Dynamic channel assignment with flexible reuse partitioning in cellular systems

Wireless Personal Communications (2007) 42:161–183DOI 10.1007/s11277-006-9172-0 c© Springer 2006

Dynamic Channel Assignment with Flexible Reuse Partitioningin Cellular Systems

STEVEN LI CHEN, PETER H. J. CHONG and MING YANGNetwork Technology Research Center, School of EEE, Nanyang Technological University, Nanyang Avenue,Singapore, 639798, SingaporeE-mails: [email protected], [email protected]

Abstract. In cellular communications, one of the main research issues is how to achieve optimum system capacitywith limited frequency spectrum. For many years, researchers have proposed and studied many dynamic chan-nel assignment (DCA) schemes to increase the capacity of cellular systems. Another proposed technique, ReusePartitioning (RP), is used to achieve higher capacity by reducing the overall reuse distance. In convention, whenRP is exploited in network-based DCA, a portion of channels will be assigned permanently to each partitionedregion. However, the number of channels assigned to each region may not be optimum due to factors like theuneven and time-varying traffics. In this paper, a new network-based DCA scheme is proposed with the flexibleuse of RP technique, named as flexible dynamic reuse partitioning with interference information (FDRP-WI). Inthis 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 canuse any channel. The scheme aims to minimize the effect of assigned channels on the availability of channels foruse in the interfering cells and to reduce overall reuse distance. Both FDRP-WI with stationary users and mobileusers are investigated. Simulation results have confirmed the effectiveness of FDRP-WI scheme. In the case withstationary users, FDRP-WI exhibits outstanding performance in improving the system capacity under both uniformand non-uniform traffic distributions. Under the uniform traffic case, the scheme can provide over 100% capac-ity 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 thecall dropping probability, Pd, is evaluated. The effect on system capacity of reserving some channels for handoffcalls is first studied. Then, we propose a new handoff scheme, called “Reverse Overflow” (RO), to improve theutilization of channels with smaller reuse distances under mobile environment. Simulation results show that, withRO handoff, the system capacity of FDRP-WI is effectively improved at the expense of higher handoff rates in thecellular system.

Keywords: dynamic channel assignment, reuse partitioning, cellular mobile communications, channel rearrange-ment, handoff, mobility

1. Introduction

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

162 S. L. Chen et al.

resource management compared to centralized DCA. In DDCA, the channel assignment deci-sion is made by each base station (BS) and/or mobile station (MS) and the information of thewhole 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, thechannel assignment is based on minimizing the impact of every assignment on channel avail-ability in all the interfering cells. Every channel is ordered and an interference informationtable (IIT) is used in each BS. It has been shown that DCA-WI out performs other existingschemes [3–5] in both uniform and non-uniform traffic distributions. However, these DDCAschemes [2–5] have not achieved the optimum performance because the assignment policiesof 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 closeto the BS, they are able to tolerate higher interference and thus can be assigned channels withsmaller cluster size to improve system capacity.

Reuse Partitioning (RP) [6] is a very useful technique to achieve high spectrum efficiencyin cellular systems by using different cluster sizes. In RP, a cell is divided into several concen-tric regions and each region has a different cluster size. A mobile close to its BS is assigneda channel with a smaller reuse distance, whereas a mobile far from its BS with low signalquality is assigned a channel with a larger reuse distance. In this way, overall reuse distanceis 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% ascompared 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 perma-nently to each partitioned region [11, 12, 6, 8]. However, there are two main design issuesrelated to the simple RP concept [1]. The first issue is the capacity allocation problem wherethe capacity allocation procedure takes place in the cell planning process. The implementeris to decide how many channels should be assigned to each reuse pattern. The problem ariseswhen the number of channels assigned to each region may not be optimum due to the unevenand 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 partitioningwith interference information (FDRP-WI), which integrates DCA-WI with flexible two-regionRP, 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 theco-channel interference (CCI) constraint. An inner region originated call will use a channelbased on a smaller reuse distance constraint, while an outer region originated call will usea channel based on a larger reuse distance constraint. The flexible use of RP in FDRP-WIhas 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 capacityis expected.

