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基于时间资源共享的分配方法在丰富的协作OFDM中的运用

基于时间资源共享的分配方法在丰富的协作OFDM中的运用
基于时间资源共享的分配方法在丰富的协作OFDM中的运用

P r

i m a r

y L i n k Figure 1. Model of the cognitive OFDM network

A Time-Sharing Resource Allocation Method in Heterogeneous Cognitive OFDM Network

Lei Li, Baoyu Zheng, Member, IEEE

Institute of Signal Processing and Transmission

Nanjing University of Posts and Telecommunications, Nanjing, P.R. China

Email: {y080601, zby}@https://www.wendangku.net/doc/e015407163.html,

Abstract —For a multiuser cognitive OFDM network, most existing adaptive resource allocation methods focus solely on fixed data-rate requirement (QoS guaranteed) or variable data-rate (no QoS guaranteed) conditions without any fairness consideration. In this paper, we investigate the resource allocation problem in a heterogeneous cognitive network with different QoS requirements. By decomposing the problem as a convex optimization, an optimal time-sharing resource allocation method is proposed to maximize the throughput of cognitive network under both subcarrier interference temperature limits and heterogeneous data-rate requirements. Finally, the performance of our proposed resource allocation algorithm is investigated by numerical results.

Keywords-Cognitive Wireless Network; Orthogonal Frequency Division Multiplexing (OFDM); Resource Allocation; Quality of Service (QoS)

I. I NTRODUCTION

The cognitive wireless network was proposed as the "NeXt generation" dynamic access technology in [1], which is considered as a reliable, seamless, high-efficient network that support a variety of different QoS guaranteed services. QoS guaranteed services such as voice transmission and video phone are very sensitive to delay and require a fixed data-rate (FDR). Whereas, no QoS guaranteed services like file transmission and web browsing could tolerate large delay and variable data-rate (VDR). Therefore, the cognitive network should dynamically allocate its resource in real-time so as to provide available QoS for different cognitive user while maintaining the performance of primary network. This restriction of primary users is equivalent to the interference temperature limit on all cognitive users' transmission power [2]. Since the design of OFDM ensures that each sub-carrier has a bandwidth less than the coherence bandwidth of the channel resulting sub-carriers experience relatively flat fading [3; 4], the system performance can be significantly enhanced by adaptive resource allocation, especially in multiuser system. Most multiuser OFDM resource allocation methods have focused solely on homogeneous QoS requirements. For a pure FDR QoS, Wong converted the problem to minimizing total transmitting power while maintaining constant rate for each user [5], which is also referred to Margin Adaption (MA). However, cognitive OFDM network usually experiences strict interference constraint by primary network, which can not provide such constant rate for all users. On the other hand, for a pure adaptive rate system, Jang formulated the problem to maximizing network throughput subjected to total transmitting

power limit [6], which is also referred to Rate Adaption (RA). Unfortunately, this technique never takes any fairness among all users into consideration and leads some user to not be assigned any subcarrier if all its subcarrier gains are relatively worse. With the consideration of fairness, Shen proposed a sub-optimal algorithm based on proportional rates constraints among all users in [7], and Tao proposed a time-sharing algorithm based on partly delay-constrained requirement in [8]. In this paper, under the interference temperature limit on each subcarrier, we discuss a time-sharing resource allocation method for heterogeneous cognitive OFDM network, where both FDR and VDR users are supported simultaneously. The rest of the paper is organized as follows: We introduce our system model and decompose the allocation problem by time-sharing in Section II. The multi-level water-filling algorithm for given time-sharing factors is given in Section III. In Section IV, we discuss the calculation of time-sharing factors based on heterogeneous requirements. The performance of our proposed resource allocation method is investigated by numerical results in Section V. Finally, conclusions are given in Section VI. II. S YSTEM M ODEL

We consider a heterogeneous cognitive OFDM network depicted in Fig.1. The system consists of N cognitive users

(CU) sharing K

subcarriers licensed to primary network. According to the "receiver-centricity" concept [2], interference caused by cognitive transmitter must keep below a certain upper-bound determined by the primary user (PU) receiver using the same subcarrier. These interference temperature limits on particular subcarriers is gathered by primary base station and delivered to cognitive control center (CCC). Cognitive channel gains ,n k g and interference channel gains

,n k h are assumed perfectly estimated at user terminal and collected by CCC via a feedback channel. Typically, CCC

This work is partly supported by National Natural Science Foundation of China (Grant No. 60972039), The National High Technology Research and Development Program of China (Grant No. 2009AA01Z241).

