Location-Quality-aware Policy Optimisation for Relay Selection in Mobile Networks
Jimmy J. Nielsen, Rasmus L. Olsen, Tatiana K. Madsen, Bernard Uguen, Hans-Peter Schwefel
AACM Wireless Networks manuscript No. (will be inserted by the editor)
Location-Quality-aware Policy Optimisation for Relay Selection in MobileNetworks
Jimmy J. Nielsen · Rasmus L. Olsen · Tatiana K. Madsen · Bernard Uguen · Hans-Peter Schwefel
Received: date / Accepted: date
Abstract
Relaying can improve the coverage and performance of wireless access networks. In presence of a local-isation system at the mobile nodes, the use of such location estimates for relay node selection can be advantageousas such information can be collected by access points in linear effort with respect to number of mobile nodes (whilethe number of links grows quadratically). However, the localisation error and the chosen update rate of locationinformation in conjunction with the mobility model affect the performance of such location-based relay schemes;these parameters also need to be taken into account in the design of optimal policies. This paper develops a Markovmodel that can capture the joint impact of localisation errors and inaccuracies of location information due to for-warding delays and mobility; the Markov model is used to develop algorithms to determine optimal location-basedrelay policies that take the aforementioned factors into account. The model is subsequently used to analyse theimpact of deployment parameter choices on the performance of location-based relaying in WLAN scenarios withfree-space propagation conditions and in an measurement-based indoor office scenario.
Keywords
Location based communications · Information quality · Location error · Relay policy optimisation
Two-hop relaying has been shown to improve throughput in WLANs. However, for traditional measurement-basedapproaches as in References [9,31,10], user movements cause link quality measurements to become outdated andinaccurate, leading to performance degradations. More frequent updates of link measurements can mitigate this
Jimmy J. Nielsen, Rasmus L. Olsen, and Tatiana K. MadsenDepartment of Electronic Systems, Aalborg University, Aalborg, DenmarkE-mail: { jjn, rlo, tatiana } @es.aau.dkBernard UguenIETR, University of Rennes 1, Rennes, FranceE-mail: [email protected] SchwefelDepartment of Electronic Systems, Aalborg University, Aalborg, Denmark, and Forschungszentrum Telekommunikation Wien - FTW, Vienna, AustriaE-mail: [email protected] a r X i v : . [ c s . N I] M a y Jimmy J. Nielsen et al.
Fig. 1
Intended use of the proposed Markov chain model as a tool for optimizing deployment parameter settings of location based relaysystems. degradation, however at the cost of signalling overhead that scales quadratically with the number of nodes. In
Reference [16], we considered a location based relay selection scheme that uses estimated node positions providedby a localisation algorithm to determine whether to relay or not and which relay to use. As the signalling overheadscales only linearly with the number of nodes and allows for movement prediction, it is useful in highly mobilescenarios and in scenarios of infrequent uplink transmissions (as would be the case in many M2M communicationscenarios with mobile sensors).While the simulation models that were used to analyse the location-based relaying scheme in Reference [16]are sufficient to evaluate the expected performance of a single scenario with a given set of parameters, it is compu-tationally infeasible to use simulations for determining system deployment settings, namely 1) location update rate,2) optimal relay policies, i.e., in which places to relay or transmit directly, and 3) required accuracy of localisationsystem.As a consequence, this paper derives a continuous-time Markov chain (MC) model that allows to numericallycalculate achievable performance of location-based two-hop relaying while capturing the impact of delays of theinformation forwarding and of localisation inaccuracies originating from the positioning approach at the mobilenodes. The location information is thereby periodically sent from the mobile nodes to the access point (AP). Suchperiodic information forwarding represents one of the three basic information access schemes that have been anal-ysed via analytic models in References [4,21]. The analysis approach of References [4,21] also inspired the modelsetup for the relay scenario in this paper.While there can be substantial further gains of PHY-layer combining of relay transmission and original APtransmission [22], such approaches require modification of the physical layer of the destination nodes. In order tobe able to deploy relaying on top of off-the-shelf physical layers, this paper considers store-and-forward relaying without additional Layer-1 symbol combining. Notice however that the contribution of this paper does not lie inthe used relaying scheme, but rather in the MC modelling framework and optimization algorithms. The consid-ered store-and-forward relaying scheme is merely a use case example. In principle, other more advanced relaying ocation-Quality-Aware Relay Selection 3 schemes can be used with the proposed model, as long as appropriate location dependent utility functions can bedefined.The diagram in Fig. 1 shows an overview of how the proposed MC model can be used to determine deploymentparameters: While the mobility model of a node, the technology dependent channel characterization, and parame-ters of the wireless technology (upper left) are considered given by the scenario, the location update rate, the actualrelaying policy and the choice of the location system (lower left) can be influenced by the deployment configura-tion. The Markov model and the algorithms in this paper provide a method for optimizing this configuration.Location-based relay selection was considered already in References [32,30,28,29] and for cooperative MIMOscenarios in Reference [13], however in all cases under the assumption of perfect non-delayed location knowledge.The impact of feedback delay on relaying has been studied in, e.g., References [27,25], but in both cases for systemsthat are not utilizing location information. Markov based models have been used for mobility modelling, location tracking and trajectory prediction as in References [11,8,15]. The mobility models from these papers can be usedto describe the movements of the mobile node(s). To the best of our knowledge only our own previous work inReferences [18,20,19] uses models of location error, information collection and mobility models to optimize relaydecisions.The Markov model for the analysis of location-based relaying performance was first introduced in Reference[18]; subsequently, it was applied to a case study using indoor measurements in Reference [20] and it was extendedwith an efficient policy optimization algorithm and applied to a mobile destination scenario in Reference [19]. Thepresent paper generalizes and extends those previous modelling approaches and provides the following additionalresults: i) The location estimation error is introduced in the model-based analysis and in the evaluation results.The new model therefore allows to consider the joint impact of errors of the localisation system and inaccuraciescaused by mobility in conjunction with information access delays. ii) The algorithm for efficient policy optimizationtargeting maximization of average throughput presented in Reference [19] is generalized so that it can be applied toscenarios with mobile destinations as well as mobile relays. Furthermore, the generalized algorithm addresses alsocases with multiple relays. iii) The measurement-based case study originally introduced and studied with heuristicpolicies in Reference [20] is analysed in scenarios that consider now also location estimation error (see Item (i))and a rigorous policy optimization is performed and analysed. iv) The extended and generalized model of this paperallows to quantitatively analyse the required accuracy level of localisation solutions such that they are beneficialfor location-based relaying scenarios.The paper is structured as follows: Section 2 introduces the general relay system and the collection of location information; the corresponding Markov models are described in Section 3. Section 4 introduces the method forcalculating the considered performance metrics. The proposed policy optimization that is generalized to work withone or more relays is presented in Section 5. Hereafter two case studies and corresponding performance results are
Jimmy J. Nielsen et al. presented: first an outdoor open field scenario in Section 6 and subsequently a realistic indoor measurement-basedcase study in Section 7. Finally, Section 8 presents conclusions and outlook.
