Dynamic Channel Assignment with Flexible Reuse ... - Springer Link

Wireless Personal Communications (2007) 42:161–183 DOI 10.1007/s11277-006-9172-0

c Springer 2006


Dynamic Channel Assignment with Flexible Reuse Partitioning in Cellular Systems STEVEN LI CHEN, PETER H. J. CHONG and MING YANG Network Technology Research Center, School of EEE, Nanyang Technological University, Nanyang Avenue, Singapore, 639798, Singapore E-mails: [email protected], [email protected]

Abstract. In cellular communications, one of the main research issues is how to achieve optimum system capacity with limited frequency spectrum. For many years, researchers have proposed and studied many dynamic channel assignment (DCA) schemes to increase the capacity of cellular systems. Another proposed technique, Reuse Partitioning (RP), is used to achieve higher capacity by reducing the overall reuse distance. In convention, when RP is exploited in network-based DCA, a portion of channels will be assigned permanently to each partitioned region. However, the number of channels assigned to each region may not be optimum due to factors like the uneven and time-varying traffics. In this paper, a new network-based DCA scheme is proposed with the flexible use of RP technique, named as flexible dynamic reuse partitioning with interference information (FDRP-WI). In this scheme, channels are open to all incoming calls and no channel pre-allocation for each region is required. As long as the channel assignment satisfies the co-channel interference constraints, any user from any region can use any channel. The scheme aims to minimize the effect of assigned channels on the availability of channels for use in the interfering cells and to reduce overall reuse distance. Both FDRP-WI with stationary users and mobile users are investigated. Simulation results have confirmed the effectiveness of FDRP-WI scheme. In the case with stationary users, FDRP-WI exhibits outstanding performance in improving the system capacity under both uniform and non-uniform traffic distributions. Under the uniform traffic case, the scheme can provide over 100% capacity improvement as compared to conventional fixed channel assignment scheme with 70 system channels at 1% blocking probability. In the case with mobile users, the impact of mobility on the new call probability, Pb , and the call dropping probability, Pd , is evaluated. The effect on system capacity of reserving some channels for handoff calls is first studied. Then, we propose a new handoff scheme, called “Reverse Overflow” (RO), to improve the utilization of channels with smaller reuse distances under mobile environment. Simulation results show that, with RO handoff, the system capacity of FDRP-WI is effectively improved at the expense of higher handoff rates in the cellular system. Keywords: dynamic channel assignment, reuse partitioning, cellular mobile communications, channel rearrangement, handoff, mobility

1. Introduction In cellular mobile communications, since the given frequency spectrum is limited, it is paramount to know how to effectively make use of the available spectrum to achieve optimum system capacity. The conventional way of allocating channels is called fixed channel assignment (FCA) [1]. But the scheme FCA is not able to adapt to the uneven and time-varying traffic nature. Hence, dynamic channel assignment (DCA) [1] is introduced to overcome such disadvantage. Further, distributed DCA (DDCA) has been paid much attention due to much simpler

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resource management compared to centralized DCA. In DDCA, the channel assignment decision is made by each base station (BS) and/or mobile station (MS) and the information of the whole service area is not required. A network-based DDCA scheme, namely DCA with interference information (DCA-WI), was introduced in [2] to increase the capacities of TDMA cellular systems. In DCA-WI, the channel assignment is based on minimizing the impact of every assignment on channel availability in all the interfering cells. Every channel is ordered and an interference information table (IIT) is used in each BS. It has been shown that DCA-WI out performs other existing schemes [3–5] in both uniform and non-uniform traffic distributions. However, these DDCA schemes [2–5] have not achieved the optimum performance because the assignment policies of these DDCA schemes rely on mobiles on the edge of the cell, where a single cluster size (CS) is assumed and it limits the efficiency of spectrum utilization. In fact, for mobiles close to the BS, they are able to tolerate higher interference and thus can be assigned channels with smaller cluster size to improve system capacity. Reuse Partitioning (RP) [6] is a very useful technique to achieve high spectrum efficiency in cellular systems by using different cluster sizes. In RP, a cell is divided into several concentric regions and each region has a different cluster size. A mobile close to its BS is assigned a channel with a smaller reuse distance, whereas a mobile far from its BS with low signal quality is assigned a channel with a larger reuse distance. In this way, overall reuse distance is decreased and channels could be used more frequently to provide larger system capacity. The performance analysis of FCA with RP (FRP) system has been studied in [7–9]. In [8], it is shown that a two-region FRP system can improve the system capacity by about 25% as compared to conventional FCA with a total of 140 system channels. Since the mid-1990s, many cellular companies have adopted RP [10] scheme. In convention, when FRP is implemented, a portion of channels will be assigned permanently to each partitioned region [11, 12, 6, 8]. However, there are two main design issues related to the simple RP concept [1]. The first issue is the capacity allocation problem where the capacity allocation procedure takes place in the cell planning process. The implementer is to decide how many channels should be assigned to each reuse pattern. The problem arises when the number of channels assigned to each region may not be optimum due to the uneven and time-varying traffic. The second issue is the actual assignment of channels to calls. In this paper, a new channel assignment scheme called flexible dynamic reuse partitioning with interference information (FDRP-WI), which integrates DCA-WI with flexible two-region RP, is proposed. In FDRP-WI, all channels are open to all incoming calls. Any user from any (inner or outer) region can use any channel as long as the channel assignment satisfies the co-channel interference (CCI) constraint. An inner region originated call will use a channel based on a smaller reuse distance constraint, while an outer region originated call will use a channel based on a larger reuse distance constraint. The flexible use of RP in FDRP-WI has eliminated the need of pre-allocation of channels for each region, which is required in [11, 12]. With the combined effect of DCA-WI and flexible RP, a much larger system capacity is expected. First, FDRP-WI with stationary users is studied. It shows that FDRP-WI can provide great capacity improvement under both uniform and non-uniform traffic distributions. Next, the impact of mobile users on FDRP-WI scheme is investigated with only uniform traffic distribution. Two mobility models are used to study the impact of mobile users on the new call blocking probability, Pb , and the call dropping probability, Pd , in the cellular system. The effect of a cutoff priority scheme for handoff calls on capacity is considered. The capacity is

