IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. -, NO. -, - 1

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1 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. -, NO. -, - QuaDRiGa: A 3-D Muti-Ce Channe Mode with Time Evoution for Enabing Virtua Fied Trias Stephan Jaecke, Member, IEEE, Leszek Raschkowski, Kai Börner, Student Member, IEEE and Lars Thiee, Member, IEEE Abstract Channe modes are important toos to evauate the performance of new concepts in mobie communications. However, there is a trade-off between compexity and accuracy. In this paper, we extend the popuar WINNER channe mode with new features to make it as reaistic as possibe. Our approach enabes more reaistic evauation resuts at an eary stage of agorithm deveopment. The new mode supports three-dimensiona (3-D) propagation, 3-D antenna patterns, time evoving channe traces of arbitrary ength, scenario transitions and variabe termina speeds. We vaidated the mode by measurements in a coherent LTE advanced testbed in downtown Berin, Germany. We then reproduced the same scenario in the mode and compared severa channe parameters (deay spread, path gain, K-factor, geometry factor and capacity). The resuts match very we and we can accuratey predict the performance for an urban macro-ce setup with commercia high-gain antennas. At the same time, the computationa compexity does not increase significanty and we can use a existing WINNER parameter tabes. These artificia channes, having equivaent characteristics as measured data, enabe virtua fied trias ong before prototypes are avaiabe. Index Terms Coherent Muti-Ce Measurements, MIMO Systems, MIMO Channe, Modeing, Parameterization, Radio Propagation, Spatia Channe Mode (SCM), Vaidation, WINNER. I. INTRODUCTION THERE are severa ways to vaidate new concepts in mobie communication systems. Ideay, everything woud be tested using rea-time prototypes. However, this is ony possibe after the standardization and product deveopment stages. In the research stage, i.e., before standardization and product deveopment, eary fied trias are often hepfu to promote new approaches towards standardization. However, the vaue of such eary trias is rather imited from a performance evauation point of view. Therefore, they are usuay combined with simuation studies taking the channe and interference statistics into account. Channe modes such as the 3GPP spatia channe mode (SCM) [], the Wireess Word Initiative Manuscript received February 8, 23; revised Juy 5, 23; revised December 9, 23; accepted February 9, 24; date of pubication -; date of current version -. This work was supported by the German Federa Ministry of Economics and Technoogy (BMWi) in the nationa coaborative project InteiSpektrum under contract ME24, by the European Space Research and Technoogy Centre (ESTEC) under contract AO/-5985/9/8/NL/LvH (Acronym: MIMOSA) and by the German Federa Ministry od Education and Research (BMBF) under contract BU63 (Acronym: EASY-C). The authors are with the Fraunhofer Institute for Teecommunications, Heinrich Hertz Institute, Einsteinufer 37, D-587 Berin, Germany (e-mai: stephan.jaecke@ieee.org). Digita Object Identifier - for New Radio (WINNER) mode [2], [3] and the European Cooperation in Science and Technoogy (COST) 273/2 channe mode [4], [5] are reiabe toos for such studies. The 3GPP SCM [], its extensions [6], [7] and the WINNER mode [2] are based on a two-dimensiona (2-D) modeing approach. However, Shafi et a. [8] pointed out the importance of a 3-D extension when studying the effects of cross-poarized antennas on the mutipe-input mutipe-output (MIMO) capacity. This was taken up in the WINNER+ project where the parameter tabes were competed with the eevation component [3]. However, a 3-D WINNER+ channe mode is not avaiabe. Meanwhie, 3-D propagation was incorporated into other modes such as the COST mode [5] or mobie-tomobie propagation modes [9]. They share simiar ideas which we use in this paper to incorporate 3-D propagation and 3-D antenna patterns into an extension of the WINNER mode. Another prerequisite for virtua fied trias is the continuous time evoution of channe traces. Xiao et a. [6] added short-term time evoution to the SCM, that was incorporated into an officia SCM extension [7]. The idea is to cacuate the position of the ast-bounce scatterers (LBSs) based on the arriva anges of individua mutipath components. Then, when the mobie termina (MT) is moving, the arriva anges, deays, and phases are updated using geometrica cacuations. However, the WINNER II mode did not incorporate this technique. Hence, the WINNER mode does not support time evoution beyond the scope of a few miiseconds, restricting the mobiity of the MTs to a few meters. The COST mode [4] incorporates time evoution by introducing groups of randomy paced scattering custers that fade in and out depending on the MT position. However, despite the effort that was made to parameterize the mode [], [], it sti acks sufficient parameters in many interesting scenarios. Czink et a. [2] introduced a simpified method that fades the custers in and out over time. The custer parameters were extracted from measurements, and the mode is we suited for ink-eve simuations. However, this random custer mode cannot be used for system-eve scenarios, because it does not incude geometry-based depoyments ike in the SCM, COST, and WINNER modes. Nevertheess, the ideas presented by [2] ed to more research on the birth/death probabiity as we as the ifetime of individua scattering custers [3]. Wang et a. [4] then proposed a mode for non-stationary channes that aows the scattering custers to be mobie. In our extension of the WINNER mode, we incorporate time evoution based on the ideas presented in [6] and [7]. We introduce the new mode under the acronym QuaDRiGa

2 2 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. -, NO. -, - Input variabes: - network ayout - termina trajectories - propagation scenario - antenna patterns Postprocessing / Anaysis A. Cacuation of correated arge scae parameter maps G. Transitions between segments B. Cacuation of initia deays and custer powers F. Appication of path gain, shadow fading and K-Factor C. Cacuation of departure and arriva anges E. Cacuation of poarized channe coefficients D. Drifting of the initia deays, anges, and phases over a short segment of the termina trajectory Fig.. Steps for the cacuation of time-evoving channe coefficients. Compared to the WINNER mode, changes were made in the gray shaded boxes. Quasi Deterministic Radio Channe Generator. A reference impementation in MATLAB is avaiabe as open source [5]. Our approach consists of two steps: A stochastic part generates arge-scae parameters (LSPs) and cacuates random 3-D positions of scattering custers. We assume that the base stations (BSs) are fixed and the MTs are moving. In this case, scattering custers are fixed as we and the time evoution of the radio channe is deterministic. Different positions of the MT ead to different arriva anges, deays, and phases for each mutipath component (MPC). Longer sequences are generated by transitions between channe traces from consecutive initiaizations of the mode. This aows the MTs to traverse different scenarios, e.g., move from indoors to outdoors. We vaidated the mode by measurements in downtown Berin, Germany. We extracted severa singe-ink and mutiink parameters and compared them with those obtained from the channe mode. The resuts agree very we. Remaining deviations can be expained by some specific characteristics of our measurement system. In this way, we show that it is possibe to emuate a rea-word scenario accuratey. The paper is organized as foows: Section II describes the mode in detai. Section III reports on the measurements. Section IV then compares the resuts from both mode and measurement. Section V concudes the paper. II. DESCRIPTION OF THE CHANNEL MODEL Our modeing approach is an extension of the WINNER mode [2]. Figure gives an overview of the modeing steps. The user needs to configure the network ayout (i.e., the positions of the BSs, antenna configurations, downtits), the positions and trajectories of the MTs, and the propagation scenarios. The channe coefficients are then cacuated in seven steps, which are described in detai in Sections II-A to II-G. Major extensions concerning 3-D propagation are made in steps C and D. Time evoution is incorporated in steps D and G, and a new 3-D mode of the poarization [6] is introduced in step E. In order to integrate these extensions, some changes are made in the other parts of the mode as we. Time evoution requires a more detaied description of the mobiity of the terminas. This is done by assigning tracks, i.e., ordered ists of positions, to each MT. Reaistic scenarios may incude acceerations, deceerations, and MTs with different speeds, e.g., pedestrian and vehicuar users. However, to minimize the computationa overhead and memory requirements, we cacuate channe coefficients at a constant sampe rate that fufis the samping theorem max v f T 2B D = 4 max f D = 4, () λ c where B D is the width of the Dopper spectrum, f D is the maximum frequency change due to the veocity v, and λ c is the carrier waveength. Thus, the appropriate samping rate is proportiona to the maximum speed of the MT. Since it is sometimes usefu to examine agorithms at different speeds, it is unfortunate to fix the samping rate in advance as the speed is then fixed as we. To overcome this probem, we cacuate channe coefficients at fixed positions with a samping rate f S measured in sampes per meter. In its normaized form, it is known as sampe density (SD). A time-series for arbitrary or varying speeds is then obtained by interpoating the coefficients in a postprocessing step. f S = SD = f T max v 4 λ c (2) f S λ c /2 2 (3) Longer time-evoving channe sequences need to consider the birth and death of scattering custers as we as transitions between different propagation environments. We address this by spitting the MT trajectory into segments. A segment can be seen as an interva in which the LSPs do not change consideraby and where the channe keeps its wide sense stationary (WSS) properties. Thus, the ength of a segment depends on the decorreation distances of the LSPs. We propose to imit the segment ength to the average decorreation distance. In the WINNER urban macro-ce (UMa) scenario, this woud be 22 m for ine-of-sight (LOS) and 48 m for non-ine-ofsight (NLOS) propagation. Channe traces are then generated independenty for each segment. In Section II-G we combine those individua traces into a onger sequence that incudes the birth and death of scattering custers. A. Correated Large-scae Parameter Maps The positions of the scattering custers are based on seven arge-scae parameters (LSPs): ) RMS deay spread (DS) 2) Ricean K-factor (KF) 3) Shadow fading (SF) 4) Azimuth spread of departure (ASD) 5) Azimuth spread of arriva (ASA) 6) Eevation spread of departure (ESD) 7) Eevation spread of arriva (ESA) Their distribution properties are directy obtained from measurement data (e.g., [7]-[9], [3], [2]). If some MTs or segments are cose to each other, their LSPs wi be correated and they wi experience simiar propagation conditions.