We consider downstream communication between a static access point (AP) and a destination node (D); there isa set of K nodes in the geographic region that can potentially act as relay nodes, see Fig. 2. Mobility is presenteither for the destination node or for the relay nodes. Even though multiple mobile nodes can be present, we forsimplicity in the following refer to the Mobile Node (MN), which has a position x ( t ) that changes over time. Viaa positioning system (e.g. GPS based), the MN can obtain an estimation of its own coordinate, labelled ˜ x ( t ) . In alocation-based relaying approach, the MN will send this coordinate estimate to the AP, so that the AP has a view ˆ x ( t ) of the MN’s coordinate, which in the general case is a sampled and delayed version of ˜ x ( t ) . The AP thenwill take a decision based on this inaccurate and delayed knowledge of the position of the mobile node: which ofthe candidate relay nodes to use or if it is better to make a direct transmission to the destination. The mapping ofthe position of the MN to the relay decision is called a relay policy , here, for the example of a mobile destinationnode, represented by π ( ˆ x ) ∈ { R = D , R , ..., R K } , where R i stands for ’relaying via node i ’ while R = D standsfor a direct transmission. In this paper, we assume that this relay decision is taken by the AP just before the nextindividual downstream data fragment transmission. The policy optimization algorithms presented later in this paperare used to determine the optimal relay policy for the AP, given the present scenario conditions.The positions of the static AP and of the static nodes are assumed to be known at the AP, hence only the MN willperiodically (with rate τ ) send position updates to the AP. It is assumed that such location information is availableat the MN through, e.g., a GPS system, however the coordinate provided by the chosen positioning solution inthe MN can show a stochastically varying error. Furthermore, the forwarding delays of positioning information inscenarios with mobile nodes lead to additional inaccuracies of the position estimate. Investigating the impact oflocation estimation errors and location information collection delay on the system performance is key to this paper.While the model in this paper can be applied to different wireless technologies, we use the terminology andprocedures subsequently from WLAN 802.11 type transmissions.The location measurements are transmitted from the MN to the AP as sketched in Fig. 3: 1) the MN obtains a,potentially erroneous, estimate of its current location, 2) wraps it into a WLAN packet and passes it to its WLANinterface. At the WLAN interfaces, there could be a queuing delay until the location message reaches the firstposition in the (finite) interface queue, 3) followed by a subsequent MAC and transmission delay. The sum of MAC and transmission delays are assumed to show a distribution with mean 1 / µ . The location update messagecan also be lost, either due to a full WLAN interface queue, or due to an unsuccessful WLAN transmission. Thelatter happens with probability p loss . Since the location update messages are very small in size, they can justifiably ocation-Quality-Aware Relay Selection 5 AP R DRR (a) Mobile relays AP R DRR (b) Mobile destination
Fig. 2
System with static AP, relays (R), and destination (D). Position uncertainty for mobile nodes is shown by the dashed circle.
APMobile node
Queue delay ... (cid:0)✁✂(cid:0)✁✄
MAC + transmissiondelay
Measurement unicastMeasurement transmission scheduled
Fig. 3
Location measurements are transmitted periodically with rate τ and are subject to queuing delay as well as MAC (Medium AccessControl) and transmission delay, represented by a distribution with mean 1 / µ . be transmitted directly from the mobile node to the AP, since a low bit-rate and hence robust modulation schemecan be used. Relaying of transmissions is thus only considered for data transmissions with much larger payload,where it is desirable to achieve as high as possible bit-rate.The AP’s estimate of the MN’s position is based on the last received location measurement. Typically thelocation estimation error of such measurements from for example satellite or local radio-based location systems isassumed to follow a 2D Gaussian probability distribution [6,24,12]. Outdoors, a zero mean distribution is oftenassumed, however indoors or in situations with shadowing effects caused by buildings, walls, furniture or otherobstructions, the distribution may be offset in some direction or even be non-Gaussian. As the relay decisiondepends on the location measurement, its location error is therefore an important influencing factor in the system.It is important to emphasize that we do not compare performance of different location systems, but rather we focuson location errors as input to the system. Even for an ideal positioning system at the MN, since the MN is mobile,its true position may differ from the AP’s estimate, depending on the stochastic mobility model of the MN.Depending on the AP’s belief on the MN’s location it will choose to either make a relayed data transmissionthrough one of the K candidate relay nodes, R i , or a direct data transmission (D). It will use the pre-computedrelaying policy to determine which transmit mode is expected to yield the highest throughput for the MN’s believed location. The resulting achieved throughput will depend on this choice since the bit rate can be adapted to thequality of each used link in either the direct or two-hop transmission. For simplicity and in order to allow relayingapproaches to be implemented on top of existing Layer 1 and 2 implementations, in this study, we do not consider Jimmy J. Nielsen et al. joint decoding of the first and second transmissions in case of relaying; however, the later introduced throughputmodels can be extended to take into account such advanced PHY-layer combining approaches.For optimal performance, it is desirable to make the choice that maximizes the overall achieved throughput. Inthe considered scenario, this optimal choice depends on the MN’s mobility model, the accuracy of the localisationsystem, on the distance-dependent propagation characteristics, and on the strategy (period of the location updates)and forwarding delays (queuing, MAC and transmission) of these location updates. The next section develops aMarkov model that subsequently will be used for evaluating relay policies and in the calculation of relay policiesthat maximize throughput.
In order to evaluate relaying performance and to later on determine optimized location-dependent relay policies,this section provides a Markov model that captures the localisation and location update procedures between mobilenode and central access point. Main target of the model is to include the localisation errors originating at thepositioning system and to capture the impact of information forwarding delays on the location knowledge at theaccess point. The Markov model in this section considers one destination node and a single relaying node, whereone of the two is mobile (called Mobile Node, MN). Whether it is the destination node or the relay node that ismobile, is in fact irrelevant for the model in this section.In short, the model in this section takes a mobility model, an information forwarding model from the MN tothe AP, a location error model and a location-dependent relay policy as input; the Markov model allows to computestate probabilities of the true coordinates conditioned on a relay or direct transmission decision at the AP; the APlooks up the decision from a given policy based on the resulting delayed and inaccurate location knowledge. Thesubsequent section then shows how, together with a geographic throughput model as input, resulting performancemetrics for this input policy can be calculated in the single relay scenario. Based on this performance model,Section 5 then develops a computationally efficient (polynomial time with respect to size of geographic region)approach to calculate optimized policies that even can be applied to scenarios of K relay nodes. The key idea inSection 5 is to use ’singular relay policies’ as input to the model of this section in order to compute the conditionalprobability of the mobile node’s true location x conditioned that the assumed location of the MN at the AP isˆ x . These conditional probabilities can then be utilized to determine optimal choices in the presence of K relaycandidates; only in that last step, the differences between the scenarios of the relays being mobile or the destinationbeing mobile will become relevant. As a first step, this section develops a Markov model that captures the node mobility, the localisation error,and the information forwarding of the positioning information to the access points. It consists of two parts: 1) acontinuous-time Markov model for the spatial mobility of the MN (the ’true’ coordinates); 2) a model of location ocation-Quality-Aware Relay Selection 7 (cid:0) m ✁✂ (cid:0) m ✁✂ (cid:0) m ✁✂(cid:0) m ✁✄(cid:0) m ✁✄(cid:0) m ✁✄ (cid:0) m ✁✄ (cid:0) m ✁✄(cid:0) m ✁✄ (cid:0) m ✁✄(cid:0) m ✁✄(cid:0) m ✁✄ (cid:0) m ✁✄ (cid:0) m ✁✄(cid:0) m ✁✄ (cid:0) m ✁✄(cid:0) m ✁✂ (cid:0) m ✁✄(cid:0) m ✁✄(cid:0) m ✁☎(cid:0) m ✁☎(cid:0) m ✁☎ (cid:0) m ✁☎(cid:0) m ✁☎(cid:0) m ✁☎(cid:0) m ✁☎(cid:0) m ✁☎ (cid:0) m ✁☎(cid:0) m ✁☎(cid:0) m ✁☎(cid:0) m ✁☎ (cid:0) m ✁✄ (N-1)*N+2 (N-1)*N+3 (a) Mobility model W a ll (b) Mobility model with wall Fig. 4 (a) Example Markov mobility model that is used in numerical results. In total N discrete grid-points represent the geographicspace. Although more general models are possible, this example uses an equidistant grid and one state per grid-point. Also, the state-leaving rate is always µ m , which facilitates the computation of an average speed parameter. (b) A similar mobility model, but with awall. update procedures and of the resulting AP view. As these two parts are not completely independent, the transitionrates in this product space require subsequent modifications, which then will depend on the positioning error modelas well as on the relaying policy, as described in this section.3.1 Markov Mobility ModelFirst element of the relaying Markov model is a continuous-time Markov model that describes the MN’s stochasticmobility. The geographic 2-dimensional space is discretised, for instance via an equidistant grid. The states thenrepresent the current true position of the MN within the grid. Transition rates between the states characterize themobility. Fig. 4(a) shows a base model without obstacles: Transitions are only allowed to the neighbouring gridstates and all states have the same overall state leaving rate µ m . As a consequence, the average movement speed ofthe candidate relay can be readily obtained as ¯ v = d / µ m , where d is the distance between neighbouring grid-points.While the considered mobility model is a special case of user mobility, its advantage is that it only has fewparameters, which facilitates conclusions from parametric studies that are performed later in the paper. Note thatmore general mobility models can be utilized (see also Reference [21]), in particular along the following lines: 1)states can be associated with any discretisation of the geographic space (so equidistant placement is not needed);2) transition rates and transition structure can be arbitrary (though for physical movement resemblance, typicallytransitions would only target geographically neighbouring states); 3) multiple Markov states can be utilized foreach discrete coordinate in order to keep memory of directional information (as in Reference [15]) or to mimicnon-exponential state-holding times via Phase-type distributions. Figure 4(b) shows an example mobility model for indoor scenarios, in which a wall blocks certain movements.The generator matrix of the Markov mobility model is in the subsequent sections denoted as Q mob and a map-ping function of the state number m to geographic coordinate is used: c : { , , ..., N } → R . Inversely, ( x i ) i = ,..., N Jimmy J. Nielsen et al. denotes the enumerations of the N coordinates of the Markov mobility model. The steady state probability dis-tribution of the mobility model is denoted by p mob . In addition to the regular grid model, a more complicatedmobility model with obstacles will be used in the measurement-based case study; this model will be explained laterin Section 7.3.2 Relay Policy Representation for Single Relay CaseBefore we model the information forwarding in the next subsection, we introduce here the notion of a relay policyfor the single-relay-candidate case, which will be input to the information forwarding model. Later, more generalpolicies and more general cases will be discussed. The simple case of one candidate relay node enables a compactmodel formulation, as it allows to reduce the state-space of the models, since only the decision (D or R transmission) and not the full geographic coordinate space needs to be encoded in the relevant Markov model states. This single-relay case will then later be the instrument to address more complex scenarios in a computationally efficient manner.This simple single-relay-candidate policy is a function that maps geographic coordinates of the MN to thebinary relaying decision, which is either a direct (’D’) or relayed (’R’) transmission. Hence, the single-relay policyis a function π : ˆ x → { R , D } . Note that the policy is implemented at the AP, hence it uses the estimated MN positionas input, i.e. both positioning errors of the location system as well as forwarding delays will impact the reliabilityof this information. The modelling of this position estimate at the AP is described in the next section.3.3 AP View and Information ForwardingIn order to model the AP view on the location information resulting from the location update process, the state-space at each coordinate (state of the mobility model) is extended as illustrated in Fig. 5. The model assumes atwo-element WLAN interface FIFO queue at the MN. First, memory of the AP on the last received coordinate needsto be introduced. Instead of keeping track of coordinates, it is sufficient to keep track of the relay decision π ( x ) that corresponds to that last communicated coordinate. Hence, the AP can be in state ’D’ (last received locationupdate was a position that is mapped to a direct transmission in the relaying policy; upper half of Fig. 5) or state ’R’(analogous for a relay transmission; lower half of Fig. 5). When the MN triggers a location update (with rate τ ), thestate-space does not need to encode the actual full coordinate contained in this location update, rather it is enoughto encode the resulting decision π ( x ) . If the current state of the mobility model (true coordinate) is associatedwith π ( x ) = ’D’, then the update in progress is memorized as such (State 2 and 9 in Fig. 5; otherwise States 3 and ocation-Quality-Aware Relay Selection 9 When queuing of state-update messages at the WLAN interface queue may occur, additional states are needed:In the shown example, the max queue-size is set to 2 (one update in progress of being transmitted, while one can bein the buffer). States 4-7 and 11-14 thereby correspond to the situation that one update is being transmitted, whilea second one is stored in the queue. The state label describes the content of the location updates, where the firstelement refers to the location update in progress. Increasing the maximum queue size is simply done by adding twoadditional states for each of the right most states, i.e. in Fig. 5 that would be state 4-7 and 11-14 and connect themin a similar way. The state space for each AP view would contain 2 N q + − N q : queue-size), and thus,the whole state space size is 2 ( N q + − ) for a single geographic grid point. For the complete grid model with N geographic grid points, the complete state space model contains ( ( N q + − )) N states.Measurements are transmitted according to the measurement transmission delay rate µ . Finally, potential lossesof update messages during the wireless transmissions are also modelled; they occur with probability p loss . Note that losses of updates due to full interface queues are modelled implicitly, as the updates with rate τ are not occurringany more in the rightmost states. Notice that the Markov model allows the measurement loss probability andmeasurement transmission rate to be location-dependent. However, for simplicity and because the small packetsize would justify using a more robust modulation scheme than for data transmissions, these parameters are in thispaper considered to be independent of location.In order to express the relay policy’s dependence on the location of the MN, i.e., whether a ’D’ or ’R’ measure-ment is sent from the MN, the τ transitions in Fig. 5 are weighted by the binary variables w D ( x ) and w R ( x ) , where w R ( x ) = − w D ( x ) . w D ( x ) = w D ( x ) = w D ( x ) and w R ( x ) will represent the proba-bility that the true location is mapped into a Direct or Relay decision, hence these factors will become real valuesbetween 0 and 1, while they at single coordinate always add up to 1.The depicted 14 states in the example shown in Fig. 5 exist for each grid point in the mobility model. Thetransitions between grid points in the mobility model, shown for the considered example in Fig. 4, are independentof the states of the AP view and information forwarding; hence they do not lead to changes of the correspondingstate in Fig. 5.3.4 Modelling of Location ErrorsThe location error is modelled as a probability distribution that describes the outcome of the location system, ˜ x , given a certain true position, x of the node. Notice that this location error only reflects inaccuracy of locationestimation, not the inaccuracy caused by collection delays. Using the discretised geographic space which is thebasis for the Markov mobility model and given the enumeration ( x i ) of all possible geographic coordinates, the (cid:0) ·w D (cid:0) ·w R (cid:0) ·w D (cid:0) ·w D (cid:0) ·w R (cid:0) ·w R ✁✁ ·p loss ✁✁ ·p loss ✁ ·p loss ✁ (cid:0) ·w D (cid:0) ·w R (cid:0) ·w D (cid:0) ·w D (cid:0) ·w R (cid:0) ·w R ✁ ·p loss ✁ ✁ ·p loss ✁✁✁ ·p loss AP view = DAP view = R ✁ ·(1-p loss ) ✁ ·(1-p loss ) ✁ ·(1-p loss ) ✁ ·(1-p loss ) ✁ ·(1-p loss ) ✁ ·(1-p loss ) Geographical grid point 1Geographical grid point 2...
