Aalborg Universitet On Radiated Performance Evaluation of Massive MIMO Devices in Multi-Probe Anechoic Chamber OTA Setups General rights

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1 Aaborg Universitet On Radiated Performance Evauation of Massive MIMO Devices in Muti-Probe Anechoic Chamber OTA Setups Kyösti, Pekka; Hentiä, Lassi; Fan, Wei; Lehtomaki, Janne; Latva-aho, Matti Pubished in: I E E E Transactions on Antennas and Propagation DOI (ink to pubication from Pubisher): /TAP Pubication date: 2018 Link to pubication from Aaborg University Citation for pubished version (APA): Kyösti, P., Hentiä, L., Fan, W., Lehtomaki, J., & Latva-aho, M. (2018). On Radiated Performance Evauation of Massive MIMO Devices in Muti-Probe Anechoic Chamber OTA Setups. I E E E Transactions on Antennas and Propagation, 66(10), Genera rights Copyright and mora rights for the pubications made accessibe in the pubic porta are retained by the authors and/or other copyright owners and it is a condition of accessing pubications that users recognise and abide by the ega requirements associated with these rights.? Users may downoad and print one copy of any pubication from the pubic porta for the purpose of private study or research.? You may not further distribute the materia or use it for any profit-making activity or commercia gain? You may freey distribute the URL identifying the pubication in the pubic porta? Take down poicy If you beieve that this document breaches copyright pease contact us at vbn@aub.aau.dk providing detais, and we wi remove access to the work immediatey and investigate your caim. Downoaded from vbn.aau.dk on: december 24, 2018

2 1 On Radiated Performance Evauation of Massive MIMO Devices in Muti-Probe Anechoic Chamber OTA Setups Pekka Kyösti, Lassi Hentiä, Wei Fan, Member, IEEE, Janne Lehtomäki, Member, IEEE, and Matti Latva-aho Senior Member, IEEE Abstract Radiated testing of massive mutipe-input-mutipeoutput (MIMO) devices in fading radio channe conditions is expected to be essentia in deveopment of the fifth generation (5G) base stations (BS) and user equipment (UE) operating at or cose to the miimetre wave (mm-wave) frequencies. In this paper we present a setup upgrading the muti-probe anechoic chamber based system designed originay for 4G UE. We describe methods for mapping radio channe modes onto the probe configuration and discuss the differences to the former 4G case. We aso propose metrics to assess the accuracy of the test setup and find key design parameters by simuations. The resuts with the utiized channe modes indicate that at 28 GHz up to panar arrays can be tested with range ength of one meter and with at minimum eight active dua poarized probes. Index Terms Antenna arrays, Anechoic chambers (eectromagnetic), antenna measurements, fading channes, miimeter wave radio propagation, MIMO systems, testing. I. INTRODUCTION New wireess teecommunication system, containing a mutitude of new technoogy components, new frequency bands to be utiized, and new radio devices, is currenty deveoped intensivey. The purpose of the new system, commony abeed as 5G, is to serve more devices, to enabe higher data rates, ower atency, ower energy consumption, and to offer many other advanced and desirabe features [1], [2]. Of the wide paette of 5G features the specia interest to this paper is the combination of mm-wave frequency bands and massive MIMO antenna arrays. Sufficient wide bandwidths to support for mobie broadband data transfer are not avaiabe at the egacy ceuar bands beow 6 GHz. Thus new bands are now investigated from 24 GHz and higher [3], despite the transmission oss chaenges inherent to the higher bands. Especiay the frequencies around 28 GHz are considered for the so caed pre-5g systems [4]. Massive MIMO technoogy is seen as a promising technoogy to enabe high rate transmission to a arge number of users P. Kyösti is with Centre for Wireess Communications (CWC), University of Ouu, Ouu, FI Finand (emai: pekka.kyosti@ouu.fi) and Keysight Technoogies Finand Oy, Ouu, Finand. L. Hentiä is with Keysight Technoogies Finand Oy, Ouu, Finand (e-mai: assi.hentia@keysight.com). Wei Fan is with the Antennas, Propagation and Radio Networking section at the Department of Eectronic Systems, Facuty of Engineering and Science, Aaborg University, Denmark. Emai: wfa@es.aau.dk. J. Lehtomäki and M. Latva-aho are with Centre for Wireess Communications (CWC), University of Ouu, Ouu, FI Finand (emai: firstname.astname@ouu.fi). in a dense network, and to compensate the severe transmission osses by substantia array gains [5]. Many experiments with massive MIMO arrays have been reported in the iterature [6], [7] and the first commercia base station products are in a deveopment phase. The expected mode of operation of arge antenna arrays is the hybrid beamforming. For practica reasons, mainy reated to the power consumption of components, each of the tens or hundreds antenna eements may not be supported by separate radio frequency (RF) chains. Instead the arrays may be connected to a base band unit by ony a sma number, e.g. eight, of RF chains. The antenna eements are divided to sub-arrays, where eements are combined to a singe RF port by an anaog weighting matrix. The matrix enabes composing a predefined set of fixed antenna beams [4]. Thus each RF port, feeding a number of antenna eements (subarray), may compose a number of predefined beam shapes. Typicay main directions of a set of beams cover the anguar sector of interest. In the ink estabishment the beam aocation and beam aignment are crucia operations to be tested. One identified chaenge on the deveopment work is the testing of mm-wave massive MIMO devices. In [8] is predicted that the testing wi move amost excusivey to radiated methods for a number of reasons. It is seen that the mmwave devices are sma in size and wi be highy integrated units. Thus they may not provide RF connectors necessary for conducted testing. Even if they did, the