First, FDRP-WI with stationary users is studied. It shows that FDRP-WI can provide greatcapacity improvement under both uniform and non-uniform traffic distributions. Next, theimpact of mobile users on FDRP-WI scheme is investigated with only uniform traffic distri-bution. Two mobility models are used to study the impact of mobile users on the new callblocking probability, Pb, and the call dropping probability, Pd, in the cellular system. Theeffect of a cutoff priority scheme for handoff calls on capacity is considered. The capacity is

Dynamic Channel Assignment 163

defined as the total offered traffic that can support in a particular cell at a certain Grade ofService (GOS) that is given by [13]

GOS = (1 − α)Pb + αPd (1)

where α ∈ [0, 1] is the GOS parameter and indicates the relative importance of Pb and Pd ina given system.

It is found that prioritized handoff can reduce Pd but it may also degrade the capacity insome cases. Also, it can be shown that the low utilization of channels with smaller reuse dis-tances 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 smallerreuse distances. Simulation results have shown that the new handoff scheme can effectivelyimprove the performance of the FDRP-WI scheme at the expense of higher handoff activity.

2. FDRP-WI Scheme

2.1. N e t wo r k S c enario

A service area of 49 regular hexagonal cells is considered as shown in Figure 1. Each cell isdivided into inner and outer concentric regions, where they are associated with CS of 3 and7 respectively. When the inner region of a cell has a CS value of 3, its neighboring cells inthe first tier are within the reuse distance range. When the outer region of a cell has a CSvalue of 7, the interference area covers the first two tier neighboring cells. It means that if achannel is assigned to an inner (outer) region originated call, that channel cannot be reusedin the neighboring cells in the first (first two) tier(s). Using Figure 1 to illustrate, the smallhexagonal 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 theouter 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

Ni/

r2i = No

/r2

o (2)

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. Inother words, the left-most and the right-most columns in the 49-cell plane as shown in Figure1 are connected with each other, so are the top and the bottom rows. Therefore, if any MSreaches the cell plane boundary, it will return to the system automatically.

2.2. I nt e r f e r e nc e I nf o rmation Table (IIT)

An IIT shown in Table 1 is used to record the channel status in each cell. Using Table 1 of cell17, 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. Thechannel reservation is only applicable when mobility is considered, i.e., Ch = 0, in the caseof stationary users. The first column lists the own cell, cell i , (hereafter referred to as OWNCELL) and all its interference cells’ (IF CELLs) numbers, in the order of cell i , cell i’s firsttier interfering cells, and cell i’s second tier interfering cells. The cells in the first tier and


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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. Allother columns contained the information of all channels available in the system, i.e., each rowindicates the channel status for a particular cell.

2.2.1. Legend explanationThe legends used in the IIT are described as follow. A letter U or U′ in the box indicates achannel is assigned based on the CCI constraint with reuse distance of 3 or 7 respectively. Forexample, in Table 1, channels 1 and ‘C-1’ are used by MS’s in cell 17 with reuse distance of3. Channels 3 and ‘C’ are assigned to MS’s in cell 17 and 22 respectively, with reuse distanceof 71. A letter L means the channel, say channel k, is locked in an IF CELL because one of theIF CELL’s interfering cells, say cell x , uses channel k. Thus, that IF CELL is not allowed touse channel k. Note that the OWN CELL is outside the interference range of channel k, whichis used in cell x with reuse distance of 3 or 7. For instance, in Table 1, channel 2 is lockedin cell 3. This is because one interfering cell of cell 3, say cell 1, has used channel 2 withreuse distance of 7, but it does not affect the availability of channel 2 for use in cell 17 withreuse distance of 3 or 7 in this particular example. Thus, from Table 1, we know that cell 3cannot use channel 2. A symbol of 2L means that two such interfering cells of IF CELL usethat 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 assignedto an inner (outer) channel’ or ‘the call uses an inner (outer) channel’ in the following context.


