A Novel Algorithm for Efficient Paging in Mobile WiMAX Shantidev Mohanty, Muthaiah Venkatachalam, and XiangYing Yang

Intel Corporation, Hillsboro, Oregon 97124, USA

Abstract − Idle mode operation is used in Mobile WiMAX

networks to conserve battery power when a mobile station (MS) is not engaged in active call sessions. An idle-mode MS is paged to alert it to pending downlink traffic. Paging latency and paging signaling overhead are the two important parameters that determine the performance of paging procedures. It is desired that a paging algorithm minimize paging signaling overhead without compromising paging latency requirements. In this paper, a novel algorithm is proposed to minimize paging signaling overhead while ensuring that paging latency is bounded by a maximum desired value, referred to as paging latency upper limit. The proposed algorithm groups the idle-mode MSs into different paging sets and aggregates their paging information into one paging message. This aggregation of paging information reduces paging signaling overhead significantly. The cardinality of each paging set is determined in such a way that paging latency is bounded by the paging latency upper limit. Therefore, the proposed algorithm achieves a good tradeoff between paging latency and paging signaling overhead. Index Terms: IEEE 802.16e, WiMAX, idle mode and paging, paging overhead, and paging latency.

I. INTRODUCTION Mobile WiMAX [4] based on IEEE 802.16e standard [1] enables high speed data communications anywhere and anytime. For significant time durations, mobile stations (MSs) are powered on in mobile WiMAX networks but are not in active call sessions. To use these durations as battery conserving opportunities, idle mode, location update, and paging operations are specified in IEEE 802.16e standard [1]. Per these procedures, an MS enters a low-power mode called “Idle mode”. Upon entering idle mode, the MS relinquishes all of its connections and states associated with the base station (BS) it was last registered with. The idle MS is tracked by the network at the granularity of a group of BSes (commonly called a paging group) as opposed to a non-idle MS which is tracked at the granularity of a BS. While in idle mode the MS periodically listens to the radio transmissions for paging messages, in a deterministic fashion that is decided apriori between the network and itself. The period for which the MS listens to paging messages is known as “paging listen interval” (PLI) and the period for which the MS powers off its radio interface is known as the “paging unavailable interval” (PUI). The amount of power saving an MS can achieve in idle mode is tightly coupled to the duty cycle of the MS, which is the ratio of paging listen to the paging unavailable interval. One paging unavailable interval and one paging listening interval constitute a paging cycle (PAGING_CYCLE) as shown in Figure 2. Therefore, once in every PAGING_CYCLE interval the idle-mode MS wakes up and listens for paging messages. When traffic arrives for the idle-mode MS the network

performs paging to locate the MS and to bring it back to active mode.

The operation of idle mode and paging, in mobile WiMAX networks, can be summarized as follows.

Maintaining the location information of an idle-mode MS: This is achieved by logically dividing the network coverage area into different paging groups. A paging group (PG) refers to the coverage area of one or more base stations (BSes). A Paging Controller (PC) administers one or more paging group(s). There could be one or more PCs in the network. When an MS goes to idle mode, a PC, referred to as anchor PC, creates an entry in its database noting the PG where the MS is initially located. When the MS moves from one PG to another, it updates the location with the anchor PC. Therefore, while in idle mode the location of an MS is known up to the granularity of one PG.

Paging an idle-mode MS: When the network wants to locate an idle-mode MS, or has incoming data buffered for it, or for administrative purposes, the PC initiates paging the MS by broadcasting mobile paging advertisement (MOB-PAG-ADV) message to all the BSes in the PG; the BSes in turn broadcast this message on the airlink. This is because when the location information stored at a PC is correct; the MS is expected to reside in the coverage area of at least one of these BSes. If the paging advertisement happens during the PLI of the MS, then the MS is expected to receive the page and perform network re-entry or location update in response to the page if it is alerted to do so.

In this paper, we develop an algorithm for efficient paging in IEEE 802.16e based mobile WiMAX networks. The performance of paging mechanism in these networks can be specified by two parameters: paging signaling overhead and paging latency.

Definition 1: Paging signaling overhead (χ) is defined as the number of bits per second used for paging one idle-mode MS.