3 JAECKEL et a.: QUADRIGA: A 3-D MULTI-CELL CHANNEL MODEL WITH TIME EVOLUTION FOR ENABLING VIRTUAL FIELD TRIALS Fig. 2. White Gaussian noise generator 2D autocorreation shaping Linear transformation to impose inter-parameter correation B DS = B ESD... c... c c 7... c 77 A DS... A ESD Principe of the generation of channe coefficients based on correated LSPs. Parameter Maps Norm. Power Loca vaues for an individua MT position Initia Deays and Custer Powers.2.4 Deay [μs].6 This is modeed by means of 2-D maps, as iustrated in Figure 2. Our method for generating these maps is adopted from [2]. The maps are initiaized with vaues obtained from an independent and identicay distributed (i.i.d.) zero-mean Gaussian random process with desired variance. The pixes are then subsequenty fitered to obtain the desired autocorreation function, i.e., a decaying exponentia function with a specific decorreation distance. In contrast to [2], we fiter the maps in the diagona direction as we to get a smooth evoution of the vaues aong the MT trajectory. Advanced methods going beyond our approach for generating such maps are discussed in [2]. Once the maps are generated, initia LSPs for each segment are obtained by interpoating the maps to match the exact position of the MT. B. Initia Deays and Custer Powers Initia deays are drawn randomy from a scenariodependent deay distribution as τ [] = r τ σ τ n(x ), (4) where X uni(, ) is an uniformy distributed random variabe having vaues between and, σ τ is the initia DS from the map and r τ is a proportionaity factor (see [2]). The term r τ was introduced in [] because σ τ is infuenced by both the deays τ and the powers P ; r τ is usuay cacuated from measurement data. Next, the deays are normaized such that the first deay is zero and then they are sorted: { ( )} τ [2] = sort τ [] min τ []. (5) The NLOS custer powers are drawn from a singe sope exponentia power-deay profie (PDP) depending on the DS σ τ and a random component Z N (, ζ 2 ) [2]. The term ζ is a scenario-dependent coefficient emuating an additiona shadowing process. It is obtained from measurements. ( ) P [] r τ = exp τ Z (6) r τ σ τ The power of the first custer is further scaed according to the initia KF from the map and custer powers are normaized so that their sum power is one: P [2] = K L =2 P [] ; P [2] 2... = P [] 2... and P = P [2] / L = P [2]. (7) In the ast step, we correct the infuence of the KF on the DS, which has changed due to the scaing. The DS after appying (7) is cacuated using (4) from Section III-C with P i set to one. This vaue is denoted as σ τ [actua]. With σ τ being the initia DS from the map, custer deays note τ = σ τ τ [2] σ τ [actua] (8) C. Departure and Arriva Anges We cacuate four anges for each custer. In addition to the azimuth ange of departure (AoD, φ d ) and the azimuth ange of arriva (AoA, φ a ) used in the 2-D WINNER mode, we aso cacuate the eevation ange of departure (EoD, θ d ) and the eevation ange of arriva (EoA, θ a ). The anges share the same cacuation method but have different anguar spreads σ φ. Hence, we use σ φ representative for σ φ a, σ φ d, σ θ a, σ θ d in the foowing. We assume that the power anguar spectrum of a custers foows a wrapped Gaussian distribution [2], [22]. P (φ) = σ φ 2π exp ( φ 2 2σ 2 φ The wrapping is appied ater by (2) when the discrete custer anges are drawn from the statistics. Since the above formua assumes a continuous spectrum, whereas the channe mode uses discrete paths, we need to correct the variance by a function C φ (L, K). This function ensures that the input variance σ φ is correcty refected in the generated anges. It is derived in the Appendix. We obtain the anges φ by first normaizing the power anguar spectrum so that its maximum has unit power. We can thus omit the scaing factor /(σ φ 2π). We aso normaize the path powers P (7) so that the strongest peak with unit power corresponds to an ange φ =. A other paths get reative departure or arriva anges depending on their power, ) (9) φ [] σ φ = C φ (L, K) 2 n(p / max(p )). () The vaue σ φ is measured in radians here. Next, we create two random variabes, X and Y, where X {, } is the positive or negative sign and Y N (,. σ 2 φ ) introduces a random variation on the ange. Then we cacuate φ [2] = X φ [] + Y. () If the power P of a path is sma compared with the strongest peak, its ange φ [2] might exceed ±π. In this case, we wrap it around the unit circe by a moduo operation: ( ) φ [3] = φ [2] + π mod 2π π. (2)

4 4 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. -, NO. -, - In case of eevation spreads, the possibe range of eevation anges goes from π/2 to π/2. In this case, we have to correct vaues of φ [3] outside of this range. φ [3] φ [4], for e. φ [3] < π 2 and a az. anges; = π φ [3], for eevation φ [3] > π 2 ; φ [3] π, for eevation φ [3] < π 2. (3) The positions of the transmitter (Tx) and receiver (Rx) are deterministic, and so are the anges of the LOS component. We correct the vaues of the anges to incorporate this position: φ [5] = φ [4] φ [4] + φlos. (4) Finay, the NLOS custer-paths are spit into 2 sub-paths to emuate intra custer anguar spreads. The LOS path has no sub-paths. φ,m = φ [5] + c φ ˆφ m, for > (5) m is the sub-path index, c φ is the scenario-dependent custerwise RMS anguar spread and ˆφ is the offset ange of the m th sub-path from Tabe I. Furthermore, each of the 2 ange pairs (θ,m d, φd,m ) at the Tx gets couped with a random ange pair (θ,m a, φa,m ) at the Rx (see [2]). D. Drifting TABLE I OFFSET ANGLE OF THE m TH SUB-PATH FROM [2] Sub-path Offset ange Sub-path Offset ange m ˆφm (degrees) m ˆφm (degrees),2 ±.447,2 ± ,4 ±.43 3,4 ± ,6 ± ,6 ±.48 7,8 ±.375 7,8 ±.595 9, ±.529 9,2 ± 2.55 After custer-deays, powers, and anges are known for the initia position, we update their vaues for each snapshot of the segment. Thus, we get an evoution of the parameters over a short time interva. Drifting for 2-D propagation was aready introduced in an extension of the SCM [7]. However, it was not incorporated into the WINNER mode and no evauation was reported. Here, we extend this idea towards 3-D propagation to incorporate time evoution into the new mode. Besides the parameters from steps B and C, drifting requires the exact position of each antenna eement. At the MT, eement positions need to be updated for each snapshot with respect to the MT orientation. The foowing cacuations are then done eement-wise. The indices r, t,, m, s denote the index of the Rx antenna eement (r) and the Tx antenna eement (t), the custer number (), the sub-path number (m), and the snapshot number (s) within the current segment, respectivey. a) NLOS drifting: We keep the scatterer positions fixed for the time it takes a MT to move through a segment. Hence, the anges (θ d, φ d ) seen from the BS do not change except for the LOS ange, which is treated separatey. Based on this assumption, the anges (θ a, φ a ) as we as the path deay ony change with respect to the ast-bounce scatterer (LBS). Hence, if the BS array size is sma compared to the BS-MT distance, ast-bounce scatterer b t,,m, Tx ocation r r r,t,s a r,,m,s a,m, q r,s MT track initia Rx ocation Rx ocation at snapshot s Fig. 3. Iustration of the cacuation of the scatterer positions and updates of the arriva anges. it is sufficient to consider ony a singe scatterer (the LBS) for the NLOS paths. We cacuate the position of the LBS from the initia arriva anges and the custer deays. Then we update the anges and path engths between the LBS and the termina for each snapshot on the track. This is done for each antenna eement separatey. Figure 3 iustrates the anges and their reations. The first deay is aways zero due to (5). Hence, we cacuate the tota ength of the th path as d = τ c + r, (6) where r is the distance between the Tx and the initia Rx ocation, and c is the speed of ight. We assume that a subpaths have the same deay and thus the same path ength. However, each sub-path has different arriva anges (θ,m a, φa,m ). We transform those anges into Cartesian coordinates and obtain â,m, = a,m, a,m, = cos φ a,m cos θa,m sin φ a,m cos θa,m sin θ a,m. (7) We approximate the drifting at the MT using ony a singe refection. Hence, Tx, Rx, and LBS form a triange. Since we know d, r, and â,m,, we can appy the cosine theorem to cacuate the distance a,m, between the Rx and LBS. b 2,m, = r 2 + a,m, 2 2 r a,m, cos β,m, (d a,m, ) 2 = r 2 + a,m, a,m, r T â,m, d 2 a,m, = r 2 2 (d + r T â,m,) (8) Now we can cacuate the vector a r,,m,s for the Rx antenna eement r at snapshot s. The eement position incudes the orientation of the antenna array with respect to the moving direction of the Rx. Hence, the vector q r,s points from the initia Rx ocation to the r th antenna eement at snapshot s. a r,,m,s = a,m, q r,s (9) We obtain an update of the arriva anges by transforming a r,,m,s back to spherica coordinates. φ a r,,m,s = arctan 2 {a r,,m,s,y, a r,,m,s,x } (2) { } θr,,m,s a ar,,m,s,z = arcsin (2) a r,,m,s We substitute cos β,m, with r T â,m,/ r since we are at the Rx position ooking towards the Tx.