number and the overa compexity of coaxia cabe connections to test devices woud increase impractica high. Attaching and detaching, e.g., one hundred coaxia cabes is a time consuming and an error prone operation. Moreover, with massive MIMO the antenna characteristics and the anaog array contro are essentia, thus it is crucia to test them atogether in a reaistic manner with emphasis on the spatio-poarimetric propagation environment. For exampe testing the beam acquisition capabiity of massive MIMO devices, which is an initia step in ink estabishing procedure, wi require emuating a spatio-poarimetric propagation environment. OTA test methods for MIMO capabe mobie terminas have been deveoped and researched for many years [9], [10]. The three main categories of methods are the reverberation chamber (RC) [11], the radiated two-stage (RTS) [12], and the muti-probe anechoic chamber based (MPAC) method [13]. Outside the referred standard documents has been introduced aso a fourth option; reconfigurabe OTA chamber [14], an RC whose was are ined with antennas, supporting for reconstruc-

3 2 tion of controabe three dimensiona power anguar spectrum (PAS). The overa purpose of OTA test setups is to generate fading radio channe conditions around the device under test (DUT) as specified by target channe modes, ike, e.g., 3GPP SCM [15], WINNER [16] or the recent 3GPP above 6 GHz mode [17]. RC emuates time averaged isotropic scattering environment, but it does not provide controabe anguar or poarimetric propagation characteristics, which makes it ess attractive for testing of beamforming based devices. The practica capabiity of the reconfigurabe RC is currenty not fuy known. RTS may in principe support aso for massive MIMO, but it has two drawbacks. Firsty, it is not we suited for adaptive antenna systems ike, e.g., for anaog beamforming. Secondy, the required probe and fading emuator resources for the second stage are directy proportiona to the number of DUT antennas. With tens or hundreds of DUT antennas the test setup may become non-feasibe. Therefore, it is expected that the MPAC has the highest potentia for being the OTA test method aso for eectricay arge 5G devices. In the iterature MPAC OTA techniques for massive MIMO or mm-wave device evauations have been discussed in [18] [23]. In the foowing we summarize the work briefy. The feasibiity of so caed pane wave synthesis and prefaded signas synthesis methods, in terms of required number of probes, is anayzed in [18] for 2-dimensiona (2D) circuar probe geometries. Preiminary investigations on probe configurations and range engths are reported in [19], with the main focus on precision of reconstructing an individua muti-path custer. Reference [22] specifies a sectored 3D probe configuration for massive MIMO testing and presents simuation resuts for the minima physica dimensions of the setup. Numerous figures of merit were used in the evauations, from direction of arriva estimation accuracy up to muti-user MIMO sum rate capacity error. Work on the physica dimensions assessment was continued in [20], where few new metrics were used and the focus was set on 28 GHz frequency. Various aspects, ike physica setup dimensions, probe configurations, and suitabe channe modes are discussed in [21]. Simuations were performed with 2D probe configurations ony with two channe mode scenarios used for 4G evauations (SCME UMi and UMa). Finay, [23] specifies seection criteria for the OTA method for testing of 5G equipment and discusses different aternatives. The identified criteria are: capabiity for rea-time performance assessment, for emuating reaistic radio channes, and for bidirectiona (up- and downink) emuation. They concude that the coherent wave fied synthesis is the ony potentia MPAC method fufiing the criteria. We agree with [23] that with the pre-faded synthesis the reconstruction of wave fronts from arbitrary directions is not possibe. However, in order to support for coherent wave fied synthesis a very high number of probes and emuator resources woud be required [18]. Given this, we may have to restrict the setup to capabiity of reconstructing wave fronts, with arbitrary fading characteristics, from the actua probe directions ony. The probe requirements for wave synthesis are further discussed in section II and capabiities of the proposed system are described in section IV. In this work we are going to introduce a compete sectored muti-probe anechoic chamber based (MPAC) over-the-air (OTA) test setup, incuding methods for mapping channe modes onto probes. Important design parameters for the setup are its dimension, dictated mainy by the measurement distance (the range ength), the configuration of switchabe probes incuding their number and ocations, and the number of active probes used for the emuation. The measurement distance has been discussed aready in [20], [22]. The main contribution of the current work is to propose an upgraded MPAC method and to assess the impact of the mentioned design criteria by a set of nove simuation metrics. The focus is on mmwave massive MIMO BS testing, but the findings are to some extent appicabe aso for eectricay smaer devices, for ower frequencies, and for non-sectored devices (ike UE). In section II is discussed the feasibiity to directy extend the conventiona uniform MPAC method for eectricay arge devices. Section III specifies system modes for the MIMO radio channe and for the corresponding OTA emuation system. Detaied description of the proposed OTA setup is given in section IV. Simuation settings and resuts are discussed in sections V and VI, respectivey. Concusions and a brief discussion on future work are presented in section VII. II. TEST ZONE SIZE The MPAC system is attractive for radiated testing of mutiantenna systems, due to its capabiity to physicay emuate reaistic RF environment in the anechoic chamber. Any adaptive antenna technoogies (e.g. massive MIMO BS in our paper) that utiize or adapt to features