Table 1. IIT of cell 17

Channel no.

C − Ch Non-reserved channels Ch Reserved channels

Cell no. 1 2 3 4 . . . C − Ch C − Ch + 1 . . . C-1 C

Own Cell

17 U U′ . . . . . . U

i-IF Cells

10... . . . L . . .

24 U L

o-IF Cells

3 L . . . . . . L

4 L...

19 U L

22 U L U′...

30 L

31 2L

2.2.2. Table updatingAny channel assignment and channel release will initiate an updating procedure. When OWNCELL assigns a call to channel j with smaller (larger) reuse distance, (i) it first updates its IIT byinserting a letter U(U′) in the [OWN CELL, channel j] box; (ii) then, it informs its IF CELLs byinserting a letter U(U′) in the [OWN CELL, channel j] box in their IITs; (iii) after that, each i-IFCELL (o-IF CELL) informs all its IF CELLs, (hereafter referred to as Other IF CELLs), whichis not one of the i-IF CELLs (o-IF CELLs), that the particular channel j is locked, i.e., a letterL is inserted in Other IF CELLs’ IITs (Note that L is additive); (iv) finally, Other IF CELLswith L inserted inform all their IF CELLs its latest number of locked cells on that particularchannel. The updating for channel release follows the same procedure, except that “removingU(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-WIscheme 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 anddirection where both parameters are independent random variables. The speed and directionof an MS are uniformly distributed in [E[V ]/2, 3E[V ]/2] and (0, 2π ] respectively, whereE[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


V1

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V3V

Cell Cell

Model BModel A

Figure 2. Two mobility models.

speed and direction after a random time interval, where the change is exponentially distributedwith 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. InModel B, the MS is more likely to changes speed and direction within a cell depending on thevalue of T . If T is small, the MS changes speed and direction more frequently within a celland 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 theinner channel and outer channel respectively. For the cluster size of an inner channel 3, it willaffect 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 ha nne l A s s i g nment

Assume that there are C available channels in a cellular system, and Ch channels are exclu-sively reserved for handoff calls. As mentioned, for the case of stationary users, the reservedchannel Ch = 0. When a new call is initiated in the inner region, it is assigned a channel basedon a smaller reuse distance of 3 (an inner channel), while an outer region originated call willuse 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 callwill be assigned an inner or outer channel from one of the C − Ch channels. The idea remainsthe same as an inner region originated call is assigned an inner channel, while an outer regionoriginated 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 itsMS exits the inner region, and it will be assigned an outer channel. The channel assignmentfor the handoff call can be chosen from all C channels. If no channel is found, the intra-cellhandoff call is dropped. A call using an outer channel can keep using the same channel as longas its MS remains within the cell because it will not violate the CCI constraints. An inter-cellhandoff is required only when its MS exits the cell. Then, the inter-cell handoff call will beassigned a suitable outer channel in the new cell. The channel assignment for the inter-cellhandoff call can be chosen from all C channels as well. If no channel is found, the inter-cellhandoff call is dropped.


As we can see, the inner channel is used for calls originated in the inner region only. How-ever, 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 outerregion (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 factorof 7, is much heavier.

In this paper, a channel is assigned to a new call (or handoff call) if there is a free channelor a channel required a single channel reassignment based on the describe cost function inthe following section. For a call which is looking for an inner channel, a free channel meansthat there is no U in i-IF CELLs and no U′ in o-IF CELLs. Single channel reassignment isconsidered when the channel is used by only one of IF CELLs, except those second tier inter-fering cells occupied by calls using inner channels. For instance, in Table 1, channels 2 and4 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, afree channel means that there is no U or U′ in any IF CELL. Single channel reassignment ispossible when the channel is used only by one of IF CELLs. For example, in Table 1, channel 2is a free channel and channels 4, ‘C −Ch’ and ‘C’ are suitable for single channel reassignmentfor calls which are looking for outer channels.