Definition 2: Paging latency (τ) is defined as the time delay between the initiation of paging operation by the network and the completion of MS’s response to the paging operation.

Most of the applications specify an upper bound for paging latency. Thus, the objective of our research is to minimize paging signaling overhead without increasing the paging latency beyond what is required by different applications. A paging architecture is proposed for mobile WiMAX networks in [2]. However, it does not analyze the tradeoff between paging signaling overhead and paging latency. To the best of our knowledge there is no existing work that investigates the

481-4244-0957-8/07/$25.00 ©2007 IEEE.

tradeoff between these two parameters of paging procedures in mobile WiMAX networks.

In our proposed paging algorithm, idle-mode MSs are grouped into different sets, referred to as paging sets, in such a way that the paging information of these MSs can be aggregated into one MOB-PAG-ADV message. This reduces the overhead associated with paging operation. However, aggregation of paging information of MSs may result in too many MSs transitioning from idle mode to normal/active mode at the same time causing high contention load during network re-entry, timeouts and potentially resulting in further retransmissions of paging broadcasts. This may increase the paging latency beyond what is required by the applications. To eliminate this, the proposed paging algorithm determines the maximum cardinality of each paging set that guarantees an upper bound for paging latency. Thus, the proposed paging algorithm achieves a good tradeoff between the paging latency and paging signaling overhead.

The remaining part of the paper is organized as follows. In Section II we describe idle mode and paging operation in mobile WiMAX networks. We present the proposed paging algorithm in Section III. We carry out performance analysis of the proposed paging algorithm in Section IV. Finally, we summarize the advantages of the proposed paging algorithm and conclude the paper in Section V.

Figure 1: Network reference model

II. PAGING OPERATION IN MOBILE WIMAX Figure 1 depicts a representative network reference model [3] used to describe the idle mode operation in WiMAX networks. It consists of the three PGs (PG1, PG2, and PG3) and two PCs (PC1 and PC2). PC1 manages PG1 and PG2. PC2 manages PG3. PG1 comprises three BSs, PG2 comprises one BS, and PG3 comprises two BSs. Each PC maintains a location database that keeps information about all the MSs that have gone into idle mode in the PG(s) managed by that PC. Figure 2 shows a snapshot at time t, for four representative MSs (MS1, MS2, MS3, and MS4). At time t, all four MSs are in coverage area of BS4, and in PG2. Prior to t, MS1 was in coverage area of BS3 (i.e. in PG1). Prior to t, MS4 was in coverage area of BS5 (i.e. in PG3). While only four idle-mode

MSs are shown in this picture, there may be several more MSs (both idle mode and active mode) in real deployments in BS4 coverage area. The entire idle mode operation in IEEE 802.16e based mobile WiMAX networks can be divided into following stages: idle mode initiation, idle mode entry, operation during idle mode, and idle mode exit [3]. Next, we provide a brief description of these states. Idle mode initiation: The idle mode can be initiated either by the BS or MS when the MS does not have any ongoing traffic. In case of MS initiated idle mode, the MS sends deregistration request (DREG-REQ) message to the BS [1] [2]. Similarly, in case of BS initiated idle mode, the BS sends deregistration command (DREG-CMD) message to the MS. When the MS receives the DREG-CMD message, it sends the DREG-REQ message to the BS [1] [2]. In either case, the BS receives a DREG-REQ message from the MS. Idle mode entry: When a BS receives the DREG-REQ message from one of its MSs, it sends a message to the anchor PC (how the anchor PC is chosen is a matter of the network configuration and is outside of the scope of this paper). This message contains certain MS service and operation information referred to as idle mode retain information (IMRI) [1]. IMRI can be used to expedite MS’s network re-entry from idle mode. PC stores the MS IMRI and transmits a backbone message to BS that includes numerical values for PAGING_CYCLE, PAGING_OFFSET, and MS Paging Listening Interval (PLI) for the MS [1]. Note that PC may use its own algorithm or negotiate with the BS and/or MS to decide the numerical values of PAGING_CYCLE and PLI. On the other hand, it can determine the PAGING_OFFSET using its own algorithm. Once BS receives the backbone message from the PC, it sends the DREG-CMD message to the MS that includes the idle mode entry time (IMET), PAGING_CYCLE, PAGING_OFFSET, and PLI values. The MS enters into idle mode at IMET.

