The Analysis of the Optimal Periodic Ranging Slot Number in IEEE 802.16 OFDMA Systems

Jihua Zhou1 2, Xin Jin1 2, Jiangtao Dong1, Jinglin Shi1, Zhongcheng Li1 1Institute of Computing Technology, Chinese Academy of Sciences

2Graduate University of the Chinese Academy of Sciences E-mail:{jhzhou, jinxin, dongjiangtao, sjl, zcli}@ict.ac.cn

Abstract

As part of the IEEE 802.16 protocol, the random access scheme is used for ranging. The ratio between the numbers of periodic ranging slots and data slots in the uplink subframe decides the contention throughput, ranging delay and data throughput, all of which are important parameters of the system performance. However no specific ratio is standardized in the protocol. So, it is necessary to determine the optimal number of periodic ranging slots which is the decisive factor of the ratio. In this paper, the three parameters above are analyzed and the optimal number of the periodic ranging slots is derived. In addition, an estimation method is proposed to predict the number of contention users. The correctness of the analysis is verified by the simulation results, and it is demonstrated that the contention throughput efficiency is high with the derived optimal number. 1. Introduction

IEEE 802.16 [1] and 802.16e [2] have been standardized to provide fixed and mobile solutions for broadband wireless access systems in metropolitan area networks. In IEEE 802.16 orthogonal frequency division multiple access (OFDMA) mode, the total available bandwidth is divided into multiple logic subchannels in frequency domain. In time domain, a frame is composed of lots of OFDMA symbols, and can be divided into a downlink subframe and an uplink subframe. A slot is one subchannel by multiple OFDMA symbols, and a region is a two-dimensional allocation of a group of contiguous subchannels, in a group of contiguous OFDMA symbols.

An uplink subframe can be divided into a periodic ranging region and a data region as shown in Fig. 1. The periodic ranging region is used for subscriber stations (SSs) to contend for transmitting CDMA

codes, in order to adjust power offset, frequency offset and timing offset, or request bandwidth resource from the base station (BS). The data region is used for transmitting data, such as user packets and management messages. For simplicity, slots in the periodic ranging region are called periodic ranging slots, and slots in the data ranging are called data slots. A SS randomly selects a slot in the periodic ranging region to transmit a CDMA code, so collisions occur when multiple SSs select the same slot. No collisions will occur in a data slot as the BS will not schedule more than one SS to transmit on a given slot.

The ratio between the number of the periodic ranging slots and the number of the data slots affects the system performance. On the one hand, increasing the number of the periodic ranging slots is highly desirable when there are excessive contention users who perform periodic ranging or transmit bandwidth requests in the periodic ranging region. However, this decreases data throughput since the number of data slots is reduced. On the other hand, decreasing the number of periodic ranging slots would increase the delay of the periodic ranging process. Evidently, a different number of periodic ranging users needs a different number of periodic ranging slots, and the BS scheduler might allocate various numbers of uplink slots according to the bandwidth requirement. Hence the number of periodic ranging slots is affected by the numbers of contention users and uplink slots, and

Figure 1. 802.16 OFDMA frame structure

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dynamic control of the number of periodic ranging slots can achieve the best system performance. In this paper, we aim at deriving the optimum of periodic ranging slots given the numbers of contention users and uplink slots. Firstly, ranging delay, contention ratio and contention throughput of the system are analyzed. After that, an objective function including ranging delay and contention ratio is defined, and then the equation for the optimal number of periodic ranging slots is derived. With the determined number, we show that the contention throughput is considerably high.

The rest of the paper is organized as follows. Section 2 outlines the related work. Section 3 introduces the system model. In section 4, we analyze ranging delay, contention ratio and contention throughput, and derive the optimal number of periodic ranging slots. Simulation and numerical results are given in section 5, which is followed by our conclusions in section 6. 2. Related work

The optimal number of periodic ranging slots can be viewed as the key parameter which decides the ranging delay and throughput of the IEEE 802.16 OFDMA system. However, to the best of our knowledge, there have been no previous proposals on this problem. To some extent, the period of ranging slots can be regarded as a reservation period [8], because these two periods have the same feature of random contention access. There have been several papers tackling the reservation period. Vinel etc. analyzed the performance of the random access in the IEEE 802.16 protocol in [3]. However, they had not presented the optimal number of ranging slots, because the contention period was assumed to be fixed in their work. In [4], Iyengar etc. derived average delay for a packet in the 802.16 system, but they ignored to analyze the ranging delay for periodic ranging process. Other authors in [5]-[9] proposed some static or adaptive reservation period allocation mechanisms. In their proposals, the reservation period is used for transmitting reservation request messages, and it is assumed that the amount of data to be transmitted during the service period [8] is tightly related to the successful reservation request messages. Nevertheless, the assumption is not applicable to our problem, because the amount of data to be transmitted in the data region is not affected by the number of users who transmit CDMA codes to perform ranging in periodic ranging region. As a result, the mechanisms they proposed can not be adopted in our system, and can

not obtain the optimum of periodic ranging slots in IEEE 802.16 OFDMA system.

