A Proactive Selection Method for Dynamic Access Points Grouping in User-centric UDN

Bo Hu,Fangxia Zuo,Chuan’an Wang,Shanzhi Chen

1 State Key Laboratory of Networking and Switching Technology,Beijing University of Posts and Telecommunications,Beijing 100876,China

2 Department of Computer Science,Anhui Science and Technology University,Anhui 233100,China

3 State Key Laboratory of Wireless Mobile Communications,China Academy of Telecommunication Technology,Beijing 100191,China

Abstract:Network densification is a promising solution to fulfill network capacity requirement and transmission rate for beyond 5G and 6G wireless communications.Ultra-dense network(UDN)integrates heterogeneous network resources and coordinates technologies on quality of service controlling,to provide users with flexible service.However,dense deployment reduces coverage radius of the cell,resulting in an increase on handover frequency,which makes a serious impact on service continuity.In this paper,we propose a proactive selection method for dynamic access points grouping (DAPGing) in accordance with“user-centric” philosophy,which selects target Access Points (AP) and reduces handover times to ensure communication continuity.This method includes two criteria:1)the user’s sojourn time,which is determined by analyzing the AP coverage area;2) neighbor relationship between APs,which is determined by coverage area and signal strength characteristics between neighboring APs.Therefore,candidate APs become the proactive selected ones to update the AP group.Stochastic geometry is used to build system model and performance metrics are analyzed,including AP group coverage probability and average update frequency.Experimental analysis shows that the proposed proactive selection method brings similar coverage probability to traditional handover method,while average update frequency is reduced more than 20%selection criteria.

Keywords:proactive selection;user-centric;ultradense network;stochastic geometry model

I.INTRODUCTION

Mobile wireless communication is facing with an everincreasing requirement of massive connectivity and data traffic for beyond 5G and 6G,mostly coming from continual growth of devices and users.Global IP traffic will increase threefold by 2022,and traffic from wireless and mobile devices will account for 71 percent of total IP traffic [1].Network densification,as one of the most prominent deployment technologies in future network,would meet the requirement of demanding data traffic growth to fulfill the unprecedented capacity goals [2,3].Hence that AP density enables cellular network to optimize network capacity and serve for more devices and users in a given area.Despite the diverse transmission fashions,viewing from the AP density,the wireless network is essentially taking the trend from traditional networks to denser networks,very dense networks and ultra-dense networks (UDNs) [4].UDN has been viewed as one of the promising technology to enhance the system capacity for 5G.Also,UDN has been considered a key issue for wireless communication network for beyond 5G and 6G[5].

In UDN,the reduced coverage radius and overlapped coverage bring challenges to handover management.Compared to the traditional network,it brings more handover through the same trajectory,including a mass of redundant handover,which results in the additional consumption on signaling overhead and the handover latency on data transmission[6].What’s more,service interruption may cause an impact on service quality.Increased handover times and connection failure rate lead to network service interruption,which risks the stability of provided service performance[7].Hence,the traditional approaches of handover are not applicable for the moving users served by a group of dense small cells.

An architecture named user-centric ultra-dense network (UUDN) [8]is proposed in from the analysis of challenges on handover management,which evolves from traditional “network-centric” to a new idea of“user-centric”.UUDN introduces the concept of DAPGing to serve seamlessly without the user’s involvement.In such a case,we define the AP group as an AP set,which organizes APs and other resources.Specifically,AP group (APG) updates dynamically following the user’s movement and adjusts adaptively to match user’s requirement in UUDN.The handover is always triggered when the user moves from one cell to another,which is quite different to traditional mobility management system.

Generally,APs are deployed densely and unevenly in ultra-dense scenario.Hence,AP deployment is more self-organized in UDN rather than uniform in traditional cellular network.Unless we have a very limited network size[9],the grid-based network model becomes idealized and impractical.A powerful and tractable model based on stochastic geometry has been proposed.Poisson Point Process (PPP)has been widely used to simulate AP spatial distribution and analyze network performance [10].In Reference [11],the authors analyze base stations cooperation with stochastic geometry model.They derive a theoretical expression on handover rate experienced by an active user with arbitrary trajectory.Further,a method on optimizing APs cluster size is put forward to illustrate the tradeoff between handover rate and data transmission rate.In Reference[12],the authors consider an alternate handover skipping approach to reduce the handover rate.Particularly,in Reference[13],the authors consider a strategy by associating user with a single base station.The decision to skip a handover is based on the upcoming cell’s topology,as a result,the efficient handover skipping strategy effectively reduce handover rate.In Reference[14],the authors propose a scheme that jointly designs DAPGing to support user’s movement and get benefits in experiencing different APs.