5 JAECKEL et a.: QUADRIGA: A 3-D MULTI-CELL CHANNEL MODEL WITH TIME EVOLUTION FOR ENABLING VIRTUAL FIELD TRIALS 5 Since we assume a static scattering environment, we use the same departure anges for a Tx eements. The phases and path deays, however, depend on the tota path ength d r,t,,m,s. To obtain this vaue, we cacuate the vector b t,,m, from the vectors r r,t,s and a r,,m,s at r = s =. b t,,m, = r,t, + a,,m, (22) d r,t,,m,s = b t,,m, + a r,,m,s (23) Finay, we cacuate the phases ψ and path deays τ. ψ r,t,,m,s = 2π λ (d r,t,,m,s mod λ) (24) τ r,t,,s = 2 c 2 m= d r,t,,m,s (25) b) LOS drifting: The direct component is handed differenty, since we have to update the anges at both the Tx and the Rx sides. We update the departure and arriva anges for each combination of Tx-Rx antenna eements based on the position of the eement in 3-D coordinates. φ d t,,s = arctan 2 {r r,t,s,y, r r,t,s,x } (26) { } θt,,s d rr,t,s,z = arcsin (27) r r,t,s φ a r,,s = arctan 2 { r r,t,s,y, r r,t,s,x } (28) { } θr,,s a rr,t,s,z = arcsin (29) r r,t,s The vector r r,t,s points from the ocation of the Tx eement t to the ocation of the Rx eement r at snapshot s (see Figure 3). The phases and deays are determined by the ength of this vector and are cacuated using (24) and (25) where d r,t,,m,s is repaced by r r,t,s. E. Poarized Channe Coefficients Next, we combine antenna patterns, poarization, and phases to cacuate initia channe coefficients for each snapshot of a segment. The antennas are defined by their 3-D poarimetric response F containing vertica and horizonta poarization in spherica coordinates [23]. ( ) FV (θ, φ) F(θ, φ) = (3) F H (θ, φ) We read the directiona antenna gains from both the Tx and Rx antennas using the previousy cacuated departure and arriva anges and cacuate the coefficient g [] r,t,,m,s = F r(θ a r,,m,s, φ a r,,m,s) T M F t (θ d t,,m,s, φ d t,,m,s). (3) The poarization is changed aong the propagation path. This is captured by the matrix M. The SCM, WINNER, and COST modes use random coefficients to hande poarization effects. However, in our separate pubication [6], we discussed how this does not account for a effects contributing to the poarization state of a MIMO radio ink. Thus, we proposed a method for cacuating M based on inear transformations, which we use here as we. Each MPC has a random initia phase ψ. Hence, by summing up the 2 sub-paths to get one path per custer, we get a random custer power. This is compensated by normaization where we first sum up the compex phases and then average the power over a S snapshots of the segment. We update the channe coefficients (3) as ψ + r,t,,m,s = exp ( jψ,m ) jψ r,t,,m,s, (32) 2 g [2] P r,t,,s = β g [] r,t,,m,s ψ+ r,t,,m,s, (33) β = S S s= m= ( 2 m= ψ + r,t,,m,s) 2, (34) where P is the initia power assigned to each custer. F. Path Gain, Shadow Fading and K-Factor Now, we appy the path gain (PG), the SF, and the KF. Hata [24] presented a simpe mode for macro-ceuar settings where the PG scaes with the ogarithm of the distance d (in units of meters) between BS and termina: PG [db] = A og d [m] B, (35) where A and B are scenario-specific coefficients that are typicay determined by measurements. The path gain exponent A often varies between vaues of 2 and 4, depending on the propagation conditions, the BS height, and other factors. Combining PG and SF resuts in the effective path gain PG [eff]. The vaues for the SF and the KF are obtained from the LSP map by an interpoation of the surrounding pixes at the position of the s th snapshot. The KF at the initia position is aready incuded due to the scaing in (7). Thus, we have to take this into account and scae the power accordingy. PG [eff] s =. ( g r,t,,s = PG [eff] s PG [db] s ) +SF s [db] + P ( Ks K { K s K g [2] r,t,,s for = ; g [2] r,t,,s otherwise. ) (36) (37) In the above equations, K s and SF [db] s are the interpoated vaues for the KF and the SF from the map, K is the KF at the initia position, PG s [db] is the path gain (without SF) at the MT position (35), and P is the power of the LOS custer (7). G. Transitions between Segments The cacuations in Sections II-B to II-F were done independenty for each segment of the MT trajectory. Here, we combine those segments into a ong, time-evoving sequence of channe coefficients. The idea comes from the WINNER II mode [2]. However, it was neither impemented nor tested. Our impementation requires that parts of the segments are overapping as depicted in the top of Figure 4. The ifetime of a scattering custer is confined within the combined ength of two adjacent segments. The power of custers from the od segment is ramped down and the power of new custers is ramped up within the overapping region of the two segments. Hence, this process describes the birth and death of custers aong the trajectory. Outside the overapping

6 6 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. -, NO. -, - segment Transitions between Segments overapping part merging area (variabe ength) segment 2 initia pos. segment 2 has a corresponding position on the MT trajectory (in units of meters). The ampitudes and phases of the channe coefficients are interpoated separatey using cubic spine interpoation. The path deays are interpoated with a piecewise cubic hermite interpoating poynomia. initia pos. segment Postprocessing / Variabe Speeds: origina constant distance interpoated constant samperate Fig. 4. Top: iustration of the overapping area used for cacuating the transitions between segments (step G), Bottom: iustration of the interpoation to to obtain variabe MT speeds (step H). region, a custers of the segment are active. We further spit the overapping region into sub-intervas to keep the computationa overhead ow. During each sub-interva, one od custer ramps down and one new custer ramps up. We mode the power ramps by a squared sine function: w [sin] = sin 2 ( π 2 w[in]). (38) Here, w [in] is the inear ramp ranging from to, and w [sin] is the corresponding sine-shaped ramp with a constant sope at the beginning and the end. This prevents inconsistencies at the edges of the sub-intervas. If both segments have a different number of custers, the ramp is stretched over the whoe overapping area for custers without a partner. For the LOS custer, which is present in both segments, we adjust ony power and phase. Custers need to be carefuy matched to minimize the impact of the transition on the instantaneous vaues of the LSPs. For exampe, the DS increases if a custer with a sma deay ramps down and a simiary strong custer with a arge deay ramps up. Hence, the DS can fuctuate randomy within the overapping region. To baance this out we pair custers from both segments that minimize these fuctuations. This is done by determining the vaues of the DS before and after the transition. Then, we cacuate a target DS for each subinterva. For exampe, if the od segment yieds a DS of 2 ns and the new segment has 4 ns, then the target DS wi be 22 ns for the first sub-interva, 24 ns for the second and so on. Then we ook for a combination of custers that best matches the target DS for each sub-interva. H. Postprocessing / Variabe Speeds In the rea word, MTs move at arbitrary speeds, incuding acceerations and deceerations. Provided that the samping theorem is fufied, we can interpoate the channe coefficients to incude such effects. This is iustrated in the bottom part of Figure 4. The white dots represent the snapshots at a constant distance. However, the sampe points (gray stars) can have unequa spacing, e.g., for an acceerated movement. Each sampe point in the time domain (given in units of seconds) III. VALIDATION METHOD To vaidate the mode, we used measurement data from our muti-ce testbed in downtown Berin, Germany. Detaied information on the testbed is avaiabe in [25]-[28]. The same scenario (in terms of BS and MT positions) was repicated using the channe mode. We extracted severa arge-scae parameters from both data sets and compared their distributions. Here, we describe the measurement and channe mode setup as we as the metrics used for evauating the data. A. Measurement Setup Our measurement setup repicated a sma pre-commercia Long Term Evoution (LTE)-advanced scenario consisting of six sectors. A sectors were equipped with commercia Kathrein XPo pane antennas 2 