978-1-4244-7554-4/10/$26.00 ?2010 IEEE

executes all resource allocation calculations and maintains the reliable communication in the cognitive OFDM network. Let ,n k R denotes the throughput of cognitive user n on subcarrier k in bits/OFDM-symbol, which depends on channel gain ,n k g and allocated power ,n k p , and can be expressed as

2

,,,22,log 1n k n k n k n k n g p R σ????=+??Γ??

, (1) where 2

,n k σ denotes the noise estimated by cognitive receiver. And n Γ

is a constant related to a given BER requirement, which is suitable for estimating practical data-rate. If practical

uncoded MQAM modulation constellation is used, according to [9], we have

()ln 51.5n n BER ?Γ=?. (2)

For a set f Φof FDR cognitive users, the QoS guaranteed constant rates ,f n R n ∈Φ

should be satisfied. And for a set v Φ of VDR cognitive users, best-effort rates ,v m R m ∈Φ should be maximized. Undoubtedly, {}1,2,,f v

N ΦΦ=∪ .

These QoS requirements were also considered in [8] without

fairness considerations among VDR users, which may make some VDR user not be able to communicate if all its subcarrier

gains are relatively worse.

In [8], the author creatively proposed a time-sharing resource allocation by relaxing the constraint that each subcarrier is used by one user only. This method introduced a sharing factor [],0,1n k ρ∈ indicating the portion of time that subcarrier k is assigned to user n during each time fragment,

which was first noticed in [5] and widely used in multiuser

OFDM systems to convert a mixed integer optimization

problem into a convex optimization [6;7;8]. In our work, we

move forward this time-sharing method by introducing

mutually exclusion in time fragment, which can be written as

{}

,,,max

n n k n n k n

k

p R ττ∑∑

(3)

subject to

,0,,n k p n k ≥?,

(4) ,,n k n k

p P n ≤?∑

,

(5) 2

,,,,n k n k k h p T n k ≤?,

(6)

,f

f

n n

R R n =?∈Φ,

(7)

::,,v

i j i j R R i j γγ=?∈Φ, (8)

{}1,2,,f v N ΦΦ=∪ ,

(9)

[]0,1,

1n n n ττ∈≤∑.

(10) The object function (3) is to maximize cognitive network throughout, where n τ denotes the time-sharing factor that the portion of time subcarriers occupied by user n . Meanwhile, ,n k R is calculated by (1) and the actual rate of user n is

,n n n k k R R τ=∑. Constraint (5) is the total transmitting power

limit of user n . Constraint (6) is the interference temperature

limit given by primary network on each subcarrier. Note that although most existing allocation methods in cognitive radio treat interference limit as a summed-up value over all subcarriers, we hold our opinion that it should be separately

considered on each subcarrier, since primary network allocates

different subcarriers for different users, and then results

different interference channel gains ,n k h .Constraint (7) denotes

the QoS requirements of FDR users. Constraint (8) is the

proportional rates requirement for VDR users, which is firstly introduced in [7] to maintain the fairness among all users.

The sharing factor n τ in (3) under constraint (10) make the resource allocation more tractable by relaxing its exclusion

on k subcarriers under our model assumption, i.e., all

subcarriers are allocated to a single user over a portion of time. This make our optimization problem significantly reduced into

two sub-problems:

? For a given sharing factor set {}n τ, objective function

(3) turn to be {}

,,max n k n k k p R ∑for each user under the power constraints (4)-(6);

? For a given maximized rate set {},,max n k n k k p n R ??????∑, find

the sharing factor n τ for each user under the QoS constraints (7)-(9). The first issue is a power allocation and control problem, as

well as the second belongs to a rate allocation and scheduling

problem. Both these issues will be solved separately and

integrated jointly as the solution of the resource allocation

problem in the following two sections.

III. M ULTI -L EVEL W ATER -F ILLING P OWER A LLOCATION As discussed above, by a given time-sharing factor set {}n τ,

maximizing network's total throughput is equivalent to maximizing each user's throughput, that is

{}

,,max ,n k n k k p R n ?∑ (11)

subject to

,,n k n k

p P ≤∑

(12) 2

,,,n k n k k h p T k ≤?,

(13)

,0,n k p k ≥?.