Fig. 5
State overview for Markov model of information forwarding, here depicted for queue length N q =
2, which is also used for thelater numerical studies. location error is given by the error matrix E with elements: E i , j = Pr ( positioning system provides coord. x j | true coord. is x i ) (1) In case of an ideal positioning system, E is the identity matrix. In relation to the full Markov chain model, the state-space of the Markov chain remains unchanged as it repre-sents the true location of the MN. The error matrix will however influence the mapping to relay choices as follows:For a given true coordinate i , the factor w R in the example of a single candidate relay of Fig. 5 is calculated as thesum of the probabilities in the location error matrix, for which the policy π dictates a relayed (R) transmission: w R ( x i ) = ∑ j with π ( x j )= ’R’ E i , j . (2) Equivalently for w D , the sum is taken over all probabilities E i , j where x j is a coordinate mapped to a Directtransmission. ocation-Quality-Aware Relay Selection 11 The complete Markov chain model, which combines the Markov chain mobility model in Fig. 4 and the informationforwarding Markov chain in Fig. 5, is created by the following two-step procedure.1. Create a full generator matrix template Q ∗ as the Kronecker product of the mobility model generator matrix Q mob and information forwarding generator matrix Q info : Q ∗ = Q mob ⊗ Q info (3)2. Adjust location dependent transition rates, by iterating over states and inserting the corresponding values. Specifically, in the presented case studies, the location dependent rates that we update are the τ · w R and τ · w D transition rates. Hereby, we get the final generator matrix Q .Having set up the Markov chain model with generator matrix Q for a single-relay policy as input, the steady-state probabilities p of this Markov chain can be obtained from the linear equation system: pQ = , ∑ i p i = . (4)Using standard numerical methods for solving linear equations, this step has time complexity O (( N · L ) ) where N is the number of geographic states utilized in the mobility model, and L represents the number of states utilizedfor the information forwarding process ( L =
14 in the above illustrated example of a interface queue at the mobilenode with two places). On a standard PC, for the case studies presented in this paper where the number of gridpoints is in the range of 100-150, the calculation of steady state probabilities takes up to a few seconds. In relationto this we note that it only takes a few minutes to determine the optimal relay policy for a specific scenario usingthe algorithms presented later in this paper. From this we conclude that the proposed modelling approach, withoutspecifically optimized code implementation, is feasible in situations where the area dimensions combined with thedesired grid resolution results in up to some hundreds of grid points. As comparison, note that the office buildingcase study in Section 7 has 147 grid points.These steady-state probabilities can now be used to numerically calculate different performance metrics forthis single-relay case with given input policy. Note that so far we have not distinguished yet, whether the mobile node is the candidate relay node or the destination node. So both cases from the introduction are still covered bythe model. For increased readability, we index the p vector corresponding to the product space representation, i.e. p m , s refers to the s th state of the information update model model in the m th grid point of the mobility model. Geographic Throughput Model
In order to calculate expected throughput of the relaying system, we here assume that this expected throughputbetween AP and destination node is only influenced by variability due to changing coordinates of the participatingnodes; statistical variations due to changing propagation environments are not considered. Hence, the model usesa mapping of node coordinate pairs to link throughput, respectively for the case of relaying, a mapping of node-coordinate triplets to throughput of the 2-hop link. As we here assume that AP and either destination or relay nodes are static and known, we only require the MN’s position as input; motivated by the discretisation of the geographicspace, we utilize the state-number rather than the geographic position as input to these throughput functions. Hence,we use two functions, one T D : ( m ) → R + for the direct transmission, and another T R : ( m ) → R + for the relayedtransmission. The specific choice of these throughput functions will now depend on the scenario; for instance, whenthe mobile node is the relay candidate and the destination node is fixed, T D will be a constant.The specific throughput models used for each of the two considered case studies in the mobile relay scenarioare described separately in Section 6 and Section 7, respectively. The mean throughput that is achieved via a certain relaying policy can be computed by the weighted sums of theachievable throughput in the correspondingly chosen relay mode; the weights are thereby the steady-state Markovchain probabilities. An ideal relay selection would pick the relay node or the direct transmission that maximizesthroughput for the current true position. In practice, this would require an ideal positioning system at the MN, azero transmission delay and an infinite location update rate. As a comparison case, it can be computed from theMarkov model as follows: S ideal ( π opt,ideal ) = N ∑ m = p mob m · max ( T D ( m ) , T R ( m )) (5)The achievable throughput from policy π under the mobility and information forwarding conditions of the model as described in the previous section is then computed as: S loc ( π ) = N ∑ m = (cid:16) ∑ s ∈ ’D’ states p m , s · T D ( m ) + ∑ s ∈ ’R’ states p m , s · T R ( m ) (cid:17) (6) ocation-Quality-Aware Relay Selection 13 which reduces for the special cases of policies that always transmit directly (dir) or always transmit via relaying(rel) to: S dir = N ∑ m = p mob m · T D ( m ) (7) S rel = N ∑ m = p mob m · T R ( m ) . (8)The state set ’D’ states refers to all Markov states at a certain coordinate, in which the AP view is ’D’ (in theexample of Fig. 5, this is the upper half of states with IDs 1 , . . . , ’R’ states . T D ( m ) and T R ( m ) are the expected throughput with the Mobile Node being at the m th grid point for direct and relayed transmissions,respectively. For constructing the throughput functions T D ( m ) and T R ( m ) , the throughput model that we presented earlier in Reference [17] can be combined with a path loss model or a database of signal strength measurements aselaborated in the considered two case studies.While the absolute throughput is interesting in relation to performance, the impact of inaccurate and delayedinformation shows as a reduction in throughput performance compared to the case where information is accurateand instantly available. Therefore we consider a so-called lost throughput metric, which measures exactly thisreduction in performance. The lost throughput metric for a certain relaying policy is the difference in throughput relative to a system that hasideal location information (i.e., no positioning errors, zero delays and infinitely high update rate) and makes theoptimal choices on this ideal location information. That is, it chooses the method that yields the highest throughputin each grid point. This metric is therefore useful for comparing the impact of different scenario parameter settings. S lost ( π ) = S ideal ( π opt,ideal ) − S loc ( π ) (9)Later, in the results section, we consider the fraction of lost throughput, which is S lost ( π ) S ideal ( π opt ) . Note that there is asecond way of comparing throughput, namely the difference of throughput achieved under a certain policy π withinstantaneous and accurate location information and the same policy π with potential location errors, delay, andinformation loss. S (cid:48) lost ( π ) = S ideal ( π ) − S loc ( π ) (10)This latter difference can also be negative for ’poor’ policies. Using the Markov model and the metrics defined in the previous sections, we now show how optimal policies canbe efficiently calculated with these ingredients. We thereby generalize to the scenario of K relay nodes. Efficientcomputation here refers