A Study of Dynamic Multipath Clusters at 60 GHz in a Large Indoor Environment
Manijeh Bashar, Katsuyuki Haneda, Alister G. Burr, Kanapathippillai Cumanan
aa r X i v : . [ ee ss . SP ] S e p A Study of Dynamic Multipath Clusters at 60GHz in a Large Indoor Environment
Manijeh Bashar ∗ , Katsuyuki Haneda † , Alister G. Burr ∗ , and Kanapathippillai Cumanan ∗∗ Department of Electronic Engineering, University of York, Heslington, York, UK, † Department of Electronics and Nanoengineering, Aalto University, Espoo, Finland,Email: { mb1465, alister.burr, kanapathippillai.cumanan } @york.ac.uk, katsuyuki.haneda@aalto.fi Abstract —The available geometry-based stochasticchannel models (GSCMs) at millimetre-wave (mmWave)frequencies do not necessarily retain spatial consistencyfor simulated channels, which is essential for smallcells with ultra-dense users. In this paper, we work oncluster parameterization for the COST 2100 channelmodel using mobile channel simulations at 61 GHz inHelsinki Airport. The paper considers a ray-tracer whichhas been optimized to match measurements, to obtaindouble-directional channels at mmWave frequencies. Ajoint clustering-tracking framework is used to determinecluster parameters for the COST 2100 channel model.The KPowerMeans algorithm and the Kalman filter areexploited to identify the cluster positions and to predictand track cluster positions respectively. The resultsconfirm that the joint clustering-and-tracking is a suit-able tool for cluster identification and tracking for ourray-tracer results. The movement of cluster centroids,cluster lifetime and number of clusters per snapshot areinvestigated for this set of ray-tracer results. Simulationresults show that the multipath components (MPCs) aregrouped into clusters at mmWave frequencies. cc Index terms — Cluster identification, Kalman filter,KPowerMeans, millimetre wave, multi path components.
I. I
NTRODUCTION
Over the past few years, an abundance of tech-niques have been proposed as a means to efficientlyscale the wireless capacity. It remains unclear whichtechnology or set of technologies can meet the de-mand. One promising set of technologies for the 5thGeneration (5G) cellular network is reviewed in [1]:the combination of large antenna arrays and shortwavelength carrier waves. This combination allowsfor a greater bandwidth availability and extremelyhigh spectral efficiency by utilizing a large numberof antennas, whilst occupying a relatively small area.This technology is known as Massive multiple-inputmultiple-output (MIMO) in the millimeter-wavelength(mmWave) spectrum [2].Most standardized MIMO channel models such asIEEE 802.11 [3] and the most recent 3GPP channelmodel [4] rely on clustering [3]. The same appliesto the recent COST channel models, e.g., the COST
The work of A. G. Burr and K. Cumanan was supported byH2020- MSCA-RISE-2015 under grant number 690750. The workon which this paper is based was carried out in collaboration withCOST Action CA15104 (IRACON). [ x, y, z ] -coordinates of the MPCs) is presented. To investigatethe performance of the proposed clustering scheme weexploit a set of ray-tracer results in Helsinki’s airportdescribed in [15], which is very accurate to presentthe propagation properties such as specular reflections,diffraction, diffuse scattering [16]. The contributions ofthe paper are summarized as follows: We study whether clusters exist or not. For the first time, we perform clustering of dy-namic multipath channels. [ x, y, z ] coordinate-based clustering. A. Outline
The rest of the paper is organized as follows. SectionII describes the ray-tracer and simulation area, andSection III provides the MPC clustering-and-trackingframework. The simulation results and discussion areresented in Section IV while Section V concludes thepaper.