of the RF environment can be therefore reiaby evauated in the MPAC setup, since it offers a reaistic test condition for the device to operate normay [24]. A key question in the MPAC design to be addressed is how arge a test zone size can be supported with a MPAC configuration. The test zone denotes a geometrica voume inside which target channes can be accuratey reproduced. Extensive efforts have been taken to characterize the test zone size as a function of required active OTA antennas in the iterature, where two techniques are often discussed, i.e. the pane wave synthesis (PWS) and the pre-faded synthesis (PFS) technique. The objective of the PWS is to synthesize pane waves with arbitrary impinging anges within the test zone, by aocating appropriate compex weights to the active OTA antennas. Compex weights can be cacuated with different techniques, e.g., the east square technique in [13], [25] or the spherica wave expansion in [26], [27]. The minimum required number of OTA antennas to synthesize an arbitrariy poarized fied with an arbitrary ange can be expressed, according to the cut-off properties of the spherica wave modes [27], as K min = 2 ( kr o + n 1 ) ( kr o + n 1 ), (1) where k is the wavenumber, r o is the radius of the minimum sphere that encompasses the device under test, n 1 is a sma integer number, and. is the cei (round upwards to cosest integer) operator. Typicay, n 1 varies from 0 to 10 [27], [28], depending on the desired accuracy of the fied synthesis. Assuming a panar DUT array with = 100 antennas

4 3 with 0.5λ spacing, which gives the minimum r o around 3.2λ and via setting n 1 = 0 and 10, we have K min = 880 and 1920, respectivey. The minimum number of probes is very high. It was aso concuded in [18], [23] that significanty more active OTA probes are needed for fied synthesis in MPAC setups for massive MIMO testing object and higher frequency scenarios. Therefore, utiizing existing OTA setups as a means to test massive MIMO BSs woud necessitate a substantia amount of additiona hardware ike probes and fading emuators, eading to cost-prohibitive designs. With the PFS technique, the focus is on reconstructing spatia profies in the test zone via aocating optima power weights for probes [13]. The target continuous PAS is approximated by the discrete PAS in the PFS technique, characterized by the probe ocations and probe weights. The arger the antenna aperture of the DUT, the higher beam resoution of the DUT is expected. Therefore, to ensure that the DUT can not distinguish the target and emuated spatia channe, we need more active probes to sampe the PAS for DUTs with arger antenna aperture. It was concuded in [29] that using the PFS technique woud yied simiar estimates of the number of required probes as in the PWS technique. Therefore, the existing MPAC configuration, i.e. with a uniform probe configuration and each probe connected to a fading emuator output port, is chaenged for massive MIMO testing for mm-wave frequency bands due to cost consideration. There is a strong need to deveop a new MPAC configurations that are adequate and cost-effective for mm-wave massive MIMO BS testing. Our proposed method is intended to address this need. III. SYSTEM MODEL In the foowing we define system modes both for the conductive MIMO radio channe emuation and the OTA emuation. A. Traditiona MIMO emuation The we known system mode for MIMO transmission (negecting noise) is Y(t, f) = H (t, f)x(t, f), (2) where t and f denote time and frequency, Y C N 1 is the received signa vector, X C M 1 is the transmitted signa vector, and N, M denote the number of receiver (Rx) and transmitter (Tx) antenna ports (or sub-arrays), respectivey. With a geometric channe mode having L discrete paths the MIMO channe transfer function H C N M is defined as H (t, f) = L =1 [ G rx (t, k rx α θθ (t)) (t, f) α θϕ (t, f) α ϕθ (t, f) α ϕϕ (t, f) ( G tx t, k tx (t) ) T, (3) where G rx C N 2 and G tx C M 2 are the poarimetric antenna (or sub-array) pattern vectors of θ and ϕ poarizations for ] Rx and Tx antenna arrays, respectivey, defined to a common phase centre. Antenna patterns are introduced with argument t to support for a time variant anaog beamforming. Further, wave vectors k rx and k tx define both the frequency and the direction of arriva/departure to sampe the radiation patterns of Rx/Tx antennas, and coefficients α ab are the compex channe gains of path for transmitted poarization b and received poarization a. It is noted that in the formuation of eq. (3) it is assumed that a Tx and Rx antenna eements experience the same propagation coefficients α. This assumption is not vaid if the far fied condition does not hod. To mode these cases the propagation coefficients have to be defined separatey for Tx/Rx eement pair, as is done, e.g., in [30]. In traditiona conducted MIMO emuation UE antenna ports and DUT (BS) antenna ports are connected to fading emuator input/output ports with coaxia cabes. Within the fading emuator the input signa X is mutipied (convoved in time domain) with the channe matrix H and the signa vector Y is fed to N ports of the DUT. For terminoogy, from now on the upink transmission is assumed, i.e. DUT (BS) is the receiver and the transmitter is UE or UE emuator. Though, the emuation can be aso to downink direction or bi-directiona, where the atter one is expected as the most typica test mode. B. OTA emuation In OTA case the transfer function H is composed by operations of the fading emuator and the MPAC setup iustrated in Fig. 1. In eq. (2) H is substituted by H(t, f) = F(t, f)w(t, f). (4) The transfer matrix from K OTA probes to N DUT antennas is with entries F(t, f) = {γ n,k (t, f)} C N K, (5) γ n,k (t, f) =G rx,n (t, k n,k ) G o (k n,k ) T L(d n,k, f)e j k n,k d n,k, where G rx,n and G o,k C 1 2 are the poarimetric antenna pattern vectors of nth DUT antenna and kth OTA probe, respectivey. Further, k n,k, d n,k and L(d n,k ) are the wave vector, the distance and the path oss term between the kth probe and the nth DUT antenna, respectivey. It is noted that the time dependency of F resuts ony from possibe time variant anaog weighting of DUT antennas. Otherwise the transfer matrix is static. The transfer matrix W C K M, containing predominanty the tempora and the frequency fading components of the channe mode, is defined as W(t, f) = L diag (Γ (t)) G id =1 [ α θθ (t, f) α θϕ (t, f) α ϕθ (t, f) α ϕϕ (t, f) ] G T ( tx t, k tx (t) ), (6) (7)