3.2. C o s t F unction

This channel assignment scheme attempts to minimize the effect of the assignment on channelavailability in all IF CELLs of any OWN CELL. The effect of any assignment is evaluatedby a cost function, C(x), where x is the channel number. An assignment with least cost isfavorable. The cost function C(x) described below can be applied for both inner and outerchannel 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) refersto 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 OWNCELL, of cell 17, are 6 and 18 respectively. Similarly, the maximum values of L(i, j) are 6 and18 for inner and outer channel assignment respectively. From (3), it is clear that cost decreasesas 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 ifL(i, j) is larger. Note that i-IF CELLs are used for I (i) and L(i, j) if channel j is assigned asan 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 functiondefined 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 lockedfor channel j and L(n, k) refers to the number of i-IF CELLs (o-IF CELLs) of cell n, whichare locked for channel k. Note that i-IF CELLs are used for both L(n, j) and L(n, k) if


channel j is used as an inner channel in cell n before switching. Otherwise, o-IF CELLs areconsidered.

When there is more than one suitable channel for assignment, the channel with least cost isselected. If there is more than one channel with the same least cost, the higher order channelis 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 CELLsare 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 reassignmentchannel. 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-numberedchannel has higher order. For instance, in Table 1, the order of channel 2 is higher thanthat 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 ha nne l R e a rrangement

Channel rearrangement means that an on-going call is switched to a just-released channelwhen the cost can be minimized. In FDRP-WI, channel rearrangements for completed callsare also considered. When a call, which is not using a reserved channel, is completed, channelrearrangement is performed. The channel selection is among the C −Ch channels. To avoid theCh reserved channels being used by calls other than handoff calls, no channel rearrangementis performed for a completed call using a reserved channel. Different rearrangement processesare 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 processis done on the lower column (second tier interfering cells, e.g., from cell 3 to cell 31 as shownin 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 channelwithout a U in the lower column could be switched. A channel j with least locked cellsin the upper column (first tier interfering cells, e.g., from cell 10 to cell 24 as shown inTable 1) is selected. If there is more than one such channel with the same least lockedcells, higher-numbered channel is preferred. The purpose of such rearrangement is tofree a channel j , which is able to support any call originated in either inner or outerregion.

(ii) If U does not exist in lower column of channel i , an on-going call using an outer channelcould be switched if the number of locked cell in the whole column of the channel isless than that of the released channel. The channel with least locked cells is selected. Ifmore than one such channel with the same least locked cells is available, higher-numberedchannel is preferred. If the number of locked cells is equal, the channel is still switchedprovided that it is higher numbered than the released channel.Note: When a call using an outer channel is completed, only process (ii) is performed.


3.4. A N e w H a ndoff Scheme

In stationary cases, calls originated from inner region will use inner channels until the call endsbecause they always stay in the inner region. However, taking mobility into account, wheninner region calls move out of the inner region, intra-cell handoffs will occur. These calls willbe switched from inner channels to outer channels. For calls using the outer channels, they willkeep using the outer channels throughout the whole cell until the calls end. It means that innerchannels will be assigned to calls with smaller reuse distance only by inner region originatedcalls. 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 thesystem channels increases as compared to the stationary cases. This is contradicting to the aimof 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 introducedto FDRP-WI to improve its performance with addition to the existing intra-cell and inter-cellhandoffs. The main purpose of this handoff scheme is to increase the utilization of inner chan-nels in the mobile environment. This handoff method is performed when an MS moves fromthe outer region into the inner region. Then, the MS will then switch from an outer channelto an inner channel. In this way, we are able to improve the utilization of inner channels. Twomethods 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 samechannel. However, the channel will be treated with a reuse distance of 3 instead of 7. There-fore, tables are updated only and no handoff activity is needed. The other method is calledOptimum 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 channelis not the same as the currently used outer channel, handoff activity is needed. RO will notintroduce any extra dropped calls because the same channel can be always used even thoughthe 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 wi t h S tationary Users

In this section, the average call blocking probability, Pb and capacity of FDRP-WI are evalu-ated for stationary users. The cellular system being simulated consists of 49 hexagonal cellsand each with two regions as shown in Figure 1. The arrival of new calls is assumed to bea 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 systemare simulated. The simulation results are presented for FDRP-WI in both uniform and non-uniform 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 forinner and outer regions are C(6, 7), C(12, 15) and C(18, 22) per cell for M = 70, 140 and210 respectively. Such combinations are chosen for the optimum performance of FRP.