with a haf-power beam width of 6 in azimuth and 6 in eevation direction (poarization ±45, 8 dbi gain). A sites were synchronized using GPSdiscipined Rubidium cocks that aowed phase-coherent operation in the same frequency band. Reference signas [29] consisting of 44 piot tones for each BS served for coherenty identifying up to six ces. Additiona orthogona sequences over four consecutive symbos aowed the identification of mutipe antennas per ce. At the Rx side, we used a customized termina equipped with a pair of dipoe-ike antennas 3 (4 dbi gain). These antennas were mounted on the roof of a car and santed by ±45. The termina was synchronized over the air to simpify the measurement procedure and to eiminate additiona caibration steps. The system automaticay adjusted the muti-ce channe impuse response (CIR) within the 4.7 µs guard interva of the underying orthogona frequency-division mutipexing (OFDM) system which removed the mean muti-ce deay from the data. The MT detected the reference signas and converted them into an Ethernet packet stream as described in [28]. This data stream was tapped at the termina and recorded to a notebook computer. Custom import fiters provide access to the stored CIRs. The import fiters extract a channe tensor every ms. The dimensions correspond to the number of Rx antennas, the tota number of Tx antennas, and the number of sampes in the frequency domain, respectivey. We use the preprocessing technique described in [3] to extract the MPCs from the CIR. Essentiay, the preprocessing estimates L h n = α e jφ e }{{} j2π τ B n N, (39) = =g where α is the ampitude, φ is the phase, τ is the deay of the th MPC, B is the measurement bandwidth of 8.36 MHz, 2 Type No HUBER+SUHNER SWA 2459/36/4/45/V; Type:

7 JAECKEL et a.: QUADRIGA: A 3-D MULTI-CELL CHANNEL MODEL WITH TIME EVOLUTION FOR ENABLING VIRTUAL FIELD TRIALS 7 y N HHI Sector, 2: Height: Downtit: Coord. (x,y): x TLabs Sector 5, 6: Height: Downtit: Coord. (x,y): Fig SE Active Sector Meas. Track 3m 5 and m or , -383 NE 3 Ernst- Reuter Patz -55 and m 8 or 23, () HHI W 4 2 Einsteinufer SE Overview map of the measurement scenario. Genera settings: Center freq.: 2.68 GHz Bandwidth: 8.36 MHz No. Carriers: 44 MIMO: 2x2 per BS Update rate: ms Max. speed: 2.8 m/s ISD: 5 m Tx power: 36.5 dbm Noise foor: -95 dbm 3 NE 4 W TUB Sector 3, 4: 55 and -7 Height: 49 m Downtit: 5 or 5 Coord. (x,y): 26, -454 and n =... N is the index of the sampe point in frequency domain. Due to the preprocessing, h has an approximatey 6 db better signa to noise ratio (SNR) than the raw measurement data. Both the preprocessed data (39) and the output of the channe mode (37) have the same format. Thus, identica routines can be used to obtain the LSPs. Figure 5 shows an overview of the measurement scenario, giving the coordinates and heights (in units of meters), the antenna orientations, and the downtit settings for each BS site. Three BSs are ocated around the Ernst-Reuter-Patz in downtown Berin, Germany. They are at the rooftop of the Heinrich Hertz Institute (HHI), the Deutsche Teekom Laboratories (TLabs) and the main buiding of the Technische Universität Berin (TUB). The 2 measurement tracks with a tota ength of 3. km are potted as thick back ines. The measurements were repeated twice with different downtit settings. In the first setting, the main beam of the high-gain antenna reached the ground at 9% of the inter-site distance (ISD) (45 m). In the second setting, this distance was reduced to 33% of the ISD (7 m). In this way, different interference scenarios can be investigated. B. Channe Mode Setup We imported the Tx-positions, sector orientations and Rxtracks into the mode and spit the measurement tracks into 9 segments. Each segment has an average ength (incuding the overapping part) of 24 m with a standard deviation of 6 m. A separation into LOS and NLOS parts was done based on the overa received power and a 3-D mode of downtown Berin. We assume that there is no inter-site correation of the LSPs due to the arge ISD and the high anguar separation at the MT [3]. However, inter-sector correation at the same BS is incuded impicity since we combine the antennas of different sectors into one array. When parameterizing the mode, we found some differences between our measurement resuts and the WINNER 2 TABLE II PARAMETERS FOR THE URBAN MACRO-CELL (UMA) SCENARIO Parameter LOS NLOS WIN. Berin Ref. WIN. Berin Ref. No. Custers L Path Gain A own data own data B own data own data SF (db) σ own data own data decorr. [m] λ 45 9 own data 5 own data Deay Spread µ own data own data (og s) σ.63.3 own data.32.2 own data decorr. [m] λ 4 3 own data 4 own data Deay factor r τ [2] [2], [] K-factor µ own data N/A -6.3 own data (db) σ own data N/A 3.7 own data decorr. [m] λ 2 23 own data N/A 4 own data ASD µ..65 [2], [8], [9] [2], [8], [9] (og ) σ [2], [8], [9] [2], [8], [9] decorr. [m] λ 5 8 [2], [9] 5 25 [2], [9] per custer c φ 6 2 [2] 2 6 [2] ESD µ.7.7 [3].9.9 [3] (og ) σ.2.2 [3].2.2 [3] decorr. [m] λ 5 5 [3] 5 3 [3] per custer c φ 3 3 [3] 3 3 [3] ASA µ.7.6 [2], [8], [9].72.5 [2], [8], [9], [7] (og ) σ.9.7 [2], [8], [9].4.6 [2], [8], [9] decorr. [m] λ 5 [2], [9] 5 45 [2], [9], [7] per custer c φ 2 2 [2] 5 5 [2] ESA µ.95.6 [8], [9], [3] [8], [9], [3] (og ) σ.6.4 [8], [9], [3].6.4 [8], [9], [3] decorr. [m] λ 5 [9], [3] 5 25 [9], [3] per custer c φ 3 3 [3] 7 7 [3] XPR µ [2], [9], [32] [2], [9], [32] (db) σ [2], [9], [32] [2], [9], [32] TABLE III CROSS-CORRELATION VALUES Cross- L O S correation DS K SF ASD ASA ESD ESA DS Berin WIN K Berin WIN. N/A.3..2 SF Berin N WIN..4 N/A L ASD Berin O WIN..4 N/A S ASA Berin WIN..6 N/A ESD Berin.4.5 WIN..5 N/A.34 ESA Berin WIN. N/A parameters. For exampe, many WINNER resuts (e.g., [2], [8], [9]) show median DS vaues of around 4 ns for LOS and 7-23 ns for NLOS. Measured resuts from the scenario with ow downtits (.9 ISD), however, show arger DS vaues of 2 and 3 ns, respectivey. This was aso reported by other authors (e.g., [7], [], []). We aso observed ower KF vaues, i.e., we found strong echoes even if the direct component was present. In some cases, the power of those echoes coud even exceed the LOS power. Therefore, we decided to adjust some parameters to increase the match with our testbed. After a, our intention is to show that the mode creates channes with simiar properties as rea word data. Tabe II ists the LSPs from the WINNER mode [2], [3] (Urban macro-ce scenario), as we as parameters that we extracted from our own measurement data (Berin scenario). Tabe III provides the cross-correation vaues between the LSPs. The cross-correation matrix must be positive definite to create correated sequences, e.g., by Choesky factorization. This is not the case for the WINNER parameters. Hence, we

8 8 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. -, NO. -, - did some minor adjustments to the parameters to make the matrix positive definite 4. To cacuate the anguar spreads, we need antenna arrays with a high spatia resoution, such as those used by [9], [33], and [34]. However, those antennas are not compatibe with our testbed. We can ony directy vaidate the vaues for DS, PG, SF, and KF. To fi the gaps we refer to measurements that we did together with our partners at the Imenau University of Technoogy using a different channe sounder [35]. Hence, Tabe II incudes the averages of the resuts from measurement campaigns in Dresden, Germany [9], Imenau, Germany, [8] and the WINNER parameters. We made sure by extensive testing and debugging that for each parameter in the tabes, our impementation of the mode produces exacty the same vaue in the output channe coefficients. However, the tabe is ony vaid for omnidirectiona radiation patterns. We incuded high-gain BS-antennas by a measured 3-D pattern provided by Kathrein. It contains the radiated power vs. azimuth and eevation ange for one poarization at a fixed eectrica downtit of. We added mechanica tits as described in [6] to obtain the same downtits as for the measurements. We aso approximated the poarization for the second port and the cross-poarization isoation between the ports. Since we had no 3-D pattern of the receive antenna, we approximated it by a dipoe antenna. However, with those antennas, the LSPs extracted from the channe coefficients differ from the vaues in the tabe. We had to remove the antenna-infuence to parameterize the mode with our own measurement resuts. This was done using an iterative method: First, we cacuate the parameter (e.g., the DS) from the measured data 5, cacuate the ognorma distribution, and obtain the median DS µ and standard deviation (STD) DS σ. We then run the mode and cacuate from the mode output. However, due to the weighting by the antenna pattern, some custers get more power and others get ess. We observed that this increases the width of the distribution of the DS. In the next step, we adjust the vaues at the input of the channe mode to account for this difference. We then repeat the procedure unti the vaues DS [mode] µ and DS [mode] σ DS [mode] µ, DS [mode] σ converge to DS µ, DS σ. The same is done for a other parameters marked with own data in Tabe II. C. Estimation of Large-scae Parameters In the foowing, we describe how the LSPs are cacuated from both, the measured data and the modeed channes. The parameters are cacuated on a per-snapshot basis. However, sma-scae fading can ead to strong fuctuations of a parameter even in subsequent snapshots. To remove the infuence of sma-scae fading, we average the resuts of the computations within a radius of 3 λ or 3.3 m [3]. 4 The corrections for the LOS scenario are: ASD-DS from.4 to.3, ASA- DS from.8 to.72, ESA-SF from -.8 to -.72, and ESD-DS from -.5 to The corrections for the NLOS scenario are: ASD-SF from -.6 to -.44, ESA-SF from -.8 to -.64, ESD-ASD from.5 to.34, and ESA-ASD from -.4 to We use the scenario where the downtit is set to maximize the gain at 9% of the ISD for this evauation. a) Effective Path Gain (PG): We estimate the PG from the data by summing up the power of a L paths and averaging over the n t transmit and n r receive antennas of the i th sector. The ampitude of a singe MPC is represented by α. P i = n r n t n r n t r= t= = L αr,t,,i 2 (4) b) Deay Spread (DS): During preprocessing, MPCs are estimated from each MIMO subink independenty. To cope with measurement noise and estimation errors, we deveoped a method to match the paths from different subinks. We spit the deay axis into L intervas of 5 ns ength 6 and add up the power of a MPCs from a inks that fa into one interva. This aso accounts for the jitter on the path deays of successive CIRs. The DS is then cacuated as [36] 2 σ τ i = L P,i (τ,i ) 2 L P,i τ,i, P i P i = = (4) where the index indicates the interva number, P is the sumpower of a paths faing into the th interva, τ is the mean deay of the interva. We evauated the performance of this approach 7 and found that at 5 db SNR, the median error is % 8. In 9% of the CIRs the error is beow 35%, i.e., the estimated DS is at most 35% onger or shorter than the actua DS from the unprocessed, noise-free channes. c) K-Factor (KF): The KF is defined as the ratio of the power of the direct path divided by the sum-power of a other paths. Some iterature sources (e.g., [37], [36]) define the KF with respect to the strongest path in the CIR which can originate from a dominant scatterer. In our mode, however, the KF is defined as the power ratio between LOS and NLOS. Hence, to estimate the KF we have to detect the LOS path. Our empirica detection of the LOS path works in three steps: First, we sum up the PDPs of a MIMO subinks of one sector. Then we ook for a peak at the beginning of this sum- PDP, i.e., we detect the first path that exceeds % of the tota power. This ensures that noise at the beginning of the CIR is excuded. The noise aso eads to jitter on the estimated deays from different subinks. In order to account for this jitter, we try to match paths from a MIMO subinks that have roughy the same deay as the peak detected in the first step. Therefore, in the second step, we ook for the strongest path on each MIMO ink separatey within a 5 ns window before and after the peak deay. If the LOS path is correct, then its deay shoud not change significanty over a short distance. Thus, 6 The interva ength corresponds to the time resoution of our measurement system, which is 54.5 ns at 8.36 MHz bandwidth. 7 This evauation was done by generating 2x2 cross-poarized MIMO channes with a known DS in the channe mode. Then we transformed the output into the frequency-domain and added noise such that the SNR was 5 db. Then we extracted the paths the same way, as we did for the measurements and cacuated the DS from the preprocessed data. 8 The percentage p is cacuated by taking the actua vaue σ τ [actua] estimated vaue σ τ [est.] and cacuating σ τ [actua] σ [est.] τ p = σ τ [actua] and the

9 JAECKEL et a.: QUADRIGA: A 3-D MULTI-CELL CHANNEL MODEL WITH TIME EVOLUTION FOR ENABLING VIRTUAL FIELD TRIALS 9 in the third step, we compare the LOS deays of successive snapshots within a 5 m radius and remove fase detections. From the remaining snapshots, we cacuate the KF as K i = P [LOS] i P i P [LOS] i, where P [LOS] i = n r n t r= t= P [LOS] r,t,i. (42) Since the KF depends on the correct detection of the LOS path, there wi be an error if this detection fais. We found that at 5 db SNR, the median error is.4 db (32%). The highest deviations occur in strong NLOS conditions. Here, the cacuated vaues for the KF can be up to 5 db higher than expected. For this reason, we evauate the KF separatey for the LOS segments of the measurement track where we can expect that our empirica estimator works we. d) Large-scae Parameter Correations: For each 3 λ interva, we get vaues for the SF, the KF, and the DS. Roughy haf of those vaues can be attributed to LOS and the other haf to NLOS propagation. The decorreation distance and the cross-correation are cacuated in the og-domain [38] using the Pearson product-moment correation coefficient [39] where a k and b k contain K sampes of a LSP, e.g., the DS, SF or KF aong the measurement tracks. K a K k b k K K K 2 a k b k k= k= k= ρ {a, b} = K a 2 k 2 K K a k K b 2 k 2 K K K b k K k= k= k= k= (43) For the decorreation distance d λ, we cacuate ρ { a, a (q)} where the superscript (q) denotes a shift of a by q entries. Two adjacent LSPs vaues are 3 λ or 3.3 m apart from each other. Hence, for q =, we get the correation coefficient at 3.3 m distance. For q = 2, we get it at 6.6 m distance. This is repeated for vaues up to q = 2 or 4 m distance. We then use those 2 vaues to fit an exponentia function ρ(d) = e d d λ, (44) where both the distance d and the decorreation distance d λ are given in units of meters. D. Estimation of Performance Metrics a) Geometry Factor (GF): The geometry factor (GF) is a ower bound for the actua signa to interference and noise ratio (SINR). It is defined as the power ratio of the serving BS to a interfering BSs pus noise: E f/t [P i ] GF = P [noise] + E f/t [P k ] E [SINR inst.], (45) k,k i where E f/t [P ] denotes the expectation vaue of the power over frequency and over the snapshots within a 3 λ radius. This ensures that the effect of fast fading is removed. The noise power P [noise] is imited either by therma noise (-95 dbm) or by the sensitivity of the measurement system. Our system is based on commercia equipment that is optimized to achieve a SNR of 3 db. For the modeed channes, we set P [noise] accordingy to make the resuts comparabe. Due to handover between ces, we aways assign the MT to the sector with the highest received power. b) Singe-User Capacity at a Fixed SNR: We cacuate the capacity C [4] measured in bps/hz of the i th sector by C [fixed] i = N N og 2 det n= ( I + σ n t P i H n,i H H n,i ), (46) where I is the 2x2 identity matrix. At a fixed SNR σ of db, the capacity depends ony on the structure of the channe matrix H and the infuence of the PG is removed. Vaues of can be in between 4 bps/hz for singuar matrices and 6.9 bps/hz for orthogona matrices. We averaged the resuts within a 3 λ radius. The median error at 5 db SNR comparing noise-free with noisy 2x2 keyhoe channes [4] is 7.6% and does not exceed.7% in 9% of the cases. c) Singe-User Capacity with Inter-Ce Interference: We cacuate the interference imited capacity using the quasistatic bock fat-fading MIMO mode [42] with y n = H n,i x n,i + H n,k x n,k + v, (47) C [fixed] i k,k i where y n is the received signa vector on subcarrier n, x n is the transmit data vector, H n,i is the channe matrix