B. Notation
The following notations are adopted in the rest ofthe paper. Uppercase and lowercase boldface lettersare used for matrices and vectors, respectively. Thenotation | x | , | X | det and | x | size stand for the absolutevalue of x , determinant of matrix X , and the size ofvector x , respectively. X − and X T denote the inverseand transpose of matrix X , respectively. Moreover, I n introduces identity matrix with size n × n . TheKronecker product of X and Y is presented by X ⊗ Y .II. T HE R AY - TRACER AND S IMULATION A REA
The in-house ray-tracer simulates multipath chan-nels for a large number of links between BS andMS [15]. Note that our ray-tracer works with accuratedescriptions of the environment in the form of pointclouds, obtained by laser scanning, and has the abilityof simulating relevant propagation properties such asspecular reflections, diffraction, diffuse scattering andshadowing [16]. For more details on our ray-tracerrefer to [15], [16]. A check-in hall of Helsinki airportas a representative small-cell scenario is considered asshown in Fig. 1. Exploiting the ray-tracer parametersin Fig. 1, we obtain the MPCs for links defined by BSand MS locations as in Fig. 1. The BS is located 1m from a wall at a height of 5.7 m whereas the MSis placed at a height of 1.5 m at every 5 cm over aroute. In total, 2639 links including 1816 line-of-sight(LOS) and 823 obstructed LOS (OLOS) are simulated.As the ray-tracer calculates interactions of MPC withphysical objects in the environments, we save the firstand last MPC interacting coordinates [ x, y, z ] insteadof the angle of departure and arrival of each MPC. Weassume downlink where BS transmits and MS receivesradio signals. The first and last interacting coordinatesare the same for a single-bounce path, and are differentfor a multiple-bounce path. The ray-tracer also derivesa complex gain for each MPC.III. C LUSTERING - AND -T RACKING F RAMEWORK
Similar to standard clustering algorithms [17], [18],we independently perform clustering at each snapshotand thereafter the clusters are tracked. Consider n =1 , · · · , N data windows, where at each data windowwe have L ( n ) MPCs. Next, we define for each MPC v ( n )1 ,l = [ x ( n ) MS,l , y ( n ) MS,l , z ( n ) MS,l ] (the position of MPCsfrom MS side) and v ( n )2 ,l = [ x ( n ) BS,l , y ( n ) BS,l , z ( n ) BS,l ] (theposition of MPCs from BS side), and finally we have χ ( n ) l = h v ( n )1 ,l i = h x ( n ) MS,l , y ( n ) MS,l , z ( n ) MS,l i . (1)The same equality hold for the BS-side compo-nents. This enables us after visualising clusters to Figure 1. Floor plan of the small-cell site in Helsinki airport. For thissimulation set-up f c = 61 GHz, BW = 2 GHz refer to the carrierfrequency and bandwidth, respectively. Moreover, the position of BSis fixed (the green triangle), while we investigates 2639 positionsfor MS (the yellow and red points demonstrate the LOS and OLOS,respectively. The total MS route is 132 m, and channels simulatedat every 5 cm. plot clusters separately for v ( n )1 ,l and v ( n )2 ,l in physi-cal three-dimensional space as well as defining thematrix χ ( n ) = [ χ ( n )1 , · · · , χ ( n ) L ] Moreover, the l thMPC in window n has a power represented by p ( n ) l which enables us to define the power vector p ( n ) =[ p ( n )1 , · · · , p ( n ) L ] . A. Cluster Parameters
In next step, we define the following parameters foreach cluster: Cluster ID c . Cluster power at time n : γ ( n ) c = P l ∈ I ( n ) c p nl ,where I ( n ) c denotes the set of MPCs belongingto cluster c at time n . Total number of MPCs in cluster c at time n : L ( n ) c = | I ( n ) c | size . Cluster centroid position: µ ( n ) c = h x ( n ) MS,c , y ( n ) MS,c , z ( n ) MS,c i T = 1 γ ( n ) c (2) X l ∈ I ( n ) c p nl x ( n ) MS,l , X l ∈ I ( n ) c p nl y ( n ) MS,l , X l ∈ I ( n ) c p nl z ( n ) MS,l T . Combined cluster centroid position and speed: θ ( n ) c = (3) h x ( n ) MS,c , ∆ x ( n ) MS,c , y ( n ) MS,c , ∆ y ( n ) MS,c , z ( n ) MS,c , ∆ z ( n ) MS,c i T . Cluster spread matrix: C ( n ) c = P l ∈ I ( n ) c p ( n ) l ( χ nl − µ nc ) ( χ nl − µ nc ) T γ ( n ) c . (4) Next, similar to terminology in [17], a Kalman filter[19] is used to both track and predict the clusterpositions over time. Moreover, an initial-guess processintroduces an appropriate initial guess for cluster cen-troids, and finally the clustering algorithm determineshe clusters in the ray-tracer results exploiting theinitial guess.