(14)

The object (11) is concave because positive linear

combination of concave function (1) is concave. Furthermore,

Subcarrier Index

W a t e r F i l l i n g P o w e r

Figure 2. Illustration of multi-level water-filling

since the inequality constraints (12)-(14) are all convex, the feasible set of this problem is convex. For that reason, the power allocation problem defined in (11)-(14) is a convex optimization problem and there exists a unique global optimal point, which can be acquired by iteration. Now we formulate the optimal power allocation. The Lagrangian of the problem is,

{}()

,2

,,2,2,log 1n

n k

n

n k n k

n n k n k

k k n J p g p p P λλ????

??=+

??????Γ????

∑∑, (15) where n λ is the Lagrange multiplier of user n . The boundary conditions in (12) and (14) will be absorbed in Karush-Kuhn-Tucker (KKT) conditions [10] for short Lagrangian ()n J i . If

we let ,n k p ?

as the optimal solution there exist for ,n k ?, applying the KKT conditions, we formulate the sufficient and

necessary conditions for ,n k p ?

by differentiating the Lagrange,

{}()

2

,,,2,,,,0,,0,0,0,0n k k n k

n

n k

n

n k k n k n k

n k p T h J p p T h k p p λ??

?

??

?>=?

??=<

. (16) Moreover, this differentiating of Lagrangian with respect to ,n k p ?

and substituting into the KKT condition (16) follows,

2,2,22,,,,,,2

,222,,,10,0

ln 211,0ln 2ln 21,ln 2n k n

n n k n k n n k n

k n k

n n n k

n k n k n k n k k n n k n k n k g T p g g h T T h g h σλσσσλ?

?Γ??

?ΓΓ?=????

,(17)

which can also be simplified as,

2,,2

2,,1min max 0,,,ln 2n k n

k n k

n n k n k T

p k g h σλ???

??Γ????=?

????????

?

. (18) Meanwhile, the Lagrange multiplier n λ is obtained when we substitute (17) into the total power constraint (12), 2,22,,1min max 0,,ln 2n k n

k n k n n k n k

T

P g h σλ??

????Γ???????

=?????????????

?

∑. (19)

This multi-level water-filling optimal power allocation method given by (17) and (19) is similar to traditional OFDM water-filling principle [11], however, being some difference summarized as follows and illustrated in Fig. 2:

?

The line sketched out the bottom is no longer channel

noise 2,n k σ, but 2

2

,,,n k n k n

n k

g σΩ=Γas Equivalent

Noise adjusted by cognitive channel gains; ?

The power filled on each subcarrier ,n k p does not only depend on the water-line 1ln 2n n L λ=, but also the interference limit 2

,,n k k

n k

I T h =, which is illustrated

in Fig. 2 as Interference Limit Line ,,n k n k I Ω+. Thus, the filled power can exceed neither the water-line nor the interference-line; ?

For different user n , the water-line n L may vary.

However, the water-line 1ln 2n L λ= given by (19) cannot

be calculated in closed-form. Thus, a numerical iterative algorithm is given as follows that incessantly pours total power n P into all subcarriers until total power is used up or interference limits are reached on all subcarriers with least algorithm complexity ()2log K K Ο: 1) Initialization,

a) Set (),min n n k k

L ←Ω as initial water-line;

b) Set 0n F ← as initial total filled-power. 2) Loop until n F approchs n P numerically,

a) Update current water-line ()n n n n L L P F ←+?;

b) Update (),,min max 0,,n n n k n k k F L I ??←?Ω??∑as

current total filled-power;

c) If ,,max()n n k n k L I >Ω+, set ,,max()n n k n k L I ←Ω+

and break the loop. 3) Obtain allocation results,

a) Return current n L as final water-line;

b) Return (),,,min max 0,,n k n n k n k p L I ??←?Ω?? as final

power on subcarrier k .

Figure 3. Procedure of time-sharing resource allocation

2C o g n i t i v e N e t w o r k T h r o u g h p u t

2Figure 4. Throughput versus cognitive and interference channel gains

IV. T IME -S HARING A LLOCATION WITH Q O S R EQUIREMTS Although the transmitting power is given by (17) and (19), the actual transmitting rate of user n also depends on its time-sharing factor n τ, i.e., ,n n n k k R R τ=∑. As discussed above, time-sharing factors denote the portion of time subcarriers occupied by user n , which play a leading role in multiuser scheduling under heterogeneous QoS requirements. Thus, the sharing factors allocation problem can be expressed as, {}

,max n n n k

n k R ττ∑∑ (20) subject to

,f f n n R R n =?∈Φ, (21) ::,,v

i j i j R R i j γγ=?∈Φ, (22)

{}1,2,,f v N ΦΦ=∪ , (23) []0,1,1n n n ττ∈≤∑, (24)

Fortunately, this convex optimization problem is a linear program (LP) without any inequality constraint, which leads to the existence of close-form solution [10]. The FDR constraint (21) should be satisfied foremost not only for its reliable requirement, but also for its equality property, which yields,

,,f f

n n n k

k R n R τ=?∈Φ∑. (25) Note that these factors may dissatisfy constraint (24) when the FDR requirements are beyond the capacity of cognitive network, which is also called service outage. In this situation, there is no feasible point for (20)-(24).