for the serving sector i, and v is additive white Gaussian noise. Without channe knowedge at the Tx, the power is equay distributed over the transmit antennas. The capacity then notes C i = N N n= Z n,i = P [noise] I + og 2 det ( I + Z n,i H n,ih H n,i), (48) k,k i H n,k H H n,k, (49) where Z is the interference covariance matrix. Without interference, we set P [noise] = Pi nt σ and get the same resuts as when using (46). However, here we use the noise power P [noise] estimated from the measured channes. This vaue aready incudes the transmit power and the factor /n t. The median error at an average SNR of 5 db is.8% and does not exceed 8.5% in 9% of the cases. IV. RESULTS AND DISCUSSION Figure 6 depicts the resuts. Each pot contains five cumuative distribution function (CDF) curves. The soid ines show the resuts for the scenario with ow downtit, i.e., the main beam reaches the ground at.9 ISD or 45 m. The dashed ines show the resuts for the high downtit (.33 ISD, 7 m). The thick ines are for the measurements, the thin ines for the mode resuts. The dotted ine shows the resuts obtained from using the WINNER parameters. For this curve, a new features (e.g., time evoution, drifting, geometric poarization, scenario transitions) were disabed, 3-D antenna patterns were incuded, and the main beam reaches the ground at.9 ISD. The pots can be grouped into two categories: singe-ink parameters (PG, DS, KF, capacity at db SNR) and mutiink parameters (GF, muti-ce DS, and interference imited capacity). The mode yieds 928 vaues (3. km track divided by 3.3 m averaging distance) for each muti-ink parameter,

10 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. -, NO. -, - P(PG < abscissa) P(DS < abscissa) P(KF < abscissa) P(Cap. < abscissa) v median PG Meas..9: Sim..9: Meas..33: Sim..33: WIN..9: a LOS A. Effective Path Gain NLOS ISD Meas..9 ISD Sim..33 ISD Meas..33 ISD Sim..9 ISD WIN UMa Effective Path Gain (PG) with Antenna [db] v C. Singe Ce Deay Spread (SNR > 5dB) SNR > 5 db: Meas..9: 9 % Sim..9: 86 % Meas..33: 74 % Sim..33: 72 % WIN..9: 66 %.4 median DS [ns] a LOS NLOS.3 Meas..9: Sim..9: Meas..33: Sim..33: WIN..9: Deay Spread (DS) [ns] v median KF Meas..9: Sim..9: Meas..33: Sim..33: WIN..9: v a E. K Factor (SNR > 5 db) LOS NLOS K Factor (KF) [db] Norma Dist. Fit: Meas. 9: N(5.4,.35 2 ) Sim. 9: N(5.38,.54 2 ) Meas. 33: N(5.2,.35 2 ) Sim. 33: N(5.36,.47 2 ) WIN..9: N(5.38,.5 2 ) G. Singe User Capacity at db SNR.9 ISD Meas..9 ISD Sim..33 ISD Meas..33 ISD Sim..9 ISD WIN UMa.4.9 ISD Meas..3.9 ISD Sim ISD Meas..33 ISD Sim...9 ISD WIN UMa Rayeigh i.i.d. Cap Capacity [bps/hz] P(GF < abscissa) P(DS < abscissa) P(KF < abscissa) P(Cap. < abscissa) v median GF Meas..9: Sim..9: Meas..33: Sim..33: WIN.9: v a B. Geometry Factor.9 ISD Meas..9 ISD Sim..33 ISD Meas..33 ISD Sim..9 ISD WIN UMa Geometry Factor (GF) [db] D. Muti Ce Deay Spread median Muti Ce DS [ns] Meas..9: 389 Sim..9: 38 Meas..33: 86 Sim..33: 36 WIN..9: Deay Spread (DS) [ns] v Norma Dist. Fit Meas..9: N(3.8, ) Sim..9: N(4.4, ) Meas..33: N(4.5, ) Sim..33: N(2.6, ) WIN.9: N(8.9, 5. 2 ) v F. K Factor (LOS ony).9 ISD Meas..9 ISD Sim..33 ISD Meas..33 ISD Sim..9 ISD WIN UMa K Factor (KF) [db] H. Singe User Capacity with Inter Ce Interference.4 Outage Cap. % 5% 9%.3 Meas..9: Sim..9: Meas..33: Sim..33: WIN..9: Capacity [bps/hz] Fig. 6. Comparison of the distributions of severa channe parameters. The thick ines are extracted from the measurements, the thin ines from the mode. Soid ines are for the ow downtit (.9 ISD), dashed ines for the high downtit (.33 ISD). The errorbars (dots around the modeed curves) indicate the standard deviation of the spread in the resuts when initiaizing the channe mode 4 times with different random seeds. Squared endings are for the ow downtit and round endings for the high downtit.

11 JAECKEL et a.: QUADRIGA: A 3-D MULTI-CELL CHANNEL MODEL WITH TIME EVOLUTION FOR ENABLING VIRTUAL FIELD TRIALS and 5568 vaues (928 6 sectors) for each singe-ink parameter. We repeated the simuation 4 times. Hence, we got 4 CDFs and 4 median vaues (2-quantie) for each parameter. The average of those 4 vaues is potted in the point where the ordinate shows a vaue of.5. The STD above and beow the mean of those 4 sampes determines the width of the errorbar. Squared endings are for the ow tit (.9 ISD) and round endings for the high downtit (.33 ISD). Generay, the resuts for the ow downtit agree better than for the high downtit since we adjusted the mode parameters in Tabe II for the ow downtit data. A. Effective Path Gain: The effective PG combines the directiona antenna gain, the SF, the distance-dependent PG, and the different propagation parameters for LOS and NLOS into one curve. The testbed resuts agree we for the ow downtits (.9 ISD). However, there are differences at high downtits. The NLOS parts have on average 6 db more power in the modeed channes compared with the measured ones. The LOS part, on the other hand, has ony 3 db more power. A possibe expanation is that at high downtits most of the radiated power is ocaized in a sma area. If the MT is cose to one of those areas, the received power is dominated by the BS serving this area. In our measurement system, the achievabe SNR is imited. Thus, weak custers from inks to other BSs often fa beow the noise foor and cannot be resoved. The mode, on the other hand, does not have this imitation. The WINNER resuts show good agreement in the LOS scenario. However, the NLOS power is on average 2 db ower than in our measurements. This can be expained by the high NLOS path oss coefficient of 3.3 in the WINNER parameters. In our measurements, we got a vaue of B. Geometry Factor: At higher downtits (.33 ISD), the coverage area of a sector is sma and itte power is radiated into the neighboring ces. Hence, the interference situation can be improved by increasing the downtit. This is predicted we by the channe mode when using our own parameterization. However, in this case the mode predicts a GF that is roughy db better compared with the measurements. Two reasons coud be behind this: First, the exact positions of the buidings on the campus are not incuded in the mode. Thus, the effective path gain at the MT positions is different for each initiaization of the mode. Second, the synthetic antenna patterns in the mode do not perfecty match the rea ones in the measurement. This changes the GF, since the power distribution on the ground differs from the measurements. The WINNER resuts show a 3 db higher GF. This can aso be expained by the high WINNER NLOS path oss coefficient. NLOS channes have significanty ess power which increases the GF in cases when there is a LOS ink to one of the BSs. We coud confirm this by adjusting the NLOS path oss coefficients for the simuations to the vaues from our testbed. This reduced the difference from 3 db to.5 db. C. Singe-Ce Deay Spread: The DS in Fig. 6C depends on the KF and the LOS probabiity, which was 5% in our testbed. At ow SNR, cacuation of the DS becomes erroneous since many MPCs fa beow the noise foor. Thus, we show ony the resuts for areas where the SNR was at east 5 db. This incudes 9% of the ow downtit data and 75% of the high downtit data. An interesting observation is that the antennas have amost no infuence on the DS. This becomes cear when comparing the DS from Tabe II with the DS in Fig. 6C. The median LOS vaue from Tabe II (excuding antennas) is 2 ns. The corresponding vaues cacuated from the mode output are 73 ns for ow and 83 ns for high downtits. For NLOS channes, Tabe II predicts 34 ns and the mode outputs are 272 ns and 285 ns, respectivey. The same hods for the measured channes except for the LOS-DS at high downtits, which is 5 ns shorter. This known effect comes from the threshoding used to remove the noise from the data [36]. In our measurement system the noise foor is 3 db beow the peak power in the muti-ce CIR. At high downtits the power difference between the serving ce and interfering ces can easiy exceed 2 db due to the antenna gain. This eaves a dynamic range of ony db for the detection of MPCs in the interfering inks. NLOS channes often fa beow the 5 db imit and are sorted out, but many LOS channes seem to have a shorter DS because weak MPCs cannot be resoved. Modeed channes do not have this imitation and thus