B. Kalman Filter to Track and Predict Cluster Posi-tions
We exploit the cluster centroid positions and clustercentroid speeds for the Kalman tracking [19]. Thefollowing state equations are used: θ ( n ) c = A θ ( n − c + B ( n ) , A = I ⊗ (cid:20) (cid:21) µ ( n ) c = D θ ( n ) c + E ( n ) , D = I ⊗ (cid:2) (cid:3) , (5a)(5b)(5c)(5d)where B ( n ) and E ( n ) refer to the state-noise withcovariance matrix Q and the observation-noise withcovariance matrix R , respectively. Note that µ ( n ) c in-troduces the observed cluster centroid position. Theprediction and update equations are given byPrediction ( θ ( n | n − c = A θ ( n − | n − c , M ( n | n − = AM ( n − | n − c + Q , (6a)(6b)and update K ( n | n ) = M ( n | n − c D T (cid:16) DM ( n | n − D T + R (cid:17) − , θ ( n | n ) c = θ ( n | n − c + K ( n | n ) (cid:16) µ c − D θ ( n | n − c (cid:17) , M ( n | n ) = (cid:16) I − K ( n | n ) D (cid:17) M ( n | n − (7a)(7b)(7c) C. Association of Clusters
Association of predicted targets to identified targetsis a substantial challenge in any multi-target tracking[17]. Based on [17], the distance between a clusterwith parameters ( µ c , C c ) and a cluster with centroid ˜ µ is called the closeness function and is given by d c (˜ µ | µ c , C c ) = 1(2 π ) | C c | det (8) exp (cid:18) − (cid:0) ˜ µ − µ Tc (cid:1) T C − c . (cid:0) ˜ µ − µ Tc (cid:1)(cid:19) , First, the closeness function between the old clusters(with the old covariance matrix) and new centroidsand the closeness function between the new clusters(with the old covariance matrix) and old centroidsare calculated. Next, for each new cluster the closestold cluster and for each old cluster the closest newcluster is determined. Note that the closest clusteris determined by finding the maximum value of thecloseness function. If the closeness function from bothdirections are exactly the same, these two clusters areassociated and assumed to be one cluster. The clusterswhich are not associated are assumed to be new ones.
D. Initial Guess for Clusters
The initial guess of the cluster centroids is a chal-lenging task in clustering algorithms. In [17], theauthors propose a novel initial guess to maximize thedistances between the cluster centroids. If there isno cluster prediction available, the path having thestrongest power is selected as the first centroid ˆ µ whereas for the case of available cluster prediction,the initial-guess centroid from the prediction is to beas the current initial guess. Note that the multipathcomponent distance (MCD) in this paper is differentfrom the one used in [17], [20]. The distance measurebetween MPCs i and j is given byMCD ij = (9) q || MCD x MS ,ij || + || MCD y MS ,ij || + || MCD z MS ,ij || . Note that in (10) we haveMCD x MS ,ij = | x MS,i − x MS,j | ∆ x MS, max , (10)where ∆ x MS, max = max {| x MS,i − x MS,j |} , and theother terms in (10) are evaluated is a the similar wayto (10). Next, the weighted distance matrix Υ ∈ C l × c between all paths and all initial-guess centroids isevaluated as follows: Υ ( χ nl − ˆ µ c ) = log (cid:16) p ( n ) l (cid:17) MCD ( χ nl − ˆ µ c ) . (11)Following the terminology in [17], we select the pathwith the maximum minimum distance to any centroidas follows: l sel = max l n min c { Υ } o . (12)We then assign all MPCs to their closest centroid andcluster power is evaluated. If we do not achieve themaximum number of clusters, and centroid powersare larger than . of the total snapshot power, werepeat the calculation of the weighted distance matrix Υ ∈ C l × c in (11). Otherwise, the last centroid isignored and the algorithm is stopped. E. Clustering Algorithm
