Geometry-Based Stochastic Channel Models for 5G: Extending Key Features for Massive MIMO

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1 Geometry-Bsed Stochstic Chnnel Models for 5G: Extending Key Fetures for Mssive MIMO Àlex Olivers Mrtínez, Ptrick Eggers, Eliseth De Crvlho Fculty of Engineering nd Science, Dept. of Electronic Systems, APNet section Alorg University, Alorg, Denmrk Emil: rxiv: v1 [cs.it] 19 Sep 2016 Astrct This pper introduces three key fetures in geometry-sed stochstic chnnel models in order to include mssive MIMO chnnels. Those key fetures consists of multiuser (MU) consistency, non-sttionrities cross the se sttion rry nd inclusion of sphericl wve modelling. To ensure MU consistency, we introduce the concept of user ur, which is circle round the user with rdius defined ccording to the sttionrity intervl. The overlp etween urs determines the shre of common clusters mong users. To model nonsttionrities cross mssive rry, su-rrys re defined for which clusters re independently generted. At lst, we descrie procedure to incorporte sphericl wve modelling, where cluster focl point is defined to ccount for distnce etween user nd cluster. I. INTRODUCTION In mssive MIMO (Multiple-Input Multiple-Output) system, the se sttion is equipped with very lrge numer of ntenn elements nd serves multiple users in the sme timefrequency resource [1]. Under certin fvorle propgtion conditions (e.g. [2]), fst fding nd uncorrelted noise t the receiver vnish, ringing huge gins in throughput, reliility nd energy efficiency [3]. Mssive MIMO is considered key technology for the development of 5G [4]. The chrcteristics of the mssive MIMO chnnel ring some chllenges for inclusion in the existing geometry-sed stochstic chnnel models (GSCM). The existing GSCM cn e divided into two groups. We nme them Winner-type nd COST-type. The first ones re the min focus of this work nd exmples re the 3GPP sptil chnnel model (SCM), extended SCM (SCME) [5], Winner (WIM1), Winner II (WIM2) [6], Winner+ (WIM+) nd QuDRiG [7]. Their min chrcteristic consists of the definition of the sctterers sed on the ngles of deprture nd ngles of rrivl, i.e. terminl perspective. On the other hnd COST-type GSCM [8] defines the physicl position of the sctterers in the simultion re. Existing work proposes n extension of COST-type GSCM for mssive MIMO [9]. The COST-type GSCM chnnel models defines the physicl position of the sctterers, not directly ngles of deprture or rrivl s seen from terminl. Consequently, it is difficult to extrct prmeters for the COST model using mesurements (contrry to the cse of the Winner type GSCM chnnel model). Those resons explin why Winnertype GSCM is currently more widespred nd is the preferred cndidte for 5G chnnel modelling in stndrdiztion efforts. One mjor drwck of Winner-type GSCM is tht it does not support multi-user (MU) consistency. MU consistency refers to the genertion of chnnels for ech users tht re consistent with the distnce etween users in terms of oserved clusters nd their correltion. Winner-type GSCM fils to represent scenrios where the users re in close proximity, s the chnnels re generted independently for ech user, regrdless of the distnce etween users. As the performnce of mssive MIMO is relted to the user chnnel vectors orthogonlity [2], Winner-type GSCM models results in overoptimistic performnce. With the increse in the numer of ntenns, the size of the rrys lso increses. Although compct rry designs re desirle for opertors, some ppers rgue tht the rel dvntges of mssive MIMO pper when the size of the rry ecome lrge [10]. Non-sttionrities hve een oserved in mesurements [10], [11] for lrge ut lso compct rrys [10], so tht it would pper tht even for compct rrys, it ecomes importnt to model non-sttionrities. The non-sttionrities re of different nture: the power cn vry, the directions of deprture/rrivl vries, different prts of the rry see different clusters, etc. Winner-type GSCM define the clusters y their ngles of deprture nd ngles of rrivl nd rely on plnr wve pproximtion. When the rry ecomes lrger or the clusters re t close proximity to the users, the plnr wve pproximtion ecomes inexct clling for sphericl wve modelling nd