5 4 where G id is K 2 idea poarimetric antenna pattern matrix of OTA probes with entries {0, 1} and the vector Γ (t) = {g,k (t)}, k = 1,..., K, is composed of weights of K probes for the th custer. In principe it is possibe to set the weights aso frequency dependent in the fading emuator by substituting each scaar g,k, e.g., by a inear fiter. However, we expect this is not necessary on the considered fractiona bandwidths (BW) ike, e.g., 0.8 GHz BW at 28 GHz or 2 GHz BW at 60 GHz. Ideay the target in faded OTA emuation woud be to reach condition H = H. On the conceptua eve this coud be achieved simpy by determining F and specifying W(t, f) = F(t, f) 1 H (t, f). (8) However, this cannot be carried out in practice. The OTA transfer matrix F(t, f) is not typicay measurabe (or otherwise determinabe), neither over frequency because the DUT may not support for measuring the S 21 parameter, nor over time because the dynamic beam aocation of a DUT is not known a priori. Instead of the aforementioned, i.e. using eq. (8), we choose active probes propery and contro weights g,k (t) to reach statisticay simiar transfer functions H and H of the reference and the OTA case, respectivey. Methods for the probe seection and the weight determination are discussed in detai in sections IV-B and IV-C, respectivey. By statisticay simiar we mean, e.g., same power deay profie, Dopper spectrum, Ricean K-factor, ampitude distribution, cross poarization power ratio, and power anguar distribution, as with the target channe mode. With the popuar geometry based stochastic channe modes [15] [17] the instantaneous channe coefficients are not specified, thus it is not feasibe to pursue for any particuar instantaneous fading channe conditions. As described in [13] the time and frequency variation of the radio channe is mosty reconstructed within the fading emuator and these dimensions do not require any specia treatment compared to the state-of-the-art conductive emuation. The chaenging part is to reconstruct the poarimetric and especiay the spatia fied within the test zone. Procedures for this are proposed in the next section. IV. MPAC OTA FOR MASSIVE MIMO DEVICES The current MPAC setup for LTE UE is composed of an anechoic chamber containing a number of probes (aso caed OTA antennas) typicay in a 2D ring formation, a fading emuator, and a communication tester. The DUT is ocated in the centre of the probe ring, which most commony contains eight dua poarized probes with 45 azimutha spacing. The intention is to synthesise time variant controabe eectromagnetic (EM) fied within a cyindrica test voume. Either PFS or PWS can be used to reconstruct the EM fieds [13] foowing the statistica propagation characteristics specified by a target channe mode. There are a number of differences between LTE UEs and the coming mm-wave massive MIMO BSs in terms of devices and typica propagation parameters, as isted in [21], [22]. Whie UEs are normay designed for isotropic reception and used Fig. 1. Components of the sectored MPAC OTA setup. cose to scatterers, BSs are typicay instaed on a wa or simiar to serve a sector of anges. So, BSs are ocated higher and farther from scatterers compared with UEs. Thus the anguar power distribution of BSs is expected to be confined in the ange region, be more specuar, and require definitey emuation of 3D propagation. The ast remark foows aso from the vertica beamforming capabiity of BSs. In the current standard LTE UE test systems [9], [10] the 2D probe configuration and fied synthesis is seen sufficient. Components of the proposed setup are iustrated in Fig. 1. Anechoic chamber serves mainy for shieding from externa signa sources, but aso for preventing unwanted refections. In Fig. 1 the test zone is ocated in one end of the chamber and DUT paced in the centre of the test zone, which is aso the origin of the coordinate system, as shown in Fig. 2. A arge number of probes is ocated on a sector of anges with approximatey equa distance R from the origin and with certain anguar spacing. In principe the variation of R across probes can be compensated by phase and ampitude caibration. In practice achieving phase coherence may be difficut in any case. For exampe the switch impementation and the ong term phase drift effects reated to the ambient temperature are concrete chaenges. Probes for 28 GHz can be fabricated on printed circuit board. They are cheap to manufacture and the major constraint on the number of them comes from the space. A number of probes can be paced on a singe board with certain size, these boards are caed probe panes from now on. Whie probes may be cheap the fading emuator resources and possiby required anaog components, ike power ampifiers and up/down converters, are not. Thus ony a sub-set of probes are switched to the fading emuator by a rea-time controabe switch. The switching and the seection of the probe sub-set, is based on the target channe mode for optimizing the usage of fading emuator resources. Fading emuator has RF input and output ports. It performs the channe moduation operation specified in eq. (2) with the definabe transfer matrix W from eq. (4). UE emuator imitates the other ink end. In practice it can be repaced by a rea UE or a number of UEs (emuators). If ony up- or downink is in the focus of fading emuation, the other ink direction can be communicated with a dedicated probe antenna and a cabe connection bypassing the fading emuator. This approach is simiar to the current LTE OTA configurations [10].

