a zero gap between the optimal values of Lagrange dual problem and original problem in OFDM system, on the assumption that there are a large number of frequency tones, but no SNR requirement is needed. An exhaustive search should be implemented over the dual problem domain which makes algorithm too complex. Besides, when the number of frequency tones is not large enough, the algorithm is imprecise. In this paper we consider a single channel scenario in which the channel is shared by a primary user and multiple D2D users (DU, equals the SU in Refs. [5–6]). We optimize D2D users’ power allocation to get the maximum capacity of the D2D network, and the corresponding problem in the multiple channels scenario can be transformed to multiple sub-problems on each channel. Different from the models in Refs. [5–7], we take the QoS of D2D users into account, and try to guarantee high SNR for all D2D users who have accessed the system. With the QoS consideration, the admission control problem of the D2D network is formulated. Every D2D user who tries to access the spectrum radio should get a QoS guarantee which means that it can satisfy a specific high SNR requirement. Based on the QoS guarantee for each accessed D2D link, the power allocation optimization algorithm can provide a power allocation scheme to optimize the capacity of the D2D system. Unfortunately, it’s a NP hard problem to get the optimal admissible D2D users set. Hence, a heuristic sorting-based mechanism is proposed to sort D2D users when accessing the spectrum, which can index a set of admissible D2D links and improve the system’s performance. The rest of this work is organized as follows. In Sect. 2, the model used in the following sections is presented, and the problem is discussed in detail. In Sect. 3, we design the algorithm and present that the precision of the algorithm is controllable. The simulation and the numerical results are given in Sect. 4. Sect. 5 summarizes the paper.

2 System model and problem formulation In this paper, the power allocation problem on a single channel is considered. The hybrid network consists of a D2D

23

links (DL) set S {1,2,..., N } and a primary user located in the cellular network. The transmitter of DLi is named as

DTx i , and the receiver is DRx i . The accessed D2D links will interfere with each other, and each of them will interfere with the primary user as illustrated in Fig. 1. Here the channel gain from DTx i to DRx j is denoted as hij . Similarly,

hiP represents the interference channel gain from DTx i to the primary user.

Fig. 1

System model

We assume that each D2D user treats the interference as noise, and signal to noise ratio (SNR) of DRx i can be expressed as

Ri

pi hii



¦

j , iSa , j z i

p j h ji  N 0

,

where

pi

denotes the transmit power of DTx i , N 0 is Gaussian noise received by DLi , and Sa represents the set of D2D links which have accessed the spectrum, Sa  S . We take the Shannon capacity expression as the utility function of each D2D link. With a specific power allocation, we get the capacity of D2D users. pi hii § · CD ¦ ln ¨1  (1) ¸ ¦ ln(1  Ri ) p h N  iSa iSa ¦ 0 ¸ j ji ¨ j , iSa , j z i © ¹ Optimal power allocation should be figured out to maximize CD , with the constraint of the interference to the primary user and QoS guarantee for each D2D user. In Ref. [8] the relationship between SNR and QoS has been testified. Hence, in this paper, we take the SNR as the index of D2D link’s QoS level. High SNR means high quality of D2D communication service. The power assigned to the D2D links which cannot achieve their QoS requirements is a waste of spectrum resource, and these D2D links should be rejected by the system. Therefore, the power control problem can be divided into two sub-problems. The first one is how to control the admission of D2D links and get an optimal set of D2D links which can access the system and reuse the spectrum to

24

The Journal of China Universities of Posts and Telecommunications

accomplish the communication. It has been proved in Ref. [9] that it is a NP hard problem. With the model in subsection 2.1, we can judge whether a new D2D link can access the system. Combining this model with heuristic sorting-based mechanism proposed in Sect. 2.3, a sub-optimal set of admissible D2D links can be obtained. The other problem is the power optimization of all D2D links which have accessed the system. The model in Sect. 2.2 solves this problem. 2.1

