Dynamic Channel and Power Allocation in Cognitive Radio Networks ...

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.

Dynamic Channel and Power Allocation in Cognitive Radio Networks Supporting Heterogeneous Services †

Renchao Xie† , Hong Ji† , Pengbo Si‡ , Yi Li†

School of Information and Telecommunication Engineering, Beijing University of Posts and Telecommunications, Beijing, P.R. China ‡ College of Electronics Information and Control Engineering, Beijing University of Technology, Beijing, P.R. China Email: [email protected], [email protected], [email protected], [email protected]

Abstract—Resource allocation problem in cognitive radio networks (CRN) is one of the key issues to improve the efficiency of spectrum utilization. Most of previous work on resource allocation mainly concentrates on the secondary users (SUs) with only one type of service requirement, without considering the scenario with heterogenous services requirement. In this paper, we study the dynamic channel and power allocation for SUs supporting heterogenous services in CRN. Firstly we classify the SUs by service requirement, i.e., SUs with minimum rate guarantee and SUs with best-effort services. Then we introduce the minimum rate constraints and proportional fairness constraints for SUs respectively. Under this setup, we formulate the problem of dynamic channel and power allocation for SUs as a mixed integer programming problem. And the heuristic optimal algorithm and suboptimal algorithm are proposed to realize the dynamic channel and power allocation. Extensive simulation results are presented to demonstrate the performance of the proposed scheme.

I. I NTRODUCTION Traditionally, the spectrum management committee takes a static spectrum assignment policy for wireless networks. However, with the development of wireless access technologies and the requirement of wireless application services, the spectrum resource has been becoming more and more crowed under this policy. On the contrary, most of assigned spectrum is still of low utilization [1]. Consequently, the FCC Spectrum Policy Task Force recommends to develop a new communication paradigm to improve the utilization efficiency of spectrum. Cognitive radio, first introduced by Joseph Mitola III [2], is a promising technique to improve the utilization efficiency of the radio spectrum. Then in [3], the authors give a comprehensive investigation. The main idea of the cognitive radio is that the secondary users (SUs) can sense the variance of surrounding environment and opportunistically utilize the temporarily unused spectrum resource licensed to primary This work was jointly supported by State Key Program of National Natural Science of China (Grant No. 60832009), Natural Science Foundation of Beijing, China (Grant No. 4102044), Innovative Project for Young Researchers in Central Higher Education Institutions, China (Grant No. 2009RC0119) and New Generation of Broadband Wireless Mobile Communication Networks of Major Projects of National Science and Technology (Grant No. 2009ZX03003-003-01).

users (PUs). In this case, dynamic resource allocation for SUs in cognitive radio networks (CRN) becomes very important. Resource allocation in CRN is drawing a lot of attention. The problem of channel and power allocation for multiple SUs in infrastructure-based cognitive radio networks is studied in [4]. Then the authors propose a joint resource allocation algorithm under the constraints condition. In [5] the authors study the resource allocation for underlay spectrum sharing technology and propose a power control scheme to guarantee that each SU has a minimum QoS requirement. The distributed multi-channel power allocation with QoS guarantee is studied in [6]. Then the authors propose a distributed power allocation algorithm based on the lagrangian dual decomposition. Authors of [7] study the distributed price-based spectrum management in CRN, then the authors model the resource allocation problem as a noncooperative game and design a price-based iterative water-filling algorithm to maximize the SU’s utility function. However, most of previous work concentrates on the resource allocation for SUs with only one type of service requirement, without considering the resource allocation for SUs with heterogenous services requirement. However, the problem of resource allocation for SUs supporting heterogenous services is meaningful and should be taken into account. In this paper, we focus on the resource allocation for SUs supporting heterogenous services. Firstly we classify the SUs by service requirement, i.e., SUs with minimum rate guarantee and SUs with best-effort services. Then for the former case, we introduce the minimum rate constraint condition. And to guarantee the fairness for SUs with best-effort services, we introduce the proportional fairness constraint condition. Then under these constraints, we model the resource allocation problem as a mixed integer programming problem and propose the heuristic optimal algorithm and suboptimal algorithm to realize the dynamic channel and power allocation for SUs. The main contributions of this paper are as follows. • We study the resource allocation problem supporting heterogenous services, which is more reasonable and meaningful. Because the SUs with heterogenous services requirement in