In this paper,we propose a proactive selection method for DAPGing in line with the definition of“user-centric”.The main objective of the method is to reduce handover frequency,on account that frequent handover brings significant impact,including massive redundant handover.We organize APG by selecting APs from the surrounding candidates and update at the location of user.The selected ones are jointly organized to provide data transmission on demand.Then,we analyze handover management and propose a proactive selection method for DAPGing,which selects the target Access Points (AP) and reduces handover times on the basis of ensuring communication continuity.Sojourn time is defined as the amount of time a mobile user spends in a cell before it is handed over to another cell [15],which is equivalent to the time of services.When the user walks into coverage of AP signal,the connection is established between the user and the AP.Until the user leaves the range of the AP,the connection will be interrupted,and the socalled sojourn time is the continuous service time for a single user provided by the connected AP.The method includes two AP selection criteria.1) The proactive selection handover method based on the user’s sojourn time,which determines sojourn time by analyzing the AP coverage area and the user’s movement path in it,then selects proactively and makes handover to the target one.2) Based on the AP neighbor relationship,the proactive selection handover method analyzes the coverage relationship and signal strength characteristics between neighboring APs,which determines candidate APs with similar characteristics to the target AP,to make AP proactive selection handover and update AP group members.Therefore,APs meeting the criteria are selected to make up the APG,and we analyze handover procedure and APG management in accordance with user-centric philosophy.

As shown in Figure1,the shadows with unique colors represent different APGs.The purple arrow line shows trajectory of the user.When the UE passes throughL1,four APs cooperate to provide network service.Along with the movement,AP3andAP4remain in APG atL2and ensure no signal interruption.APG updates fromL2toL3is similar to the process described above.Stochastic geometry model is presented to simulate performance metrics of the proposed proactive selection method.

Figure1.Dynamic AP group organization in UUDN Architecture.

We verify the performance of the proposed proactive selection method for DAPGing by simulations.For comparison,we consider a benchmark APG update solution,which updates APG without considering any selection criterion and all candidate APs will be added into APG.We show that the proposed method can achieve lower update frequency than that of existing handover method without selection,about 20%handover can be optimized.Simulation results quantify the benefits and show that handover management efficiency can be improved.

The rest of this paper is organized as follows.We introduce the network architecture of UUDN and stochastic geometry model on propagation in Section II.Then,we describe the proactive selection method for DAPGing in detail in Section III.In Section IV,we analyze performance metrics on coverage probability and average update frequency with formula derivations.We validate our analysis with simulation in Section V.Finally,the paper is concluded in Section VI.

II.SYSTEM MODEL

In this section,we introduce our network model architecture of UUDN to analyze selective updating APG method along the user’s movement.On propagation system,locations of APs are sampled from an independent and single tier of PPP.

2.1 Network Model

Considering that dense APs deployment inevitably results in decrescent signal coverage,strong intercell interference,and negative effects on network system performance.In UUDN architecture,control plane and user plane are decoupled from cellular network,which is foreseen as a potential solution to reduce handover rate and control burden.

In UUDN,the control plane takes responsibility to establish signal connection and data link for users.It is composed of many control nodes in control center.In the light of limitation on node control scope,nodes are divided into two categories:local control node and network control node.Moreover,local control node takes charge of APs within local coverage area.Network control node plays a key role during APG updating process.When different APs in APG are controlled by several different local control nodes,network control node collects AP information and groups the APG via UUDN control center.