Admission control of D2D users & QoS guarantee

In this part, the problem whether a D2D link can access the spectrum is discussed. An important factor of this problem is the QoS requirement. We assume that each D2D link has its specific QoS requirement and D2D users access the system one by one. If a new D2D link tries to reuse the spectrum, it should meets its minimum SNR requirement and the D2D links which have accessed the system should get the minimum SNR guarantee too. In our model, we try to optimize the new D2D link’s SNR with the guarantee of the QoS requirement of all the D2D links in Sa . If the optimal SNR of the new D2D link can achieve its QoS requirement, it can be admitted into the system. Combining all these conditions, we model the problem as follows: Problem 1 pn hnn ½ max Rn p ¦ pi hin  N0 °° iSa ° s.t. °° (2) ¾ RiıQi ; i  Sa ° ° pi İPmaxi ; i {Sa , n} ° pi hiP İI P ° ¦ i{ Sa , n} °¿ where i {Sa , n} means i  Sa or i n , n is the index of new D2D link, Rn is the SNR of the new D2D link and p is the power vector of D2D transmitters. Qi represents the minimum SNR requirement of the already accessed D2D links, and Pmaxi represents the power target of DLi where I P is the limitation of the interference from the D2D links to

the primary user. It’s neither a linear nor a standard convex problem. However, by using the geometric programming [10], we can transform the problem to a convex problem. Make pi e xi and Eq. (2) can be expressed as:

¦e

2011

½ ° ° x e xn hnn ° ° s.t. ° xj ° e h ji  N 0 ¦ (3) ¾ 1 j zi Q fi  İ0; j , i  Sa ° xi e hii Qi ° xi p ° f i e  Pmaxi İ0; i {Sa , n} ° ° fI e xi hiP  I P İ0 ¦ °¿ i{ Sa , n} It is obvious that f i p ( i {Sa , n} ) and f I are convex

min f n

1 Rn

iSa

xi

hin  N 0

functions. To testify the problem is a convex model, we have to prove that f i Q ( i  Sa ) and f n are convex functions. Without loss of generality, we discuss the convexity of f n . According to Ref. [11], H n , the Hessian matrix of f n , is a diagonal matrix with a form like diag(H n1 , H n2 ,..., H nj ,..., H nm ) where H nk is the kth diagonal element. We assume that m  1 is the number of elements in the set of Sa . We denote

the kth elements of set {Sa , n} as sk , so n

Hnk

sm . Here m1

hsk ne sk (exn hnn )(1İkİm 1) and Hnm N0 (exn hnn )  ¦Hnk . x

k 1

For any non-zero vector a  \ m , we have a T H na m

¦H

k n

ak2 ! 0 , which implies that H n is a positive definite

k 1

matrix and function f i

f n is a convex function. The convexity of Q

( i  Sa ) can be proved in a similar way, and the

problem can be solved by the convex programming. If the optimal SNR of new D2D link is larger than its minimum SNR requirement, this new D2D link can access the system; otherwise, it should be rejected by the system. 2.2 Power optimization for the admissible D2D users The model proposed in Sect. 2.1 formulated the process of D2D links’ admission control. In this section, power allocation scheme is employed to optimize the capacity of aggregate of admissible D2D links, whose QoS requirements are guaranteed and interference to primary user is limited. Assuming that Sa {1,2,..., m}, mİN , the problem is formulated as follows: Problem 2

Issue 5

FU Zi-xi, et al. / Quality of service aware admission control in cognitive device-to-device network

pi hii ·½ ¦ p j h ji  N 0 ¸¸ °° j , iSa , j z i ¹° °° ¾ RiıQi ; i  Sa ° ° pi İPmaxi ; i  Sa ° pi hiP İI P ° ¦ iSa °¿

§ max ¦ ln ¨1  p ¨ iSa © s.t.