to polynomial time with respect to the size of the geographic region, expressed by numberof states N of the mobility model in our case. Given that there are N geographic locations and K relay candidates,each geographic location has K + K mobile nodes, see further below.As the relaying system is formulated as Markov chain model, the policy optimization can be formulated asa partially observable Markov Decision Process; however, the toolbox of algorithms for policy optimization inMarkov Decision Processes [23] are based on numericals search algorithms with risk of convergence to sub-optimal solutions. As the relaying policy in our case does not influence the transition structure of the Markov model, moreefficient, exact policy optimization approaches can be utilized.The basic approach of the optimal policy search is: (1) Use the Markov model with ’singleton’ helper policies(i.e. policies that perform relaying in exactly one geographic coordinate) to obtain the conditional probabilities thatthe true coordinate of a single mobile node is x conditioned on AP view is ˆ x . Do this for all K relays. (2) Use thenthe throughput model together with the conditional probabilities from Step 1 to obtain the optimal choices for agiven coordinate.Step (1) is the computationally more demanding one, so the resulting overall time complexity will result fromStep (1) as O ( K · N · ( N · L ) ) , as we will see further below. As before, K is the number of mobile nodes, N is thenumber of grid points, and L is the number of states utilized for the information forwarding process. Step (2) willbe different in cases of mobile relays as opposed to mobile destinations; consequently, the subsections 5.2 and 5.3will now differentiate these two cases. The first step however is still common to both scenarios and hence describedin a general manner.In addition to optimizing the mean throughput also the k-th percentile throughput can be optimized. Reference[19] analyses this metric for the scenario of a mobile destination, using a heuristic policy optimisation. A rigorouspolynomial-time optimal policy search can also be defined for this metric, following the same approach as the meanthroughput optimisation presented in the following.5.1 Calculation of conditional probabilities We introduce the random variable X representing the true coordinate of the mobile node, and ˆ X as the randomvariable representing the knowledge of the AP about the MN coordinate. ( x i ) is the enumeration of the uniquegeographic coordinates, corresponding to state i of the Markov mobility model. ocation-Quality-Aware Relay Selection 15 As a first step, we determine the probability that the true position of the mobile node is x j conditioned that theknowledge of the access point is x i : Pr [ X = x j | ˆ X = x i ] . This calculation forms the first step of the policy optimisationalgorithm in the following way:
Step 1: Iteration for i = . . . N do : Create a singleton policy π sgl ( i ) which is everywhere set to 0 (D) except at coordinate x i , where the policyis set to 1 (R). Determine the Markov chain model (with generator Q ) from the mobility model and information collectionparameters; use the single entry vector π sgl ( i ) as the policy and calculate the steady-state solution p of theMarkov chain. Thereby we can obtain the desired Pr [ X = x j | ˆ X = x i ] for the i th coordinate by conditioning on the AP’s knowledge of the mobile node’s state being ’R’ in the following way: Pr [ X = x j | ˆ X = x i ] = ∑ s ∈ ’R’ states p j , s end for Note that propagation and throughput models are not needed in this step.5.2 Calculating optimal policies in mobile destination scenarioWe now consider the case of a single mobile destination and K static relay nodes. This scenario then requires K + T n ( x ) , n = , , ..., K , where T ( x ) should reflect the direct transmission and T n ( x ) for n = , ..., K , the transmission through relay node n to the mobile node at coordinate x .Having obtained the conditional probabilities in Step 1, we can determine the optimal policy for a given opti-misation metric. We first describe the procedure to optimise mean throughput, where we can just take the optimaldecision for each coordinate locally as follows: Step 2 for mean throughput and mobile destination for i = . . . N do : π mean ( x i ) : = arg max n (cid:40) N ∑ j = T n ( x j ) · Pr [ X = x j | ˆ X = x i ] (cid:41) end for Optimising percentiles of the throughput follows an analogous approach to optimising the mean throughput,though it requires a somewhat more elaborate search algorithm.
Moving to multiple mobile destinations is possible without any extra computational effort, if the stochasticmobility models of these nodes are the same and they have the same receiver (so that the throughput model isalso the same across all nodes). In that case, the access point just applies the decision which it obtains from the relay policy that it has calculated for one of the nodes. If the destination nodes show different stochastic mobilitypatterns or different receivers, optimal policies for each of the mobility patterns need to be obtained; this is doablewith linear effort increase. Note however, that also delay and loss parameters for the location updates may need tobe adapted for an increasing number of nodes.5.3 Calculating optimal policies in mobile relay scenarioIn the case of K mobile relays, calculating the whole policy would require a table with N K entries of value range0 , , ..., K , representing the relay node choice in case of a specific coordinate allocation of the K relay nodes. Toavoid this large table representation, an efficient representation can make use of the fact that the resulting throughputthrough relay node r is independent of the other relay node coordinates; so it would be sufficient to create K + tables of size N , in which the resulting average throughput for a specific relay r at assumed position x , ..., x N is calculated. During run-time, the AP would then need to search for the maximum of the K + Step 2’ for mean throughput and mobile relays for i = . . . N do : for r = . . . K do : Γ r ( i ) : = N ∑ j = T n ( x j ) · Pr [ X = x j | ˆ X = x i ] end for end for where Γ r ( i ) is a throughput table for relay r at coordinate x i .Note that the system definition which is basis for the policy optimisation is not using any location prediction.Location prediction would not even be needed to be algorithmically included explicitly, but it would instead be suf-ficient to look at relay policies that can use the current assumed coordinate and the previously assumed coordinateas input. The Markov model could be extended to include some memory on previous coordinates for such morepowerful policies. Such extensions are for future study. For demonstrating the application of the proposed model, we consider first an ideal case study that reflects thescenario in Fig. 2. Access point AP and destination node D are static, whereas the relay node R moves accord-ing to the Markov mobility model presented in Section 3.1. The scenario assumes IEEE 802.11a communication ocation-Quality-Aware Relay Selection 17
Table 1
Default scenario and simulation parameters.
Parameter Value
Dimensions 80 ×
80 m No. of grid points 10 × d × AP coordinate ( , ) Destination coordinate ( , ) Data transmission interval 25 sMeasurement delay rate µ / ( . · − ) s − Wireless link error probability p loss K n . B MSDU
Scenario A: low dynamics
Measurement update rate τ / − Location error std. dev. σ loc-err Scenario B: high dynamics/challenging
Average movement speed ¯ v τ /