3. System model

The periodic ranging slots are used to perform periodic ranging or contend for requesting bandwidth resource. All SSs need periodic ranging process for channel parameters correctness. Besides, a SS may use periodic ranging slots to request bandwidth from BS especially when no special bandwidth request opportunity is available for this SS in data region.

At the start of each frame, a SS who prepared to perform periodic ranging or request bandwidth in contention manner randomly selects a slot in periodic ranging region to transmit a CDMA code. If more than one CDMA code is concurrently transmitted in a periodic ranging slot, a collision is generated in the slot. Then the collided SS randomly reselects a ranging slot to retransmit the CDMA code in the next frame.

The users who perform periodic ranging are called periodic ranging users. The users who transmit CDMA bandwidth requests in periodic ranging region are called CDMA BWR users. To analyze the system performance and derive the optimal number of periodic ranging slots, the following is assumed.

1) The CDMA code is uniformly distributed during periodic ranging slots.

2) The contention users are composed of the periodic ranging users and the CDMA BWR users.

3) In a frame, the contention users include collided users in the previous frames and new contention users in the current frame.

4) BS allocates the periodic ranging region at the start of each frame.

4. Performance analysis

The frames needed until a SS successfully transmits a CDMA code to complete a ranging process are called ranging frames. The slots used to transmit CDMA codes successfully are called successful slots. Ranging delay, contention ratio and contention throughput are defined as follows.

( )Ranging Delay D The number of ranging frames =

( )( )

The number of periodic ranging slots SContention Ratio R

The number of data slots

=

( )( )

( )

The number of successful slots AContention Throughupt T

The total number of periodic ranging slots S

=

There is a trade-off between ranging delay and

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contention ratio. Moreover, the ranging delay and contention throughput interact with each other. Hence we will define the objective function that includes ranging delay and contention ratio, and derive the optimal number of the periodic ranging slots, with which the contention throughput is obtained. In addition, the estimation method for predicting the number of contention users in a frame is presented.

4.1. Ranging delay analysis

Since the CDMA code is uniformly distributed during S periodic ranging slots, the probability that one user selects a particular slot is 1/S. Collisions will not occur only if no other user selects this slot. Thus, given W users, the probability of transmitting a CDMA code successfully in a slot can be expressed as:

( ) 1' 1 1( , ) 1

W

P W SS S

−

= − . (1)

Let P’’(W,S) be the probability of transmitting a CDMA code successfully in a frame. Applying the probability (1) to all S slots, P’’(W,S) can be derived as:

( ) 1'' ' 1( , ) ( , ) 1

W

P W S SP W SS

−

= = − . (2)

Therefore, the probability of a user colliding with others in a frame is given by:

( ) 1''' 1( , ) 1 1

W

P W SS

−

= − − . (3)

The probability of successfully transmitting a CDMA code in the kth frame PW,S(k) can be derived as:

( )( ) 1'' ''', ( )

k

W SP k P P−

= . (4)

Using ( )21 1

kk k γ

γγ

∞

=−

∑ , the ranging delay D is

given by:

( ) ( )

( ) ( )

'''''

, '''1 1

'' '''

''' 2 11'''

111

k

k W S k

WS

PD kP k k PP

P PP P

∞ ∞

−

= =

= =−−

∑ ∑. (5)

4.2. Contention ratio analysis

According to the definition of contention ratio, it can be denoted by R as:

SRN S

=− (6)

where N is the total number of uplink slots. Notably, with the increase of S, (N-S) decreases,

whereas R increases, and data throughput is in the direct proportion to (N-S) which is the number of data slots. Therefore, data throughput and contention ratio have an inverse correlation.