The KPowerMeans clustering algorithm is investi-gated in [21], and it performs as follows: the initial-guess algorithm is applied, and the KPowerMeansclustering algorithm is run only once as the initialguess as are constant. For more details on the KPow-erMeans clustering algorithm refer to [21]. Note thatif any cluster occupies less than of total clusterpower, we re-start the clustering algorithm with theinitial guess, with the number of clusters is reduced byone. Therefore, it is possible that the algorithm endswith a single cluster. igure 2. Tracked Rx-side clusters in Helsinki airport in snapshot3.Figure 3. Tracked Rx-side clusters in Helsinki airport in snapshot4. IV. R
ESULTS AND D ISCUSSION
The joint clustering-and-tracking algorithm is ap-plied to the ray-tracer results at Helsinki airport,explained in Section II, where we have 2639 links.Figs. 2- and 6 present the exemplary plots for differentsnapshots. The MPCs are shown by dots, where theirpower is shown by light blue (weak power) and violet(strong power). The clusters are shown by ellipsoidsand always of the total power is carried by theMPCs within clusters. We use different colors forellipsoids just to make the cluster recognition easier.Each cluster is identified by a cluster ID which iswritten on each cluster. As these exemplary figuresshow for snapshots 2,3 and 4, cluster 2 is alwaystracked while the other clusters are determined as newclusters.Next, the lifetime of clusters for the available sets of
Figure 4. Tracked Rx-side clusters in Helsinki airport in snapshot5.Figure 5. Tracked Tx-side clusters in Helsinki airport in snapshot12. ray-tracer results is investigated, for Tx-side clustersand Rx-side clusters separately. Figs. 7 and 8 showthe histograms of cluster lifetimes for Rx-side (BS-side) and Tx-side (MS-side) scenarios, respectively.The figures show that in most cases clusters are activeonly for a few snapshots for this set of ray-tracerresults. This requires more investigation. Moreover, thenumber of clusters per snapshot is presented in Figs. 9and 10 for Rx-side and Tx-side clusters, respectively.The other interesting phenomenon is the movementof the tracked cluster centroids, which is shown in Fig.11. Based on these figures the cluster centroids movesrapidly in the x or y direction while its speed is verylow in other direction. Moreover, the figure show forthese clusters that the centroid’s speed is very low inthe z direction. Finally, Figs. 12 and 13 investigate the igure 6. Tracked Tx-side clusters in Helsinki airport in snapshot13. Lifetime (snapshots) of clusters N u m b e r o f O cc u r e n ce s Figure 7. Histogram of Rx-side clusters cluster lifetimes (snap-shots). distribution of the percentage of power in Tx-side andRx-side clusters. V. C
ONCLUSIONS
In this paper, we have worked on parameterizationfor the COST 2100 channel model at 60 GHz band.We have worked on a ray-tracer, which has beenoptimized to match measurements, to get double-directional channels at mmWaves. We have combinedclustering and tracking to improve the performance ofconsistent clustering. The results showed that the jointclustering-and-tracking allows for cluster identificationand tracking for the ray-tracer results. Cluster lifetimeand number of clusters per snapshot have been inves-tigated.
Lifetime (snapshots) of clusters N u m b e r o f O cc u r e n ce s Figure 8. Histogram of Tx-side cluster lifetimes (snapshots).
Number of clusters per snapshot N u m b e r o f O cc u r e n ce s Figure 9. Histogram of Rx-side cluster lifetimes (snapshots).
Number of clusters per snapshot N u m b e r o f O cc u r e n ce s Figure 10. Histogram of Tx-side cluster lifetimes (snapshots) . .66141.68 13.8 54.81.7 z ( m ) y (m) x (m) Figure 11. Tracked centroid of exemplary moving cluster.
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