25 s − Location error std. dev. σ loc-err with a relay-enabled MAC-layer as mentioned in Reference [16]. Table 1 lists the used scenario and simulationparameters.The value of the network delay rate, µ , has been calculated using the formulas from Reference [7], given anassumed frame payload of 28 bytes for location coordinate and node identifier as specified in Reference [16].6.1 Throughput ModelIn order to calculate the expected throughput for the 802.11a based case study, we use first a standard log-distancepath loss model (e.g., [5]) to determine the path loss on the direct and two relay links, given the distances betweenthe nodes for different relay positions: PL = PL d + n log ( d / d ) [dB] (11)where PL d is the path loss at a reference distance d , n is the path loss exponent, and d is the link distance.Based on the path loss and the scenario parameters given in Table 1, we use the throughput model we havedeveloped previously in Reference [17] and slightly updated in Reference [14]. Throughput is given by the ratioof expected delivered data divided by expected transmission time. By using bit-error-rate models to calculate theframe error probabilities (see [17,14] for details), the throughput for the direct link can be calculated as: S dir = P suc · B MSDU E [ T tx ] (12) where P suc is the probability of a successful MAC layer frame delivery, E [ T tx ] is the duration of a MAC framedelivery attempt, and B MSDU is the MAC payload size given in octets. In the following, we use the indices 1 and 2 x grid id y g r i d i d (a) Relayed transmission x grid id y g r i d i d (b) Direct transmission Fig. 6
Throughput [Mbit/s] per grid point. The black dots show where the relayed throughput is higher than direct throughput; this isdenoted the standard policy . The green square is the AP and the red cross is the destination. to indicate the AP-R and R-D transmissions. The throughput for the two-hop relaying algorithm is calculated as: S rel = ( P pri,1suc P pri,2suc + P sec,1suc P sec,2suc ) · B MSDU E [ T pri,1tx ] + E [ T pri,2tx ] + E [ T sec,1tx ] + E [ T sec,2tx ] . (13)The throughput model is used in this work to estimate the transmission throughput functions T D ( m ) and T R ( x i ) for each of the N grid points x i . Fig. 6 shows the throughput for a 10 ×
10 grid realisation of the Case Study 1scenario.Notice that the path loss, bit error and throughput models presented above can be exchanged to fit other sce-narios or systems for which relaying is considered. The simple models above are however advantageous for a firstcase study, as they use a small number of parameters.6.2 Location ErrorIt is assumed that it is possible to obtain a description of the location error from the used localisation system.Ideally, this would be a likelihood distribution function of the considered area, for example based on the outcomeof a particle filter localisation algorithm. Often, only a measure of the variance is provided, and in such cases it isnecessary to make some assumptions on the error. Commonly and in this work for simplicity, it is assumed thatthe location error of the positioning system follows a symmetric, truncated multi-dimensional Normal distribution:˜ x ( t ) = x ( t ) + N ( µ err , ∑ err ) , where µ err is the bias introduced by the position system and ∑ err is the covariancematrix. In our examples, we assume that µ err = σ loc-err , the latter called the location error standard deviation. However, the probability mass that falls outside the considered geographic region is cut away. This corresponds to a location system in which an invalid locationestimate is discarded. Specifically the location error probability distribution matrix is built in the following way:1. Let x i be the center coordinate of the i -th grid point corresponding to the relay’s true position. ocation-Quality-Aware Relay Selection 19
2. For this i th grid point, draw the probability density value of each grid center point x j from the Gaussian 2-dimensional location error function for the given value of σ loc-err , and store these probabilities in the element E i , j of the error matrix E . Note that E has dimensions N xN when the Markov mobility model covers N geographic states.3. Re-normalise the rows of E , so that the sum of all entries in a row is 1.6.3 Parametric Studies and Simulation ValidationFor model validation and performance evaluation, this work uses the parameters listed in Table 1 with the proposedMarkov chain model and a simulation model. The simulation model is Matlab based and implements the system model presented in Section 2. Previous work in Reference [18] presented results for a subset of the parametersstudied in the following. For both the Markov chain model and simulation model, the considered mobility modelgrid size is 10x10, which was determined heuristically from comparisons to continuous mobility simulations inReference [18].In all simulation results, the so-called standard policy (std. policy) is determined by comparing the expectedthroughput of direct or relayed transmissions for the believed relay position and then use the mode whose through-put is highest. This std. policy is exemplified by the dots in Fig. 6 and it is the only policy that is used for thesimulation results. Here it serves to validate the corresponding Markov chain curve MC model - std. policy . Forthe MC model, also the location independent policies of always transmitting directly or relayed are shown ( direct or relaying ). The inv. policy is simply the inverse of the standard policy, providing a poor choice as reference forcomparison. Finally, the curve named opt. policy , uses the optimisation algorithm from Section 5 to determine theoptimal policy, with average throughput as the optimisation criterion.Results are in the following presented for two different Scenarios A (low dynamics) and B (high dynamics), asdefined in Table 1.The plots in Fig. 7 show the impact of adding a random 2D Normally distributed location error to the coordinateof the mobile relay’s location that is sent periodically from the mobile relay to the AP. This corresponds to the errorthat would arise with an actual location system based on for example GPS or indoor radio localisation.Besides the accurate resemblance of the simulation and Markov chain results for the standard policy, the mostnoteworthy result here is for the optimal policy in Fig. 7(a). This shows that policy optimisation can achieve asubstantial reduction of lost throughput, especially when the location error increases above 12 m, which could occur in harsh indoor environments with many metallic objects that make the location estimation difficult. Here,the 33% reduction in lost throughput from 0 .
15 to 0 .
10 (at 20 m) demonstrates the benefit of policy optimisation. Inabsolute terms, this improvement amounts to around 0 . (cid:0) ✁ ✂ ✄ ☎ ✆(cid:0) ✆✁ ✆✂ ✆✄ ✆☎ ✁(cid:0)(cid:0)(cid:0)✝(cid:0)✞(cid:0)✝✆(cid:0)✝✆✞(cid:0)✝✁(cid:0)✝✁✞(cid:0)✝✟(cid:0)✝✟✞(cid:0)✝✂(cid:0)✝✂✞ ✠✡☛☞✌✍✡✎ ✏✑✑✡✑ ✒✓✌✔✝ ✔✏✕✝✖ ✗✘✙✚✛✜✢✣✤✥✦✧★✩✪✩✣✫✩✬✧✧✭✤✩✮✜✭✯✮✧ ✰✍✘✱✲☞✌✍✡✎ ✳ ✓✌✔✝ ✴✡✲✍☛✵✶✷ ✘✡✔✏✲ ✳ ✔✍✑✏☛✌✶✷ ✘✡✔✏✲ ✳ ✑✏✲☞✵✍✎✸✶✷ ✘✡✔✏✲ ✳ ✓✌✔✝ ✴✡✲✍☛✵✶✷ ✘✡✔✏✲ ✳ ✡✴✌✝ ✴✡✲✍☛✵✶✷ ✘✡✔✏✲ ✳ ✍✎✕✝ ✴✡✲✍☛✵ (a) Low dynamics scenario A (cid:0) ✁ ✂ ✄ ☎ ✆(cid:0) ✆✁ ✆✂ ✆✄ ✆☎ ✁(cid:0)(cid:0)(cid:0)✝(cid:0)✞(cid:0)✝✆(cid:0)✝✆✞(cid:0)✝✁(cid:0)✝✁✞(cid:0)✝✟(cid:0)✝✟✞(cid:0)✝✂ ✠✡☛☞✌✍✡✎ ✏✑✑✡✑ ✒✓✌✔✝ ✔✏✕✝✖ ✗✘✙✚✛✜✢✣✤✥✦✧★✩✪✩✣✫✩✬✧✧✭✤✩✮✜✭✯✮✧ ✰✍✘✱✲☞✌✍✡✎ ✳ ✓✌✔✝ ✴✡✲✍☛✵✶✷ ✘✡✔✏✲ ✳ ✔✍✑✏☛✌✶✷ ✘✡✔✏✲ ✳ ✑✏✲☞✵✍✎✸✶✷ ✘✡✔✏✲ ✳ ✓✌✔✝ ✴✡✲✍☛✵✶✷ ✘✡✔✏✲ ✳ ✡✴✌✝ ✴✡✲✍☛✵✶✷ ✘✡✔✏✲ ✳ ✍✎✕✝ ✴✡✲✍☛✵ (b) High dynamics scenario B F r a c t i on o f g r i d po i n t s w he r e r e l a y i ng i s p r e f e rr ed . Standard policyOpt. policy − scen. BOpt. policy − scen. A (c) Fraction of positions where relaying is preferred for optimalpolicy
Fig. 7
Lost throughput and fraction of positions where relaying is preferred for varying location error. with exact location information and no access delays is 1.65 Mbit/s. The plot in Fig. 7(c) shows that the policyoptimisation achieves a gain by reducing the number of points in which relaying is used.The plots for the high dynamics scenario in Fig. 7(b) show similar results, but here the possible reduction in lostthroughput is from 0 .
18 to 0 .
10, i.e., a reduction of almost 45%. The corresponding curve for the high dynamicsscenario in Fig. 7 shows that location information becomes less useful with increasing dynamics, so that relaydecisions based on it are taken in fewer places.Overall we can conclude that policy optimisation is necessary to ensure that location based relay selection is atleast as good as a fixed policy (always direct or always relay) when location error increases. In the latter case, thenon-optimised location-based relay selection can turn out worse than a fixed policy.Fig. 8 shows results for varying the movement speed. The nearly identical curves for the standard policy withsimulation and MC model in Fig. 8(a) show that the impact of movement speed is also accurately accounted for in the model. Further, since the optimal policy brings only a modest gain of 0 .