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defined as the total offered traffic that can support in a particular cell at a certain Grade of Service (GOS) that is given by [13] GOS = (1 − α)Pb + α Pd

(1)

where α ∈ [0, 1] is the GOS parameter and indicates the relative importance of Pb and Pd in a given system. It is found that prioritized handoff can reduce Pd but it may also degrade the capacity in some cases. Also, it can be shown that the low utilization of channels with smaller reuse distances in the mobile environment has limited the performance of FDRP-WI scheme. As such, a new handoff scheme “RO” is introduced to improve the utilization of channels with smaller reuse distances. Simulation results have shown that the new handoff scheme can effectively improve the performance of the FDRP-WI scheme at the expense of higher handoff activity.

2. FDRP-WI Scheme 2.1. N e t w o r k S c enario A service area of 49 regular hexagonal cells is considered as shown in Figure 1. Each cell is divided into inner and outer concentric regions, where they are associated with CS of 3 and 7 respectively. When the inner region of a cell has a CS value of 3, its neighboring cells in the first tier are within the reuse distance range. When the outer region of a cell has a CS value of 7, the interference area covers the first two tier neighboring cells. It means that if a channel is assigned to an inner (outer) region originated call, that channel cannot be reused in the neighboring cells in the first (first two) tier(s). Using Figure 1 to illustrate, the small hexagonal region in solid line describes the interference range for the inner region of cell 17, and the two bigger hexagonal areas which are drawn in dotted line and dash line refer to the outer region of cell 17’s and 25’s interference range respectively. From [8], the radii for inner, ri , and outer, ro , regions are given by

(2) Ni ri2 = No ro2 where Ni (No ) is the CS for inner (outer) region. In order to avoid the boundary effect, wrap-around of the 49-cell plane in both dimensions is used when uniform traffic distribution simulation is evaluated in Section 4 and Section 5. In other words, the left-most and the right-most columns in the 49-cell plane as shown in Figure 1 are connected with each other, so are the top and the bottom rows. Therefore, if any MS reaches the cell plane boundary, it will return to the system automatically. 2.2. I n t e r f e r e n c e I n f o rmation Table (IIT) An IIT shown in Table 1 is used to record the channel status in each cell. Using Table 1 of cell 17, in any IIT of cell i, the first row lists all available channels in the system. For example, there are C channels in total in the system and Ch channels are reserved for handoff calls. The channel reservation is only applicable when mobility is considered, i.e., Ch = 0, in the case of stationary users. The first column lists the own cell, cell i, (hereafter referred to as OWN CELL) and all its interference cells’ (IF CELLs) numbers, in the order of cell i, cell i’s first tier interfering cells, and cell i’s second tier interfering cells. The cells in the first tier and

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38 38

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23 23

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25 24 24

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3 2

1

Figure 1. A 49-cell system layout with 2-region reuse partitioning.

first 2 tiers are referred to i-IF CELLs and o-IF CELLs respectively as shown in Table 1. All other columns contained the information of all channels available in the system, i.e., each row indicates the channel status for a particular cell. 2.2.1. Legend explanation The legends used in the IIT are described as follow. A letter U or U in the box indicates a channel is assigned based on the CCI constraint with reuse distance of 3 or 7 respectively. For example, in Table 1, channels 1 and ‘C-1’ are used by MS’s in cell 17 with reuse distance of 3. Channels 3 and ‘C’ are assigned to MS’s in cell 17 and 22 respectively, with reuse distance of 71 . A letter L means the channel, say channel k, is locked in an IF CELL because one of the IF CELL’s interfering cells, say cell x, uses channel k. Thus, that IF CELL is not allowed to use channel k. Note that the OWN CELL is outside the interference range of channel k, which is used in cell x with reuse distance of 3 or 7. For instance, in Table 1, channel 2 is locked in cell 3. This is because one interfering cell of cell 3, say cell 1, has used channel 2 with reuse distance of 7, but it does not affect the availability of channel 2 for use in cell 17 with reuse distance of 3 or 7 in this particular example. Thus, from Table 1, we know that cell 3 cannot use channel 2. A symbol of 2L means that two such interfering cells of IF CELL use that corresponding channel. 1

Note that, when a call is assigned a channel with reuse distance of 3 (7), we would say that ‘the call is assigned to an inner (outer) channel’ or ‘the call uses an inner (outer) channel’ in the following context.

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Table 1. IIT of cell 17 Channel no. C − Ch Non-reserved channels

Ch Reserved channels

4 ...

C − Ch + 1 . . . C-1

Cell no. 1

2

3

Own Cell 17 U U ... i-IF Cells 10 .. . ... 24 o-IF Cells 3 L ... 4 .. . 19 U 22 U .. . 30 L 31 2L

C − Ch

...

U

L L

U

...

...