2.2 Propagation Model

In this section,we introduce a wireless network,composed of APs with different transmit powersPk.We assume that all APs and the receiving user are equipped with a single antenna in the downlink of network.The locations of all APs are distributed in a two-dimensional EuclideanR2,and they are modelled by a PPP Φ={x1,x2,...,xk...}with densityλ.Performance metrics of selective updating method can be obtained based on the PPP model,which is stationary and spatially ergodic to simplify the analysis.Further,the coverage area of each AP can be represented by Voronoi cell size.PPP does not explore any correlation between its points,so that APs are mutually independent.We model small-scale fading channels via independent Rayleigh variablesgk ～CN(0,1)[6],[16].The rationality of Rayleigh fading assumption in UDN has been verified via experimental results in Reference[16].In this work,the channel fading model includes Rayleigh fading and pathloss with pathloss exponentη >2.Therefore,the received power at a typical location iswhererkdenotes the distance fromk-th AP.Our mathematical notations used in this paper are summarized in Table1.

Table1.Summary of the notations.

III.PROACTIVE SELECTION METHOD

In this section,we provide a proactive selection method for dynamic AP grouping in UUDN framework.Considering the user’s movement in an arbitrary direction,the user is surrounded by alternative and available APs.When APG updates,multiple nearby APs are selected into APG candidate set.Moreover,we divide APG updating process into three parts to describe in detail.

3.1 APG Initialization

As soon as a user appears in wireless network for the first time,APG will be initialized at an arbitrary position(wherever inside the cell or on the border).We set the RSS threshold to ensure the signal strength received,which is denoted by a variableTRSS,assumed as a designed parameter to weigh the limitation of signal strength.Compared to the received power from a user,if,thek-th AP at the distance ofrkwill be added to APG.For this reason,the subset of cooperative APs can be expressed as follows:

For the sake of simplicity,we propose a straightforward method to ensure the user access to network as soon as possible.Under the limited time condition,the user will connect to an AP with highest transmission power.If RSS of all APs is lower than the threshold,that is to say,APG=φ,two APs with highest power are directly chosen to form a group and cooperate to provide service at the very beginning.As shown in the Figure2,APG is initialized with the nearest two APs covered by blue shadow,AP3andAP4.

Figure2.AP group initialization with the two nearest APs.

After APG initialization,it’s assumed that when the user moves across the cell from a current boundary to another,it’s time to update APG members.We denoteGas the APG of thei-th user before updating.From the network’s perspective,a new APG is organized by control nodes,including adding and deleting APs.According to the user’s current location,the nearestn(n ≥2) APs will be taken as candidates of new APG,denoted byC.C′is the determined APG at the next moment.Here,it’s assumed that location of the user is origino.According to Reference[17],the Probability Distribution Function (PDF) of distancerk,denoted by originoto thek-th nearest point,can be expressed by:

and joint PDF of distances from the first nearest to thek-th nearest points is:

where location of the user is assumed at the origino.Then,the nearestkAPs are prepared to associate to initiate service.Therefore,the set of cooperative APs can be expressed by the following form:

3.2 APG Proactive Selection Criterion

To the best of our knowledge,ultra-dense network is overlaid with multiple small cells and same technology to realize complete coverage.Although overlapping coverage ensures a high coverage probability,updating process brings a great deal of signaling overhead of system from control plane and resource cost.Hence,we consider two proactive selection criteria in this section.

Figure3.Proactive selection method considering user’s sojourn time.

3.2.1 User’s Sojourn Time

Sojourn time refers to service time provided by the AP.When the area of a cell is small enough,the sojourn time is quite limited in that cell.If the user moves through a small area cell,the cell will provide service for a limited time and the user moves to the next cell quickly.That is to say,APG needs to update inevitably,and short time service must bring unnecessary handovers.We set a thresholdTson the area of a cell.If the current AP area is larger thanTs,it will be selected and participate to APG updating.As shown in Figure3,hollow circles denote user’s locations,L1andL2denote locations before updating and after updating.APs are represented by simplified network symbols,where the grey ones are inactive and white are active.Blue curves show the cell boundaries;purple dotted line with arrow represents user’s moving trajectory;blue and green shadows represent the APG coverage before updating and after updating,respectively.According to selective updating method,AP1,AP2,AP6are selected to add in APG at locationL1,because their larger coverage area compared to thresholdTs.WhileAP3becomes inactive at locationL1.Situation at locationL2is similar withL1,AP4,AP5,AP6become members of APG.

