Finite Large Antenna Arrays for Massive MIMO: Characterization and System Impact
Cheng-Ming Chen, Vladimir Volski, Liesbet Van der Perre, Guy A. E. Vandenbosch, Sofie Pollin
66712 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 65, NO. 12, DECEMBER 2017
Finite Large Antenna Arrays for Massive MIMO:Characterization and System Impact
Cheng-Ming Chen ,
Student Member, IEEE , Vladimir Volski,
Member, IEEE ,Liesbet Van der Perre,
Member, IEEE , Guy A. E. Vandenbosch,
Fellow, IEEE ,and Sofie Pollin,
Senior Member, IEEE
Abstract — Massive MIMO is considered a key technologyfor 5G. Various studies analyze the impact of the numberof antennas, relying on channel properties only and assuminguniform antenna gains in very large arrays. In this paper, weinvestigate the impact of mutual coupling and edge effects onthe gain pattern variation in the array. Our analysis focuses onthe comparison of patch antennas versus dipoles, representativefor the antennas typically used in massive MIMO experimentstoday. Through simulations and measurements, we show that thefinite patch array has a lower gain pattern variation comparedwith a dipole array. The impact of a large gain pattern variationon the massive MIMO system is that not all antennas contributeequally for all users, and the effective number of antennas seenfor a single user is reduced. We show that the effect of this atsystem level is a decreased rate for all users for the zero-forcingMIMO detector, up to 20% for the patch array and 35% for thedipole array. The maximum ratio combining on the other hand,introduces user unfairness.
Index Terms — Antenna array mutual coupling, antennameasurements, antenna radiation patterns.
I. I
NTRODUCTION M ASSIVE MIMO proposes a new wireless communi-cation concept relying on an excess number of base-station (BS) antennas, relative to the number of active userterminals. The technique allows for very efficient spatialmultiplexing, attainable using linear processing in a time-division duplex mode [1]–[3]. It has been demonstrated toachieve a record spectral efficiency (SE) [4]. Moreover, thetechnology has the potential to drastically improve energyefficiency [5]. Consequently, massive MIMO addresses severalkey 5G requirements [6]: it offers a great capacity increase,can support more users, and enables significant improvementin energy efficiency.Massive MIMO operation has been studied exten-sively relying on omnidirectional profiles and homogeneous
Manuscript received December 30, 2016; revised June 27, 2017; acceptedJuly 25, 2017. Date of publication September 19, 2017; date of current versionNovember 30, 2017. This work was supported in part by the European UnionSeventh Framework Program (FP7/2007-2013) through MAMMOET underGrant 619086 and in part by the Flemish Hercules Foundation under GrantAKUL1318. (Corresponding author: Cheng-Ming Chen.)
The authors are with the ESAT-TELEMIC Research Division, Department ofElectrical Engineering, Katholieke Universiteit Leuven, 3001 Leuven, Bel-gium (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]).Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TAP.2017.2754444 arrays [7]–[10]. Most of these studies neglect the impactof the directional array gain pattern on the massive MIMOsystem performance. These assumptions are overoptimistic forrealistic scenarios with compact antenna arrays. These featurea finite-number of antennas that are spaced relatively closeto each other (a typical example is half a wavelength) andhence can experience significant mutual coupling. In [13]and [20], the analytic massive MIMO sum-rates has takenmutual coupling into account and show that channel correla-tion is dependent on mutual impedance. However, the mutualimpedance was derived from single element, so there is nogain pattern variation in the considered model. It has also beenshown that in most realistic scenarios the channels deviatefrom the i.i.d. Rayleigh assumption, and the gain variationof the channels impacts the overall system capacity becausenot all antennas contribute equally [8]. These studies wereeither on a virtual array, neglecting the mutual coupling, orstudy the gain variation combined with the multipath channel.The impact of gain variations caused purely by the antennaarray is not yet studied. Moreover, measuring the impact ofthe array topology on the active or embedded gain patternof a single element requires an antenna measurement facilitywhere multiple antennas can be active at the same time. Mostantenna measurements create a virtual array, by moving theantenna along a plane [9], [10] or measure antennas in anarray where only a subset of antennas are active at the sametime [10]–[12]. Active array antenna measurements have tothe best of our knowledge not yet been reported.The realized gain of a single antenna is a very importantparameter. Typically, it is one of the parameters specified inthe datasheets. However, in the case of arrays, the realized gainof identical elements can significantly vary due to the mutualcoupling, or in other words the electromagnetic interactionbetween elements. Mutual coupling is a changing of currentsin one element, which creates a field that changes the currentson adjacent elements. Hence, this changes the realized gainof each antenna element. These parasitic-induced currentsaffect all parameters of the elements: S-parameters and embed-ded gains. So the description of mutual coupling based onS-parameters is related to power flows between the elements,while embedded gain patterns also involve the directions inspace where the power radiates. The latter depends strongly oninduced currents and on the type of interference: constructiveor destructive [18], [19].