show a arger DS. The resuts from the WINNER parameters show a significant difference. First, ony 66% of the channes are above the 5 db SNR imit. This is another consequence of the high NLOS path oss coefficient. Hence, most of the DS vaues in the distribution come from LOS channes which owers the overa DS. Second, as we mentioned in Section III-B, many WINNER resuts (e.g., [2], [8], [9]) show too itte vaues for the DS, whereas other iterature sources (e.g., [7], [], []) confirm our resuts. D. Muti-Ce Deay Spread: The muti-ce DS (Fig. 6D) is cacuated from the combined PDP of a BSs. Hence, it incudes the different mean-deays. This is important if a MT is connected to severa BSs at the same time, e.g., when using soft handover or joint transmission. For the ow downtits, the measurement and mode resuts agree perfecty. The median DS amost doubes compared with singe-ce transmission, but the maximum deay spread does not increase. The resuts for the high downtits, however, differ significanty. The reason is ikey to be the same as discussed above: Our measurement setup cannot resove sufficient MPCs if the power difference between serving and interfering inks is high. As for the WINNER resuts, the ow singe-ce DS is aso refected in the muti-ce DS. Vaues from the mode are roughy 4% smaer than in the measured channes. E. K-Factor: The KF (Fig. 6E) is infuenced by the LOS probabiity and the antenna gain. As for the DS, we imited the evauation to areas where the SNR was at east 5 db. In the mode, ower downtits (.9 ISD) resut in a 2.3 db higher KF compared with the data set with high downtits. This is reasonabe, because at high downtits the beam of the high-gain antenna iuminates ony a sma area cose to the BS. The KF is reduced in a other areas because the direct component is attenuated. In the measured data, on the other

12 2 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. -, NO. -, - hand, high downtits resut in a better KF. However, this can aso be expained by the missing MPCs due to the reduced resoution of our measurement system. The WINNER parameters show high vaues for the KF (see Tabe II). This expains the ow vaues for the DS. When the KF is high, the DS is short since more energy is concentrated on the direct path. The WINNER mode aso incudes no KF modeing for NLOS channes. In this case, our estimation method uses the first custer that exceeds % of the tota power as the direct one. Even then, however, the estimated KF from the modeed channes is 7 db higher than in the measurements. F. K-Factor (LOS ony): If the KF is sma, the detection of the LOS custer might fai because a ater, stronger custer may be taken as the first one by accident. For this reason, in Fig. 6F, we imited the evauation to areas where there is a LOS connection between Tx and Rx. Here, the match between the four curves is better, especiay in the scenario with ow downtits (.9 ISD) where the curves amost agree perfecty. The effect of the high-gain antennas on the KF can be seen when comparing the parameters in Tabe II with the resuts in Fig. 6F. The LOS-KF in Tabe II foows a norma distribution with N (2.7, ) for our own parameterization and N (7, 3 2 ) for the WINNER scenario. The inserted text in the figure gives the fitted parameters N (µ, σ 2 ) for the empirica resuts. In some areas the weighting by the antenna pattern ampifies the direct component, and the KF increases. In other areas, outside the ce, the direct component is attenuated, and the KF decreases. This expains the arger spread in the empirica distributions. G. Singe-User Capacity at a db SNR: The capacity (Fig. 6G) depends on a the channe parameters and the antennas. We imited the evauation to areas where the SNR in the data was at east 5 db. We aso potted the distribution of an i.i.d. channe for comparison. There are significant fuctuations in a the resuts. Ceary, it is important to adjust the transmission mode to the channe rank [43]. The median capacity of 5.3 bps/hz is predicted we by the channe mode. However, the width of the modeed distributions is wider compared with the measurements. A reason for this coud be discrepancies in the vaues for the anguar spreads. However, it is difficut to quantify this infuence without access to accurate anguar spread measures. It is aso possibe that our measurement system causes some random phase fuctuations within different MIMO subinks due to the over-the-air synchronization. Such a random component woud expain the steeper distribution of the measurement resuts. We need a higher number of antennas and synchronized receivers to correcty vaidate the capacity distribution. This woud provide more insight into the spatia structure of the channe and aow us to cacuate the anguar spreads, e.g., by using the method from [3]. However, such additiona measurements are beyond the scope of this paper. H. Singe-User Capacity with Inter-Ce Interference: The distribution of the interference imited capacity is potted in Fig. 6H. The inserted text shows the outage capacity for each curve. In genera, the simuations with our own parameterization tend to predict a sighty higher capacity. However, this is consistent with the geometry factors (Fig. 6B) which are aso sighty higher. The simuations from the WINNER parameters, however, predict a 6% higher capacity. I. LSP Correations: Tabe IV summarizes the resuts for the decorreation distance and cross-correation. It contains the vaues obtained from the measured channes (Meas. vaue), the parameterization of the channe mode (Mode setup), and the cacuated vaues from the mode output. The average (AVG) and the standard deviation (STD) resut from the 4 repetitions of the simuations. The ast coumn contains the vaues from the WINNER urban macro-ce scenario [2]. The effect of the high-gain antennas can be seen when comparing the mode setup with the mode output. In both scenarios (LOS and NLOS) the decorreation distance increases for the SF and decreases for the DS. The vaues for the KF increase ony in the LOS scenario. The crosscorreations DS-KF and KF-SF are in good agreement for LOS. For both scenarios, however, the mode output for DS- SF is significanty ower. This indicates that the true crosscorreation between DS and SF might even be smaer than -.6, but that woud destroy the positive definiteness of the cross-correation matrix. The NLOS cross-correations DS-KF and KF-SF show significant differences when measurements, mode setup, and mode output are compared. This can be attributed to the fact that KF estimation is very inaccurate when the KF is beow db. The decorreation distances from the WINNER mode are ony haf as big as in our setup. However, our resuts agree very we with [38]. TABLE IV MEASURED AND SIMULATED VALUES DECORRELATION DISTANCE AND CROSS-CORRELATION VALUES Scen. Parameter Meas. Mode Mode output WIN. vaue setup AVG STD UMa SF Decorr. Dist. [m] L DS Decorr. Dist. [m] O KF Decorr. Dist. [m] S DS-KF Cross-corr DS-SF Cross-corr KF-SF Cross-corr SF Decorr. Dist. [m] N DS Decorr. Dist. [m] L KF Decorr. Dist. [m] N/A O DS-KF Cross-corr N/A S DS-SF Cross-corr KF-SF Cross-corr N/A V. CONCLUSION In this paper, we extended the popuar WINNER channe mode with new features that aow the generation of channe traces with tempora evoution. The new mode supports freey configurabe network ayouts with mutipe transmitters and receivers, and it is scaabe from singe-ink singe-antenna systems to heterogeneous muti-ink MIMO scenarios. We further improved the mode by merging the methods for cacuating LOS and NLOS channes (WINNER uses different methods) and by impementing a new poarization mode. We vaidated the evoved mode by measurements in a reevant scenario, i.e., by using BS positions and antennas that are