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 resultsshown in this paper, the 95% confidence intervals are within ±5% of the average values shown.

4.1.1. Uniform traffic distributionFigure 3 presents the average call blocking probability for FDRP-WI with M = 70, in auniform traffic distribution. It can be seen in various scheme proposed, FDRP-WI yields thelowest Pb. Using the Erlang B formula, we can obtain the blocking probability for FCA. Thecapacity value of FCA at Pb = 1% is 4.46 Erlangs. The traffic loads that can be supported byLP, DCA-WI, FRP and FDRP-WI are 6.79, 7.27, 5.31 and 8.97 Erlangs respectively. Thesevalues correspond to the increase of 52%, 63%, 19% and 101% respectively compared to theFCA scheme.

Figure 4, illustrated the performance of FDRP-WI for M = 210. Obviously from thefigure, it is shown that FDRP-WI outperforms all other schemes. The traffic loads that canbe supported at Pb = 1% by FCA is 20.3 Erlangs. The corresponding capacity values forLP, 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%, and59% respectively. As we have noted, the improvement of LP, DCA-WI and FDRP-WI withM = 210 over FCA is lower than that in the case for M = 70. This is because the trunkingefficiency 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 variousschemes with different values of M in uniform traffic distribution. Comparing to FCA, LP andDCA-WI, the capacity of FRP increases in greater gradient as M increases. When the numberof 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 signifi-cant capacity gain. Hence by increasing M from 70 to 140 and finally to 210, FDRP-WI canimprove 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.


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 distributionComparison of results for non-uniform traffic distributions for M = 70 and 210 channels aredone using distributions in [5, Figure 2] (“distribution A”) and [4, Figure. 6] (“distributionB”) respectively. Note for non-uniform traffic distributions, wrap-around is not used. In dis-tribution A, the call arrival rates range from 20 to 200 calls/hour and the average offered loadsover 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 thatof LP and EBCA. However, FDRP-WI provides much lower blocking probability than oth-ers. The capacity for FCA, DCA-WI and FDRP-WI are 3.0, 7.3 and 9 Erlangs. The capacityimprovements 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. Theperformance of FDRP-WI under non-uniform traffic distribution B is shown in Figure 7. The


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 wi 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 theplane 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 assumedto 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 thesystem are simulated. Mobility model A and B will be used to simulate the cellular systemwith mobile users. The value of T for Model B is 5 s. This value is chosen because the MSchanges its speed and direction often within a cell. System performance measures such as


Pb, Pd, handoff activity and capacity are evaluated. Different user speeds are considered insome 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 areobtained from the analysis in [9]. The channel allocations for inner and outer regions in FRPare C(2, 9) and C(7, 27) per cell for M = 70 and 210 respectively. Such combinations arechosen for the FRP optimum performance when mobility is considered. It is noted that thecombinations are different from those used in Section 4.1.1. The reason behind the differenceis because other than traffic distribution, mobility is also considered a factor for the optimumchannel pre-allocation imposed by fixed RP. In [9], it is also shown that channel allocations forthe optimum performance of FRP with mobility and without mobility are different. With flex-ible RP implementation, FDRP-WI is able to eliminate such disadvantages. For the simulationshown for this section, the 95% confidence intervals are within ±5% of the average values.