(4)

½ ° x ° ° ° s.t. ° xj ° e h ji  N 0 ¦ ¾ 1 jSa , j z i Q  İ0; i  Sa ° Fi xi ° e hii Qi ° xi p Fi e  Pmaxi İ0; i  Sa ° ° F I ¦ e xi hip  I P İ0 ° iSa ¿ · e xi hii ¸ xj e h ji  N 0 ¸ ¦ jSa , j z i ¹

(5)

we develop the convexity testifying of F0 . Assuming the Hessian matrix of the lth item of F0 is H l : [ H l (v, w)], 1İvİm, 1İwİm , where

­0; v l | w l ° xv  xw °  hvl hwl e ; vzwzl ° N  e xk h 2 ¦ 0 kl ° k zl H l (v, w) ® (6) ° e xv h N 0  ¦ e xk hkl  (e xv h ) 2 vl al ° k zl ; v w 2 ° xk N 0  ¦ e hkl ° k zl ¯ H l (v, w) is the element located in row v and column w of











H l . The Hessian matrix of

¦ a H (v, w)a ¦ E a v

l

w

v,w

v zl

2 v v

 N  ¦ E  ¦ E a

e xv hvl , and making D v

0

k zl

k

v zl

Ev av and E v

2

v v

(7) Ev ,

F0

which proves that H l is a positive definite matrix and so is

H F0 . The convexity of F0 is proved. The original problem can be solved as a convex optimization problem. 2.3

The order of D2D links accessing the spectrum

Obviously, the D2D system’s performance is affected seriously by the accessing order of D2D links when they access the system. Ideally the D2D links with better link quality should access the system with high priority. In this paper we consider to propose a criterion to sort the D2D links to access the spectrum. We take two facts into account: interference and quality of D2D links. The interference of a D2D link includes two kinds of interference. One is the interference that the D2D link generates to the other links including D2D links and primary link, and the other kind of interference is the one that a D2D link suffers from other D2D links. Combining all this factors, we proposed a heuristic criterion named as gain to interference ratio (GIR) to sort D2D links accessing the spectrum, where the GIR of DLi ,

Gi

the convexity of Fi p and F I are easily proved too. Here



aT Hla

Gi is:

The convexity of Fi Q has been verified in Problem 1, and

Hl

. For any non-zero vector a  \ m , we have:

using Cauchy-Schwartz inequality, we have a T H l a ! 0

We can use new utility function ln R as the D2D links’ capacity function. One advantage of this method that has been mentioned in Ref. [12] is that the new utility function can result in a more fair power allocation. Considering all these advantages, we use this method to solve the Problem 2. The problem can be viewed as a convex optimization problem with the geometric programming method. Make pi e xi we have: min F0

l

l 1

Here Ev

Though through the geometric programming the feasible set of the problem can be transformed into a convex set, it’s not a concave problem since the object function is not a concave function. With the minimum SNR guarantee for each accessed D2D link, when Qi !! 1 (i  Sa ) , ln(1  Ri ) | ln Ri .

§  ¦ ln ¨ ¨ iSa ©

m

¦H

H F0

25

is

H F0 , where

hiP

¦

j S , j z i

hii h ji

¦

jS , j z i

hij

(8)

The D2D links with high GIR values will get high priority to access the spectrum, which means that high communication gain, and low interference will make it easier to access the system for the D2D links. Another method proposed in Ref. [8] indexes a D2D links set whose D2D links can all satisfy the QoS requirement. With this method, first, the power optimization method is firstly used to maximize the capacity of D2D links without the QoS guarantee. Thus, not all D2D links will satisfy their QoS requirement when too many D2D links try to access the spectrum, and the bad D2D links are removed until all left D2D links can satisfy the QoS requirement with the power optimization algorithm. In Ref. [8] two sub-optimal algorithms based on removing bad D2D links were proposed to get the set of accessed D2D links. The first one is named as

26

The Journal of China Universities of Posts and Telecommunications

2011

one-step algorithm in which all bad D2D links that cannot satisfy their QoS requirement would be removed after the power optimization process while the other one is named as one-by-one algorithm in which just the worst D2D link will be removed after one power optimization process, and then optimization-removal process will be carried out repeatedly until all left D2D links’ QoS requirements are satisfied.

3

Algorithm design

We have showed that Problem 1 and Problem 2 can be both transformed to convex optimization problems with inequality constrain. Considering the algorithm design, there is no difference between these two problems. We use a standard convex optimization model to illustrate the algorithm we proposed. The standard convex optimization model with inequality constrain is expressed as: Problem example min f 0 ( x ) ½° x (9) ¾ s.t. fi ( x )İ0; i 1,2,..., m °¿

where x  \

n

and f i ( x ) (i 1,2,..., m) is convex function.