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CRN can simultaneously contend the network resource. • We model the resource allocation problem as a mixed integer programming problem. And we propose the heuristic optimal algorithm and suboptimal algorithm to realize the dynamic resource allocation. The rest of the paper is organized as follows. The system model and problem formulation are given in section II. In section III, the heuristic optimal algorithm and suboptimal algorithm are proposed respectively, then the computation complexity is analyzed. In section IV, the simulation results are shown. Finally, we conclude this study in section V.

ρk,n pk,n ≤ Ptotal

(1)

n=1

• Minimum rate guarantee: Let Rkmin denotes the minimum rate requirement for SU k in KA . Thus we have Rk ≥ Rkmin , ∀k ∈ KA

2

pk,n |hk,n | 1+ n0

, ∀k ∈ KA ∪ KB (4)

where hk,n denotes the sub-channel gain for SU k in channel n, n0 is the additive gaussian white noise with zero mean and variance σ 2 . Therefore the optimization problem which is to maximize the total capacity of CRN under the constraints condition can be expressed as. K N 1 +K2 k=1

ρk,n log2

n=1

pk,n |hk,n | 1+ n0

2

(5)

Subject to : K1 +K2 N ρk,n pk,n ≤ Ptotal k=1

n=1

pk,n ≥ 0, ∀k, ∀n ρk,n = {0, 1} , ∀k, ∀n K1 +K2 ρk,n = 1, ∀n k=1

Rk ≥ Rkmin , ∀k ∈ KA Rk Ri = γk ,∀k ∈ KB i∈KB

The first inequality denotes that there is a total power constraint in CRN. The third constraint condition denotes whether sub-channel n is occupied by the SU k. The fourth equality constraint represents that each sub-channel can only be assigned to one SU. And the last two constraints condition denote that the SUs with heterogeneous services requirement have the different constraints respectively. III. H EURISTIC O PTIMAL A ND S UBOPTIMAL S UB -C HANNELS A ND P OWER A LLOCATION In this section, we propose the heuristic optimal algorithm and suboptimal algorithm to realize the resource allocation for SUs. In subsection III.A, we firstly give a heuristic optimal algorithm. Then due to the computation complexity for heuristic optimal algorithm, a suboptimal algorithm is proposed and realized by two steps: suboptimal sub-channels allocation in subsection III.B and optimal power allocation in subsection III.C. Finally, the computation complexity of the heuristic optimal algorithm and suboptimal algorithm are analyzed respectively in subsection III.D. A. Heuristic Optimal Sub-Channels and Power Allocation

(2)

• Proportional fairness constraint: To guarantee the fairness for SU k in KB , we introduce the normalized proportional fairness factor γk . Therefore, we have R k = γk , ∀k ∈ KB Ri

ρk,n log2

n=1

pk,n ,ρk,n

We assume that the PUs and SUs in CRN operate based on a time-slotted. In each time slot, the PUs and SUs use orthogonal frequency-division multiplexing (OFDM) modulation technology [8]. When the sub-channels are not occupied by the PUs, the SUs can opportunistically utilize these idle subchannels. To sense the idle sub-channels refers to the spectrum sensing technologies which are widely studied in [9]. Assuming that there is a common control unit (i.e. cognitive BS) to coordinate the resource allocation for SUs. And the SUs can be classified by heterogenous services requirement: SUs with minimum rate guarantee and SUs with best-effort services. Therefore we simply assume that in each time slot there are N idle sub-channels, K1 SUs with minimum rate guarantee and K2 SUs with best-effort services respectively. The corresponding set of these two classes SUs can be denoted as KA and KB respectively. The number of N , K1 and K2 can vary dynamically in different time slot. Therefore, to realize the feasible resource allocation problem, we give the assumption as follows. • Let each sub-channel is assigned to one SU. We use the binary index ρk,n ∈ {0, 1} to represent the sub-channel allocation. The ρk,n = 1 denotes the sub-channel n occupied by the SU k, otherwise ρk,n = 0. • Total power constraints: Let Ptotal denotes the total power available for the SUs, pk,n denotes the transmit power for SU k in sub-channel n. Thus, we have