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In the existing literature [2], [3], there are clear no guide-lines of how to select a basic element for a massive MIMOantenna array, although this is really a crucial aspect of amassive MIMO array and system. One thing that is knownfrom the basic MIMO theory is that it is always better if anantenna element in such an array receives as much multipathfrom all directions as possible. Hence, it has often beenassumed that using a quasi-omnidirectional dipole is alwaysbetter than the more directive patch element.In this paper, for the first time, the effect of mutual couplingin larger arrays on embedded gains, and specific the conse-quent impact on the system performance in a massive MIMOsystem is investigated, both for the more omnidirectionaldipole element, and the well-known and widely used patchelement. This is done by, including the gain variation intothe small-scale fading channel model. The study of howthese realized gain variations (a problem more understood inthe antenna and propagation community) impact system-levelperformance (a problem formulation approach typically usedin the massive MIMO signal processing community) is noveland of great interest to both communities.We first study the active gain pattern variation of individualantenna elements in a large massive MIMO array, causedby the mutual coupling between the closely located elementsand the edge effects in finite arrays. Both dipoles and patchantennas are considered in the simulation-based assessment,and for the latter results of real-life experiments are alsopresented. Our antenna measurements rely on measuring32 active elements in an array, which is enabled by relyingon a massive MIMO test bed placed in an anechoic chamber.Consequently, the impact of the gain pattern variation onthe achievable SE is highlighted. While a dipole individuallyfeatures a better omni-directionality, when composed in anarray their severe mutual coupling causes drastic directionalityon the elements and gain variations over the array. The patcharray is shown to be the better choice from the system capacitypoint of view.This paper is further organized as follows. First, we intro-duce a massive MIMO system model with an extended chan-nel model that takes into account the 3-D antenna gain inSection II. Next, the simulation-based assessment of antennagain variation and directivity of a representative finite largearray composed of either dipoles or patch antennas is providedin Section III. The experimental validation is presented inSection IV. The impact of the gain variation on SE at systemlevel is illustrated in Section V. Finally, we conclude this paperby reviewing the main findings, and provide recommendationsfor the design of large antenna arrays to be used in massiveMIMO systems.The notation used in this paper is as follows: We denotebold face upper (lower) letters as matrices (vectors). Super-scripts H , T , and − I K denotes an K × K identity matrix. Moreover, ⊗ denotes as Kroneckerproduct, vec { . } represents vectorization of a matrix, det (.) isthe determinant of a matrix, and cofactor (.) means the cofactoroperation of a matrix. The element in the k t h row and m t h column of matrix A is denoted by [ A ] k , m . II. 3-D S YSTEM M ODEL
In this section, we introduce the system model bringing intoaccount a 3-D gain pattern for the antenna elements in thearray. The actual 3-D gain pattern at each antenna elementdepends both on the embedded gain pattern, as well as thevarious multipath reflections. This requires the establishmentof a fairly detailed channel model, including propagationand array gain patterns. To access the impact from the gainvariation to the system performance, we later plug the resultsof arrays consisting of dipoles or patch antennas in Section IVinto this channel model and simulate the impact of gainvariation to the user achievable rate in Section V-B.A massive MIMO BS equipped with M antennas communi-cates with K single-antenna user terminals in the same time–frequency unit. The symbols transmitted from the K users arerepresented as a vector s = [ s , . . . , s K ] T , where E {| s k | } = y after transmission over the channel anddisturbance by noise is y = D X / s + w (1)where y ∈ C M , X = diag { x , . . . , x K } with x k denoting theaverage transmit power of user k , while w ∼ CN ( , I M ) is thei.i.d. complex Gaussian distributed noise. D = [ d , . . . , d K ] represents the channel, with the channel vector between theM-antenna BS and the k th user d k ∈ C M . Originating from thecorrelation channel model in [14], we decompose the channelvector d k into three terms, namely, large-scale fading, antennagain variation, and small-scale fading d k = √ α k C k C k (cid:2) c = G (θ c , k , φ c , k ) (cid:6) c a (θ c , k , φ c , k )v c , k (2)where α k represents the large-scale fading and shadowingeffect of user k seen by the whole antenna array and C k stands for the number of multipath components. Thearray gain pattern is a diagonal matrix G (θ c , k , φ c , k ) = diag { ( g (θ c , k , φ c , k )) / , . . . , ( g M (θ c , k , φ c , k )) / } , which repre-sents the different active antenna patterns from different angleof arrivals for each antenna m due to mutual coupling andthe edge effect. To represent the rich multipath environment, (cid:5) c is an M × M matrix with binary diagonal elements [ (cid:5) c ] m , m = (cid:3) , belongs to cluster0 , otherwise (3)specifying whether the reflection belongs to the multipathcluster c . This matches the fact that for a large antennaarray, reflections from one cluster do not contribute to allantennas. The steering vector a (θ k , φ k ) of a rectangular matrixis modeled as a (θ k , φ k ) = vec (cid:4)(cid:5) , e j π γλ sin θ k , . . . , e j π( √ M − ) γλ sin θ k (cid:6) T ⊗ (cid:5) , e j π γλ sin φ k , . . . , e j π( √ M − ) γλ sin φ k (cid:6)(cid:7) (4)where γ is the antenna spacing, λ is the carrier wavelength,and φ k denotes a azimuth of arrival angle. Moreover, v c , k ∼ CN ( , ) represents a standard complex