6 5 Fig. 2. An iustration of the sectored probe configuration. A. Mechanica rotation of DUT In the case of sectored probe configuration the probe panes are covering ony a imited sector of anges. With BS devices the broad side of DUT array is known. In order to utiize the anguar sector covered by probes the DUT is first rotated mechanicay with respect to the probe panes based on a priori information of the channe mode. For exampe the probe panes may be ocated to an eevation sector of and the strongest propagation paths in the channe mode to be emuated may be specified to beow 30. In this case it is beneficia to rotate the DUT such that directions of main paths fit the probe panes. Aternativey, the DUT may be attached to a fixture with a specifiabe rotation ange. Thus the first step of estabishing an OTA emuation is to cacuate, e.g., a centre of gravity of the mode PAS and to rotate the DUT such that maxima amount of PAS coincides with the probe sector. Optionay the rotation may be performed such that the strongest path ange turns to the probe cosest to the positive x axis direction in the coordinate system specified in Fig. 2. B. Probe aocation The next step is to choose a sub-set of probes from the fu set avaiabe in the setup. Typicay the sub-set size is determined by the avaiabe fading emuator resources. Aocation of probes is performed by connecting the seected ones to fading emuator ports with the switch iustrated in Fig. 1. In a practica setup the switch impementation may aso restrict the degrees of freedom of probe aocation. For exampe it may not be feasibe to impement a switching matric from a probes to a fading emuator ports. However, in the simuation section of this work a fu freedom is assumed. Here we propose an agorithm for seecting at maximum K probes from the fu set for emuating a channe mode with known custer nomina anges β, i.e. anges of k rx, and custer powers P. Assume that the DUT is rotated as defined in IV-A. Now K probes are aocated as foows. Sort custer powers P to descending order. Aocate the cosest probe to each ange β unti K probes are aocated. However, do not aocate a probe to a custer if the anguar distance between β and the probe direction is above a threshod, say e.g. 10. This is mainy to prevent aocating probes to custers outside the probe panes. If ess than K probes is aocated at this point a second round is started. Now again take power sorted custers and aocate as many probes as possibe around the strongest custer within imit of the mentioned threshod. Repeat the procedure with weaker custers unti K probes are seected. Fig. 3 shows an exampe of probe aocation. Other, more compex and sophisticated, aocation agorithms can be deveoped. For this purpose different criteria and cost functions can be defined. The optimization can be based, e.g., on minimizing a spatia correation function error or a reconstructed PAS error. The above described method is simpe, but sti rather competent, at east when the per-custer anguar spreads of the emuated channe mode are not arge. The defined probe aocation is based on anguar characteristics of the propagation channe. Some custers may stay without dedicated probes, if, e.g., the probe panes do not cover wide enough anguar sector of if K is ess than the number of custers. In this case aso these remaining custers are mapped to the seected probes, as described in the foowing subsection. This conserves the power deay profie (PDP) of the propagation channe, but may distort the PAS and the joint power anguar deay profie, if the probe aocation is not sufficient. C. Probe weighting The next task is to find weights g,k of eq. (7) for the aocated probes. A straightforward method woud be to sampe the known mode PAS with the known probe ocations. Here is assumed that the reference channe mode specifies for each custer a continuous PAS P (Ω) for space anges Ω, that can be samped by probe directions. This is the case with most geometry based stochastic channe modes, where typicay custers have 2D Lapacian function shaped PAS with specific spread parameters. Now the direct samping is simpy g 2,k = P (ξ k ) P (Ω)dΩ, (9) where ξ k is the space ange of the kth probe (ange of wave vector k 0,k from probe k to the origin). However, this procedure does not consider the imited aperture of DUT and does not ead to optima weighting. Another weighting method, aiming to minimize the spatia correation error, is defined in [13] in context of PFS method. There a cost function is composed of the spatia correation function of the reference mode and the aocated probe configuration within voume of the test zone. The spatia correation function is Fourier transform pair with PAS P (Ω) and carries the same information with it. For any pair of spatia ocations q = (p q1, p q2 ) defined by ocation vectors p, the spatia correation can be written as ρ q = P (Ω) exp (jω (p q1 p q2 )) dω, (10) where Ω is the wave vector from space ange Ω. The spatia correation function achievabe with an MPAC setup, considering the number, directions, and distances of probes, can be cacuated according to [21] as

7 6 ˆρ q = K k=1 g2 k L(d p1,k)l(d p2,k ) exp (j Ω (d p1,k d p2,k )) K k=1 L2 (d p1,k )gk 2 K k=1 L2 (d p2,k )gk 2 (11) where K is the number of probes, g k is the ampitude weight of the kth probe, d p1,k and L(d p1,k ) are the distance and the path oss term between the kth probe and the ocation p q1, respectivey. Now for each custer is searched the set of weights g,k that minimizes the cost function Γ = arg min Q ρ q ˆρ q 2, (12) q=1 where Q is the number of ocation pairs. Finay each weight vector Γ is normaized to unity gain. This method was seected for the simuation part of this work. Aternativey the cost function can be composed, e.g., to minimize the deviation of the reference PAS and the PAS constructed by the OTA setup, both as observed by a imited aperture of the DUT. It is important to notice that in a practica system the weights g,k may contain aso phase and ampitude compensation for impairments on signa paths, probe gains, etc. The compensation coefficients can be determined by a caibration procedure performed in an initia step with, e.g., a network anayzer and a known caibration antenna paced within the test zone. Beneficiay, with PFS the phase accuracy between probes is not mandatory as stated in [31]. However, the phase coherence is required between co-ocated orthogonay poarized probe eements, even with PFS, if target is to contro poarization states. The steps described above can be extended to muti-ue case. There the rotation and probe aocation is optimized for the joint PAS of a UEs, whie probe weighting procedure is repeated for each UE separatey, but keeping the reative powers of UE custers baanced. Of course, resources in terms of channe emuators (active ports and ogic channes), RF spitters and combiners, and the required ange region might be increased. D. Probe pane design In this work we discuss and evauate mainy the reconstruction of spatia/anguar characteristics of radio channe modes for OTA emuations. These aspects affect the design of arrays of probes on probe panes. Especiay the range ength, the covered sector of anges, the anguar spacing of probes, and the number of seectabe probes. The first three design criteria, together with possibe manufacturing constraints, determine the dimensions of probe panes and the ocations of probes within panes. Another radio channe dimension to be covered is the poarization. Each probe antenna must support for transmission/reception of controed poarization state. This can be achieved simiary to the existing LTE MPAC OTA setups, by utiising co-ocated orthogonay poarized probe eements. Both poarizations have separate feed and the phase difference between eements must be abe to be compensated out after, a caibration measurement. The poarization contro is important, especiay if the spatia mutipexing in the coming pre-5g systems wi be performed utiizing orthogona poarization. In some 5G performance measurements the OTA emuation of both upink and downink fading may be crucia. This requirement affects the probe pane design, particuary when the fu reciprocity of upink and downink fading channes is aimed at. In the present study we assume idea conditions and do not specify whether the probes are in receiving or transmitting mode. An interesting topic for a future work is to investigate refections from probe panes, as they may contribute distortion to the reconstructed PAS. In [32] a compensation at 1.5 GHz setup was performed. However, in the present work we assume idea chamber conditions. V. SIMULATION SETTINGS The simuation system foows the description of section IV. Purpose of the simuations is to evauate the performance of MPAC OTA setup with different probe configurations and other parameters, utiizing metrics described in section VI-A. A. Simuation parameters The parameters varied in simuations are isted in Tabe I. The range ength R was between 1 and 10 metres, where the simuated 4 and 10m range engths woud be very chaenging for a practica setup due to ink budget issues. Here they are considered mainy for comparison. The maximum number of probes seected for reconstruction of the anguar power distribution was between 4 and 16. In a cases the panes of probe antennas covered 120 in azumuth anges and in eevation either 30 or 60. The anguar spacing of probes in panes was either 7.5 or In tota seven channe modes were simuated. They are a 3GPP custered deay ine (CDL) modes specified in [17], without any scaing in anguar or deay domains. The first three modes M1 M3 are for non-ine-of-sight (NLOS) condition as shown in Tabe I, whie the ast four M4 M7 are for ineof-sight (LOS) condition. Ricean K-factor of M4 and M6 is 3 db and with M5 and M7 it is 9 db. In a modes the LOS direction of the UE was in AoD = 31 and EoD = 31 and the NLOS path directions orientate according to it. We do not expect the CDL modes of [17] to be the best possibe or the most representative modes for 5G radio inks, but they were chosen to have a cear and we defined reference. Finay, four different DUT array configurations were taken as specified in Tabe II. In a cases the DUT has uniform rectanguar array with haf waveength spacing between eements. DUTs D1 and D2 have 64 verticay poarized eements. Array D1 is ocated in the centre of the test zone (origin of the coordinate system), whie D2 is dispaced by 2.1 cm to directions of the positive y and z axes. DUTs D3 and D4 are anaogous, but with in tota 256 eements and dispacement of 4.3 cm. The dispacement offset is chosen to imitate cases where the DUT may have severa sub-arrays off from to DUT centre, e.g., sub-arrays with different orthogona poarizations are possiby not co-ocated. The offset shoud

8 7 TABLE I LIST OF VARIED PARAMETERS IN SIMULATIONS. Parameter Vaues and unit Range ength R 1, 2, 4, 10 m Max num. of active probes 4, 8, 12, 16 Eev. range of probe panes 30, 60 Anguar spacing of probes 7.5, 3.75 Channe mode M1, M2, M3, M4, M5, M6, M7 (NLOS A, B, C, LOS D3, D9, E3, E9) DUT arrays D1, D2, D3, D4 TABLE II SIMULATED DUT ARRAYS. DUT dimensions offset width height diag. [cm] [cm] D y = 0, z = 0 D y = 2.1, z = 2.1 D y = 0, z = 0 D y = 4.3, z = 4.3 reduce the emuation accuracy ony in the cases where the far fied criterion is not fufied. B. Simuation procedure The procedure of evauating different setup configurations is as foows. As the first step 1000 time sampes of the idea reference channe transfer matrices of eq. (3) were generated with Keysight Geometric Channe Modeing Too T M for different mode and DUT combinations. Secondy the transfer matrices of eq. (4) for OTA setups were generated in a Matab T M simuation environment for a parameter combinations of Tabe I. As intermediate operations of the second step the probe aocation and weighting was performed according to the description of section IV. Probes are assumed isotropic verticay poarized eements. In practice it is a requirement that the probe eements have sufficient fat radiation pattern to the direction of the test zone. Finay different metrics were cacuated comparing the reference and OTA cases as described in the foowing section. In the simuations was assumed isotropic radiation pattern G tx for the Tx (UE) antenna. Thus the UE iuminated a custers present in the channe mode. The resuting PAS for the Rx (DUT/BS) woud have been more confined if aso the UE side performed beamforming. Currenty the operationa mode of the other ink end, e.g. UE emuator in this case, in the coming OTA performance evauations is not defined. In other words, it is not specified whether the other ink end shoud operate in cose to isotropic mode, or in beamforming mode with a singe static beam, or in its norma adaptive beamforming mode. These aternatives are expected to set different requirements for the probe configurations. The first option woud require many probes spread to directions of a custers. In the second option probaby ony one or few custers are iuminated and ess active probes are needed in a confined sector of anges. In the third option ony one or few custers are iuminated simutaneousy, but the iuminated custers may change over time according to active beam states. In this case the switching capabiity, used to change the active probes Fig. 3. Reference PAS of mode M3 and the corresponding probe seection (in the coordinate system of probes). dynamicay, might be very usefu to save fading emuator resources. Figure 3 iustrates the theoretica PAS of mode M3 (NLOS C). In the figure is aso shown the avaiabe probes with white circes in the case of 60 eevation range and 3.75 probe spacing. The seected probes, at maximum 16 in this exampe case, are denoted with back circes. Notice that in the exampe figure the PAS is rotated to the broad side of DUT, i.e. the poar coordinate system in the figure is that of the probe sector, not of the DUT. VI. SIMULATION METRICS AND RESULTS A. Evauation metrics 1) Tota variation distance of PAS: The purpose of this and the next metric is to evauate how we the OTA setup is capabe