L L

C

L L

U

2.2.2. Table updating Any channel assignment and channel release will initiate an updating procedure. When OWN CELL assigns a call to channel j with smaller (larger) reuse distance, (i) it first updates its IIT by inserting a letter U(U ) in the [OWN CELL, channel j] box; (ii) then, it informs its IF CELLs by inserting a letter U(U ) in the [OWN CELL, channel j] box in their IITs; (iii) after that, each i-IF CELL (o-IF CELL) informs all its IF CELLs, (hereafter referred to as Other IF CELLs), which is not one of the i-IF CELLs (o-IF CELLs), that the particular channel j is locked, i.e., a letter L is inserted in Other IF CELLs’ IITs (Note that L is additive); (iv) finally, Other IF CELLs with L inserted inform all their IF CELLs its latest number of locked cells on that particular channel. The updating for channel release follows the same procedure, except that “removing U(U )” is operated instead of “inserting U(U )” and an L is subtracted rather than added. 2.3. M o b i l i t y M o dels In this paper, two mobility models will be used to evaluate the performance of FDRP-WI scheme with mobile users. The mobility models are shown in Figure 2. (i) Model A [14]: The MS is moving in a straight line without changing its speed and direction where both parameters are independent random variables. The speed and direction of an MS are uniformly distributed in [E[V ]/2, 3E[V ]/2] and (0, 2π ] respectively, where E[V ] is the mean speed of the MS. (ii) Model B [15]: The speed and the direction of an MS are independent random variables, uniformly distributed in [E[V ]/2, 3E[V ]/2]and (0, 2π ] respectively. The MS changes its

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Cell V2 V3

V V1

Model A

Model B

Figure 2. Two mobility models.

speed and direction after a random time interval, where the change is exponentially distributed with a mean of T seconds. Model A can be a special case of Model B with T = ∞. We can see, in Model A, the MS does not change speed and direction within a cell. In Model B, the MS is more likely to changes speed and direction within a cell depending on the value of T . If T is small, the MS changes speed and direction more frequently within a cell and vice verses. Further, we noticed that as T decreases, the MS tends to stay in a cell longer.

3. Channel Assignment Strategy In FDRP-WI scheme, there are two CCI constraints that associated with CSs 3 and 7 for the inner channel and outer channel respectively. For the cluster size of an inner channel 3, it will affect its neighboring cells in the first tier. Similarly, for the cluster size of an outer channel 7, it will affect its neighboring cells of the first two tiers. 3.1. C h a n n e l A s s i g nment Assume that there are C available channels in a cellular system, and Ch channels are exclusively reserved for handoff calls. As mentioned, for the case of stationary users, the reserved channel Ch = 0. When a new call is initiated in the inner region, it is assigned a channel based on a smaller reuse distance of 3 (an inner channel), while an outer region originated call will use a channel based on a larger reuse distance of 7 (an outer channel). In the case of mobile users, when a new call arrives in the inner or outer region, the new call will be assigned an inner or outer channel from one of the C − Ch channels. The idea remains the same as an inner region originated call is assigned an inner channel, while an outer region originated call is assigned an outer channel. If no channel is available, the new call is blocked. An on-going call currently using an inner channel requires an intra-cell handoff when its MS exits the inner region, and it will be assigned an outer channel. The channel assignment for the handoff call can be chosen from all C channels. If no channel is found, the intra-cell handoff call is dropped. A call using an outer channel can keep using the same channel as long as its MS remains within the cell because it will not violate the CCI constraints. An inter-cell handoff is required only when its MS exits the cell. Then, the inter-cell handoff call will be assigned a suitable outer channel in the new cell. The channel assignment for the inter-cell handoff call can be chosen from all C channels as well. If no channel is found, the inter-cell handoff call is dropped.

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As we can see, the inner channel is used for calls originated in the inner region only. However, there are three situations in which a call might use an outer region channel in a cell: (i) a new call arrives in the outer region; (ii) a call moves from the inner region to the outer region (intra-cell handoff); or (iii) a call moves from a neighboring cell into the outer region (inter-cell handoff). Therefore, the traffic load for outer channels, which require reuse factor of 7, is much heavier. In this paper, a channel is assigned to a new call (or handoff call) if there is a free channel or a channel required a single channel reassignment based on the describe cost function in the following section. For a call which is looking for an inner channel, a free channel means that there is no U in i-IF CELLs and no U in o-IF CELLs. Single channel reassignment is considered when the channel is used by only one of IF CELLs, except those second tier interfering cells occupied by calls using inner channels. For instance, in Table 1, channels 2 and 4 are free channels for calls which are looking for inner channels. Channels ‘C − Ch ’ and ‘C’ are suitable for single channel reassignment. For a call searching for an outer channel, a free channel means that there is no U or U in any IF CELL. Single channel reassignment is possible when the channel is used only by one of IF CELLs. For example, in Table 1, channel 2 is a free channel and channels 4, ‘C − Ch ’ and ‘C’ are suitable for single channel reassignment for calls which are looking for outer channels.

3.2. C o s t F u n ction This channel assignment scheme attempts to minimize the effect of the assignment on channel availability in all IF CELLs of any OWN CELL. The effect of any assignment is evaluated by a cost function, C(x), where x is the channel number. An assignment with least cost is favorable. The cost function C(x) described below can be applied for both inner and outer channel assignment. The cost for assigning a free channel j in an OWN CELL i is expressed as C( j) = I (i) − L(i, j)