modifiction of Winner-type GSCM models. The present study proposes solutions to extend Winner-type GSCM to include MU consistency, non-sttionrities cross the se sttion rry nd sphericl wve modelling. We introduce the concept of ur ssocited to ech user, which is circle centered on the user with rdius defined y the sttionrity intervl. When users re t close proximity, their urs overlp nd the overlpping surfce defines the common clusters shred mong users. An exmple is presented in Fig. 1. We propose n lgorithm to compute the numer of clusters to e shred mong pirs of users, then groups of multiple users. As pre-step, n lgorithm to divide the users into connected groups is used to increse the speed of the process. The lrge scle prmeters (LSP) of one of the users shring the cluster re used to compute the prmeters of the cluster. Finlly the cluster prmeters re shred with the other users shring the cluster. Then the prmeters or the position of the

2 Fig. 1. Left: Existing GSCM with independent clusters for users closely locted. Right: Proposed extension with multiuser consistency where closely locted users hve common clusters clusters (depending on the distnce etween user nd cluster) is reclculted ccording to the position of the new user. To ccount for non-sttionrity effects, the se sttion is divided into su-rrys with size defined y the sttionrity distnce (i.e. correltion or coherence distnce with regrd to visile clusters). Different reliztions of the LSP t ech surry re used to generte the clusters. Sphericl wve modeling, (similrly to QuDRiG s drifting procedure [7]) supports ner field clusters t the se sttion side, y fixing focl points derived from the delys nd ngles of the clusters. This work uses QuDRiG, Winner-type GSCM, s reference model on top of which to uild the proposed extensions. However the ides in the pper cn lso e pplied to other Winner-type GSCM. A. Segments II. DEFINITION OF BASIC CONCEPTS From WIM1 onwrds the trjectory of the users is divided into smller segments. These segments re defined such s the LSP of the chnnel remin constnt (i.e. the segment length equls the sttionrity intervl). Therefore the numer of clusters tht ech user hs nd the correspondent prmeters cn only chnge segment wise. This pper proposes n lgorithm tht checks the reltive position of the users t the eginning of ech segment nd defines the numer of common cluster for the rest of the segment. The proposed extension of the GSCM cn only e pplied if the user segment trnsitions re synchronized. B. Clusters In GSCM, physicl ojects re modeled s sctterers where the trnsmitted wves re reflected. These sctterers re divided into groups ccording to their dely nd ngle of deprture or rrivl, forming clusters. Ech cluster is composed y 20 sctterers. The ngles of the sctterers re smples of Lplcin function, s shown in Fig. 2. The prmeters of the clusters of ech user define the chnnel properties of tht user. The proposed extension proposes to shre some of the clusters etween users tht re ner to ech other to chieve the desired multiuser consistency. The numer of shred clusters is relted to the distnce etween users, ut which clusters re shred cn vry ccording to the implementtion. Fig. 2. Angulr representtion of the clusters in Winner-type GSCM. The AoA defines the men ngle of the cluster nd the ngles of the sctters hve deterministic offset from this ngle. All the sctterers in the cluster hve the sme dely (Not represented in this figure) Users Common Cluster Common Cluster Angles [deg] Fig. 3. Common cluster oserved etween user 1 nd 3 in n indoor NLoS scenrio. Red dots mrk the ngle of mximum power The common clusters etween users hve een oserved in mssive MIMO chnnel mesurement descried in [10]. Due to lck of spce the mesurement cmpign is not descried here (for detil see [10]). In the mesurement cmpign the se sttion rry hs 64 elements divided in sets of 8 elements. There re 8 users holding hndset with 2 elements clled nd. The ngle of rrivl is estimted using steeringvector emforming t ech set of 8 elements. The 8 element set hs 13 3 db emwidth nd mx. sideloe level of 14.7 db. We focus on the mximum power cluster to void misinterprettion of the side loes. This cluster is mrked with red dot. In Fig. 3 the power ngulr spectrum for the 8 users in non-line-of-sight scenrio (clled S-NLoS in [10]) is presented. Fig. 3 shows tht user 1 nd user 3 seprted 2.2 m hve cluster t 104 nd 110 respectively. Due to the 13 resolution of the emforming this cn e considered common cluster. C. User ur Where COST-type GSCM provide nturl cluster shring s it is cluster centric, the Winner-type GSCM re user centric. Despite QuDRiG mde mpping of the prmeters to db