4.3. Contention throughput analysis

Note that the number of successful slots is equal to the number of contention users who do not collided with others. Thus, according to (2), the number of successful slots in a frame denoted by A is given by:

( ) 111W

A WS

−

= − . (7)

Therefore, the contention throughput denoted by T is

( ) 111WA WT

S S S

−

= = − . (8)

To obtain the maximum contention throughput denoted by Tmax, we differentiate (8) with respect to S. Then it is revealed that the contention throughput reaches its maximum when the number of periodic ranging slots S equals to the number of contention users W. The maximum contention throughput in theory is given by:

( ) 111W

maxTW

−

= − . (9)

4.4 Optimum of the Periodic Ranging Slots

According to the analysis above, note that as the number of ranging slots increases, the ranging delay D decreases, whereas contention ratio R increases. Nevertheless, the increase of R will decrease data throughput. So, there is a trade-off between D and R in terms of the system performance. In order to get the optimal number of periodic ranging slots, we define the objective function denoted by f(W,N,S) including D and R as:

( ) ( )11( , , )

1W

S

Sf W N S DRN S−= =

− −. (10)

Function f(W,N,S) produces the optimal value when both D and R are small. Thus, the optimal number of the periodic ranging slots can be obtained when f(W, N, S) is the minimum value. We differentiate (10) with respect to S, and then derive the optimal number of the periodic ranging slots is

1NWS

N W=

+ − . (11)

When (N+W) >> 1, NWS

N W≈

+ .

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4.5 Estimation of the contention user number

At the start of a frame, the BS can not know the exact number of contention users in this frame, because periodic ranging and bandwidth request decision is made by a SS on its own, which is not controlled by the BS. From (11), it is observed that the number of contention users W is important for the optimal number of the periodic ranging slots. Therefore, the number of contention users in the current frame should be estimated before the periodic ranging region is allocated.

The BS knows the total number of registered users denoted by Utot in a frame. Let Upr be the number of periodic ranging users, and let Ubwr be the number of CDMA BWR users. We define ranging ratio (α’) and request ratio (β’) in a frame as:

( ))

( )'

pr

tot

Number of the period ranging users URanging ratio

Total number of the registered users Uα

( =

,

( ))

( )'

bwr

tot

Number of the CDMA BWR users URequest ratio

Total number of the registered users Uβ

( =

.

Because the ranging ratio is statistically stable, the ranging ratio (αk) in the kth frame can be estimated from the ranging ratios in the previous λ frames. λ is a system parameter which determines the estimation precision. αk can be expressed as:

11 'k

k i ik λ

α αλ−

−

= ∑ , (12)

where α’i is given by: 'pr

ii tot

i

UU

α = . (13)

Similarly, the request ratio βk can be expressed as: 11 '

k

k i ik λ

β βλ−

−

= ∑ , (14)

where β’i is given by: 'bwi

i toti

UU

β = . (15)

According to (12), (13), (14) and (15), the number of contention users in the kth frame denoted by Wk is derived as:

( )(

)1 1 1

1 1 1

' '' '

totk k k k

k k ktot

k k k k

W U

Uλ

λ

α βα α αβ β β

− − − −

− − − −

= + = + − + + −

. (16)

Therefore, the optimal number of periodic ranging slots in the kth frame denoted by Sk is given by:

1k k

kk k

N WS

N W=

+ − , (17)

where Wk is expressed as (16) and Nk is a known number which is determined by the BS scheduler.

5. Numerical and simulation results

In this section, we analyze the mathematical results of the ranging delay, contention throughput, objective function, and the optimal number of ranging slots. In order to verify the correctness of the analysis, we conduct extensive simulations. The analytical results match the simulation ones quite well, which validates the correctness of our analysis in this paper. In the following figures, the analytical results are represented as lines and the corresponding simulation results are represented as symbols near the lines. In the discussion below, N (e.g. 100, 200, 400, 800) denotes the total number of uplink slots, W (e.g. 10, 20, 50, 100, 200, 400) denotes the total number of the registered users, and S denotes the number of periodic ranging slots. Besides, the ranging ratio α equals to 0.4, and the request ratio β also equals to 0.4.

5.1 Ranging Delay

Fig. 2 shows ranging delay for various S and W. It is observed that the mathematical results are very close to the simulation results. In Fig. 2, the ranging delay rapidly decreases while the number of periodic ranging slots increases, and it is not larger than 5 frames when S exceeds 50 and W becomes less than 100.

5.2 Objective Function

Fig. 3 illustrates the objective function with the number of uplink slots equals to 400. Fig. 4 illustrates the objective function with the number of the registered users is equal to 200. It is observed that the value of S, with which the objective function reaches its minimum, meets the expression given by (11).

Figure 2. The ranging delay

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In Fig. 3, when the number of the registered users is fixed, the objective function rapidly decreases at first and then increases slowly. Consequently, we can find the optimal value of S when the value of the objective function decreases to its minimum.

5.3 Optimal Number of Periodic Ranging Slots

Fig. 5 illustrates the optimal number of periodic ranging slots for different number of the registered users. The figure depicts that as the numbers of uplink slots and registered users increase, the optimum of S increases, whereas the increasing rate of the optimum becomes slow when the number of registered users gets larger.