To get the optimal solution of problem example (PE), we transform the original problem to the unconstrained problem. An ideal price function u ( x) is introduced in the model: ­0; xİ0 u ( x) ® ¯f; x ! 0

(10)

m

f 0  ¦ u ( f i ( x ))

(11)

m t sub-optimal solution means that the gap between the optimal values of Eq. (13) and PE is less than m t . Assume that x * (t ) is the optimal solution of

Proof

Eq. (13), we have: m 1 § · ’f i ( x * (t )) ¸ 0 ’f 0 ( x * (t ))  ¦ ¨ * i 1 © tf i ( x (t )) ¹ Make Oi*

(14)

1 (tf i ( x * (t ))) , then m

’f 0 ( x * (t ))  ¦ (Oi*’f i ( x * (t ))) 0

(15)

i 1

Ȝ*

(O1* , O2* ,...Om* ) is a feasible solution of Lagrangian dual m

f 0 ( x )  ¦ Oi fi ( x ) , we have

the dual function of PE: g ( Ȝ) min L( x, Ȝ) , and from Eq. (15) we know that: x

i 1

not solvable either. A similar but derivable function is proposed to approximate u ( x) : 1  ln( x) (12) t Here t is a parameter that determines the deviation between u1 ( x) and u ( x ) . As illustrated in Fig. 2 we know that with

u1 ( x)

larger value of t, u1 ( x) gets a better approximation to u ( x ) . Then the original problem transforms to: m

f 0  ¦ u1 ( fi ( x ))

Theorem 1 The optimal solution of problem formulated by Eq. (13) is the m t sub-optimal solution of PE where

i 0

But the function u ( x) is not derivable, and the problem is

min f *

Influence of t

problem of PE. Make L( x , Ȝ)

And the original problem is equivalent to: min f

Fig. 2

(13)

i 1

Then the function f * is derivable, and we can treat the problem as a no-constrain convex optimization problem. u1 ( x) is an approximation of u ( x) , so the optimal solution of Eq. (13) is a sub-optimal solution of PE. Theorem 1 gives the gap between sub-optimal solution and optimal solution of original convex optimization problem.

g ( Ȝ* )

m

f 0 ( x * (t ))  ¦ Oi* f i ( x * (t ))= f 0 ( x * (t ))  i 1

m t

(16)

Assume V * is the optimal value of PE, according to the Lagrangian dual theory, V *ıf 0 ( x * (t ))  m t , so f 0 ( x * (t ))  V *İ m t . Theorem 1 shows that the parameter t determines the precision of the problem’s optimal solution. As mentioned in Ref. [11], large t may make the algorithm unstable. To enhance the stability of the optimization algorithm, the value of t can change from small to large gradually, and we can balance the stability with the precision of the algorithm. In Refs. [5–6], the asynchronous distributed and synchronous centralized algorithms have been proposed to solve the capacity optimization problem without the consideration of D2D users’ QoS requirement. In this paper, the centralized algorithm is used while considering the requirement of quick decision in D2D users’ admission control. As illustrated in

Issue 5

FU Zi-xi, et al. / Quality of service aware admission control in cognitive device-to-device network

Fig. 1, the network is a cellular-D2D hybrid network. The cellular base station is considered as the central node which controls the power allocation of D2D links. It’s beneficial for interference control from D2D links to primary users because the cellular base station has the information of primary link. To get the channel information, D2D transmitters can measure the interference channel gains through beacons periodically broadcasted by each receiver, and using the similar method, the primary user can get D2D interference channel gain. According to the channel information acquired by D2D transmitters and primary user, the cellular base station can figure out the power allocation scheme for the D2D links. According to Theorem 1 we introduce a precision controlled algorithm through changing the value of t . With low t value, the algorithm can calculate the sub-optimal solution quickly with low precision but high stability. When t becomes larger, the precision of solution gets higher while the convergence speed turn lower. This characteristic especially benefits solving Problem 1 because for D2D links, only a feasible but not optimal solution is needed to satisfy the accessing D2D link’s SNR requirement. For some D2D links with good quality, a feasible solution can be obtained quickly with a low t value. The precision controlled algorithm (PCA) is described in Algorithm 1. Algorithm 1 Precision controlled algorithm (PCA) Step 1 Initialize t t0 , u ! 1 , [ ! 0 , K ! 0 , H m t , xt00

x0 .