3 Computtion of common clusters Genertion of prmeters Computtion of focl points Reclcultion of prmeters Shring the clusters Fig. 4. Trck of two users divided into segments. sux is the first position of user U in segment numer X Fig. 6. Modifiction of the QuDRiG step 3 into 5 su-steps Fig. 5. Division of the se sttion rry into su-rrys ccording to the sttionrity intervl geometric positions to provide time evolution of the chnnel, it is still locl to ech user. To fcilitte possile shring of clusters etween users, we introduce the concept of n ur. The user ur is defined s the circle surrounding the users with rdius equl to the sttionrity intervl. When two users re seprted more thn the sttionrity intervl they hve independent chnnel vectors nd their urs re disjoint. If two users re close to ech other their urs overlp. The mount of overlpping re is proportionl to the distnce etween the users. This proportion is used to define the mount of clusters tht need to e shred etween users. The overlpping of the urs is computed in the first position of ech segment nd the numer of common clusters is kept constnt long the segment. Fig. 4 shows n exmple users lyout. D. Aur t the se sttion To generte non-sttionries from the se sttion perspective, the rry is divided into su-rrys in the sme wy the user trjectory is divided into segments. In the sme wy ech user hs defined n ur, the su-rrys in the se sttion hve lso defined n ur of rdius equl to the sttionrity intervl. The su-rrys hve the length of the sttionrity intervl, nd the ur is centered t the center of the su-rry. Notice tht the sttionrity intervl long the se sttion rry might differ from the user perspective. To generte the nonsttionrities over the rry, the exposed extension proposes to chose different prmeters of the cluster t the trnsmitter for ech su-rry. See n exmple in Fig. 5. The urs of djcent su-rrys cn e overlpped to produce grdul shre of the clusters. However, in this work it is not implemented. E. Drifting One contriution of QuDRiG is the time evolution chnnel consistency. It mens tht in ech snpshot the chnnel is consistent with the previous nd the following snpshot. At the initil position of the segment the prmeters of the clusters re clculted. These prmeters re updted ccording to the movement of the user in the susequent snpshots of the chnnel. To chieve this time evolution the position of the sctterers hs to e defined nd kept constnt through the segment. Then, the reltive position etween the user nd the sctter cn e computed, nd the new prmeters of the sctter cn e updted. The proposed extension uses this concept to define the position of the sctters oth t the receive nd the trnsmit side nd therefore the sphericl wves cn e used. A. Simultion flow III. EXTENSION OF GSCM Winner-type GSCM chnnel model follows nine steps to generte the chnnel coefficients [7]: 1) Define the prmeters of the simultion (Positions of the users nd se sttions, Antenn rrys, Trcks of the users, Segments, Scenrios) 2) Genertion of the correltion mps using the scenrios configurtion files 3) Genertion of clusters for ech segment 4) Genertion of the sctterers inside the clusters nd clcultion of the vector for ech sctterer nd ech position of the user 5) Clculte ntenn response for ech ngle 6) Clculte the phses using the position of the clusters nd the ntenns 7) Sum of the coefficients of the 20 sctterers. The chnnel mtrix for ech cluster is creted 8) Merge the djcent segments (irth/deth process) 9) Formtting of chnnel coefficients nd delys To otin the multi-user consistency, non-sttionrities cross the rry nd the sphericl wves propgtion, Alorg University (AAU) modifies step 3 of the nine steps. B. Description of extensions The modified step 3 hs 5 su-steps. These su-steps re presented in Fig. 6: 1) Clculte proportion of common clusters 2) Genertion of initil prmeters 3) Computtion of the focl points of the clusters 4) Shring the clusters 5) Reclculting prmeters