4.2.1. FDRP-WI without reserved channelsThis section illustrates the results of FDRP-WI scheme without reserved channels. Figure 8presents the Pb and Pd for FDRP-WI with M = 70 and E[V ] = 50 km/h for mobilitymodel A. We can see that FDRP-WI yields the lowest Pb. However, when the traffic load isheavy, FDRP-WI has higher Pd than LP and DCA-WI. The reason is because when trafficload is high, more handoffs are required for FDRP-WI since RP is used. It can be also seenthat FRP is less effective to handle handoff calls as compared to FCA. Similar observation isalso 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 isshown in Figure 9. for M = 210 and E[V ] = 50 km/h. It can be seen in the mobility modelsthat the Pb for both of LP and DCA-WI is close, while FDRP-WI has a lower Pb in modelB. Pd of LP, DCA-WI and FDRRP-WI is lower in model B than in model A because the MStends to stay longer in a cell and thus requires fewer handoffs procedures. In general, Pb andPd 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 inmodel A for the same scheme because of longer residual time in a cell for model B. These find-ings agree with [9]. Also, the figure shows that, when the mobility model is same, the handoffactivities 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, thehandoff 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/hand α ranging from 0.1 to 0.9. It can be seen that FDRP-WI provides the highest systemcapacity over the whole α range. We also found that the capacity of FRP is even lower thanthat of FCA when α > 0.53. This is because RP technique in FRP induces higher handoff rateand results in higher Pd as compared to FCA. The system capacity of FCA at α = 0.5 (i.e., Pband Pd are equally important) is 4.72 Erlangs. The values for FRP, LP, DCA-WI and FDRP-WIare 4.732, 7.072, 7.602 and 7.98 Erlangs respectively, which corresponds to the improvementof 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 12with parameters E[V ] = 50 and 25 km/h for α ranging from 0.1 to 0.9. We can see that forE[V ] = 50 km/h, the system capacity of FCA at α = 0.5 is 20.97 Erlangs. The system capaci-ties 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


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 is21.46 Erlangs. The capacities of FRP, LP, DCA-WI and FDRP-WI are 23.67, 26.2, 26.63 and30.23 Erlangs, which are equivalent to 10.3%, 22.1%, 24.1% and 40.9% improvement overFCA. It shows that FRP and FDRP-WI provide higher capacity for slower user speed. This isbecause higher user speed results in higher handoff activity and reduces the effectiveness of RP.

4.2.2. Effect of reserved channels on FDRP-WIThe effect of number, Ch, of reserved channels for handoff calls on Pb and Pd is simulated forsystem for M = 70 and 210 with mobility model A at E[V ] = 50 km/h. The results are shownin Figure 13. It is found that as Ch increases, Pd decreases, but Pb increases. The increasednumber 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 maxi-mize the system capacity at a given GOS value. The capacities at GOS = 0.01 for FDRP-WIwith different Ch values are shown in Figures 14 and 15. In Figure 14, the simulation is basedon mobility model A. For M = 70, the maximum capacity is obtained with Ch = 0 for0.1 ≤ α ≤ 0.65 and thus the optimum number, Copt, of reserved channels for handoff calls is


Figure 9. Comparison of mobility model A and B for FDRP-WI in (a) blocking probability and (b) droppingprobability 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.


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.


Figure 13. Blocking probability and dropping probability of FDRP-WI with different Ch values for mobility modelA 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 and6 respectively. Hence, when M = 210, the Copt values for 0.1 ≤ α ≤ 0.65, 0.65 ≤ α ≤ 0.77and 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 overallcapacities 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. ForM = 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 usersIn 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 aretaken into consideration, the improvement is decreased to 69% and 37.2% for E[V ] = 50 km/has shown in previous section. Results also show that the capacity improvement of FDRP-WIdecreases when E[V ] changes from 25 to 50 km/h. When the user speed is low, the channelutilization based on a smaller reuse distance criterion increases because more inner channels


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 withuser speed of constant 0 km/h. In this section, the effectiveness of the new proposed handoffschemes using RO, based on IS and OS, is examined.