k=1

max

II. S YSTEM M ODEL AND P ROBLEM F ORMULATION

K N 1 +K2

Rk =

N

(3)

i∈KB

The γk , ∀k ∈ KB is a predetermined value. Therefore the unit bandwidth capacity of SU k can be expressed as

The direct solution of optimization problem in (5) is very computation complexity. This is because the optimization problem is a mixed binary integer programming problem, which involves the continue variable pk,n and discrete binary index ρk,n . Furthermore, the optimization problem in (5) is not a convex optimization problem, thus it can not use the convex optimization method directly to find the optimal solution. However, we can give a heuristic optimal algorithm to realize optimal sub-channels and power allocation for SUs as follows. We firstly exhaustively search over all possible sub-channels

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combination for SUs. Then for each combination, we can do the optimal power allocation under the constraints condition. The optimal power allocation scheme will be proposed in section III.C. Finally we can select a optimal solution from all possible combination. However, the heuristic optimal algorithm induces the problem of computation complexity. B. Suboptimal Sub-Channels Allocation for SUs In this subsection, we give a suboptimal sub-channels allocation for SUs based on [10]. We first assume that the power is allocated equally to all idle sub-channels and let the channel|h |2 to-noise ratio is Gk,n = k,n n0 . Then the detail sub-channels allocation algorithm is as follows Algorithm1: Suboptimal Sub-Channels Allocation 1) Initialization: Let Rk = 0, Ωk = ∅ for ∀k ∈ KA ∪ KB and N = {1, 2, . . . , N }. 2) For k = 1 to K1 + K2 do a) Calculate the Gk,n and find n∗ = arg max |Gk,n |, n∈N

b) Let Ωk = Ωk ∪{n∗ } and N = N −{n∗ }, then calculate the capacity Rk as (4). 3) While N = ∅ do a) Find the SU k ∗ = arg min Rk , k

b) Find the n∗ = arg max |Gk∗ ,n |, n∈N ∗

c) Let Ωk∗ = Ωk∗ ∪ {n } and N = N − {n∗ } for the selected k ∗ and n∗ , and calculate Rk∗ as (4). In the algorithm 1, we always assign the sub-channels to the SU with best channel-to-noise ratio. And in the iteration process, we allocate the sub-channels to the SU with low rate. Furthermore, we let K1+K2 ≤ N to guarantee that each SU can obtain at least one sub-channel. And this condition can be easily satisfied in the phase of admission control. Alternatively, for the case of K1+K2 ≥ N , we may relax the sub-channel constraints condition and allow each sub-channel shared by SUs which will be considered in the future. C. Optimal Power Allocation for SUs Based on the algorithm 1, we let Ωk denote the set of subchannels assigned to SU k. Now we can do the optimal power allocation for SUs to support heterogenous services and we rewrite the optimization problem in (5) as K 2 1 +K2 pk,n |hk,n | (6) log2 1 + max pk,n n0 k=1

n∈Ωk

Subject to : pk,n ≤ Ptotal

K1 +K2 k=1

n∈Ωk K 2

R1 : R2 : ... : RK2 = γ1 : γ2 : ... : γK2 , ∀k ∈ KB

K1 +K2 log2 (1+ pk,n Gk,n )+ L(λ, βk , μk , pk,n ) = k=1 k n∈Ω K1 +K2 K 1 λ pk,n−Ptotal + βk log2 (1+pk,n Gk,n)−Rkmin n∈Ωk k=1 n∈Ωk k=1 K 2 γ1 + μk log2 (1+p1,n G1,n)−γk log2 (1+pk,n Gk,n) n∈Ω1

k=2

k=1 n∈Ωk

Rk,n

= γk ,∀k ∈ KB

n∈Ωk

(8) where λ, βk and μk are the Lagrangian multiplier factors. For ∀k ∈ KA , we can differentiate (8) and get ∂L ∂pk,n