13 JAECKEL et a.: QUADRIGA: A 3-D MULTI-CELL CHANNEL MODEL WITH TIME EVOLUTION FOR ENABLING VIRTUAL FIELD TRIALS 3 reaistic for a commercia setup. A evauated parameters, for both singe-ink and muti-ink setups, are in good agreement. We have shown that it is possibe to generate channe traces with simiar characteristics as measured data. This wi speed up the evauation of new agorithms, since we can now obtain reaistic performance resuts in an eary stage of deveopment. A existing WINNER parameter tabes can be used. Hence, the new mode aows us to perform virtua fied trias in many scenarios. We performed simuations with the origina WIN- NER parameters and compared the resuts with our findings. There were some differences. Due to this, we woud suggest carefuy checking the WINNER parameter tabes against reaword scenarios. However, this woud exceed the scope of this paper. Further extensions can be made regarding the generation of departure and arriva anges. Currenty, azimuth and eevation anges are cacuated independenty (see Section II-C). It might be preferabe to extract both anges from a bivariate distribution. This is expected to yied better resuts if the eevation of some paths is cose to ±9. Another improvement coud be made by incuding the custer mode from Czink and Oestges [44]. This woud aow the tracking of departure anges for different positions of the Tx-antenna. However, how to generate the departure anges of the so-caed twin custer in order to achieve a given power anguar spectrum is sti an open issue. In the COST mode, which aso uses this approach, the anguar dependency of the power is not considered. How the pubished findings on the birth/death probabiity of individua scattering custers [3], [4] can be mapped to the tempora evoution of the LSPs is aso an open issue. For exampe, randomy creating and removing paths as suggested by [2] woud significanty ater the deay and anguar spread. Finay, inter-site correations of the LSPs can be incuded by incorporating more advanced agorithms [45], [46], [2] for generating the parameter maps for the initia parameters. ACKNOWLEDGMENTS The authors thank V. Jungnicke, A. Forck, F. Bauermeister, S. Schiffermueer, S. Schubert, S. Wahs, T. Haustein [Heinrich Hertz Institute (HHI), Berin, Germany], W. Kreher, J. Mueer, H. Droste, G. Kade [Deutsche Teekom AG, T- Labs, Darmstadt, Germany], and V. Braun [Acate-Lucent Be Labs, Stuttgart, Germany] for their hep with setting up the testbed and assistance during the measurements. We further thank G. Sommerkorn, C. Schneider, M. Kaeske [Imenau University of Technoogy (IUT), Imenau, Germany], E. Eberein and F. Burkhardt [Fraunhofer IIS, Erangen, Germany] for the fruitfu discussions on the QuaDRiGa channe mode and the manuscript of this paper. APPENDIX The correction function C φ (L, K) takes the infuence of the KF and the varying number of custers on the anguar spread into account. To approximate the function, we generate the anges using () to (3) with the correction function set to C =. Then we cacuate the spread σ φ as proposed in [36]: σ φ = 2π F 2 F 2, (5) L F n = P exp( j φ n), = where φ is the ange cacuated by (3), and F n is the n th compex Fourier coefficient. The correction function now foows from comparing σ φ with σ φ. However, two aspects need to be considered:. Due to the randomization of the anges in (), we have to take the average ange over a sufficienty arge quantity ( reaizations) of σ φ. This vaue is denoted as σ φ. 2. There is a noninear reationship between the anguar spread in the simuated data σ φ on the initia vaue σ φ. This comes from the ogarithm in () and the moduo in (2). However, for sma vaues, the reationship can be approximated by a inear function. We define the maximum anguar spread σφ max as the point where the error between the corrected σ vaue φ C φ (L,K) and σ φ is. 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14 4 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. -, NO. -, - [4] W. Wang, T. Jost, U. Fiebig, and W. Koch, Time-variant channe modeing with appication to mobie radio based positioning, Proc. IEEE GLOBECOM 2, pp , 22. [5] [Onine]. Avaiabe: [6] S. Jaecke, K. Börner, L. Thiee, and V. Jungnicke, A geometric poarization rotation mode for the 3-D spatia channe modeja, IEEE Trans. Antennas Propag., vo. 6, no. 2, pp , 22. [7] A. Agans, K. Pedersen, and P. Mogensen, Experimenta anaysis of the joint statistica properties of azimuth spread, deay spread, and shadow fading, IEEE J. Se. Areas Commun., vo. 2, no. 3, pp , 22. [8] C. Schneider, M. Narandzic, M. Käske, G. Sommerkorn, and R. Thomä, Large scae parameter for the WINNER II channe mode at 2.53 GHz in urban macro ce, Proc. IEEE VTC Spring, 2. [9] M. Narandzic, C. Schneider, M. Käske, S. Jaecke, G. Sommerkorn, and R. Thomä, Large-scae parameters of wideband MIMO channe in urban muti-ce scenario, Proc. EUCAP, 2. [2] K. Bakowski and K. 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Nicewander, Thirteen ways to ook at the correation coefficient, The American Statistician, vo. 42, p , 988. [4] I. E. Teatar, Capacity of muti-antenna gaussian channes, Europ. Trans. Teecommun., vo., no. 6, pp , 999. [4] D. Chizhik, G. Foschini, and M. Gans, Keyhoes, correations and capacities of mutieement transmit and receive antennas, IEEE Trans. Wireess Commun., vo., pp , Apr. 22. [42] E. A. Jorswieck and H. Boche, Performance anaysis of capacity of MIMO systems under mutiuser interference based on worst-case noise behavior, EURASIP J. Wireess Commun. Netw., vo. 2, pp , 24. [43] M. Schemann, L. Thiee, T. Haustein, and V. Jungnicke, Spatia transmission mode switching in muti-user MIMO-OFDM systems with user fairness, IEEE Trans. Veh. Techno., vo. 59, no., pp , 2. [44] N. Czink and C. Oestges, The COST 273 MIMO channe mode: Three kinds of custers, Proc. IEEE ISSSTA 8, 28. [45] T. Kingenbrunn and P. Mogensen, Modeing cross-correated shadowing in network simuations, Proc. IEEE VTC 99 Fa, vo. 3, pp. 47 4, 999. [46] X. Cai and G. B. Giannakis, A two-dimensiona channe simuation mode for shadowing processes, IEEE Trans. Veh. Techno., vo. 52, no. 6, pp , 23. Stephan Jaecke (S -M 2) was born in Freiberg, Germany, in 982. He received the B.Eng. and M.Eng. degrees in information and communications technoogy from Hochschue für Teekommunikation, Leipzig, Germany, in 25 and 27, respectivey. He is currenty working toward the Dr. Ing. (Ph.D.) degree in eectrica engineering at the Imenau University of Technoogy (IUT). In 26, he was a summer student at CERN, Geneva, Switzerand, where he worked on the software for the LHCb partice detector. In 27, he joined the Fraunhofer Heinrich Hertz Institute, Berin, Germany, where he worked on the measurementbased performance anaysis of cooperative mobie communication systems. His current research interests incude measurements and data anaysis in heterogenous muti-ce networks incuding reays as we as channe modeing for terrestria and sateite systems. Leszek Raschkowski was born in Pietersburg, South Africa, in 983. He received the Dip.-Ing. (M.S.) degree in eectrica engineering in 22 from Technische Universität Berin, Germany. Currenty, he is empoyed as a research associate at Fraunhofer Heinrich Hertz Institute in Berin, Germany. His research interests incude modeing and simuating radio propagation channes, as we as performance anaysis of wireess communication systems. Kai Börner (S 2) received the Dip.-Ing. (M.S.) degree in eectrica engineering from the Technische Universität Berin, Germany, in 29. Currenty, he is working toward the Dr.-Ing. (Ph.D.) degree in eectrica engineering at the Technische Universität Berin. He joined the Fraunhofer Heinrich Hertz Institute (HHI) in Apri 29. His research interests ie in channe modeing, energy efficient transmission and sef-organization in heterogeneous mutipe-input mutipe-output (MIMO) orthogona frequency-division (OFDM)-based networks. Lars Thiee (S 6-M 9) received the Dip.-Ing. (M.S.) degree in eectrica engineering from the Technische Universität Berin, Berin, Germany, in 25. He joined the Fraunhofer Heinrich Hertz Institute (HHI), Berin, Germany, in September 25. In 23 he received the Dr.-Ing. (Ph.D.) degree from the Technica University of Munich (TUM), Munich, Germany. He has contributed to receiver and transmitter optimization under imited feedback, performance anaysis for mutipe-input mutipeoutput (MIMO) transmission in ceuar orthogona frequency-division mutipexing (OFDM) systems, fair-resource aocation, and cooperative muti-point (CoMP) transmission under constrained channe state information at the transmitter (CSIT). Lars has authored and coauthored about 5 conference and journa papers as we as a coupe of book chapters in the area of mobie communications. He eads the System Leve Innovation research group at Fraunhofer HHI and is activey participating in the GreenTouch consortium.