(3)

where I (i) is the total number of i-IF CELLs (o-IF CELLs) of OWN CELL i and L(i, j) refers to the number of i-IF CELLs (o-IF CELLs) of OWN CELL i, which are locked for channel j. For example, as shown in Figure 1, the total number of i-IF CELLs and o-IF CELLs of OWN CELL, of cell 17, are 6 and 18 respectively. Similarly, the maximum values of L(i, j) are 6 and 18 for inner and outer channel assignment respectively. From (3), it is clear that cost decreases as the number, L(i, j), of locked cells increases since I (i) remains constant. In other words, an assignment of channel j affects the availability of channel j on the interfering cells less if L(i, j) is larger. Note that i-IF CELLs are used for I (i) and L(i, j) if channel j is assigned as an inner channel. If channel j is used as an outer channel, o-IF CELLs are used only. In the case of a single channel reassignment, if channel j is used by an IF CELL, cell n, and OWN CELL, cell i, wants to use channel j, then cell n might switch the on-going call (currently using channel j in cell n) from channel j to channel k depending on the cost function defined as C( j) = [I (i) − L(i, j)] + [L(n, j) − L(n, k)]

(4)

where L(n, j) refers to the number of i-IF CELLs (o-IF CELLs) of cell n, which are locked for channel j and L(n, k) refers to the number of i-IF CELLs (o-IF CELLs) of cell n, which are locked for channel k. Note that i-IF CELLs are used for both L(n, j) and L(n, k) if

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channel j is used as an inner channel in cell n before switching. Otherwise, o-IF CELLs are considered. When there is more than one suitable channel for assignment, the channel with least cost is selected. If there is more than one channel with the same least cost, the higher order channel is selected. The ordering of outer channel assignment is described with following examples. Note, similar rules are also applied to inner channel assignment except that only i-IF CELLs are taken into account when locked cells are calculated. (1) A channel with larger number of locked cells has a higher order. For example, in Table 1, the order of channel 2 is higher than that of channel 4. (2) If it is a tie in (1), the order of a free channel is higher than that of single reassignment channel. For example, in Table 1, the order of channel 2 is higher than that of channels ‘C − Ch ’ and ‘C’. (3) If there is more than one free channel with equal number of locked cells, a lower-numbered channel has higher order. For instance, in Table 1, the order of channel 2 is higher than that of channel ‘C − Ch + 1’. (4) If there is more than one single reassignment channel with equal number of locked cells, a lower-numbered channel has higher order. For example, in Table 1, the order of channel ‘C − Ch ’ is higher than that of channel ‘C’. 3.3. C h a n n e l R e a rrangement Channel rearrangement means that an on-going call is switched to a just-released channel when the cost can be minimized. In FDRP-WI, channel rearrangements for completed calls are also considered. When a call, which is not using a reserved channel, is completed, channel rearrangement is performed. The channel selection is among the C −Ch channels. To avoid the Ch reserved channels being used by calls other than handoff calls, no channel rearrangement is performed for a completed call using a reserved channel. Different rearrangement processes are performed when calls, which use inner channels or outer channels, are completed. When a call using channel i as an inner channel is completed in cell x, a pre-scan process is done on the lower column (second tier interfering cells, e.g., from cell 3 to cell 31 as shown in Table 1) of the released channel i. (i) If U exists in lower column channel i, an on-going call in cell x using an inner channel without a U in the lower column could be switched. A channel j with least locked cells in the upper column (first tier interfering cells, e.g., from cell 10 to cell 24 as shown in Table 1) is selected. If there is more than one such channel with the same least locked cells, higher-numbered channel is preferred. The purpose of such rearrangement is to free a channel j, which is able to support any call originated in either inner or outer region. (ii) If U does not exist in lower column of channel i, an on-going call using an outer channel could be switched if the number of locked cell in the whole column of the channel is less than that of the released channel. The channel with least locked cells is selected. If more than one such channel with the same least locked cells is available, higher-numbered channel is preferred. If the number of locked cells is equal, the channel is still switched provided that it is higher numbered than the released channel. Note: When a call using an outer channel is completed, only process (ii) is performed.

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3.4. A N e w H a n doff Scheme In stationary cases, calls originated from inner region will use inner channels until the call ends because they always stay in the inner region. However, taking mobility into account, when inner region calls move out of the inner region, intra-cell handoffs will occur. These calls will be switched from inner channels to outer channels. For calls using the outer channels, they will keep using the outer channels throughout the whole cell until the calls end. It means that inner channels will be assigned to calls with smaller reuse distance only by inner region originated calls. Therefore, when mobile users are considered, due to the intra- and inter-handoff calls, more traffic will be served by outer channels as compared to the case with stationary users. Thus, the utilization of inner channels is less. Therefore, the overall reuse distance of the system channels increases as compared to the stationary cases. This is contradicting to the aim of RP where its attempts to reduce the overall reuse distance of the system channels. Hence, the effectiveness of RP is reduced in the mobile environment. In this section, a new handoff scheme, namely “Reverse Overflow” (RO), is introduced to FDRP-WI to improve its performance with addition to the existing intra-cell and inter-cell handoffs. The main purpose of this handoff scheme is to increase the utilization of inner channels in the mobile environment. This handoff method is performed when an MS moves from the outer region into the inner region. Then, the MS will then switch from an outer channel to an inner channel. In this way, we are able to improve the utilization of inner channels. Two methods are proposed to implement the RO. The first method is called Intuitive Switching (IS). In IS, when an MS enters the inner region from the outer region, it will use the same channel. However, the channel will be treated with a reuse distance of 3 instead of 7. Therefore, tables are updated only and no handoff activity is needed. The other method is called Optimum Switching (OS). In OS, when an MS enters the inner region from the outer region, the optimum inner channel, i.e. inner channel with least cost, is searched. If the inner channel is not the same as the currently used outer channel, handoff activity is needed. RO will not introduce any extra dropped calls because the same channel can be always used even though the mobile is moved from larger reuse distance to smaller reuse distance area.