4 Fig. 7. Simultion lyout with six users converted into grph nd n edges description C. Clculte proportion of common clusters The proposed solution uses simple preprocessing lgorithm nd n lgorithm designed y AAU to compute the numer of common cluster etween users depending on their proximity. These lgorithms re simple to implement. We wnt to remrk tht n lgorithm for computing the overlpping of circles with exct precision lredy exist in [12]. The implementtion of such lgorithm cn e complex nd the processing time long. The ccurcy provided y such lgorithm is not necessry. Therefore we develop simplified method. First there is preprocessing of the lyout to cluster the users in connectivity groups. This lgorithm mkes groups of users whose urs re overlpping [13]. This step is necessry to increse the efficiency of the lgorithm to compute the numer of common clusters. This lgorithm uses grph theory to find connected components. Ech user is represented s vertex of the grph. If the distnce etween two users is smller thn the sum of its rdius their urs re overlpping nd there is n edge etween the two vertices representing the two users. An exmple cn e seen in Fig. 7. The lgorithm performs deep serch on ech connected component. Ech new vertex reched is mrked. When no more vertices cn e reched long edges from mrked vertices, connected component hs een found. An unmrked vertex is then selected, nd the process is repeted until the entire grph is explored. This lgorithm requires memory spce liner with mx(v, E), nd time liner with mx(v, E). Where V is the numer of vertices (i.e. users in the lyout) nd E is the numer of edges of the grph (i.e. overlpping urs in the lyout). The lgorithm to compute the common clusters is designed y AAU nd it is sed on finding the men distnce of the groups of users to the centroid of the groups. Then using liner reltionship (or nother reltionship) this distnce gives proportion of clusters to e shred mong the group of users. This procedure is repeted for groups of two, three, four, etc. users until the mximum is reched. This lgorithm is presented in Algorithm 1 nd Fig. 8 shows n exmple. In the previous lgorithm the centroid of the group of users (i.e. m) is computed s, m = (x 1, y 1, z 1 ) + + (x N, y N, z N ) (1) N where (x n, y n, z n ) is the position of user n in Crtesin coordintes (lets cll it P os n ). forech group of N users (N {1,..., mx(users)}) do if N = 1 then proportion of clusters for the individul users = 1; else find centroid of the group of users: m; if (ll distnces to m)<r then find men distnce to m: md; proportion of clusters = md + 1: p; p N 1 sutrct from the groups contining N 1 users; else the users with (distnce to m)>r re too fr wy nd no clusters re shred in this group; end end end Algorithm 1: Compute the numer of common clusters Pos 1 =(x 1,y 1,z 1 ) m Pos 2 =(x 2,y 2,z 2 ) Pos 1 m R m Pos 2 Pos 3 Pos 3 Fig. 8. Exmple of the clustering lgorithm for groups of 2 users (N = 2). User 1 in green, user 2 in red nd user 3 in lue Compute the distnces from the users to the centroid nd find if the urs re overlpping using: m P os n < R (2) To compute the men distnce of the group of users to the centroid use: md = m P os m P os N N The proportion of clusters to shre corresponds to liner reltionship with the men distnce to the centroid (proportion of clusters p = md R +1). This liner function hs een chosen for its simplicity. However, empiriclly derived cluster shring functions cn esily e sustituted here. After the explined lgorithm, ech user hs proportion of individul clusters nd ech intersection of urs hs proportion of common clusters. Knowing the proportion of clusters to shre nd the totl numer of clusters, ech user nd group of users is ssigned with numer of clusters s seen in Fig. 9. Notice tht the prmeters defining ech cluster (i.e. ngles, dely, position) hve not een computed yet. The clusters re only defined y its numer, nd the prmeters re computed in the following su-step. (3)