On the other hand, all VDR users share the remaining

throughput of cognitive network under the proportional rate fairness constraint (22). Their total sharing factors must satisfy,

1,,v f

m n m n m n ττ=??∈Φ?∈Φ∑∑. (26) Additionally, proportional rates constraint (22) implies ,,:(/):(/)i j i i k j j k k k R R ττγγ=∑∑, ,v i j ?∈Φas the

proportional sharing factors constraint, which yields, ()

,,,m m k

v

k m m

m m m k

m k R m R γττγ=?∈Φ∑∑∑∑. (27) Hence, the time-sharing factors allocation including both FDR and VDR users and given by (25) and (27) respectively.

As a summarization, the diagram of our time-sharing resource allocation is given in Fig. 3, where the right dashed box represents the heterogeneous QoS requirements of cognitive users. Furthermore, each resource allocation cycle must be finished in a stable cognitive period, during which the

channel parameters and interference limit do not change.

V. S IMULATION AND A NALYSIS

In our simulations, we consider a heterogeneous cognitive

OFDM network with 8 users and 64 subcarriers. Uncoded

MQAM constellation is used and the BER for both FDR and VDR users are set to 510?. Noise gap 2

,n k σ for every cognitive

receiver on each subcarrier in normalized to unit, i.e. 0dB. In

addition, all cognitive and interference channel gains are treat

as i.i.d. Rayleigh variables with mean square 2,E[||]n k g and

2,E[||]n k h respectively. Thus, Monte Carlo simulations are applied over 310 times to reduce the influence of various channel realizations.

Fig. 4 shows the relation between cognitive network

throughput ,n n k n k R τ∑∑ in unit bits/OFDM-symbol and two average channel gains. We vary one channel gain from -20 dB to 0 dB and lock another at -10 dB. Meanwhile, all users

are set as VDR equal proportional rates (1:1::1 ) on power

constraint n P =+∞

for a independent comparison between different k T . We see that throughput rises when 2,E[||]n k

g

increases or 2,E[||]n k h decreases for fixed k T . This is because

cognitive network enjoys advantageous access capacity in good

cognitive or bad interference channel conditions. Moreover, as expected, throughput rises with k T since more interference

primary network can endure. Last but not least, the gaps grow

up as shown in the figure for the joint beneficial impact of

interference limit and channel gains. Owing to the direct constraint of cognitive transmitting

power by (5) and (6), cognitive network throughput definitely

depends on both user power constraint n P and subcarrier interference limit k T . This relation is given in Fig. 5 as a mesh plot with all channel gains at a same mean value -10dB. Above

10

20

30P n

(dB)

T k

(dB)

C o g n i t i v e N e t w o r k T h r o u g h p u t

Figure 5. Throughput versus sub-carrier interference temperature limit and

user transmitting power limit

5

101520

2500.20.40.60.81Average Throughput of FDR Users

S e r v i c e O u t a g e P r o b a l i t y

Figure 6. Service outage probability versus average throughput requirement

of each fixed data-rate user

all, at small value of n P or k T , no matter how large the other is, the throughput hardly increases. This trend is expected because the low value constraint plays a dominant role in transmitting power limitation. In addition, for a fixed large k T (corresponding large 2,E[||]k k n k I T h =), the throughput's variation can be generalized into three phases: Power Limited Phase — small n P restricts transmitting power and then makes the cognitive network in a low throughput, i.e., n k P I <; Boost Phase — median n P brings effective multi-level water-filling among all subcarriers and then makes rapid growth in throughput, i.e., k n k k I P I <<∑; Interference Limited Phase — large n P

exceeds the interference temperature limit and then makes little change in throughput, i.e.,n k k P I >∑.Note that a similar phenomenon occurs if we extend the value range

of k T for a fixed large n P .