According to Reference [18],the cell size PDF of a Poisson-Voronoi tessellation is accurately expressed by a gamma distribution withK=3.575:f(s)=where,sdenotes the cell size,andrefers to Gamma Function.Consequently,we define a thresholdTsfor the cell size,

the probability of AP selection is derived as above.In this case,the proactive selection method reduces handover from short service time APs under the proposed criterion on AP coverage.

3.2.2 Neighbor Relationship between APs

Due to random AP deployment in UDN,there may be overwhelmingly short distance between the two adjacent APs.The two APs can achieve similar data transmission effciiency,so that one of the adjacent APs becomes unnecessary in APG.ThresholdThis denoted as criterion of distance between APs.If the distance between APs out of reach ofTh,choose one of them to add into APG.The probability density function of distancehfrom the point to medium edges is simplifeid in Reference[19]:where erfc(x)is the complementary error function,defined byAccording to the symmetry of geometry stochastic model,distance between two APs are double of distanceh.Thus,the relation between thresholdThand the PDF of ignored APs is as follows:

Figure4.Proactive selection method considering neighbor relationship between APs.

In Figure4,L3andL4represent locations before updating and after,we consider the distance betweenAP2andAP3.Due to overwhelmingly short distance between them,onlyAP3is selected.Under this method,data transmission efficiency is not affected,APG becomes streamlined and the update frequency can be efficiently reduced,which contributes to successive connectivity on APG for users.

3.3 APG Organization

In accordance with user-centric philosophy,APG updates dynamically following the user’s movement and adjusts adaptively to match user’s requirement in UUDN.Communication service is realized via signaling interaction among control nodes.Information of coverage area of an AP and distance between neighboring APs is gathered and transmitted towards control node in control layer.When APG updates,control plane exchanges signals for adding or deleting APs.APs situation in new APG are demonstrate in Table2.WhenG ∩C′ /=φ,this situation is quite common.

Table2.APs trend during updating.

It means,when the user comes from previous location to the current,some APs still meet the requirements of RSS and selective criteria.On the one hand,if APs belong to bothGandC′,scilicetAP ∈G∩C′,they should remain previous connection with the control node.On the other hand,some APs are not members ofGbutC′,namely,AP ∈(C′ −G ∩C′).In our strategy,the control node will get connection with APs of this subset.Similarly,APs are inGbut notC′,which meansAP ∈(G −G ∩C′),will be interrupted connection to the user.

If there are no common APs inGandC′,and that is,G ∩C′=φ,all APs inGshould be replaced because none of them reach to RSS standard.The user may move across a cell with a very large area or a long path,which makes APG members totally different from the former one.So that,all APs inGneed be deleted and other new APs are taken into consideration.

Moreover,the APG relationship ofG=C′indicates thatGandC′share the same APs.Actually,APs are unevenly distributed in different places.The distance may be quite short between two consecutive updating locations,in this situation,the surrounding APs may not change and APG keeps the same members.

After these signaling interaction,we denoteC′as the newGAPG to start the next updating cycle.The overall APG updating process is written by pseudo code as follows.

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Under orderly management,the APG members are updated along the user’s movement.As soon as he moves towards an arbitrary direction across an AP,control node will prepare to take control of the APG management.The node collects information of surrounding APs and select appropriate APs referring to updating criteria.After that,these APs are organized as the members of the APG.Compared to control simultaneously by several local control node and network control node,in our simulations,local control node will deal with the most connections during APG updating process,which can greatly improve the efficiency in mobility management.After determination,control node is ready to establish signal connection and data link between APs and the user.In addition,APs cooperate via non-coherent joint transmission in the same APG to enhance the received signal quality and decrease the received spatial interference[20].

IV.PERFORMANCE METRICS

In this section,we firstly portray a character of the SINR for downlink transmission to a typical user with different APGs of operation.Then,we derive ergodic and closed integral-forms of coverage probability with multi-APGs for the proposed selective updating method.

4.1 Coverage Probability

The wireless network performance critically depends on SINR levels at the receivers.Throughout the paper,coverage probability is denoted as the probability of sending signals successfully.We definePCPas the probability that the signal-to-interference-plusnoise(SINR)is larger than a given thresholdTat the receiver.The set of AP group has the form Φ={x1,x2,...,xn}and the set of cooperating APs in APG denoted asGis a subset of APs in Φ.At the typical user,the definition of SINR is as follows:

where

•S=denotes the received signal power,

•σ2is a variance of the additive white noise.