5 we explin how to dpt their procedure to the trnsmit side. Fig. 10 shows the prmeters used. First the totl length (from trnsmitter, to cluster, to receiver) is otined from the dely, d c = τ c c 0 + r 0,,k (4) = U 1 = U 2 = U 3 U x nd U y = C z U 1 = C 1, C 2, C 3, C 4 U 2 = C 5, C 6, C 7 U 3 = C 8, C 9, C 10 U 1 nd U 2 = C 11 U 1 nd U 3 = C 12 U 2 nd U 3 = C 13, C 14 U 1, U 2 nd U 3 = C 15 Fig. 9. Exmple of the clustering lgorithm with 7 clusters (C) per user(u). First compute the proportion of common clusters for ech group, then compute the numer of clusters nd finlly ssign set of cluster nmes where r 0,,k is the distnce etween su-rry nd user k (i.e. AP os P os k,s, where AP os is the centrl position of the su-rry nd P os k,s is the first position of the user k in the segment s), τ c is the excess dely nd c 0 is the speed of light. Then the deprture ngles of the cluster re converted into Crtesin coordintes. ê c,,s is the vector defining the direction of the cluster c of su-rry t segment s. f c,,s defines the vector from the user to the cluster. Considering the tringle with vertices t the center of the su-rry, t the user position, nd t the focl point of the cluster, nd using the cosine theorem we cn compute the distnce from the su-rry to the cluster. D. Genertion of initil prmeters The initil delys, powers nd ngles (i.e. zimuth of deprture nd rrivl, elevtion of deprture nd rrivl) re generted for ech cluster (Cx) in ech segment following QuDRiG s procedure explined in [7]. To crete nonsttionrities cross the rry, we modify this procedure to hve one zimuth ngle nd one elevtion ngle of deprture for ech su-rry. There re 4 + 2A prmeters for ech cluster (eing A the numer of su-rrys). This procedure uses user (U x) specific prmeters (drwn from the lrge scle prmeter mps) to generte the cluster prmeters. If the cluster elongs only to one user (e.g. C 3 in Fig. 9) the prmeters of tht user re used to generte the cluster. On the other hnd if the cluster elongs to more thn one user (e.g. C 11 in Fig. 9) one of the users is picked to use its prmeters to generte the cluster. We propose to pick the users rndomly with uniform distriution, ut other methods re possile. The vlues of the deprture ngles re drwn independently for ech su-rry. E. Computtion of the focl points of user side clusters QuDRiG s drifting procedure determines the position of the Lst Bounce Sctterer (LBS) nd keeps it fixed during the whole segment, [7], glol step 4. In this su-step only the first prt of the QuDRiG s drifting procedure is used to find the focl point of the LBS nd dd it to the tle of prmeters for ech cluster. Even if the cluster elongs to more thn one user (e.g. C 11 in Fig. 9) the focl point is referenced to the user used to generte the prmeters of the cluster. Then it is necessry to find the focl point t the trnsmitter side. We cll the focl point t the trnsmit side First Bounce Sctterer (FBS) nlogous to the QuDRiG nomenclture. We propose to use the sme procedure used y QuDRiG to find the focl point of the clusters t the trnsmit side. Next f 2 c,,s = r 0,,k 2 + e c,,s 2 2 r 0,,k e c,,s cos(β c,,s ) (5) (d c e c,,s ) 2 = r 0,,k 2 + e c,,s 2 +2 e c,,s r T 0,,kê c,,s (6) e c,,s = d2 c r 0,,k 2 2(d c r T 0,,kêc,,s) The vector from the trnsmitter position to the focl point of the cluster t the trnsmit side is, (7) e c,,s = e c,,s ê c,,s (8) And using this vector nd the position of the trnsmit rry we cn find the position of the focl point of the cluster t the trnsmit side (FBS) s BCP os c,,s = e c,,s + AP os (9) After dding the focl points, the clusters hve 5+3A prmeters in their tles (i.e. power, dely, zimuth of rrivl, elevtion of rrivl, focl point t receiver nd for ech surry: zimuth of deprture, elevtion of deprture nd focl point t trnsmitter). F. Shring the clusters In su-step III-C we showed tht ech cluster could hve more thn one owner, ut in su-step III-D the prmeters of only one user hve een used to generte the cluster. In this su-step the clusters re shred with the other users tht they elong to, ccording to the results of III-C. In other words, the clusters nd their generted prmeters re duplicted to the prmeter tles of the corresponding users. See n exmple in Fig. 11.

