Dynamic User Scheduling For OFDMA Uplink System Sai Qian Zhang

Abstract—User scheduling in a multicell OFDMA uplink system is considered. In this work, we propose a novel frequency subcarrier allocation algorithm based on the proportional fair scheme. To reduce the communication between the base stations and improve the feasibility, other three suboptimal user scheduling methods are further proposed and evaluated. Simulation results show that the four methods achieve a significant improvement on the intercell interference mitigation.

I. I NTRODUCTION OFDMA (orthogonal frequency division multiple access) is one of the very promising multiple access schemes, and has been treated as the best candidate among the multiple access schemes for the cutting-edge wireless communication system such as WiMAX and IEEE 802.16e. However, it is widely known that the intercell interference is one of the main limiting factor of the performance of the OFDMA wireless system and a lot of scheduling techniques has been developed to mitigate the effect on the overall performance of the wireless network taken by the intercell interference. There are a lot of previous work which focus on the single cell scheduling. In [1,2,3] the power allocation problem is separated with the user scheduling problem: a set of users with the best channel conditions are picked first and the power is allocated to these users based on the water-filling algorithm. To increase the fairness of the scheduling method, some utility functions are further proposed to ensure the users receive the fair amount of power and fair number of subcarriers. In [4], the logarithm of the transmission rate of the users is regarded as the object function, which effectively ensure the fairness of the algorithm. Some other previous work concentrates on the multi-cell scenario and try to mitigate the effect taken by the intercell interference. Several techniques are proposed, including fractional frequency reuse scheme, dynamic frequency reuse scheme. For the Fractional Frequency Reuse (FFR) scheme, one cell is divided into an inner region and three outer regions [5]. All the inner regions in the different cells share a common frequency subcarrier and the rest of the subcarriers are allocated to the different outer regions according to their geometric location. A more sophisticated scheme of FFR was further proposed in [6], which divides each cell into three regions, and a similar frequency reuse scheme was applied. This enhanced FFR scheme shows a better result of interference mitigation. Dynamic frequency reuse scheme allows the subcarriers to be allocated anywhere in the cell and several techniques are proposed based on that. In [7], a power allocation and a user

scheduling algorithm are proposed to mitigate the intercell interference by deactivating the base stations in the cell as long as the cell cannot provide enough uplink rate for users to compensate the intercell interference caused to the overall wireless network. Moreover, game theory and pricing theory have been widely used for mitigating the intercell interference, such as [8],[9]. However, these works assume the user knows the channel state information, the power allocation and the subcarrier allocation of all the other users in the network. Besides the techniques mentioned above,there are some other general techniques for the uplink scheduling.In the Round robin method, the subcarriers are assigned to every user randomly which ensures that every user has at least one subcarrier for uplink and downlink transmission. However, this method completely neglects the intercell interference and the performance is not ideal. The other general technique is the downlink duality method, which figures out the downlink scheduling by using the proportional fair method, and applying the same scheduling scheme for the uplink scheduling. This method improves the overall uplink performance to some extent. However, this is certainly not the optimal scheduling method. In this work, a greedy iteration algorithm of user scheduling which effectively improves the log utility of average uplink rate is proposed for OFDMA system. This algorithm is much simpler than the algorithms presented in the previous work and it gives a very promising results. Furthermore, in order to reduce the amount of co-operations between the base stations, another three suboptimal user scheduling methods are further proposed and evaluated. II. S YSTEM M ODEL This work assumes an multicell cellular system with L cells, S sectors per cell and K users per sector, and an OFDMA scheme with N frequency tones over a limited bandwidth, an example of such a model is shown in Fig1.The work also assumes that both the base stations and the mobile users are equipped with single antenna and a fixed amount of power is allocated to user antenna and base station antenna. Finally, this work assumes that the wireless network can generate a suitable fading channel model between every pair of user antenna and the base station antenna across every frequency tone. The dynamic frequency reuse technique is employed in this design, means that several users across the sectors are served at the same frequency tone and time slot.