4. Simulation Results and Analysis 4.1. F D R P - W I w i t h S tationary Us ers In this section, the average call blocking probability, Pb and capacity of FDRP-WI are evaluated for stationary users. The cellular system being simulated consists of 49 hexagonal cells and each with two regions as shown in Figure 1. The arrival of new calls is assumed to be a Poisson process, and the call duration is exponentially distributed with a mean of 180 s. Three cases, where total number, M, of 70, 140 and 210 channels available in the system are simulated. The simulation results are presented for FDRP-WI in both uniform and nonuniform traffic distributions and compared to available results for the FCA, Local Packing (LP) [3], EBCA [5], DCA-WI [2] and FRP [8] schemes. In FRP, the channel allocations for inner and outer regions are C(6, 7), C(12, 15) and C(18, 22) per cell for M = 70, 140 and 210 respectively. Such combinations are chosen for the optimum performance of FRP.

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Since Pb = 1% is considered as a reasonable design target, the results of system capacity (or supported traffic load) used in this section are set to Pb = 1%. For the simulation results shown in this paper, the 95% confidence intervals are within ±5% of the average values shown.

4.1.1. Uniform traffic distribution Figure 3 presents the average call blocking probability for FDRP-WI with M = 70, in a uniform traffic distribution. It can be seen in various scheme proposed, FDRP-WI yields the lowest Pb . Using the Erlang B formula, we can obtain the blocking probability for FCA. The capacity value of FCA at Pb = 1% is 4.46 Erlangs. The traffic loads that can be supported by LP, DCA-WI, FRP and FDRP-WI are 6.79, 7.27, 5.31 and 8.97 Erlangs respectively. These values correspond to the increase of 52%, 63%, 19% and 101% respectively compared to the FCA scheme. Figure 4, illustrated the performance of FDRP-WI for M = 210. Obviously from the figure, it is shown that FDRP-WI outperforms all other schemes. The traffic loads that can be supported at Pb = 1% by FCA is 20.3 Erlangs. The corresponding capacity values for LP, DCA-WI, FRP, and FDRP-WI are 25.13, 25.65, 25.85 and 32.28 Erlangs respectively. Compared to FCA scheme, the various schemes improvements are 24%, 26%, 27%, and 59% respectively. As we have noted, the improvement of LP, DCA-WI and FDRP-WI with M = 210 over FCA is lower than that in the case for M = 70. This is because the trunking efficiency is higher for FCA when M is large. This observation agrees with [2]. In Figure 5, it illustrates the traffic loads that can be supported at Pb = 1% for various schemes with different values of M in uniform traffic distribution. Comparing to FCA, LP and DCA-WI, the capacity of FRP increases in greater gradient as M increases. When the number of system channels is 210, FRP is able to outperform DCA schemes like LP and DCA-WI. When the flexible RP is implemented in DCA-WI, i.e. FDRP-WI, it can provide a significant capacity gain. Hence by increasing M from 70 to 140 and finally to 210, FDRP-WI can improve the capacity by about 101%, 71% and 59% respectively over a conventional FCA.

Figure 3. Pb of FDRP-WI for uniform traffic distribution with M = 70.

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Figure 4. Pb of FDRP-WI for uniform traffic distribution with M = 210.

Figure 5. System capacity of different schemes at Pb = 1% for uniform traffic distribution with M from 70 to 210.

4.1.2. Non-uniform traffic distribution Comparison of results for non-uniform traffic distributions for M = 70 and 210 channels are done using distributions in [5, Figure 2] (“distribution A”) and [4, Figure. 6] (“distribution B”) respectively. Note for non-uniform traffic distributions, wrap-around is not used. In distribution A, the call arrival rates range from 20 to 200 calls/hour and the average offered loads over the 49 cells is 4.59 Erlangs. Figure 6 shows the Pb over 49 cells for FCA, LP, EBCA, DCA-WI and FDRP-WI schemes. We can see that Pb for DCA-WI is slightly lower than that of LP and EBCA. However, FDRP-WI provides much lower blocking probability than others. The capacity for FCA, DCA-WI and FDRP-WI are 3.0, 7.3 and 9 Erlangs. The capacity improvements for DCA-WI and for FDRP-WI over FCA are 143% and 200% respectively. For distribution B, the offered load per cell, averaged over the 49 cells is 21.9 Erlangs. The performance of FDRP-WI under non-uniform traffic distribution B is shown in Figure 7. The

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Figure 6. Pb of FDRP-WI for non-uniform traffic distribution A with M = 70.

Figure 7. Pb of FDRP-WI for non-uniform traffic distribution B with M = 210.

capacity supported by FCA is 14 Erlangs. The values for LP, DCA-WI and FDRP-WI are 22.6, 23.2 and 29.72 Erlangs, which are equivalent to 61%, 66% and 112% improvement over FCA. 4.2. F D R P - W I w i t h M o b i l e U s e r s The assumptions for FDRP-WI with mobile users are described as follows. Each cell in the plane √ has radius ro = 2 km. According to (2) in Section 2, the radius of an inner region is ri = 2 3/7 km. The user distribution is assumed to be uniform. The arrival of new calls is assumed to be a Poisson process, and the call duration is exponentially distributed with a mean of 120 s. Two cases, where total number, M, of 70 channels and 210 channels are available in the system are simulated. Mobility model A and B will be used to simulate the cellular system with mobile users. The value of T for Model B is 5 s. This value is chosen because the MS changes its speed and direction often within a cell. System performance measures such as