G

G

k,n k,n 1 = ln12 1+Gk,n pk,n +λ+βk ln 2 1+Gk,n pk,n , ∀n∈Ωk

(9)

For ∀k ∈ KB , we differentiate (8) and get G1,n ∂L 1 ∂p1,n = ln 2 1+G1,n p1,n

K 2 G1,n +λ+ μk ln12 1+G1,n p1,n ,∀n∈Ω1

Gk,n ∂L 1 ∂pk,n = ln 2 1+Gk,n pk,n

(10)

k=2

G

k,n +λ−μkγγk1 ln12 1+Gk,n pk,n ,∀n∈Ωk

(11)

Let the (9), (10) and (11) are equal to 0, then for a specific SU k and the corresponding sub-channel set Ωk we have Gk,m Gk,n = 1 + Gk,n pk,n 1 + Gk,m pk,m

(12)

where m, n ∈ Ωk and k ∈{1, 2, . . . , K1 + K2 }. If we assume that the number of sub-channels allocated to SU k is Nk and let Gk,1 ≤ Gk,2 ≤ ... ≤ Gk,Nk without loss of the generality, we can get from (12) pk,n = pk,1 +

Gk,n − Gk,1 , ∀n = {1, 2, . . . , Nk }, ∀k (13) Gk,n Gk,1

So let the total power allocated to SU k is Pk,total , according to (13) we have

n∈Ωk

Rk,n

(7)

Now relying on the [12], the optimization problem in (6) is equivalent to solve the following Lagrangian dual problem

Pk,total =

pk,n ≥ 0, ∀k, ∀n Ωk ∩ Ωi = ∅, ∀k, i ∈ KA ∪ KB Ω 1 ∪ Ω2 ∪ ... ∪ ΩK1 +K2 = {1, 2, ..., N } Rk,n ≥ Rkmin ,∀k ∈ KA n∈Ω k

The optimization problem in (6) is still complex for the last constraint condition. However, inspired by the [11], we can rewrite the last constraint condition equivalently as

Nk

pk,n = Nk pk,1 +

k=1

Nk Gk,n − Gk,1 , ∀k (14) Gk,n Gk,1 n=2

Therefore we can realize the sub-channels power allocation for SU k as (13) and (14). If we transfer the inequality constraint condition of minimum rate guarantee to the equality constraint, according to (13) we can get N k n=1

log2

Gk,n Gk,1 (1

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+ Gk,1 pk,1 ) = Rkmin , ∀k ∈ KA

(15)


1 γ1

=

N1

log2

G1,n G1,1 (1

n=1 N k 1 log2 γk n=1

+ G1,1 p1,1 )

Gk,n Gk,1 (1

+ Gk,1 pk,1 ) , ∀k ∈ KB

(16)

are NP-hard computation complexity. However, for the suboptimal algorithm, the sub-channels allocation requires

O 2N (K1 + K2 ) − (K1 + K2 )2 operations which can reduce the computation complexity significantly.

Then let

IV. S IMULATION R ESULTS Qk =

Nk Gk,n − Gk,1 , ∀k ∈ KA ∪ KB Gk,n Gk,1 n=2

N1 N k k Gk,n Zk = , ∀k ∈ KA ∪ KB Gk,1 n=2

(17)

(18)

In this section, the simulation results are given. We assume that all SUs randomly located in a rectangular area and communication with common control unit. The size of rectangular area is 100 × 100. All SUs experience slow fading in all channels in a time slot. 4

Substitute the (14), (17) and (18) into (16) we have

−Q1 P log2 (1 + G1,1 1,total = ) + log Z 1 2 N 1 Pk,total −Qk log2 (1 + Gk,1 ) + log2 Zk , ∀k ∈ KB Nk