n SIN RU,lsk =

2.5 Base Station Mobile User

2

n n PU |Hls,lsk(l,s,n) |2 n |H n P |2 (v,t)̸=(l,s) U ls,vtk(v,t,n)

∑

n Here, RU,l,s,k(l,s,n) is the instantaneous uplink rate the base station of the lth cell and the sth sector receive from the kth user of the lth cell and the sth sector on frequency tone n n. Hls,vtk(v,t,n) denotes the complex channel gain between the cochannel user of the vth cell, tth sector and the base station of the lth cell, sth sector on frequency tone n. PUn is the power allocated on the user antenna on frequency tone n, and is assumed to be a fixed value in this work. δ 2 is the background noise.

1.5 1 0.5 0 −0.5 −1 −1.5 −2

III. M ETHODOLOGY

−2.5 −2.5

The crucial problem of the uplink user scheduling is how ˜ n in each sector such that to select a set of co-channel users k every user has the satisfactory uplink rate. It is reasonable to apply log utility function as the object function, and it is well known that a proportional fair allocation maximizes the sum of logarithmic average user rates because the derivative of the log function is R¯ n 1 .Therefore, for each frequency tone, U,l,s,k(l,s,n) the users should be activated to maximize the proportional fairness function. That is: 1 wk(l,s,n) = ¯ n (4) RU,l,s,k(l,s,n)

−2

−1.5

−1

−0.5

Fig. 1.

0

0.5

1

1.5

2

System Model.

The work wants to address the following problem: Assume the fixed amount of power is allocated to every user antenna, and given the total amount of frequency tones in each sector, how to allocate the frequency tones to the users across the cells such that the log utility function is maximized. Seeing that several users are served in the same frequency and time slot, the uplink transmission rate from the user antenna to the base station antenna are seriously limited by the strong interference between the user antennas, therefore, a suitable frequency allocation algorithm is necessary to improve the uplink transmission performance. Indicate with k(l,s,n) the user served by base station of the lth cell, sth sector on tone n, so a set ˜n = of co-channel users can be further defined as k (k(1, 1, n), k(1, 2, n), ...., k(L, S, n))T . Moreover, a set of ac˜ = vec(k ˜1, k ˜ 2 , ...., k ˜n) tive users can be further defined as k The uplink optimization problem can be formulized as following: arg max ˜ k

L ∑ S ∑ N ∑

n wk(l,s,n) RU,l,s,k(l,s,n)

(1)

l=1 s=1 n=1

˜ n such that Or find k L ∑ S ∑

¯n Where R U,l,s,k(l,s,n) is the long-term averaged uplink rate that the base station of the lth cell, sth sector receive from the kth user of the lth cell, sth sector on frequency tone n. And we can update the long-term average uplink rate by using n ¯n ¯n R U,l,s,k(l,s,n) = aRU,l,s,k(l,s,n) + (1 − a)RU,l,s,k(l,s,n) (5)

A. Problem Statement

n wk(l,s,n) RU,l,s,k(l,s,n)

(2)

l=1 s=1

is maximized for n=1,2....,N where n n RU,l,s,k(l,s,n) = log(1 + SIN RU,lsk )

and

δ2 +

∀l, s, k

(3)

for some 0 < a < 1. Here are some methods to solve this optimization problem: (For the ease of explanation, define the total number of the sectors in the system to be ST .) A. Greedy iteration method This algorithm is described by the following steps: Step0 Set n=1; Step1 Randomly select one user from each sector which forms a ST dimensional vector of cochannel users; Step2 Set s=1; Step3 Fix the cochannel users in sector p (p ∈ [1, 2, ...., ST ], p ̸= s) and find the user in sth sector by exhaustive search such that the weighted sum rate of (2) get maximized; Step4 Given the approximated expression of the weighted sum rate (6), find the user in the sth sector by exhaustive search who maximizes (6),by fixing the cochannel users in sector p; Step5 Set s=s+1; Step6 Go to step3 and stop when s = ST + 1; Step7 Go to step2 and stop when (2) converges; Step8 Update the long term average according to (5);