The sum of the numbers of registered users and uplink slots is much larger than 1 in a practical system, so we can conclude that the optimum of S is approximately the product of the numbers of the registered users and uplink slots divided by the sum of these two numbers. If BS allocates periodic ranging

Figure 3. The objective function

with 400 uplink slots

Figure 4. The objective function

with 200 registered users

slots in view of this optimal number, the system is able to achieve the best performance.

5.4 Contention Throughput

Fig. 6 presents the contention throughput for different number of registered users. Because the analytical and mathematical results are well matched, the contention throughput represented by (8) as derived in section Ⅳ is correct. According to Fig. 6, as S increases, the contention throughput increases rapidly at first and then decreases slowly. Furthermore, the fewer the registered users are, the sooner the contention throughput reaches its maximum and the more rapid the decreasing rate becomes.

In Fig. 7, the top line represents the theoretical optimum of contention throughput given by (9), about 37%. The other lines depict the contention throughput for different number of uplink slots (N) with the optimum of S given by (11), and the cross symbol on each line indicates the average throughput.

Figure 5. The optimal number of periodic

ranging slots for different uplink slots

Figure 6. The contention throughput

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Figure 7. The contention throughput with optimal number of ranging slots

To analyze the effect of optimal S on contention

throughput, we define contention throughput efficiency ε as:

( )( )

avg

opt

The average contention throughput TThe optimal contention throughput T

ε

= .

Table 1 summarizes the contention throughput efficiency for different N.

TABLE 1 Contention Throughput Efficiency

with the Optimal Number

According to Tabel 1, the contention throughput

efficiency ε increases with the number of uplink slots N. When N is 100, ε is near to 60%, and when N is larger than 400, ε exceeds 90%. We hereby conclude that the contention throughput is considerably high with the optimal number of periodic ranging slots. 6. Conclusion

IEEE 802.16 system performance is affected by the number of periodic ranging slots in uplink subframe. To maximize the performance of the system, it is required to obtain the optimal number of periodic

ranging slots. In this paper, we analyzed the ranging delay, contention ratio and contention throughput of the system, and then defined an objective function including ranging delay and contention ratio, and derived the optimal number of periodic ranging slots. In addition, we proposed an estimation method to predict the number of contention users which is a decisive factor of the optimal number. By comparing the analytical and simulation results, we verified the correctness of the analysis. It is found that the optimal number of periodic ranging slots is approximately the product of the numbers of contention users and uplink slots divided by the sum of these two numbers. Based on the optimal number, we demonstrate that the contention throughput efficiency is considerably high. References [1] IEEE, “Standard for local and metropolitan area networks part 16: air interface for fixed broadband wireless access systems,” IEEE 802.16-2004, Oct. 2004. [2] IEEE, “Amendment 2: Physical and medium access control layers for combined fixed and mobile operation in licensed bands,” IEEE 802.16e, Dec. 2005. [3] A. Vinel, Y. Zhang, M. Lott and A. Tiurlikov, “Performance analysis of the random access in IEEE 802.16,” Proc. IEEE Int Personal, Indoor, and Mobile Radio Communication Systems, 2005, pp. 1596-1600. [4] R. Iyengar, P. Iyer, and B. Sikdar, “Delay analysis of 802.16 based last mile wireless networks,” Proc. IEEE GLOBECOM, Nov. 2005, pp. 3123-3127. [5] K. Sriram, and P. D. Magil, “Enhanced throughput efficiency by use of dynamically variable request minislots in MAC protocols for HFC and wireless access networks,” Kluwer academic publishers, Telecommunication Systems Journal, vol. 9, issue 3, 1998, pp. 315-333. [6] D. Sala, J. Limb and S. Khaunte, “Adaptive control mechanism for cable modems MAC protocols,” Proc. Infocom, March, 1998, pp. 1392-1399. [7] W. M. Yin and Y. D. Lin, “Statistically optimized minislot allocation for initial and collision resolution in hybrid fiber coaxial networks,” IEEE Journal on Selected Areas in Communications, vol. 18, issue 9, Sept. 2000, pp. 1764-1773. [8] A. Doha and H. Hassanein, “Opportunistic performance enhancement of reservation multiple access protocols of wireless broadband networks,” Proc. IEEE BROADNETS, Oct. 2005, pp. 511-520. [9] A. Doha, H. Hassanein and G. Takahara, “Performance Evaluation of Reservation Medium Access Control in IEEE 802.16 Networks,” Proc. IEEE International Conference on Computer Systems and Applications, Mar. 2006, pp. 369-374.

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