Idle mode operation: While in idle mode the MS alternates between PUI and PLI. The idle mode operation of two MSs (MS1 and MS2) is illustrated in Figure 2. In this case both MS1 and MS2 have same PAGING_CYCLE and PLI (which is the case in most of the network deployments). However, MS1 and MS2 have different PAGING_OFFSETs of T1 and T2, respectively. Therefore, when the network wants to page MS1 and MS2, it does so through two different MOB-PAG-ADV messages at different times. It may be noted that the network needs to send two different MOB-PAG-ADV messages although it wants to page these two idle-mode MSs at the same time because the MSs have non-overlapping paging listening intervals. Idle mode exit: An MS in idle mode exit from idle mode if it has data to send to the BS or it receives a paging message indicating that its traffic is waiting at the BS. In this case, the MS terminates idle mode operation and carries out network re-entry procedures as specified in IEEE 802.16e [1]. As a part of network re-entry the idle-mode MS may perform contention

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based initial ranging. In another instance the BS may assign dedicated ranging region to the MS for initial ranging [1].

Figure 2: Idle mode operation of MS1 and MS2

Next, we analyze the paging overhead and paging latency associated with paging operation according to IEEE 802.16e specifications. Paging overhead: The format of MOB-PAG-ADV message is shown in Table 1. This message is appended with a 48 bit MAC header and transmitted over the air link. Out of all the bits in a MOB-PAG-ADV message the number bits that carry information specific to a particular MS is

∑=

==

8

6

i

iis Ll (1)

The number of bits in a MOB-PAG-ADV message that does not carry MS specific information is

∑∑=

=

=

=+=

10

9

5

11

L

Li

i

ii LLl (2)

Therefore, using (1) and (2), when n numbers of MAC addresses are present in a MOB-PAG-ADV message, the total length of the MOB-PAG-ADV message is

snlll += 1 (3)

Thus, when the paging information of n number of idle-mode MSs are aggregated into one MOB-PAG-ADV message, the number of bits used for paging one idle-mode MS is given by

nnll s+

= 1ψ (4)

Therefore, when the paging information of n number of idle-mode MSs are aggregated into one MOB-PAG-ADV message, paging signaling overhead (define in Section I) is given by

)( 1 snlln

+== λλψχ (5)

where λ is the average call arrival rate, i.e., number of calls arrived per second, for idle-mode MSs.

Table 1: Format of MOB-PAG-ADV message [1]

Syntax Size (bits) Note Generic MAC header 48 (L1) The generic MAC header [1] MOB-PAG-ADV_Format () { Management Message Type 8 (L2)

=62 Num_Paging_Group_IDs (N_PG)

16 (L3) Number of paging group IDs in this message

For ( i=0; i< N_PG; i++) { Paging Group ID 16 (L4) } Num_MACs 8 (L5) Number of MS MAC

addresses For ( j=0; j< N_MACs; j++) { Depends on the PHY

specification MS MAC Address hash 24 (L6) The hash is obtained by

computing a CRC24 on MS 48 bit MAC address

Action Code 2 (L7) Paging action instruction to MS [1]

Reserved 6 (L8) } Padding Variable

(L9) Padding bits to ensure octet aligned

TLV encoded information Variable (L10)

TLV specific [1]

}

0

2

4

6

8

10

12

0 20 40 60 80 100Number of idle-mode MSs whose paging

information is aggregated

Pagi

ng s

igna

ling

over

head

in b

its/s

ec

Call arrival rate = 1/3600

Call arrival rate 1/1800

Call arrival rate 1/900

Figure 3: Paging signaling overhead for different amount of paging information aggregation

Figure 3 shows the relationship between paging signaling overhead and the number of MS whose paging information is aggregated into one MOB-PAG-ADV message for different call arrival rate (λ). The results show that significant paging overhead reduction is achieved even with the aggregations of paging information of small number of MSs. Paging latency: After successful paging an idle-mode MS performs network re-entry via initial ranging access [1]. After initial ranging access the MS carries out other network entry procedures such as registration, authentication, and IP address acquisition etc. Paging latency which is defined as the time delay between the initiation of paging operation by the network and the reception of MS’s response to the paging operation (i.e., completion of network entry) is given by