3

(19)

Then we add the following total power constraint K

Capacity (bit/s/Hz)

N1 γ1 Nk γk

Heuristic Optimal Scheme Suboptimal Scheme Existing Scheme

3.5

2.5

2

1.5

Pk,total = Ptotal

(20)

k=1

1

0.5

Therefore we can solve the (K1 +K2 ) equations in (15), (19) and (20) to find the optimal power allocation for SUs. Alternatively, we can use the Newton-Raphson iterative method [11] or [13] to find the power allocation for SUs. After the power allocation for SUs, each SU can realize the optimal subchannels power allocation as (13) and (14). However, if there is Qk > Pk,total for a particular SU k , we know that there is no power allocation by observing (14). In this case, it needs to reallocate the sub-channels and power for SUs. Therefore the suboptimal resource allocation is as follows Suboptimal Sub-Channels and Power Allocation Algorithm 1). Initialization: Determine the number of sub-channels N and SUs K1 and K2 . 2). For k = 1 to K1 + K2 , do Suboptimal channel allocation for SU k as algorithm 1. End for 3). Do the power allocation for SUs 4). If Qk > Pk,total , ∀k, reallocate the sub-channels and power for SUs. 5). Allocate the sub-channels power for each SU as (13), (14). The above suboptimal algorithm can realize the subchannels and power allocation for SUs supporting heterogenous services. And the computation complexity can be reduced which is analyzed in subsection III.D. D. Computation complexity Analysis In this subsection, the computation complexity for heuristic optimal algorithm and suboptimal algorithm are analyzed respectively. Firstly the heuristic optimal algorithm is to exhaustively search over all possible sub-channels combination for SUs. For (K1 + K2 ) SUs and N idle sub-channels, there are (K1 + K2 )N possible combinations. This requires O (K1 + K2 )N operations which

Fig. 1.

0.2

0.4

0.6 Total Power (w)

0.8

1

Total Capacity for Cognitive Radio Networks.

In Fig. 1, we evaluate the performance of proposed algorithm in term of the total capacity over different total power constraints. In the simulation, we assume that there are 2 SUs, 3 idle sub-channels and the K1 /K2 = 1. The existing scheme in the figure means to allocate the sub-channels for SUs randomly. In the figure, we know that the total capacity by the suboptimal scheme is better than the existing scheme. This is because that the suboptimal scheme takes the sub-channels allocation as subsection III.B. Though the performance by heuristic optimal scheme is better than the performance by the suboptimal scheme, the heuristic optimal scheme induce the computation complexity. . In the fig. 2, we evaluate the performance of minimum rate for SUs with minimum rate guarantee. In the simulation, we assume that the number of SUs with minimum rate guarantee is 6 and there are 10 idle sub-channels. The reference minimum rate denotes the minimum rate requirement for SUs. In the figure 2, we know that the minimum rate requirement for SUs is guaranteed by suboptimal scheme. However, method in [4] which is to solve the resource allocation for SUs with only one type of service requirement can not guarantee the minimum rate requirement. In the fig. 3 and fig. 4, we evaluate the performance of total capacity for different ratio of SUs with heterogenous services. The simulation parameters are same with above. From the figure 3, we know that the total capacity is increasing with the total power increasing. Furthermore, when the ratio of SUs increase or the number of K1 increasing, the total capacity is also increasing. This is because that there is a trade-off

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5.8

0.7 Reference Minimum Rate Suboptimal Scheme Method in [5]

(K1+K2)=12 (K1+K2)=18

5.4

0.5

0.4

0.3

0.2

5.2 5 4.8 4.6

0.1

4.4

0

1

2

Fig. 2.

3 4 SUs Index

5

4.2 0.1

6

Minimum Rate for Each SU

Fig. 4.

0.2

0.3

0.4

0.5 0.6 K1/(K1+K2)

0.7

0.8

0.9

Total Capacity for Different Number of SUs.