of reconstructing a target PAS. The metrics shoud refect both the PAS itsef and aso the DUT size and resoution. The tota variation distance of power anguar spectra is defined as foows. First the PAS is estimated utiizing the cassica Bartett beamformer [33] with the assumed DUT array. This corresponds to fitering the actua power anguar distribution of the propagation channe by the imited aperture of the DUT array. The PAS estimate is cacuated for the idea reference mode as ( ˆP r (Ω) = a H (Ω) a(ω )P (Ω )a H (Ω )dω ) a(ω) (13) and the discrete impementation of the reference mode by the OTA setup as ˆP o (Ω) = a H (Ω)R o a(ω), (14) where a(ω) is the array steering vector of DUT array to the space ange Ω and P (Ω ) is the PAS of the reference channe mode. Further, R o = {ˆρ q } is the correation matrix which entries are the spatia correation coefficients between DUT eement ocations specified in eq. (11). An exampe of ˆP r (Ω) estimated with DUT D1 is shown in Fig. 4. Next, both estimated spectra are normaized to sum power of unity such that they can be interpreted as 2D probabiity

9 8 Fig. 4. PAS of mode M3 (in the coordinate system of DUT) estimated by Bartett beamforming with DUT D1 in the reference case (eft) and OTA case (right). distribution functions. Finay the tota variation distance between the normaized PAS is cacuated D p = 1 ˆP r (β) 2 ˆPr (β )dβ ˆPo (β) dβ. (15) ˆPo (β )dβ The range of D p is [0, 1], where zero denotes fu simiarity and one maxima dissimiarity, respectivey. 2) Spatia correation error: The intention of the test system is to reconstruct the PAS of the origina channe mode as accuratey as possibe. We need a metric to evauate how we the reconstruction succeeds. Comparing a continuous target PAS to the inevitaby discrete PAS achievabe by a imited number of probes is probematic [13]. With this metric we aim to evauate the spectra indirecty via the spatia correation function. The idea is to assess the spatia correation error on a particuar test zone within the setup. The error indicates deviation of the idea target PAS and the PAS achievabe with an MPAC setup, specified in eq. (10) and (11), respectivey. The weighted RMS correation error is defined as e ρ = 1 Q ρ q ˆρ q 2 max ( ρ q, ˆρ q ). (16) Q q=1 Weighting by the corresponding correation eve is performed to emphasize the significance of the deviation. Namey, even sma deviation on the magnitude of correation coefficient when it shoud be cose to unity has impact on, e.g. the spatia mutipexing performance, whie possiby arger deviations at ow correation eves are ess significant. 3) Beam peak distance: The motivation of beam seection metrics, this and the next one, is the assumption that the DUT is utiizing fixed beams having a discrete code book of antenna weights. We assume the DUT array can at east party perform anaog combining of eements (anaog beamforming) to compose beams to a pre-defined set of directions. This mode of operation is expected with devices in so caed pre-5g systems [4]. It is further assumed the DUT array is we caibrated and the fixed main beams are targeted to a certain grid of directions. Like, e.g., in Fig. 5 the grid has 56 directions, four in eevation and 14 in azimuth. In the figure and in the beam seection metrics is assumed that the beam with highest power is seected per time instant among the a fixed beam. The Fig. 5. Fixed beam directions and their probabiities with the reference mode M3 (bue) and in the OTA case (red). strongest beam is found by sequentia scanning of a beam powers. Fig. 5 shows probabiities of certain beam found as the strongest. The DUT in simuations for the figure was D1 and the other settings were as described with the Fig. 3. In NLOS modes the tempora variation, i.e. fading, of propagation paths spreads the probabiity distribution. In LOS modes, especiay with high Ricean K-factor, typicay the beam of LOS direction carries constanty the highest power and the distribution is a singe peak. It is worth of noticing that comparing instantaneous beam seection between the reference and the OTA case is not possibe in the simuations. However, this shoud not be interesting either, because typica channe modes are essentiay describing statistica characteristics of propagation channes and the instantaneous channe reaizations are not specified. Beam peak distance is the anguar distance between probabiity weighted average directions of the aocated beams with the unit of degrees, B D b = Ω b p r (Ω b ) Ω b p o (Ω b ) (17) b=1 where B is the number of fixed beams i.e. the pre-aocation code book size of the DUT, Ω b = (ϕ b, θ b ) is the azimuth and eevation ange of the bth beam, p r and p o are probabiities of the beam aocation on the reference and the OTA case, respectivey. 4) Tota variation distance of beam aocation distributions: is another beam seection metric. Here the tota variation distance is cacuated for 2D beam aocation distributions as D s = 1 2 B p r (Ω b ) p o (Ω b ) (18) b=1 Simiary to eq. (15) D s has vaues in range [0, 1], with the same interpretation. 5) Fixed beam power oss: In addition to the four genera metrics, we use the fixed beam power oss to evauate the range ength ony. The metric assumes a communication system with fixed beams, i.e. with a discrete code book of DUT antenna

10 9 weights. The purpose is to determine how much power is ost in average, due to curvature of wavefronts at the test zone. The power oss for a wave from direction of nth probe is Q n and the average power oss Q av is the mean over a n. The metric is defined in [20] and we eave the detaied description to be found there. B. Simuation resuts The mentioned four metrics were determined from simuations with the parameters defined in Tabe I. The number of parameter combinations, i.e. simuation cases, is high, in tota Due to space imitation it is not possibe to show the resuts for this high number of cases. Instead of trying to visuaize the six dimensiona data set we present the resuts as foows. We observe the trends and typica behaviour from the whoe data set and describe the findings in this section. For visuaization of the impact of a certain configuration parameter we fix the other variabes, except DUT types, and choose one exampe figure for a NLOS mode and one for a LOS mode. The fixed configuration parameter vaues are: range ength 2 m, eight active probes, eevation sector 60, and the anguar probe spacing in panes 7.5. Finay we show the simuated metrics for combinations of DUTs and channe modes, with a configuration parameters fixed to the recommended vaues. In each of the Fig the four bar diagrams are as foows: top eft is the Tota variation distance of PAS, top right is the Spatia correation error, bottom eft is the Beam peak distance, and bottom right is the Tota variation distance of beam aocation distributions. 