δγτ +++++= arirpb DDDD (6)

where Dpb is the delay in the backbone network between the PC and BS, γ is processing delay at the BS (including scheduling and queuing delays), and Dir is the initial ranging delay. Dr, Da, δ are the time required for MS’s registration and authentication, and IP address acquisition, respectively. As pointed out earlier, Dir depends on the number of MSs that

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perform initial ranging at the same time. As our focus is the effect of Dir on paging latency, we assume that other parameters in (4) are un-affected when the paging messages of many idle-mode MSs are aggregated. Therefore, the desired Dir to meet the required τ can be calculated using (6).

III. PROPOSED PAGING ALGORITHM FOR WIMAX The objective of the proposed paging algorithm is to decide the maximum number of MSs who’s paging information can be aggregated in one MOB-PAG-ADV message. Once this number is determined, the idle-mode MSs can be grouped into different sets with each set containing the maximum number of MSs. These sets are referred as paging sets. The proposed paging algorithm also develops methodologies to assign the idle-mode MSs into these paging sets.

For the following description, we assume that the numerical values of PAGING_CYCLE and the PLI for each MS are already known to the PC. Moreover, we consider that the numerical values of PAGING_CYCLE and PLI are same for all idle-mode MSs.

We define the following parameters:

T: The upper limit for paging latency, i.e., the paging latency should be limited to T N: average number of idle-mode MSs in a PG R: maximum number of idle-mode MSs in a cell that can perform initial ranging simultaneously such that paging latency does not exceed its upper limit T λ: call arrival rate (number of calls per second) of each idle-mode MS K: number of cells in a PG L: maximum cardinality of a paging set p: probability that an idle-mode MS is paged in a paging cycle. This is the probability that one or more calls are arrived for the idle-mode MS during a paging cycle. The expression for p is given by

)_(1 CYCLEPAGINGep λ−−= (7)

Therefore, assuming that idle-mode MSs are uniformly distributed among the cells in a PG, the number of idle-mode MSs of a particular paging set that are paged simultaneously in a cell in one paging cycle is

KLp=α (8)

To ensure that the paging latency is limited to T, α should be equal to R. Now the question is how to determine the numerical value of R. We will answer this question in Section IV. Therefore, using (7) and (8), the expression for L is given by

)_(1 CYCLEPAGINGeKR

pKRL λ−−

=≤ (9)

Therefore, the number of paging sets, m, to accommodate N number of idle-mode MSs in a PG is

=

LNm (10)

The expression for N is given by

ηωπρ )( 2rKN = (11)

where ρ is the population density of the area where a WiMAX network is deployed, r is the radius of one WiMAX cell, ω is the fraction of population using WiMAX network, and η is the fraction of WiMAX users in idle mode. We denote the paging sets as {S1, S2, S3, ….Sm}. Once, m and L are determined the PC uses the following steps to assign idle mode users to individual sets.

1. Upon cold start of the system, when a PC receives the first idle mode initiation message for an MS, it assigns the corresponding MS into the first paging set and assigns the PAGING_OFFSET value corresponding to this paging set to the MS. This set is referred as the current paging set. A current paging set is defined as the paging set to which a new idle mode user can be added. The cardinality of the current paging set is at least one less than L.

2. When during normal operations, another idle mode initiation message arrives at the PC; the PC adds the new MS to the current paging set and assigns the corresponding PAGING_OFFSET to the MS. Then, the PC checks if the number of idle-mode MSs in the current paging set reached the maximum value L, such that adding one more MS will cause the expected contention latency to exceed T. If no, PC keeps the current paging set unchanged. If yes, then the PC creates chooses another paging set as the current paging set. Therefore, at any given time there are Sc (c < m) number of paging sets that are occupied with idle mode users. These paging sets, {S1, S2, …., Sc} are referred as active paging sets. One of these active paging set is the current paging set that a new idle-mode MS can be assigned to. The remaining paging sets {Sc+1, S c+2, ….,Sm} are referred as empty paging sets.