1.8

4.5 K1/K2=1/2

4

γ(1:1:1:1:1:1) γ(2:1:1:1:1:1) γ(4:1:1:1:1:1)

1.6

K /K =1 1

2

Capacity of each SU (bit/s/Hz)

K1/K2=2

3.5 Capacity (bit/s/Hz)

(K1+K2)=6

5.6

Capacity (bit/s/Hz)

Minimum Rate of each SU(bit/s/Hz)

0.6

3

2.5

2

1.4 1.2 1 0.8 0.6 0.4

1.5

1

Fig. 3.

0.2 0 0.2

0.4

0.6 Total Power (w)

0.8

1

Fig. 5.

Total Capacity for Different SUs’ Ratio.

between the total capacity and the proportional fairness due to the fairness proportional constraint condition. However, in figure 4 with the total number of SUs increasing, the total capacity decreases due to the power and sub-channels resource allocated to each SU decreasing. In fig. 5, we assume that there are not SUs with minimum rata guarantee in CRN and we evaluate the capacity of each SU over the different proportional fairness factor. The simulation parameters are same with the above. From the figure, we know that we can guarantee the proportional fairness for SUs and obtain the expectation capacity for particular SU by adjusting the proportional fairness factor. V. C ONCLUSIONS In this paper, we have studied the problem of resource allocation in cognitive radio networks supporting heterogenous services. The problem of resource allocation was formulated as a mixed integer programming problem. Specifically, we have proposed the heuristic optimal resource allocation algorithm and suboptimal sub-channels and power allocation algorithm. Finally simulation results have shown that the proposed scheme can significantly improve the system performance. R EFERENCES [1] F. C. Commission, “Spectrum policy task force report,” Nov. 2002.

1

2

3

4 SU Index

5

6

Capacity for Each SU.

[2] J. Mitola, “Cognitive radio: An integrated agent architecture for software defined radio,” Ph.D. Dissertation, KTH Royal Institute of Technology, Stockholm, Sweden, 2000. [3] S. Haykin, “Cognitive radio: Brain-empowered wireless communications,” IEEE J. Select. Areas Commun, vol. 23, no. 2, Feb. 2005, pp. 201220. [4] F. F. Digham, “Joint power and channel allocation for cognitive radios.” in Proc. IEEE WCNC’08, Jan. 2008. [5] L. B. Le and E. Hossain, “Resource allocation for spectrum underlay in cognitive radio networks,” IEEE Trans. Wireless Commun., vol. 7, no. 12, Dec. 2008, pp. 5306-5315. [6] Y. Wu and D. H.H., “Distributed power allcation algorithm for spectrum sharing cognitive radio networks with qos guarantee.” in Proc. IEEE INFOCOM 2009, Jan. 2008, pp. 981-989. [7] F. Wang, M. Krunz, and S. g. Cui, “Price-based spectrum management in cognitive radio networks,” IEEE Journal of Selected topicsin signal processing, vol. 2, no. 1, Feb. 2008, pp. 74-87. [8] H. Sampath, S. Talwar, and p. J. Tellado adb V, Erceg abd A, “A fourth-generation mimo-ofdm broadband wireless system: Design, performance, and field trial results,” IEEE Commun. Mag., vol. 40, no. 9, Sep. 2002, pp. 143-149. [9] S. Haykin, D. J. Thomson, and J. H. Reed, “Spectrum sensing for cognitive radio,” Proceedings of the IEEE, vol. 97, no. 5, May. 2009, pp. 849-877. [10] W. Rhee and J. M. Cioffi, “Increasing in capacity of multiuser ofdm system using dynamic subchannel allocation,” vol. 2. in Proc. IEEE Int. Vehicular Tech. CXonf. [11] Z. Shen, J. G. Andrews, and B. L. Evans, “Adaptive resource allocation in multiuser ofdm systems with proportional rate constraints,” IEEE Trans. Wireless Commun., vol. 4, no. 6, Nov. 2005, pp. 2726-2737. [12] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U. K : Cambridge Univ. Press, 2004. [13] R. baldick, “Optimization of engineering systems course notes.” Austin, TX: Univ. Texas.

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