Step7 Step8 Step9 Step10

3500

weighted sum rate

3000

Go to step2 and stop when (2) converges; Update the long term average according to (5); Set n=n+1; Go to step1 and stop when n = N+1;

2500

This method significantly reduces communication between the base stations during every iteration because while exhaustively searching the uplink user in one sector, the base station only need to talk with a part of the base stations (q out of ST base stations) to make the user selection decision. q users with the lowest long-term average uplink rate are chosen because they are the dominant factors of (1).

2000

1500

1000

500

1

2

3

4

5 6 iteration times

7

8

9

10

C. Single activated suboptimal iteration method Fig. 2.

Step9 Step10

Convergence of weighted sum rate on 10 random frequency tones

Set n=n+1; Go to step1 and stop when n = N+1;

(2) must converge to local maximum after some iterations because the greedy iteration method promises that (2) keeps increasing after each iteration, and we know that (2) cannot increase without any limitation, it inevitably converges to the local maximum (Fig2). The disadvantage of this method is that it requires a lot of co-operation and communication between base stations while doing the iteration process because to select the user in one sector, the base stations in this sector has to ask n for the instantaneous uplink rate RU,l,s,k(l,s,n) and the longn ¯ term average uplink rate RU,l,s,k(l,s,n) of each user of the other sectors. To reduce the communication among the base stations, a suboptimal method is proposed next. B. Suboptimal iteration method This algorithm is described by the following steps: Step0 Set n=1; Step1 Randomly select one user from each sector which ˜n; forms a ST dimensional vector of cochannel users k Step2 Set s=1; Step3 Assume for each sector there are S ′ neighbour ˜ n′ ⊆ k ˜ n to be the sectors. Define S ′ dimensional vector k S set of cochannel users in the neighbour sectors of sector s, ˜ n ′ , i.e. k ˜n ⊆ k ˜ n ′ who have choose q (q < S ′ ) users from k q S S the highest weight wk(s,n) , and define the weighted sum rate of the q users to be ∑ n wk(l,s,n) RU,l,s,k(l,s,n) (6) ˜n (l,s):k(l,s,n)∈k q

Step4 Given the approximated expression of the weighted sum rate (6), find the user in the sth sector by exhaustive search who maximizes (6),by fixing the cochannel users in sector p(p ∈ [1, 2, ...., ST ], p ̸= s); Step5 Set s=s+1; Step6 Go to step3 and stop when s = ST + 1;

This algorithm is described by the following steps: Step0 Set n=1; Step1 Randomly select one user from each sector which ˜n; forms a ST dimensional vector of cochannel users k Step2 Set s=1; Step3 define the weighted uplink rate of a user in sth n sector and lth cell to be wk(l,s,n) RU,l,s,k(l,s,n) ,find the user in the sth sector by exhaustive search who has the largest weighted uplink rate. Step4 Set s=s+1; Step5 Go to step3 and stop when s = ST + 1; Step6 Go to step2 and stop when (2) converges; Step7 Update the long term average according to (5); Step8 Set n=n+1; Step9 Go to step1 and stop when n = N+1;

This method requires no communication between the base stations since all the cochannel users are selected based on the internal channel state information. D. Comparison method Before going to the detail of this method, we need define some terms: Define the user of lth cell and sth sector with maximum self-weighted uplink rate as: max k(l,s,n)

L ∑ S ∑

n wk(l,s,n) RU,l,s,k(l,s,n)

l=1 s=1

Where n n RU,l,s,k(l,s,n) = log(1 + SIN RU,lsk )

And n SIN RU,lsk =

n n PU |Hls,lsk(l,s,n) |2 δ2

(7)