1) Range ength: Fig. 7 and 8 show the impact of range ength R on the four metrics with NLOS mode M3 and LOS mode M7, respectivey. With the NLOS mode R does not affect the PAS based metrics (Tota variation distance of PAS and Spatia correation). It has a sma impact on the beam seection metrics with D2 and D4, i.e. with the DUTs off from the test zone centre. Simiary the DUTs with ocation offset gain from arger R with the LOS mode, but in LOS this is observabe aso on the Tota variation distance of PAS metric. We can concude that for D1 and D3, i.e. for DUT arrays up to without offset, the range ength of R = 1 m is sufficient with a simuated channe modes. OTA emuation of DUT D2 woud give sighty higher precision if R > 1 m. Distincty D4, representing a very arge DUT, woud require R = 2 m or higher. Simiar concusions can be drawn from the fixed beam power oss simuations of Fig. 6 (eft). There DUTs D1 D3 have acceptabe Q av < 2 db with R = 1 m, which was chosen as the threshod of the average fixed beam power oss in [20]. D4 has above 2 db oss even with R = 2 m. Further, we can observe that with this metric R = 0.5 m may be too short for D2 D4. The maximum fixed beam power osses, among a directions of the probe sector, are iustrated in Fig. 6 (right). Even these are beow 1 db with D1 D3 and R = 1 m. 2) Number of active probes: The diagrams of Fig. 9 and 10 iustrate how the number of probes that can be simutaneousy switched to the fading emuator affects the metrics with NLOS mode M3 and LOS mode M5, respectivey. In the LOS case there is practicay no performance difference with different probe numbers. This foows mainy from the dominant roe of the LOS path. The other paths have such an insignificant contribution that adding more probes does not perform consideraby better. With NLOS modes, however, the increased probe number has a positive impact. The PAS based metrics indicate remarkabe improvement when taking eight probes instead of four. The beam seection metrics do not show a cear trend. There, in some cases the more probes resuts to worse accuracy. The beam peak distance, being based on the centre of gravity of 2D probabiity histograms, is quite sensitive even to sma changes of reconstructed discrete PAS, when the mode has many cose to equa strong custers (see Fig. 5). This may expain the unstabe behaviour of that metric in the simuated case. Four simutaneousy active probes is a sufficient number for LOS channe modes. With NLOS modes the adequate number with a DUT types is eight. Though, some accuracy gain is achievabe utiizing even 12 or 16 simutaneous probes. It is important to remember that this configuration parameter is heaviy dependent on the channe mode to be emuated. If the target PAS is highy spread, i.e. it has high azimuth and eevation anguar spreads, and possiby has numerous equa strong directions, then many active probes are required. 3) Eevation sector covered by probes: The eevation coverage by probe panes is investigated in Fig. 11 and 12 for the NLOS mode M3 and the LOS mode M6, respectivey. Simiary to the probe numbers, the LOS mode is insensitive to the eevation coverage. Aso the reason is same, i.e. the strong centraization of PAS to the LOS path. In the seected NLOS mode there is a sight performance enhancement with 60 eevation sector, except with the metric of Tota variation distance of beam aocation distributions. This is another setup configuration parameter that is strongy dependent on the channe mode, in particuar the target PAS. In 3GPP mode [17] the composite eevation spreads are rather narrow and the power may be confined to a 30 eevation sector. The 30 eevation sector can be considered sufficient for the singe UE emuations. However, when emuating mutipe users, e.g., MU-MIMO systems, the need for eevation coverage of probe panes may easiy increase to 60. 4) Anguar spacing of probes within panes: Impact of the spacing of seectabe probes with the NLOS mode M3 and the LOS mode M4 is depicted in Fig. 13 and 14, respectivey. With NLOS modes the tota variation distances show some gain with increased anguar resoution by probe panes. The spatia correation error has no difference on smaer DUTs D1 and D2, but has cear improvement with the two arger DUTs. Again the beam peak distance is somewhat unstabe whie the resuts indicates opposite trend. With LOS modes there is no remarkabe difference between 7.5 and 3.75 resoutions. At east with 8 8 DUT arrays the 7.5 spacing of seectabe probes is adequate. The arger DUTs with NLOS modes benefit from denser spacing, but the gain is not necessariy significant. 5) Genera remarks: As a genera observation from simuation resuts we can remark that LOS channe modes are more

11 10 Fig. 6. Impact of range ength on the metric average (eft) and maximum (right) fixed beam power oss. sensitive to the range ength whie NLOS modes are more sensitive to the other probe setup configuration parameters. This is a consequence of the dispersion of power in anguar domain. In LOS modes the PAS is typicay more impuse ike and in NLOS modes there is a wider spread. In principe the more dispersed the PAS is the more probes are needed, which is a very intuitive concusion too. Based on the findings the recommended configuration parameters for DUTs sized up to without dispacement, i.e. D1 D3, are as foows: range ength R = 1 m, eight simutaneousy active probes, 30 eevation sector covered by probe panes, and with 7.5 anguar spacing of probes. The range ength of 1 m is supported aso by simuations of [20]. There a metric caed Fixed beam power oss was used for a panar array and the minimum R = 1 m was concuded. The metric assumes DUT array using a code book of fixed beams and it indicates the amount of ost power due to curvature of the received wave fronts. The overa recommended configuration aims to save in the cost and size of the test setup whie sti keeping the accuracy on an appropriate eve. Performance of a DUT and channe mode combinations with the recommended parameter set is shown in Fig. 15. We can observe that LOS modes can be reconstructed with higher precision in a cases than the NLOS modes. The ony exception to this is the tota variation distance of PAS with DUT D4. As discussed earier D4 suffers from short range engths in LOS cases. Further, mode M1 shows the worst performance when measured by the PAS based metrics. This foows from the PAS shape of M 1 whose eevation spread is more than ten-fod compared to the other modes. It has one strong custer and the other custers are very widey spread outside the probe panes both in azimuth and eevation. The other custers are such weak, on the other hand, that beams are never aocated to them and thus the beam seection metrics perform decenty. Moreover, mode M 2 has highest inaccuracies with the beam seection metrics. In M2 the PAS is composed of severa cose to equa strong custers and in the reference case more than 20 different beams get aocated. Reconstruction of this condition with imited probe resources in the anechoic chamber is evidenty difficut. Fig. 7. Impact of range ength on performance metrics, NLOS M3. Fig. 8. Impact of range ength on performance metrics, LOS M7. Fig. 9. Impact of active probe number on performance metrics, NLOS M3.