Figure 16 shows the capacity improvement for FDRP-WI for the cases with M = 70 andM = 210 when RO is deployed. In the simulation, mobility model A is considered and nochannel is reserved for handoff calls. The capacities for FDRP-WI without RO, FDRP-WI withIS and FDRP-WI with OS in M = 70 channel system at α = 0.5 are 7.98, 8.665 and 8.802Erlangs. 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. Thesevalues are corresponded to the increase of 37.15%, 51.17% and 54% respectively comparingto FCA. The capacity improvement is substantial with RO implementation. It is also noticedthat, as GOS parameter increases, the capacity decreases slightly because Pd is slightly higherthan Pb for GOS = 0.01. Figure 17 shows the handoff activities for FDRP-WI with the intro-duction of RO in the system with M = 70 and M = 210. When M = 70, the average ofhandoff activity for FDRP-WI, FDRP-WI with IS and FDRP-WI with OS are 0.833, 0.988 and1.248 respectively. When M = 210, the average of handoff activity for FDRP-WI, FDRP-WIwith IS and FDRP-WI with OS are also 0.833, 0.988 and 1.248 respectively. Thus, we can


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 a210-channel system. In both cases, it is found that with RO implementation, the handoff ratesare increased. This is expected because both IS and OS introduce extra intra-cell handoffswhen MS’s move out of the inner region after they have performed RO. OS has even higherhandoff 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 inte-grates 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 eachpartitioned region, which is required in the conventional RP implementation.

Simulation results have confirmed the effectiveness of FDRP-WI scheme with station-ary users. With the combination of DCA-WI and flexible RP, FDRP-WI improves the systemcapacity tremendously over FCA, LP, DCA-WI and FRP. Under uniform traffic, FDRP-WI canprovide more than 100% improvement over FCA for 70 system channels, thus, a substantial


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-WIis able to show its efficiency on spectrum utilization and it can provide a great capacity gaincompared to FCA and other DCA schemes.

FDRP-WI with mobility is further investigated on the effectiveness of this channel assign-ment scheme. The impact of mobile users on the new call blocking probability, the calldropping probability, system capacity and handoff activity are studied by using two differentmobility models with different user speeds. Moreover, a new handoff scheme called “RO” isintroduced to improve the performance of FDRP-WI under mobile environment by increasingthe utilization of channels with smaller reuse distances.

In conclusion, with only stationary users in the system, FDRP-WI performs very well inboth uniform and non-uniform traffic distributions to provide higher capacity for TDMA cel-lular systems. When mobility is considered, FDRP-WI is still able to achieve large systemcapacity as compared to other schemes like FCA, FRP, LP and DCA-WI. Its performance canbe further enhanced by introducing “RO” handoff scheme but at the expense of higher handoffrates in the system.


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

References

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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 fromNanyang Technological University, Singapore, in 2002 and 2004, respectively. His researchinterests are wireless communication systems and radio resource allocation and optimizationfor 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 (cur-rently 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.


Between July 2000 and January 2001, he worked with Advanced Networks Division at AgilentTechnologies Canada Inc., Vancouver, BC, Canada. Between Feburary 2001 and May 2002,he was a Research Engineer in the Radio Communications Laboratory at Nokia Research Cen-ter, Helsinki, Finland, and was involved in research on WCDMA and standardization. SinceMay 2002, he has been with the School of Electrical and Electronic Engineering, NanyangTechnological University, Singapore, as an Assistant Professor. He was a Technical ProgramCommittee Chair for IEE 2nd Mobility Conferecne 2005. His research interests are in the areasof wireless and mobile communications systems including channel assignment schemes, radioresource 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 inInformation engineering (English intensive) from Dalian University of Technology, China, in2002. Since October 2002, he has been pursuing his Ph.D degree at the School of Electrical andElectronic Engineering, Nanyang Technological University, Singapore. His research interestsinclude handoff, channel allocation, and radio resource management for present and futuremobile communication systems.

Dynamic channel assignment with flexible reuse partitioning in cellular systems

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