According to the definition of coverage probability,PCPcan be represented by the formula:

Using the fact thatgk ～exp(1) and the independence property,can be got in[[18],theorem 5].Letsuch that,coverage probability can be written as:

In (9),Laplace transformLI(s) is evaluated atsconditioned on the distance to thek-th closest BS from the origin.Signal interference source includesIrfrom APs outside the APG candidate set andIkfromk-th AP ignored in APG.In the light of the definition of the Laplace transform yields,LIr(s)can be further illustrated as:

The calculation process of the function2F1(a,b;c;z) is given in Reference [21].To simplify the derived expressions,we assumeη=4,σ2=0,then,

Proof.Refer to the Appendix.

According to the APG selective updating method,some APs are filtered out when we determine the final APG.Therefore,we have different AP combination within APG.For sake of simplify,we assume a maximum of three APs in APG candidate set.Signals from the nearest AP will be generally strongest,in this case,these APs the nearest three ones,and APG candidate set is composed ofC={x1,x2,x3}.On the basis of selective criteria,all possible AP combinations are:APG1={x1,x2,x3}with all APs selected,APG2={x1,x2},APG3={x1,x3},andAPG4={x2,x3},except the 3rd,2ndand 1stnearest AP,respectively.The interference of nearby closed-access APs can be removed using successive interference cancellation(SIC)[21].Formula of coverage probability with a single AP has been derived in Reference [11],and coverage probability ofAPGi(i ∈{1,2,3,4})is analyzed as follows.

• IfAPG1={x1,x2,x3},coverage probabilityAPG1can be simplified as:

where,f(r1,r2,r3)=(2πλ)3exp(−πλr23)r1r2r3can be got from(4),and

• IfAPG2={x1,x2},we haves2=and

• IfAPG3={x2,x3}.Apart fromIrfrom APs outside the APG candidate set,interferenceI1from ignoredx1is under consideration as well.The conditional PDF off(r1|r2)=is obtained by dividingf(r1,r2) byf(r2),which is proven in detail in [22]andf(r2,r3)is got by integratingf(r1,r2,r3) wherer1is bounded as 0

So,coverage probability is given by:

• IfAPG4={x1,x3},we setWe getf(r1,r3) by integratingf(r1,r2,r3)wherer2is bounded asr1

f(r1,r3).The formula of coverage probability is:

4.2 Average Update Frequency

In this section,we define average update frequency on the number of adding APs and deleting APs during per trajectory and unit time.Formula (17) is derived to update frequency expression with each trajectory:

whereNadddenotes the number of new added APs andNdelis the number of the deleted.Considering irregularity and randomness of cells,we use average values to simplify formula (17).LetA ⊂R2.The number of APs falling in Borel set A is distributed asE[Φ(A)]=λ|A|,where|A|denotes the area of cell.In this case,the overlapping part area ofGandC′isSG∩C′.In order to simplify the calculation,we assume the coverage of the APG candidate set as a circle.We havenAPs in the APG,so thatn=λπR2and the radius of APG candidate set isThe trajectory is denoted byL,andNdelcan be expressed:

According to symmetric characteristic,we assumeE[Nadd]=E[Ndel]in our simulation.The distance of trajectory in a cell can be simulated as the chord lengthLfor simplicity.The mean chord length iscomputed by the PDF of the cell chord.It is derived in[23]in arbitrary Poisson-Voronoi cell:

where,V2(α,β)=(1 +ρ2β −2ρβcosα)(1−andc0=Average moving timetscales asL/v.More precisely,after AP selection with crite-average update frequency can be derived as (20) and (21),whereandL=.

Table3.Simulation parameters and values.

V.NUMERICAL RESULTS

In our simulation,performance parameters are considered to conduct the evaluation.Here,path loss exponentη=4 is assumed and the background noiseσ2is negligible.We consider the APs with different transmit powers have the same densityλ=1000unit/km2.All the simulation parameters shown in Table3.