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Pb , Pd , handoff activity and capacity are evaluated. Different user speeds are considered in some cases as well. The simulation results will then be compared with other schemes, FCA, fixed reuse partitioning (FRP) [8], LP [3] and DCA-WI [2]. The results for FCA and FRP are obtained from the analysis in [9]. The channel allocations for inner and outer regions in FRP are C(2, 9) and C(7, 27) per cell for M = 70 and 210 respectively. Such combinations are chosen for the FRP optimum performance when mobility is considered. It is noted that the combinations are different from those used in Section 4.1.1. The reason behind the difference is because other than traffic distribution, mobility is also considered a factor for the optimum channel pre-allocation imposed by fixed RP. In [9], it is also shown that channel allocations for the optimum performance of FRP with mobility and without mobility are different. With flexible RP implementation, FDRP-WI is able to eliminate such disadvantages. For the simulation shown for this section, the 95% confidence intervals are within ±5% of the average values. 4.2.1. FDRP-WI without reserved channels This section illustrates the results of FDRP-WI scheme without reserved channels. Figure 8 presents the Pb and Pd for FDRP-WI with M = 70 and E[V ] = 50 km/h for mobility model A. We can see that FDRP-WI yields the lowest Pb . However, when the traffic load is heavy, FDRP-WI has higher Pd than LP and DCA-WI. The reason is because when traffic load is high, more handoffs are required for FDRP-WI since RP is used. It can be also seen that FRP is less effective to handle handoff calls as compared to FCA. Similar observation is also noted in the case for M = 210 system channels. The comparison of Pb and Pd of FDRP-WI with different mobility models A and B is shown in Figure 9. for M = 210 and E[V ] = 50 km/h. It can be seen in the mobility models that the Pb for both of LP and DCA-WI is close, while FDRP-WI has a lower Pb in model B. Pd of LP, DCA-WI and FDRRP-WI is lower in model B than in model A because the MS tends to stay longer in a cell and thus requires fewer handoffs procedures. In general, Pb and Pd of FDRP-WI are lower than those of LP and DCA-WI in both models. Figure 10 shows a general trend that the handoff activity [13] is lower in model B than in model A for the same scheme because of longer residual time in a cell for model B. These findings agree with [9]. Also, the figure shows that, when the mobility model is same, the handoff activities are very close for schemes without RP implementations we see in LP and DCA-WI. The result is expected because when RP technique is used in the scheme like FDRP-WI, the handoff activity is increased since there will be extra intra-cell handoffs required. Figure 11 shows the capacity of FDRP-WI in a 70-channel system, with E[V ] = 50 km/h and α ranging from 0.1 to 0.9. It can be seen that FDRP-WI provides the highest system capacity over the whole α range. We also found that the capacity of FRP is even lower than that of FCA when α > 0.53. This is because RP technique in FRP induces higher handoff rate and results in higher Pd as compared to FCA. The system capacity of FCA at α = 0.5 (i.e., Pb and Pd are equally important) is 4.72 Erlangs. The values for FRP, LP, DCA-WI and FDRP-WI are 4.732, 7.072, 7.602 and 7.98 Erlangs respectively, which corresponds to the improvement of 0.25%, 49.8%, 61% and 69% respectively as compared to FCA. The capacity of FDRP-WI with M = 210 at GOS = 0.01 is presented in Figure 12 with parameters E[V ] = 50 and 25 km/h for α ranging from 0.1 to 0.9. We can see that for E[V ] = 50 km/h, the system capacity of FCA at α = 0.5 is 20.97 Erlangs. The system capacities for FRP, LP, DCA-WI and FDRP-WI are 22.28, 26.1, 26.55 and 28.76 Erlangs respectively. These values correspond to the increase of 6.2%, 24.5%, 26.6% and 37.2% respectively as

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Figure 8. (a) Blocking probability and (b) dropping probability of FDRP-WI for mobility model A with E[V ] = 50 km/h and M = 70.

compared to FCA. And when E[V ] = 25 km/h, the system capacity at α = 0.5 for FCA is 21.46 Erlangs. The capacities of FRP, LP, DCA-WI and FDRP-WI are 23.67, 26.2, 26.63 and 30.23 Erlangs, which are equivalent to 10.3%, 22.1%, 24.1% and 40.9% improvement over FCA. It shows that FRP and FDRP-WI provide higher capacity for slower user speed. This is because higher user speed results in higher handoff activity and reduces the effectiveness of RP. 4.2.2. Effect of reserved channels on FDRP-WI The effect of number, Ch , of reserved channels for handoff calls on Pb and Pd is simulated for system for M = 70 and 210 with mobility model A at E[V ] = 50 km/h. The results are shown in Figure 13. It is found that as Ch increases, Pd decreases, but Pb increases. The increased number of reserved channels can effectively reduce the call dropping probability in the system. Similar findings are observed for mobility model B as well. Thus, to determine the optimum value of Ch to be used for a given system, we can maximize the system capacity at a given GOS value. The capacities at GOS = 0.01 for FDRP-WI with different Ch values are shown in Figures 14 and 15. In Figure 14, the simulation is based on mobility model A. For M = 70, the maximum capacity is obtained with Ch = 0 for 0.1 ≤ α ≤ 0.65 and thus the optimum number, Copt , of reserved channels for handoff calls is

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Figure 9. Comparison of mobility model A and B for FDRP-WI in (a) blocking probability and (b) dropping probability with E[V ] = 50 km/h and M = 210.

Figure 10. Handoff Activity of FDRP-WI for mobility models A and B with E[V ] = 50 km/h and M = 210.

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Figure 11. Capacity of FDRP-WI for mobility model A at GOS = 0.01 with E[V ] = 50 km/h and M = 70.