For a cognitive heterogeneous network, access availability of FDR users can only be guaranteed in a probabilistic manner for the variable cognitive conditions and finite transmitting power. The service is said to be in an outage if FDR users' requirements exceed system capacity and then cannot be satisfied. This relation is illustrated in Fig. 6 with parameters n P =∞ and 0dB k T =. We define the range of average FDR users' requirements with outage probability lower than 1% as

Non-Outage Range, and the range with outage probability between 1% and 99% as Partial-Outage Range. Undoubtedly, FDR users' requirements by (7) can be supported in probability 1out P ? in both these ranges, but hardly guaranteed after the partial-outage range. In our simulation, both these two ranges shrink with the growth in FDR users' amount rapidly. This characteristic tells us that FDR users' requirements should be set at most in the non-outage range or low values of partial outage range to reduce service outage probability in a real system.

VI. C ONCLUSION

A time-sharing resource allocation method for cognitive heterogeneous OFDM network under the constraint of each subcarrier interference limit is considered in this paper. FDR and VDR users are simultaneously supported by constant rate and proportional rate access respectively. We investigated the problem of maximizing network throughput while satisfying both interference and total power constraints. This problem was transformed into two sub-problems of convex optimization by introducing the time-sharing factor, and solved separately. Simulation results showed that network throughput increases with the increasing of cognitive channel gains, the decline of interference channel gains, the increment of each subcarrier interference temperature limit, and the growth of user power constraint. Moreover, the upper-bound of FDR requirements is determined in a service outage probabilistic manner.

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Index Terms—Cellular networks,device-to-device,D2D,peer-to-peer,resource sharing,underlay. I.I NTRODUCTION T HE increasing demand for higher data rates for local area services and gradually increased spectrum conges-tion have triggered research activities for improved spectral ef?ciency and interference management.Cognitive radio sys-tems[1]have gained much attention because of their poten-tial for reusing the assigned spectrum among other reasons. Conceptually,cognitive radio systems locally utilize“white spaces”in the spectrum for,e.g.,ad hoc networks[2][3] for local services.Major efforts have been spent as well on the development of next-generation wireless communication systems such as3GPP Long Term Evolution(LTE)1and WiMAX2.Currently,the further evolution of such systems is speci?ed under the scope of IMT-Advanced.One of the main concerns of these developments is to largely improve the services in the local area scenarios.Device-to-Device (D2D)communication as an underlaying network to cel-lular networks[4][5]can share the cellular resources for Manuscript received November26,2010;revised February11,2011and March23,2011;accepted April20,2011.The associate editor coordinating the review of this paper and approving it for publication was N.Kato. C.-H.Yu and O.Tirkkonen are with the Department of Communi-cations and Networking,Aalto University,Finland(e-mail:{chiahao.yu, olav.tirkkonen}@aalto.?). K.Doppler and C.B.Ribeiro are with Nokia Research Center,Nokia Group (e-mail:{klaus.doppler,cassio.ribeiro}@https://www.wendangku.net/doc/e015407163.html,). Digital Object Identi?er10.1109/TWC.2011.060811.102120 1see https://www.wendangku.net/doc/e015407163.html,/ 2see https://www.wendangku.net/doc/e015407163.html,/better spectral utilization.In addition to cellular operations where the network services are provided to User Equipment (UE)through the Base Stations(BSs),UE may communicate directly with each other over D2D links while remaining control under the BSs.Due to its potential of improving local services,D2D communication has received much attention recently[6][7][8][9][10][11][12][13][14][15][16]. The idea of enabling D2D connections in cellular networks for handling local traf?c can be found in,e.g.,[17][18][19], where ad hoc D2D connections are used for relaying pur-poses.However,with these methods the spectral utilization of licensed bands cannot be improved as D2D connections take place in license-exempt bands.Furthermore,ad hoc D2D connections may be unstable as interference coordination is usually not possible.In[20],non-orthogonal resource shar-ing between the coexisting cellular and ad hoc networks is considered.As the operations of both types of networks are independent(with independent traf?c loads),interference coordination between them considers only the density of transmitters.Recent works on D2D communication assume the same air interface as the underlaying cellular networks. In[21],the cellular resources are reused by D2D connections in an orthogonal manner,i.e.,D2D connections use reserved resources.Although orthogonal resource sharing eases the task of interference management,better resource utilization may be achieved by non-orthogonal resource sharing.In[4][5],a non-orthogonal resource sharing scheme is assumed.Cellular users can engage in D2D operation when it is bene?cial for the users or system.Further,D2D power control when reusing Uplink(UL)cellular resources,where cellular signaling for UL power control can be utilized,is addressed to constrain the interference impact to cellular operations. 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