Step 2

Get the optimal solution xt*w of f * with the

specific t value: t w ( w 0,1,2,... ), using Newton method or other gradient descent method. 1) If f * ( xtnw )  f * ( xtnw1 ) ıH , turn to 2), otherwise xt*w

xtnw .

clusters randomly distribute in the area. We consider the network with multiple links, which can be configured as 4, 6, 8 or more links. The channel gain hij d ijD , where dij is the distance between DTx i and DRx j , D

Step 3

QoS requirement of D2D links is 10 dB, and the interference to primary users should not be larger than  120 dBm. As illustrated in Fig. 3, the simulation consists of two parts. In the first part, the admission problem is simulated, and the set of accessed D2D links is obtained. Two kinds of algorithms are in use to get the admissible D2D set. The first algorithm in which the D2D links access the spectrum in some order is named as sorting-based algorithm. All D2D links in the simulation area will try to access the spectrum one by one, in a random accessing order or sorted by GIR criterion. With the PCA algorithm, we can judge whether a D2D link can access the system, and then a D2D link set whose D2D links is admitted into the system is obtained. Another algorithm used to index the admissible D2D links set is removal-based algorithm proposed in Ref. [8]. The ‘One-step’ algorithm and ‘One-by-One’ algorithm are both in use to get the admissible D2D links set. In the second part, the power optimization algorithm is used to maximize the aggregate of the admissible D2D links’ capacity. Then the performance of the systems using different method (sorting-based, removal-based, no admission control) to index the admissible D2D links is compared in this part. We use the Monte Carlo method to evaluate the system’s performance: With a fixed D2D links number, a large number of simulations are implemented, and in different simulations the distribution of D2D links are different. Three features of the D2D system are illustrated in the following figures.

1

If 2m t İ[ , xt*w is the optimal solution of the

problem, otherwise make t w 1

utw , xt0w1

xt*w , w w  1 ,

and turn to Step 2.

4 Simulation and numerical results In this section, we study the performance of the D2D system with QoS guarantee. The network is contained in a 100 m ×100 m square area. The primary user is located in the centre of the area, and the D2D transmitter and receiver of one D2D link are located in a cluster whose radius is 5 m. The

4 . The channel

gain hiP is defined similarly. Minimum SNR defined as the

xtnw  ª H f * ( xtnw ) º ’f * ( xtnw ) where H f * ( xtnw ) is ¬ ¼ * the Hessian matrix of f at point xtnw . Turn to 1).

2) xtnw1

27

Fig. 3

Simulation procedure

28

The Journal of China Universities of Posts and Telecommunications

Fig. 4 shows the convergence process of calculating optimal SNR of the new D2D user which tries to access the system. When increases, the precision of the algorithm improves and the suboptimal SNR converges to the optimal value. In the simulation, we have tried different t0 values, and the simulation results show that if the t0 value is too high, the algorithm may fail to converge, since it influences stability of the algorithm. In the simulation, t0 is set as 5 u 104

and u

is 2, which can make the algorithm

converge in all simulation cases.

2011

of D2D links in the network increases as illustrated in Fig. 6. The system with ‘One-by-One’ removal algorithm gets less D2D links accessing the system than the ‘sorting-based’ algorithmˈbut when D2D links number increases to 26, the system with ‘One-by-One’ removal algorithm gets more admissible D2D links than the system with random accessing sort. This shows that a good sorting criterion is important for the system’s performance. In Fig. 6 we can see that regardless of the number of D2D links configured, the system with GIR sort criterion has the most admissible D2D links.