Figure 12. Capacity of FDRP-WI for mobility model A at GOS = 0.01 with (a) E[V ] = 50 km/h and (b) E[V ] = 25 km/h for M = 210.

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Figure 13. Blocking probability and dropping probability of FDRP-WI with different Ch values for mobility model A at GOS = 0.01 with E[V ] = 50 km/h for (a) M = 70 and (b) M = 210.

0. For 0.65 ≤ α ≤ 0.75, 0.75 ≤ α ≤ 0.85 and 0.85 ≤ α ≤ 0.9, the Copt values are 2, 4 and 6 respectively. Hence, when M = 210, the Copt values for 0.1 ≤ α ≤ 0.65, 0.65 ≤ α ≤ 0.77 and 0.77 ≤ α ≤ 0.9 are 0, 5 and 10 respectively. Next, we considered the mobility model B, quite similar findings are observed as shown in Figure 15. As we have expected, the overall capacities in model B are higher than that in model A. When M = 70, for 0.1 ≤ α ≤ 0.65, 0.65 ≤ α ≤ 0.77 and 0.77 ≤ α ≤ 0.9, the Copt values are 0, 2 and 4 respectively. Hence, we can considered that the capacity for Ch = 6 is always lower than that for Ch = 4. For M = 210, the Copt values for 0.1 ≤ α ≤ 0.65, 0.65 ≤ α ≤ 0.82, and 0.82 ≤ α ≤ 0.9 are 0, 5 and 10 respectively. 4.2.3. Proposed handoff scheme in FDRP-WI with mobile users In Figure 5, it is shown that with only stationary users, FDRP-WI can have 101% and 59% capacity improvement over FCA for M = 70 and 210 respectively. When mobile users are taken into consideration, the improvement is decreased to 69% and 37.2% for E[V ] = 50 km/h as shown in previous section. Results also show that the capacity improvement of FDRP-WI decreases when E[V ] changes from 25 to 50 km/h. When the user speed is low, the channel utilization based on a smaller reuse distance criterion increases because more inner channels

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Figure 14. Capacity of FDRP-WI with different Ch values for mobility model A at GOS = 0.01 with E[V ] = 50 km/h for (a) M = 70 and (b) M = 210.

can be used more often as described in Section 3. Note that stationary user is a special case with user speed of constant 0 km/h. In this section, the effectiveness of the new proposed handoff schemes using RO, based on IS and OS, is examined. Figure 16 shows the capacity improvement for FDRP-WI for the cases with M = 70 and M = 210 when RO is deployed. In the simulation, mobility model A is considered and no channel is reserved for handoff calls. The capacities for FDRP-WI without RO, FDRP-WI with IS and FDRP-WI with OS in M = 70 channel system at α = 0.5 are 7.98, 8.665 and 8.802 Erlangs. As compared to FCA, the improvements are 69%, 83.6% and 86.5% respectively. In the case with M = 210 channels, the capacities are 28.76, 31.7 and 32.29 Erlangs. These values are corresponded to the increase of 37.15%, 51.17% and 54% respectively comparing to FCA. The capacity improvement is substantial with RO implementation. It is also noticed that, as GOS parameter increases, the capacity decreases slightly because Pd is slightly higher than Pb for GOS = 0.01. Figure 17 shows the handoff activities for FDRP-WI with the introduction of RO in the system with M = 70 and M = 210. When M = 70, the average of handoff activity for FDRP-WI, FDRP-WI with IS and FDRP-WI with OS are 0.833, 0.988 and 1.248 respectively. When M = 210, the average of handoff activity for FDRP-WI, FDRP-WI with IS and FDRP-WI with OS are also 0.833, 0.988 and 1.248 respectively. Thus, we can

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Figure 15. Capacity of FDRP-WI with different Ch values for mobility model B at GOS = 0.01 with E[V ] = 50 km/h for (a) M = 70 and (b) M = 210.

see that there is no obvious difference in handoff activity between a 70-channel system and a 210-channel system. In both cases, it is found that with RO implementation, the handoff rates are increased. This is expected because both IS and OS introduce extra intra-cell handoffs when MS’s move out of the inner region after they have performed RO. OS has even higher handoff rate than IS because OS introduces extra handoffs when RO is performed.

5. Conclusions This paper presents a new network-based channel assignment scheme, FDRP-WI, which integrates DCA with interference information (DCA-WI) and flexible reuse partitioning (RP). The merit of FDRP-WI is that it eliminates the need for pre-allocation of channels to each partitioned region, which is required in the conventional RP implementation. Simulation results have confirmed the effectiveness of FDRP-WI scheme with stationary users. With the combination of DCA-WI and flexible RP, FDRP-WI improves the system capacity tremendously over FCA, LP, DCA-WI and FRP. Under uniform traffic, FDRP-WI can provide more than 100% improvement over FCA for 70 system channels, thus, a substantial

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Figure 16. Capacity of FDRP-WI with RO for mobility model A at GOS = 0.01 with E[V ] = 50 km/h for (a) M = 70 and (b) M = 210.

capacity improvement for cellular systems. Under non-uniform traffic distributions, FDRP-WI is able to show its efficiency on spectrum utilization and it can provide a great capacity gain compared to FCA and other DCA schemes. FDRP-WI with mobility is further investigated on the effectiveness of this channel assignment scheme. The impact of mobile users on the new call blocking probability, the call dropping probability, system capacity and handoff activity are studied by using two different mobility models with different user speeds. Moreover, a new handoff scheme called “RO” is introduced to improve the performance of FDRP-WI under mobile environment by increasing the utilization of channels with smaller reuse distances. In conclusion, with only stationary users in the system, FDRP-WI performs very well in both uniform and non-uniform traffic distributions to provide higher capacity for TDMA cellular systems. When mobility is considered, FDRP-WI is still able to achieve large system capacity as compared to other schemes like FCA, FRP, LP and DCA-WI. Its performance can be further enhanced by introducing “RO” handoff scheme but at the expense of higher handoff rates in the system.