3. When an MS in idle mode decides to terminate the idle mode and become active by re-entering the network, it is removed from the corresponding paging set. Therefore, the number of MSs in each active paging set changes when some of the idle-mode MSs terminate their idle mode. These vacancies can be used to accommodate new idle-mode MSs. As pointed out earlier, a new idle-mode MS is assigned to the current available paging set. When the current paging set attains its optimum capacity, the following procedures are used to update the current paging set.

Case I: When the current paging set attains it optimum capacity, i.e., the number of users in this set becomes equal to L, all other active paging sets are checked for any vacancies (Note that these vacancies are created when some of the idle-mode MSs terminate their idle state). If an active paging set

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with vacancies is found then that become the current paging set.

Case II: If all the active sets are full, then an empty set is added to the active paging set and this set becomes the current paging set.

Figure 4: Flow chart showing the operation of the proposed paging algorithm.

When the need to page idle-mode MSs arises, the PC aggregates the paging information of all the MSs that need to be paged and that share the common PAGING_OFFSET value into one paging announcement message (Note that all these MSs belong to one paging set). Then, the PC broadcasts this paging announcement message to all the BSs in it PG. Each of these BSs sends the MOB-PAG-ADV message over the air link during the corresponding PAGING_OFFSET. The idle mode users that are addressed in this MOB-PAG-ADV message initiate their network re-entry procedures and perform initial ranging in the next available initial ranging opportunity.

The operational steps of the proposed algorithm are illustrated in the flow chart shown in Figure 4. A PC calculates the maximum number of paging sets (Sm) and the optimum number of members for each paging set (L). When a new idle mode initiation message arrives at the PC, the PC adds the new idle-mode MS to the current paging set and updates the current paging set if the size of the current paging set becomes equal to its optimum capacity L after adding the new MS. When an MS terminates its idle mode, the PC removes that MS from the corresponding paging set. Moreover, the PC carries out the paging operations to locate the desired MSs.

IV. PERFORMANCE EVALUATION We considered the parameters shown in Table 2 to investigate the performance of our proposed paging algorithm for a specific deployment scenario of mobile WiMAX networks. It may be noted that these parameters depend on a particular

network deployment scenario and may vary from one network deployment to another. However, the proposed paging algorithm can be used for all such scenarios. The results may vary depending on the deployment scenario.

Table 2: Parameters used for simulation

Parameter name Value Dpb (defined in Eq (6) ) 20 ms γ (defined in Eq (6) ) 10 ms

Dr (defined in Eq (6) ) 40 ms Da (defined in Eq (6) ) 50 ms δ (defined in Eq (6) ) 500 ms

PAGING_CYCLE 1 s K 10 r 2 km ω 0.6 η 0.9 ρ 500 – 5000 per sq. km. [5] T 1.5 s λ 1/3600, 1/1800, and 1/900

For the parameters specified in Table 2, using τ = T in Eq (6), the upper limit for initial ranging delay Dir is 880 ms. Therefore, the number of MSs that are trying to perform initial ranging at the same time, α, should be such that Dir is less than or equal to 880 ms. As we are interested in finding the maximum possible value (optimal value) for α=R, we determine R such that Dir = 880 ms. R is so far not discussed explicitly. Next, we investigate the correct value for R. In our simulations to investigate the relationship between the Dir and α, we consider 64 CDMA codes for the initial ranging sub-channel of the OFDMA-PHY frame [1]. However, the number of resolvable codes, C, in one initial ranging sub-channel depends on the cross-correlation properties of these codes. We consider three different values for the number of resolvable codes; 8, 10, and 12. We consider that binomial exponential back off algorithm with maximum contention window exponent of 10 is used for contention resolution. Moreover, we consider that the average number of initial ranging requests from MSs other than those transitioning from idle mode to active mode is S= 4. This is realistic based on our experience with mobile WiMAX system level simulations. Figure 5 shows the relationship between Dir and α for different number of resolvable codes, C. As discussed earlier for the considered scenario desired Dir =880 which is shown as a solid line in Figure 5. Therefore, the point of intersection of the solid line with the Dir curves indicates the maximum number of MSs that can perform initial ranging at the same time without increasing Dir beyond the desired value of 880 ms. It may be noted that this number includes MSs that are performing initial ranging during their idle mode to active mode transition and other MSs that may perform initial ranging for other purposes such as after lost connectivity or after powering up for the first time. As pointed out earlier, we have considered that the average number of latter category of MSs is S=4. Thus, optimum number of idle-mode MSs that

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can perform initial ranging at the same time can be calculated by subtracting S from the value of α at the intersection points. Thus, R=9-4=5 for C=8, R=13-4=9 for C=10 and R=15-4=11 for C=12.