Fig. 6 The number of accessed D2D links Fig. 4

Change of precision of PCA algorithm with t varying

Fig. 5 shows that the D2D system’s capacity with different D2D links number. We can see that D2D performance of the system without the admission control which is labelled as ‘NoAC’ is the worst in the five cases. The capacity of D2D system with ‘One-step’ algorithm is better than the system without admission control but is worse than other systems. The D2D system sort by GIR criterion performs better than the D2D system with random accessing order which is labelled by ‘AC-Random’. The best performance on the capacity of D2D links is provided by the system with ‘One-by-One’ algorithm.

Fig. 5

In Figs. 7 and 8 the fairness of the proposed algorithm is compared. The Jain’s fairness index is used to index the fairness of the algorithms. The Jain’s fairness index is defined § r · as: F ( x1 , x2 ,...xr ) ¨ ¦ x j ¸ ©j1 ¹

2

§ r 2· ¨ r ¦ x j ¸ where x is the SNR © j1 ¹

of a D2D link and r is the number of D2D links. Two types of fairness are compared: the first one considers the whole D2D system’s fairness, and the number of admissible D2D links is an important issue in this type of fairness; the other one just takes the accessed D2D links into account, and the fairness of resource allocation between different accessed D2D links is indexed.

The D2D capacity comparison

When we compare the admissible D2D links number, only the system with ‘One-step’ algorithm decreases if the number

Fig. 7 D2D system fairness comparison

Issue 5

FU Zi-xi, et al. / Quality of service aware admission control in cognitive device-to-device network

Fig. 8

Fairness index of accessed D2D links

The comparison of first type of fairness between different algorithms is illustrated in Fig. 7. All D2D links’ SNR including the admissible and no accessed D2D links. The SNR of D2D links which cannot access the system is zero. The systems’ fairness of all algorithms decreases when the number of D2D links increases in the network, because there are more and more D2D links that cannot access the spectrum, which induces large unfairness. Fig. 7 shows that the D2D system with GIR sort criterion gets the best fairness, and the sorting-based algorithms have better fairness than the removal-based algorithm. The D2D system’s fairness has high correlation with accessed D2D links number, as illustrated in Figs. 6 and 7. The sorting-based algorithm tries to get every D2D link access the system, so the algorithm will try to balance the resource allocated to the admissible D2D links, which results in more D2D links accessing the system. The removal-based algorithm tries to optimize the whole D2D links’ capacity without considering the QoS requirement but just removing the D2D link with lowest SNR when allocating D2D links’ power. However, if the D2D links with higher SNR sacrifice some power and SNR, the low SNR D2D link may get higher power to satisfy its QoS requirement and access the system. Hence, the GIR sorting-based algorithm will introduce more D2D links accessing the system and higher system’s fairness. It’s easy to deduce that, with resource balancing in admissible D2D links, the sorting-based algorithm will get higher fairness of admissible D2D links than the removal-based algorithm. In Fig. 8, the fairness of resource allocation between admissible D2D links is considered. As has been deduced, the sorting-based algorithms still perform better than the removal-based algorithm. When the D2D links’ number increases, the fairness with sorting-based algorithm gets better, but the system with ‘One-by-One’ removal algorithm performs worse.

29

The numerical results prove that the sorting-based algorithms has better fairness than the removal-based algorithms proposed in Ref. [8], when we consider the admission control of D2D links and the resource balance between different admissible D2D links. Different to the removal-based algorithm, the sorting-based algorithm try to make every D2D link access the system successfully when considering the QoS guarantee, and it will result in better balance between D2D system’s capacity and service fairness. With a slight loss of D2D system’s capacity, the sorting-based algorithm can make more D2D links suitable for communication. The One-by-One removal algorithm is more suitable to maximize the D2D system’s capacity, but if we aim to get the D2D links access the system as many as possible, the sorting-based algorithm with GIR criterion is much more suitable.

5

Conclusions

In this paper, we provide a framework to solve the admission control problem considering the QoS guarantee and capacity optimization in spectrum sharing network (D2D network). A precision controlled algorithm is derived to control the optimization’s precision and convergence speed while a heuristic sorting-based algorithm is proposed to index the accessed D2D links. The numerical results show a significant improvement on the system fairness and communication rates. Acknowledgements This work was sponsored by Renesas, the National Natural Science Foundation of China (60572120, 60602058), the National Basic Research Program of China (2009CB320400), the Joint Funds of NSFC-Guangdong (U1035001), and the Chinese Major Science and Technology Projects (2009ZX03007-004).