6 APos BCPos c,,s r 0 Pos k,s Fig. 10. Computtion of the focl point of the cluster t the trnsmitter side Group{U 1 } = C 1, C 2, C 3, C 4 Group{U 2 } = C 5, C 6, C 7 Group{U 3 } = C 8, C 9, C 10 Group{U 1, U 2 } = C 11 Group{U 1, U 3 } = C 12 Group{U 2, U 3 } = C 13, C 14 Group{U 1, U 2, U 3 } = C 15 U 1 = C 1, C 2, C 3, C 4, C 11, C 12, C 15 U 2 = C 5, C 6, C 7, C 11, C 13, C 14, C 15 U 3 = C 8, C 9, C 10, C 12, C 13, C 14, C 15 Fig. 11. Exmple of the cluster shring Fig. 12. If the cluster is ner to the users to shre the prmeters cn result in very different clusters (right). It is etter to shre the focl point (left) G. Reclculting prmeters As some clusters hve een generted using the prmeters of one user, ut fter su-step III-F they hve een shred with nother user, it is necessry to reclculte the prmeters for the new user. The reson is ecuse the focl point of the cluster hs een clculted using the ngles nd positions of one user, ut the position of the other user cn e different. There re two options to reclculte the prmeters, oth shown in Fig. 12. The first option is to keep the sme prmeters generted in su-step 3 nd reclculte the two focl points of the cluster for the new user. The second option is to keep the sme focl point nd reclculte the other prmeters (including the ngles of deprture). If the clusters re fr wy from the users it is possile to keep the sme prmeters nd void reclculting the focl point ecuse the reltive position does not chnge very much. However, if the cluster is ner the users, we hve to reclculte the focl point, else it would result in effectively different clusters for the users. We propose tht if the clusters re less thn 3 segment lengths wy the focl point is kept nd the other prmeters re reclculted. Otherwise, the opposite hppens. IV. CONCLUSION This pper extends the frmework of the existing Winnertype GSCM towrds the evolution of 5G chnnel models for mssive MIMO. Winner-type GSCM re hevily employed y the industry, so modifiction is necessry to continue uild on existing knowledge se. The pper focuses on the three min limittions of the existing models tht prevents the proper simultion of mssive MIMO systems. First of ll the lck of method to model the multiuser consistency. Then, the impossiility to generte non-sttionrities over the se sttion rry. Finlly the limittion of using the plnr wve pproximtion. Using QuDRiG s reference model, severl modifictions re proposed to overcome these limittions. ACKNOWLEDGMENT The reserch presented in this pper ws prtly supported y the Dnish Council for Independent Reserch (Det Frie Forskningsråd) DFF This work ws supported y Huwei Technologies Co. Ltd. (Huwei Sweden) in the frmework of the coopertion project No REFERENCES [1] T. L. Mrzett, Noncoopertive Cellulr Wireless with Unlimited Numers of Bse Sttion Antenns, Wireless Communictions, IEEE Trnsctions on, vol. 9, no. 11, pp , Nov [2] H. Q. Ngo, E. G. 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