Define the mutual-weighted uplink rate Aq of a user ˜ n with q users inside as: group k q ∑ n wk(l,s,n) RU,l,s,k(l,s,n) (8) Aq = ˜n (l,s):k(l,s,n)∈k q

Where n n RU,l,s,k(l,s,n) = log(1 + SIN RU,lsk )

And n SIN RU,lsk =

n n PU |Hls,lsk(l,s,n) |2 n n 2 ˜ n (v,t)̸=(l,s) PU |Hls,vtk(v,t,n) | (v,t):k(v,t,n)∈k

∑

δ2 +

q

This algorithm is described by the following steps: Step0 Set n=1; Step1 Find the user who has the largest self-weighted uplink rate in every sector, which forms a ST dimensional ˜n; vector of cochannel users k Step2 Initialize an empty user set B n ; ˜ n who has the largest selfStep3 Find the user in k weighted uplink rate, add the user to B n ,denote the sector where the user is located by p1 ; Step4 Set q=2; Step5 Randomly pick another sector pq , find the user in sector p with the largest self-weighted uplink rate, add this user to B n ; Step6 Calculate the mutual-weighted uplink Aq of B n ; Step7 Set q=q+1; Step8 Go to step5 and stop when q = ST + 1 or Aq < Aq−1 ; Step9 Update the long term average according to (5); Step10 Set n=n+1; Step11 Go to step1 and stop when n = N+1;

This method significantly reduces the communication between the base stations because every base station only need to know the channel state information of the users who has the largest self-weighted uplink rate. By comparison, the greedy iteration method assumes the base stations know the channel state information of every user of every sector. E. Greedy comparison method This algorithm is described by the following steps: Step0 Set n=1; Step1 Initialize an empty user set B n ; Step2 Set q=1; Step3 Randomly select a sector p1 and randomly select a user k1 in this sector, add this user to B n ; Step4 Set q=q+1; Step5 Randomly select another sector pq , randomly select a user kq in this sector, add this user to B n ; Step6 Set s=1; Step7 Fix the cochannel users in all the sectors selected in step 3 and 5 except the cochannel user in sector ps , find

the user in sector ps such that mutual-weighted uplink Aq of Bn get maximized; Step8 Set s=s+1; Step9 Go to step7 and stop when s=q+1; Step10 Go to step6 and stop when (8) converges; Step11 Go to step4 and stop when q = ST + 1 or Aq < Aq − 1; Step12 Update the long term average according to (5); Step13 Set n=n+1; Step14 Go to step1 and stop when n=N+1; This method significantly reduces communication between the base stations during every iteration because while exhaustively searching the uplink user in one sector, the base station only need to talk with a part of the base stations (q out of ST base stations) to make the user selection decision. q users with the lowest long-term average uplink rate are chosen because they are the dominant factors of (1). IV. S IMULATION The performance of the proposed algorithms together with the baseline algorithms are evaluated in a cellular system with 7 cells, 3 sectors per cell, 20 users per sector, and the cells are wrapped around to make sure there are 6 neighbors for each cell. Each base station is equipped with single antenna, each user is equipped with single antenna. Detailed settings are contained in table I: TABLE I BASIC SIMULATION SETTING

Cellular layout BS-to-BS Distance Number of users per sector Power allocated to each antenna Background Noise FFT Size BS antenna No. User antenna No.

Hexagonal, 7 cells 3 sector/cell 1.5km 20 -27dbm/Hz -162dbm/Hz 64 1 1

The cumulative distribution curves of the following seven methods are compared in Fig3, round robin method and downlink duality method which are presented in the introduction part are used as the benchmark of the proposed methods: 1. 2. 3. 4. 5. 6. 7.

Round robin Downlink duality Suboptimal iteration method Single activated suboptimal iteration method Greedy comparison method Greedy iteration method Comparison method

As you can see in Figure 3, the greedy iteration gives

TABLE III LOG UTILITY FOR THE FOUR METHODS

1 0.9 round robin comparison greedy iteration downlink duality greedy comparison single activated suboptimal iteration method

0.8 0.7

cdf

0.6 0.5

method

number of communications

Greedy iteration method Suboptimal iteration method Greedy comparison method Comparison method

1852200 205800 10672000(worst case) 40320(worst case)

0.4 0.3

V. C ONCLUSION

0.2 0.1 0

0

1

Fig. 3.