References 1. Mitola J, Maguire G. Cognitive radio: making software radios more personal. IEEE Personal Communications, 1999, 6(4), 1318 2. Haykin S. Cognitive radio: brain-empowered wireless communications. IEEE Journal on Selected Areas in Communications, 2005, 23(2): 201220 3. Akyildiz I F, Lee W Y, Vuran M C, et al. Next generation/dynamic spectrum access/cognitive radio wireless network: a survey. Computer Networks Journal, 2006, 50(13), 21272159 4. Smith A G, Jafar S A, Maric I, et al. Breaking spectrum gridlock with cognitive radio: an information theoretic perspective. Proceedings of the IEEE, 2009, 97(5): 894914

To p. 36

36

The Journal of China Universities of Posts and Telecommunications

Miami, FL, USA. Piscataway, NJ, USA: IEEE, 2010: 5p 9. Qu Q Q, Wang A G, Fu J L. A novel scheme of spatial modulation based on generalized space shift keying (GSSK) modulation. Proceedings of the 2010 International Conference on Broadcast Technology and Multimedia Communication (BTMC’10): Vol 1, Dec1 314, 2010, Chongqing, China. Piscataway, NJ, USA: IEEE, 2010: 130133 10. Fu J L, Hou C P, Xiang W, et al. Generalised spatial modulation with multiple active transmit antennas. Proceedings of the 2010 IEEE GLOBECOM Workshop (GC Wkshps’10), Dec 610,2010, Miami, FL, USA. Piscataway, NJ, USA: IEEE, 2010: 839844 11. Mesleh R, Haas H, Sinanovic S, et al. Spatial modulation. IEEE

Transactions on Vehicular Technology, 2008, 57(4): 22282241 12. Jeganathan J, Ghrayeb A, Szczecinski L. Spatial modulation: optimal detection and performance analysis. IEEE Communications Letters, 2008, 12(8): 545547 13. Lee K, Chun J, Hanzo L. Optimal lattice-reduction aided successive interference cancellation for MIMO systems. IEEE Transactions on Wireless Communications, 2007, 6 (7): 24382443

(Editor: ZHANG Ying)

From p. 29 5. Zhao J, Chen X, Luo J, et al. An improved resource allocation method based on convex optimization in centralized wireless network. Proceedings of the 5th International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM’09), Sep 2426, 2009, Beijing, China. Piscataway, NJ, USA: IEEE, 2009: 4p 6. Lu Q X, Wang W B, Wang W, et al. Asynchronous distributed power control under interference temperature constrains. Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM’08), Nov 30Dec 4, 2008, New Orleans, LA, USA. Piscataway, NJ, USA: IEEE, 2008: 5p 7. Yu W, Lui R, Cendrillon R. Dual methods for non-convex spectrum optimization of multicarrier systems. IEEE Transactions on Communications, 2006, 54(7): 13101322 8. Kim D I, Le L B, Hossain E. Joint rate and power allocation for cognitive

2011

9.

10.

11. 12.

radios in dynamic spectrum access environment. IEEE Transactions on Wireless Communications, 2008, 7(12): 55175527 Andersin M, Rosberg Z, Zander J. Gradual removals in cellular PCS with constrained power control and noise. Wireless Networks Journal, 1996, 2(1): 2743 Xing Y, Mathur C N, Haleem M A, et al. Dynamic spectrum access with QoS and interference temperature constraints. IEEE Transactions on Mobile Computing, 2007, 6(4): 423433 Boyd S, Vandenberghe L. Convex optimization. Cambridge, UK: Cambridge University Press, 2004 Etkin R, Parekh A, Tse D. Spectrum sharing for unlicensed bands. IEEE Journal on Selected Areas in Communications, 2007, 25(3): 517528

(Editor: ZHANG Ying)