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Figure 17. Handoff activity of FDRP-WI with RO for mobility model A with E[V ] = 50 km/h for (a) M = 70 and (b) M = 210.

References 1. I. Katzela and M. Naghshineh, “Channel Assignment Schemes for Cellular Mobile Telecommunication Systems: A Comprehensive Survey,” IEEE Pers. Commun., Vol. 3, No. 3, pp. 10–31, Jun. 1996. 2. P.H.J. Chong and C. Leung, “A Network-Based Dynamic Channel Assignment Scheme for TDMA Cellular Systems,” Int. J. Wireless Inform Networks, Vol. 8, No. 3, pp. 155–165, Jul. 2001. 3. C.-L. I and P.-H. Chao, “Local Packing – Distributed Dynamic Channel Allocation at Cellular Base Station,” In Proc. IEEE GLOBECOM ’93, pp. 293–301, 1993. 4. K. Yeung and T. Yum, “Compact Pattern Based Dynamic Channel Assignment for Cellular Mobile Systems,” IEEE Trans. Veh. Technol., Vol. 43, No. 4, pp. 892–896, Nov. 1994. 5. K. Chang, J. Kim, C. Yim, and S. Kim, “An Efficient Borrowing Channel Assignment Scheme for Cellular Mobile Systems,” IEEE Trans. Veh. Technol., Vol. 47, No. 2, pp. 602–608, May 1998. 6. S.W. Halpern, “Reuse Partitioning in Cellular Systems,” In Proc. IEEE Veh. Technol. Conf., Toronto, Canada, pp. 322–327, May 1983. 7. J. Zander and M. Frodigh, “Capacity Allocation and Channel Assignment in Cellular Radio System Using Reuse Partitioning,” Electron. Lett., Vol. 28, No. 5, pp. 438–440, Feb. 1992. 8. P.H.J. Chong and C. Leung, “Capacity Improvement in Cellular Systems with Reuse Partitioning,” J. Commun. Networks, Vol. 3, No. 3, pp. 280–287, Sep. 2001. 9. P.H.J. Chong and C. Leung, “Performance of Reuse Partitioning in Cellular Systems with Mobile Users,” Int. J. Wireless Inform. Networks, Vol. 10, No. 1, pp. 17–31, Jan. 2003.

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10. T. Halonen, J. Romero, and J. Melero, GSM, GPRS and EDGE Performance, Evolution Towards 3G/UMTS, West Sussex: John Wiley & Sons, 2002. 11. A. Pattavina, S. Quadri, and V. Trecordi, “Reuse Partitioning in Cellular Networks with Dynamic Channel Allocation,” Wireless Networks, pp. 299–309, 1999. 12. S.L. Chen and P.H.J. Chong, “Capacity Improvement in Cellular Systems with Dynamic Channel Assignment and Reuse Partitioning,” In Proc. IEEE PIMRC ’03, Vol. 2, pp. 1441–1445, Sep. 2003. 13. D. Hong and S. Rappaport, “Traffic Model and Performance Analysis for Cellular Mobile Radio Telephone Systems with Prioritized and Nonprioritized Handoff Procedures,” IEEE Trans. Veh. Technol., Vol. VT-35, No. 3, pp. 77–92, Aug. 1986. 14. R. Thomas, H. Gilbert, and G. Mazziotto, “Influence of the Movement of the Mobile Station on the Performance of a Radio Cellular Network,” In Proc. 3rd Nordic Seminar, Copenhagen, Paper 9.4, Sep. 1988. 15. R. Guerin, “Channel Occupancy Time Distribution in a Cellular Radio System,” IEEE Trans. Veh. Technol., Vol. VT-36, pp. 89–99, Aug. 1987.

Steven L. Chen was born in Guangdong, China, on December 3, 1979. He received the B. Eng. (1st Class Honors) and M. Eng degrees in electrical and electronic engineering from Nanyang Technological University, Singapore, in 2002 and 2004, respectively. His research interests are wireless communication systems and radio resource allocation and optimization for the systems.

Peter H. J. Chong was born in Hong Kong, China, on June 4 1970. He received the B.Eng. (with distinction) in electrical engineering from the Technical University of Nova Scotia (currently Dalhousie University), Halifax, NS, Canada, in 1993, and the M.A.Sc. and Ph.D. degrees in electrical engineering from the University of British Columbia, Vancouver, BC, Canada, in 1996 and 2000, respectively.

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Between July 2000 and January 2001, he worked with Advanced Networks Division at Agilent Technologies Canada Inc., Vancouver, BC, Canada. Between Feburary 2001 and May 2002, he was a Research Engineer in the Radio Communications Laboratory at Nokia Research Center, Helsinki, Finland, and was involved in research on WCDMA and standardization. Since May 2002, he has been with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, as an Assistant Professor. He was a Technical Program Committee Chair for IEE 2nd Mobility Conferecne 2005. His research interests are in the areas of wireless and mobile communications systems including channel assignment schemes, radio resource management, multiple access, and mobile ad hoc networks.

Ming Yang was born in Shenyang, China, on October 18, 1978. He received the B.S degree in Information engineering (English intensive) from Dalian University of Technology, China, in 2002. Since October 2002, he has been pursuing his Ph.D degree at the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. His research interests include handoff, channel allocation, and radio resource management for present and future mobile communication systems.