In this section,to evaluate the performance of the proposed proactive selection method,a benchmark APG update solution is considered for comparison.In this solution,the closest k APs make up the candidate set and all of them are added into the APG,which means the APG is updated without considering any selection criteria.Meanwhile,candidate set and the APG are identical.

Figure5.Coverage probability on AP group versus threshold SINR T.

Figure6.Average update frequency affected by user’s sojourn time.

Figure7.Average update frequency affected by relationship between APs.

Considering the performance of SIC,we simplify our model and eliminateLIk(s) of interferenceIk.In the certainty thatAPG1={x1,x2,x3}has the best coverage performance.Under the proactive selection method,APG selects some APs from the set{x1,x2,x3},which damages performance of coverage probability.The analysis of coverage probabilities is illustrated in Figure5.When the thresholdT >−2dB,coverage probability decreases about 10%to 20%,but each APG under proactive selection method is still superior to the closest single AP.When the thresholdT≤−2dB,{x2,x3}is more negatively affected,even it is inferior to single APx1.However,others drop to a certain extent,maintaining the same range as the impact ofT >−2dB,which is also in the range of 10% to 20%.After all,although there is a certain loss in coverage probability relative to{x1,x2,x3},the proactive selection method still maintains the advantage in coverage probability,compared with the closest single AP to the user.

Based on these considerations,we use the developed analytical model to evaluate the performance of selective updating method.Simulation results are carried out in (20) and (21).As is shown in Figure6,which clearly shows criteria of area impact the average update frequency plots conditioned withλ=1000unit/km2for different values of velocityv.As expected,small cells selection can reduce APG average update frequency.When threshold value of area isTs=0,which means the APG updates without selection.Compared withTs=5×10−4km2andTs=8×10−4km2,update frequency decreases by 16.1%,41.0%,respectively.Simulation results are carried out that average update frequency can be reduced considering selective updating APG method.As a precondition for the method,APG can’t be an empty collection and AP selection probability must be more than 33.3%.According to selection probability,the threshold range is 0～1.1×10−3km2,average update frequency decreases by 22%,compared with the benchmark APG update solution shown as the solid red line in Figure6.

Figure7 depicts the average update frequency depending on relationship between APs,comparing the thresholdThwith distance between APs.AS shown results of four curves,it is obvious that denser AP deployment brings higher AP updated frequency.We consider the special case with velocityv=15km/h.Note that the decreased update frequency stems from the increased thresholdTh.WhenTh=4×10−2kmand 2×10−2km,it decreases 40.7%and 24.5%,compared to no selection cases.Similarly,this proactive selection method also needs to ensure the number of APs in the APG,which can be calculated in the range of 0～5.7×10−2km2.The points on the leftmost axis show the average update frequency of the benchmark APG update solution.We get the average update frequency is about 28%with selection probability calculation,compared with the benchmark APG update solution.

We also make simulation experiment to compare results with numerical analysis.The simulation includes two AP sets in experiment with 40 and 70 user trajectories,and each trajectory triggers and handover 5 to 10 times.It can be seen that the simulation of the average update frequency is in the same trend as the numerical analysis,and it is more consistent with the numerical analysis results when the amount of data increases.

VI.CONCLUSION

Network densification is one of the crucial solutions to satisfy the capacity requirements for mobile wireless communications beyond 5G and 6G.In this paper,we propose a proactive selection method based on the design of DAPGing in UUDN architecture.This allows users to select optional APs intelligently and make organization automatically in APG,with all connections completed through control nodes in control plane.During the selection process,we estimate coverage area probabilities of candidate APs and distance probabilities between two neighboring APs by using probability calculation with stochastic geometry model.Moreover,the process keeps the idea of“user-centric” that APG adjusts dynamically following the user’s movement and members are updated adaptively to match a user’s service demand.Simulation results were presented to demonstrate that the proposed method can achieve significant performance improvement compared with the existing handover solutions by analyzing coverage probability,and average update frequency simplified by average AP densityλ.According to the simulation results,the proposed method can achieve similar coverage probability as the benchmark APG update solution,but the average update frequency reduces more than 20%.

ACKNOWLEDGEMENT

This work was supported by the National Natural Science Foundation of China (NSFC) under Grant 61931005.

APPENDIX

Sincegi ～exp(1),we have