02 at 20m/s we can conclude thatthe standard policy (black dots in Fig. 6) is sufficient in this scenario. Fig. 8(c) shows the number of grid pointsin which relaying is preferred for the determined optimal policy and we see that direct transmissions are preferred ocation-Quality-Aware Relay Selection 21 (cid:0) ✁ ✂ ✄ ☎✆ ☎(cid:0) ☎✁ ☎✂ ☎✄ (cid:0)✆✆✆✝✆✞✆✝☎✆✝☎✞✆✝(cid:0)✆✝(cid:0)✞✆✝✟✆✝✟✞✆✝✁✆✝✁✞ ✠✡☛☞✌☞✍✎ ✏✑☞☞✒ ✓✌✔✏✕✖✗✘✙✚✛✜✢✣✤✥✦✥✚✧✥★✣✣✩✛✥✪✘✩✫✪✣ ✬✭✌✮✯✰✎✭✡✍ ✱ ✏✎✒✝ ✑✡✯✭✲✳✠✴ ✌✡✒☞✯ ✱ ✒✭✵☞✲✎✠✴ ✌✡✒☞✯ ✱ ✵☞✯✰✳✭✍✶✠✴ ✌✡✒☞✯ ✱ ✏✎✒✝ ✑✡✯✭✲✳✠✴ ✌✡✒☞✯ ✱ ✡✑✎✝ ✑✡✯✭✲✳✠✴ ✌✡✒☞✯ ✱ ✭✍☛✝ ✑✡✯✭✲✳ (a) Low dynamics scenario A (cid:0) ✁ ✂ ✄ ☎✆ ☎(cid:0) ☎✁ ☎✂ ☎✄ (cid:0)✆✆✆✝✆✞✆✝☎✆✝☎✞✆✝(cid:0)✆✝(cid:0)✞✆✝✟✆✝✟✞✆✝✁✆✝✁✞ ✠✡☛☞✌☞✍✎ ✏✑☞☞✒ ✓✌✔✏✕✖✗✘✙✚✛✜✢✣✤✥✦✥✚✧✥★✣✣✩✛✥✪✘✩✫✪✣ ✬✭✌✮✯✰✎✭✡✍ ✱ ✏✎✒✝ ✑✡✯✭✲✳✠✴ ✌✡✒☞✯ ✱ ✒✭✵☞✲✎✠✴ ✌✡✒☞✯ ✱ ✵☞✯✰✳✭✍✶✠✴ ✌✡✒☞✯ ✱ ✏✎✒✝ ✑✡✯✭✲✳✠✴ ✌✡✒☞✯ ✱ ✡✑✎✝ ✑✡✯✭✲✳✠✴ ✌✡✒☞✯ ✱ ✭✍☛✝ ✑✡✯✭✲✳ (b) High dynamics scenario B F r a c t i on o f g r i d po i n t s w he r e r e l a y i ng i s p r e f e rr ed . Standard policyOpt. policy − scen. BOpt. policy − scen. A (c) Fraction of positions where relaying is preferred for optimalpolicy
Fig. 8
Lost throughput and fraction of positions where relaying is preferred for varying movement speed. more often as the movement speed increases. This result corresponds with the intuition that a wrongly chosen relaytransmission may be more expensive than a wrong direct transmission (if a direct transmission is possible), sincethe direct transmission quality is guaranteed in the considered scenario where the AP and destination nodes arestatic, whereas a wrongly chosen relay transmission may give close to zero throughput, c.f. Fig. 6.In Fig. 8(b) we show similar results, however for the considered high dynamics scenario with longer measure-ment update intervals. The optimised policy brings a slight improvement compared to the standard policy, which isachieved by further limiting the number of relay transmissions as shown in Fig. 8(c).Decreasing the rate of location update messages turns out to show a similar impact as increasing the movementspeed of the mobile node. Corresponding results are not shown here for space reasons.6.4 Policy choices
Fig. 9 shows the change in choices of optimised policies when increasing the location error for two different valuesof τ , corresponding to a slow and a fast update of location information. Each unique policy has been assigned anID, which is used on the y-axis of the plot. From the plot it is clear that the policies with IDs 1-7 are used for both ! !" , - ./ (cid:0) G$H ✁ $ IAB7"2B-./01C2J6;72EB<679;2F (cid:0)
G ✁ $ I Fig. 9
Choices in optimised relay policies for increasing location error. The scenario is based on Scenario B ( v = m / s ), using thespecified τ and location error values. The policy with ID=1 is all-zero, i.e., relaying is never used. τ [ s − ] v [m/s] Frac. of Lost TP = 0.05Frac. of Lost TP = 0.1Frac. of Lost TP = 0.2Frac. of Lost TP = 0.3 Fig. 10
Required τ for different mobility speeds to achieve certain levels of lost throughput, assuming no location error. values of τ , however only for the fast updates the policies with IDs 8 and 9 are used. In this case, when the updaterate is fast, the policy optimisation is better able to mitigate the effect of mobility than with a slow update rate.However, as the location error increases, this becomes the dominant factor and at 2.5 m location error, the optimalpolicy is in both cases to use only direct transmissions.6.5 Model-based adaptive update rateA possible application of the proposed model is to use it for adjusting parameters such as the measurement updatefrequency according to the scenario conditions. Since measurement updates generate signalling overhead, it isdesirable to be able to determine the update rate to achieve a required level of performance. In Fig. 10 we haveused the MC model to calculate the update rate τ that is required to achieve a certain level of lost throughput,for varying movement speeds, assuming zero location error. The figure shows that this required update rate τ is approximately linearly dependent on the average movement speed, however the slope depends on how much lostthroughput can be tolerated. In principle, the transmission delay µ makes the curves not completely linear, however,since µ is very small compared to τ the curves visually appear linear. ocation-Quality-Aware Relay Selection 23 −2 −1 τ [ s − ] loc. err. std. dev. [m] std. policy, v=0.5 m/sopt. policy, v=0.5 m/sstd. policy, v=2 m/sopt. policy, v=2 m/sstd. policy, v=5 m/sopt. policy, v=5 m/s Fig. 11
Required τ for different mobility speeds and policies to achieve 5% of throughput benefit. By also taking into account the location error, a similar analysis can be conducted to answer the question: ”Howaccurate should localisation be for location based relay selection to be beneficial?”. It is necessary to specify aprecise condition that must be fulfilled to answer this question. As an example, we specify this condition as beingable to achieve at least a certain percentage of additional throughput than with a non-location based direct or relayedrelaying policy. Specifically, we use: γ benefit < S loc max ( S dir , S rel ) (14)where γ benefit > ( S dir , S rel ) is the maximum achievable throughput with a constantrelaying policy, and S loc is the achievable throughput with a location based policy. For the latter, we will considerboth the standard policy and the throughput optimised policy. For this analysis, we use the Markov chain modelto iteratively search for the τ -value that gives us exactly γ benefit benefit, given the scenario outlined earlier in thissection, for a few selected movement speeds with the standard and optimised policies.The plot in Fig. 11 shows the obtained values of τ for a benefit of 5%, i.e., γ benefit = .