0

1000

2000

3000

4000

5000

6000

7000

8000

1 3 5 7 9 11 13 15

Dir

C=8C=10C=12Desired Dir

α Figure 5: Average paging latency for different cardinality of a paging set

After we determine R, we calculate the maximum cardinality of paging sets, L, using Eq (9). We present L for different C and λ in Table 3. Results show that for a particular value of C, L decreases as λ increases. Moreover, for a particular value of λ, L increases as C increases. Table 4 shows the number of paging sets (m) required for different deployment scenarios. We want to point out that a small number of paging sets are enough to accommodate most of the deployment scenarios. Table 3: Table showing L for different scenarios

C λ L 1/3600 180000 1/1800 90000

8

1/900 45000 1/3600 324000 1/1800 162000

10

1/900 81000 1/3600 396000 1/1800 198000

12

1/900 99000 Once PC determines the maximum cardinality of paging sets for a given C and λ, it creates paging sets and allocates idle MSs into these sets as discussed in Section III. Then during paging it aggregates the paging information of all the MSs that belong to one paging set in to one MOB-PAG-ADV message. Such paging information aggregation achieves paging overhead reduction as shown in Figure 6. Figure 6 shows that using the proposed paging algorithm aggregated paging overhead (summation of paging overhead of all the idle-mode MSs that are paged) in a PG can be reduced up to 66 % compared when idle-mode MSs are paged individually.

Table 4: Number of paging sets required for different scenarios.

ρ per sq. km.

N using Eq. (11))

m for C=10, λ = 1/3600

m for C=10, λ = 1/1800

m for C=10, λ = 1/900

500 33928 1 1 1 1000 67856 1 1 1 1500 101784 1 1 2 2000 135712 1 1 2 2500 169641 1 2 3 3000 203569 1 2 3 3500 237497 1 2 3 4000 271425 1 2 4 4500 305353 1 2 4 5000 339282 2 3 4

0

1000

2000

3000

4000

5000

6000

500 1500 2500 3500 4500Population density per sq. km

Agg

rega

te p

agin

g ov

erhe

ad in

a

pagi

ng g

roup

in b

its p

er s

ec Proposed algorithm

Separate paging for idle-mode MSs

Figure 6: Aggregate paging overhead in a paging group for different population density.

V. SUMMARY AND CONCLUSIONS In this paper, a novel paging algorithm is proposed to

carry out efficient paging in mobile WiMAX networks. The proposed paging algorithm strikes a very good balance between two important parameters of paging procedure: paging signaling overhead and paging latency. Using the proposed algorithm a PC groups the idle-mode MSs into different paging sets. PC aggregates the paging information of the MSs that belong to a particular paging set in one MOB-PAG-ADV message. The proposed algorithm also provides methodology to decide the maximum cardinality of each paging set for different network deployment scenarios. Performance investigation shows that such aggregation of paging information of idle-mode MSs is efficient to reduce paging signaling overhead without increasing paging latency beyond a specified upper limit.

REFERENCES [1] Part 16: Air interface for fixed and mobile broadband wireless access

systems. Amendment 2: Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands, IEEE standard for local and metropolitan area networks.

[2] H. S. Roh, S. Lee, and S. Lee, “Paging scheme for high-speed portable Internet (HPi) system,” The 8th International Conference on Advanced Communication Technology, ICACT 2006, pp. 1729-1732, vol. 3, Feb. 2006

[3] “WiMAX end-to-end network system architecture,” Stage 3: detailed protocols and procedures, WiMAX Form, Aug. 2006.

[4] “WiMAX ForumTM Mobile System Profile v1.0.0,” WiMAX ForumTM, Technical Working Group, April 2006.

[5] http://www.census.gov/population/www/documentation/twps0027.html

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