2 3 uplink rate(bps)

4

5 6

x 10

cdf plots for the six methods

the best performance, followed by the suboptimal iteration method, greedy comparison method, comparison method and single activated suboptimal iteration method. The figure also shows that these five methods give a significant improvement on the log-utility compared with two baseline methods. Table II shows the log utility for the four methods with different B2B distance. As you can see from table II, the B2B TABLE II LOG UTILITY FOR THE FOUR METHODS

method/distance

0.7km

1.5km

Greedy iteration method Suboptimal iteration method Greedy comparison method Comparison method Single activated

8309.9 8200.3 8122.2 8007.1 7996.1

8316.1 8218.8 8172.8 8041.4 8020.2

distance also affects the performance of the wireless uplink network, the wireless network with a smaller B2B distance performs worse than the wireless network with a larger B2B distance. This is because a smaller B2B distance causes the increase on the intercell interference which seriously impairs the quality of the uplink signal. Complexity analysis: TableIII shows the total number of communication that has been made between base stations which is under scheduling and the other base stations for total 64 frequency tones assignment: From the aspect of calculation complexity, besides from the single activated iteration method which does not require communication among the base stations, the comparison method and suboptimal iteration method require relatively less communication among the base stations. By comparison, the greedy iteration method and greedy comparison method require too much communication among the base stations.

In this work, a greedy iteration method for the user scheduling in the OFDMA multicell schemes is proposed which effectively mitigates the intercell interference. To reduce the communications among the base stations, three suboptimal user scheduling methods are further proposed and evaluated. These three suboptimal methods show satisfactory results of intercell interference mitigation, and require much less cooperations between the base stations across the sectors.

R EFERENCES [1] G. Song and Y. Li, “Cross-Layer Optimization for OFDM Wireless Networks-Part I: Theoretical Framework” IEEE Trans. Wireless commun., vol. 4, no.2, pp. 614-624, March 2005 [2] G. Song and Y. Li, “Cross-Layer Optimization for OFDM Wireless Networks-Part II: Theoretical Framework” IEEE Trans. Wireless commun., vol. 4, no.2, pp. 625-634, March 2005 [3] G. Song and Y. Li, “Adaptive Subcarrier and Power Allocation in OFDM Based on Maximizing Utility” IEEE VTC-Spring 2003, vol. 2, pp. 905909, April 2003 [4] P.Viswanath, D.N.C. Tse, R Laroia, “Opportunistic Beamforing Using Dumb Antennas” IEEE Trans. Inform. Theory, vol. 48, no. 6, pp. 12771294, June. 2002. [5] H. Fuijii and H. Yoshino, “Theoretical Capacity and Outage Rate of OFDMA Cellular System with Fractional Frequency Reuse” IEEE VTCSpring 2008, May. 2008. [6] R. Kwan and C. Leung, “A survey of Scheduling and Interference Mitigation in LTE” Journal of Electrical and Computer Engineering, Article ID 273486, Vol. 2010,2010. [7] S.G. Kiani, G.E. Oien, and D. Gesbert, “Maximizing Multicell Capacity Using Distributed Power Allocation And Scheduling” IEEE WCNC 2007, March. 2007. [8] J, Huang R.A. Berry, and M. L. Honig, “Distributed Interference Compensation for Wireless Networks” IEEE J.Sel.Areas Commun., vol. 25, no.5, pp. 1074-1084, May 2006 [9] Q. Jing and Z. Zheng, “Distributed Resource Allocation Based on Game Theory in Multi-cell OFDMA Systems” International Journal of Wireless Information Networks, vol. 16, pp. 44-50, 2009