05. Notice that τ -valueslarger than 1000 were not considered, as sub-millisecond sample rates are unlikely in a practical system.It can be seen in this plot that for the given scenario and the specified benefit conditions, the maximum accept-able location error is around 1 . − . τ -value, where up to a certain levelof location error, the required τ -value does not increase very much, but beyond this level of location error, it growswith a vertical asymptote. Notice that the optimal policy in Fig. 11 is able to shift the asymptote of this rapid in-crease, meaning that a slightly higher level of location error can be tolerated with the optimised policy compared to the standard policy. The sudden rapid increase of these curves is contrary to the results in Fig. 10, where the updaterate τ can directly counteract the impact of increasing mobility speed. However, the negative impact of locationerror cannot be similarly mitigated by increasing the update rate τ . What actually happens in Fig. 11 is that the update rate τ is used to mitigate the mobility induced errors so that the combined mobility error and location errorallows the benefit condition to be fulfilled. When investigating Fig. 11 closely, the horizontal distance between thetwo asymptotes is approximately 0 . block, as it could most likely benefit from being able to increase location accuracy on demand by using additionalmeasurements and processing resources, when policy optimisation alone is not sufficient to meet the desired per-formance goal. On the other hand, it would also be possible to use fewer measurements and processing resourceson the location estimation, in cases where a slight increase in update rate could allow the desired performance goalto be reached. For demonstrating the application of the proposed model in a more complex scenario, we consider a case study thatreflects an indoor scenario in Fig. 12. The AP and D nodes are static, whereas the R node moves according to theMarkov mobility model shown in Fig. 13. The nodes are assumed to use 802.11g based radios, with a relay-enabledMAC-layer as mentioned in Reference [16]. Notice that this case study assumes 802.11g and not 802.11a as in thefirst case study. Furthermore, since the geographic area is relatively small compared to the typical range of 802.11g,the transmission parameters have been scaled down to imitate a scenario in which relaying is usable. Table 1 liststhe used scenario and simulation parameters. The specific scenario is described in the following.7.1 Ray Tracing SimulationA ray tracing simulator named PyLayers [2] has been used to produce a large set of realistic received signals on auniform grid of 51 pseudo Access Points ×
363 Mobile Stations (MSs), which covers the office building described in [26]. Each grid point is 1 m × ocation-Quality-Aware Relay Selection 25 Fig. 12
The indoor Layout with furniture and the used grid of points (pseudo AP and destination nodes are in red.)
Fig. 13
Mobility model in room layout. Red lines are possible movements between states (blue dots) and black dashed lines are walls.
For our simulations the IEEE 802.11g channel 1 was assumed, corresponding to a center frequency of 2 .
412 GHzand channel bandwidth of 20 MHz. For a more extensive description of the ray tracing for this scenario, see Refer-ence [3].7.2 Used Throughput ModelGiven the extracted path loss for a narrow band corresponding to IEEE 802.11g channel 1, we estimate the achiev-able throughput from the path loss using the throughput model described in Section 6.1.7.3 Candidate PoliciesFor evaluation we define first a reference (Ideal) policy that assumes instantaneous collection and perfect infor-mation and that the best possible choice direct/relay is always made. Besides the ideal, we consider three locationbased policies, a heuristic one which relies on a coarse room-level localisation accuracy (Heuristic) and two others that both require grid-level accuracy; one uses the locally optimal standard policy (Locally Optimal), i.e., whichmode has the highest expected throughput in the currently believed position, and another (Optimised Policy), whichfurthermore uses the policy optimisation algorithm described in Section 5.1. For comparison we consider also the
Fig. 14
AP and D positions are marked by a black square ( , ) and black cross ( , ) , respectively. The colour of each grid point showsthe achievable relay throughput [Mbit/s], if the mobile relay is in that position. The green circles mark the grid points in which the relaythroughput exceeds the direct throughput. Table 2
Default scenario parameters for use case study.
Parameter Value
Measurement delay rate µ s − Network loss probability p loss −
85 dBmRicean K B MSDU v . τ − two fixed policies of always transmitting directly or always using the relay. Since the information collection hasan impact on the performance when using the location-based policies, the three latter policies will be analysedconsidering delayed information collection. A summary is given in the table below: Name Loc. accuracy Info. collection
Ideal grid level instantaneousOptimised policy grid level delayedLocally optimal grid level delayedHeuristic room level delayedAlways direct - -Always relay - -
For the heuristic scheme we have defined that the relay will only be used when within the two rooms delimitedby the rectangle between the two corners (8;1) to (11;6).7.4 Results and DiscussionFor evaluating the performance of the different schemes described in the section above, we have applied the con- strained mobility model shown in Fig. 13, the two throughput models shown in Fig. 14 and the default parameterslisted in Table 2 on the Markov chain model described in Section 3. The results obtained when varying the locationerror and relay movement speed are presented in Fig. 15. ocation-Quality-Aware Relay Selection 27 A v g . t h r oughpu t [ M b i t/ s ] Location error (std. dev.) [m] IdealOptimized policyLocally optimalHeuristicAlways directAlways relay (a) Location error A v g . t h r oughpu t [ M b i t/ s ] mobility speed [m/s] IdealOptimized policyLocally optimalHeuristicAlways directAlways relay (b) Relay movement speed Fig. 15
Average throughput for varying location error and relay speed.
Fig. 16
Optimised relaying policy, and the change in optimised relaying policy for selected location accuracies. Blue dots in the policymatrix show the geographic points where relaying is used – direct transmissions are used in the rest. In the change matrix, green plusesare added relaying points and red crosses are removed relaying points.
For both parameters being varied with the optimised policy and locally optimal schemes, the results show thatoptimised relaying does provide a significant benefit of more than 20% compared to using a static relay strategy(always direct or always relay). The gain compared to using the locally optimal strategy is around 10%.Since the ray-tracing based data set introduces a high level of variability in the policy decision process, wehave looked beyond the ”fraction of points where relaying is preferred” to study specifically what happens to therelay policies. An example is detailed in the plots in Fig. 16, which shows the full relay policies for three selectedlocation error values, as well as the change in policy between these values.These results show that even though the fraction of points where relaying is preferred does not change much, the policy optimisation can actually imply both additions and removals of points to the relay policy. Consequently,the policy optimisation does not just generally reduce or increase the number of relaying points, but adds andremoves points based on the individual conditions.
Location information can be useful for optimising networking functions such as relaying. As location data is neededfor each mobile node, such information can be collected by access points in linear effort with respect to number ofmobile nodes, while the number of links grows quadratically. However, the localisation error and the chosen updaterate of location information in conjunction with the mobility model affects the accuracy of location informationand hence all these parameters need to be taken into account in the design of optimal policies.This paper develops a Markov model that can capture the joint impact of localisation errors and inaccuracies oflocation information due to forwarding delays and mobility. The Markov model can be the tool for parametric stud-ies and hence deployment optimisations of relaying solutions. Furthermore, the Markov model is used to develop algorithms that determine optimal location-based relay policies that take the aforementioned factors into account.Applying the model to analyse the impact of deployment parameter choices on the performance of location-basedrelaying in WLAN scenarios with free-space propagation conditions shows that both the increase of location errorsand the increasing speed of node mobility can be compensated by higher update rates in order to maintain relayingperformance. However, location errors can only be compensated by fresher location information up to some maxi-mum, at which location information becomes useless for relay choice optimisation. Similar results are shown in anmeasurement-based indoor office scenario with more complex mobility model and multipath propagation.The presented analysis framework is particularly useful for off-line deployment optimisation, where the deter-mined optimal relay policies can be stored in the access point and an appropriate location information update ratecan be determined for the used localisation system. Alternatively, the benefit of using a more accurate localisationsystem can be analysed and based on the results, one can decide if such an upgrade is worthwhile.While the examples and the model setup in the paper optimises relaying policies with respect to throughput,other target metrics can be easily included as long as those are determined by the geographic positions of thetwo end-points of the transmission link. For instance, the target metric could also take distance-dependent energybudgets of the transmission by the relay nodes into account, i.e. use a weighted combination of throughput max-imization and relay transmission energy minimization. Such choice of optimisation metric can increase networklifetime. For explicit optimisation of network lifetime, further extensions of the Markov model can be investigatedto also include uplink forwarding of energy levels of nodes to the access point.
Acknowledgements
This work has been performed in the framework of the ICT project ICT-248894 WHERE2, which is partly fundedby the European Union. The Telecommunications Research Center Vienna (FTW) is supported by the Austrian Government and by theCity of Vienna within the competence center program COMET.ocation-Quality-Aware Relay Selection 29
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