714 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 65, NO. 12, DECEMBER 2017
Gaussian vector. When there is only a single line-of-sight (LoS) cluster, the model simplifies to d k = √ α k G (θ k , φ k ) a (θ k , φ k ). (5)For the simulation results in Section V, we use the simplifiedchannel model in (5) to consider the effect of pure antennapatterns. However, we develop a more general channel modelin (2) illustrating that the assessment of system-level impactof gain variations is not trivial.III. G AIN P ATTERN IN L ARGE A RRAYS :D IPOLES V ERSUS P ATCH A NTENNAS
It is favorable for each antenna element in massive MIMOto have equal gain from all directions so as to efficientlyexploit the multipath in the wireless environment. Typically,researchers assume an antenna element that preserves itscharacteristics in an array environment [9], [10]. However, inpractice the mutual coupling between closely spaced elementsmay noticeably affect the embedded element radiation pattern,making it different from the pattern of a single element.An accurate computational analysis of such influencerequires a full wave solver, which is capable of taking intoaccount the mutual coupling between elements and is able tocalculate the embedded gain pattern of each element. In thispaper, CST microwave studio has been used to compare thegain patterns of a single-antenna element, a finite array, andan infinite phased array. Since it is of interest to compare thequalitative performance of different types of antenna element,a more directional and a more omnidirectional antenna elementhave been considered. The first type is a microstrip patchantenna and the second type is a half wavelength dipole thatgenerates an omnidirectional pattern in the H-plane.The microstrip patch prototype consists of a square patchof 31 mm with two merged U-slots with width 1 . . . . ×
70 mm. The dimension ofdipole is about 51 . × with an element spacing of 71 mm.A first estimation of mutual coupling can be obtained fromthe analysis of the simulated S-parameters as shown in Fig. 3for the elements in the center and in the corner. All elementsin the array are consecutively numbered from the left bottomcorner as shown in Fig. 2. The simulated reflection coefficientfor a single element are also plotted with curves labeled singlein superscript. The simulated mutual coupling between thedipoles in Fig. 3(b) is higher in comparison with the simulatedmutual coupling between patch antennas in Fig. 3(a) by around6 dB. Furthermore, in order to illustrate the accuracy of these The spherical coordinate system used in the paper is based on theconvention accepted in physics and in the antenna community. The thetaangle is counted from the z-axis. The Cartesian coordinate system is definedin Fig. 2. Fig. 1. Detailed view of the microstrip patch antenna.Fig. 2. Two finite 32-element antenna arrays: dipoles (left) andpatches (right). simulations, representative measurements were performed inan anechoic chamber using a spectrum analyzer KeysightN9344C with a tracking generator; a typical agreement isillustrated in Fig. 3(a) for s , .Consider the k t h user and a single element in the BS in aLoS scenario. The power p ( r ) k received by the element can beestimated using the well-known Friis transmission formula p ( r ) k = p ( t ) k g ( t ) k r k g ( r ) k (6)where p ( t ) k is the transmit power from the user and g ( t ) k is itsrealized gain. g ( r ) k is the embedded realized gain or active gainpattern of the element in the BS, and r k = (λ/( π(cid:5) r k )) isthe inverse of free-space pathloss with distance (cid:5) r k betweenthe kth transmitter and the element.As for an array, the variation in the received power perelement is coupled with the embedded gain variation of theelements, so from now on we will focus only on the receiverealized embedded gain. For simplicity, the superscript ( r ) isomitted. For an infinite array, the embedded gain is identicalfor all elements and can be easily calculated. The calculationreduces to the analysis of a unit cell taking into account a phaseshift between neigboring elements. This phase shift dependson the main Floquet harmonic in the direction (θ k , φ k ) . Theembedded realized gain g ∞ m , k in the infinite array of m th element is modulated by the reflection coefficient (cid:9) ∞ [15]. HEN et al. : FINITE LARGE ANTENNA ARRAYS FOR MASSIVE MIMO: CHARACTERIZATION AND SYSTEM IMPACT 6715
Fig. 3. Mutual coupling between elements selected in the array center andat the edges. (a) Patch array. (b) Dipole array.
The simulation result is shown in Fig. 4. When the reflectioncoefficient goes to 1 for some direction(s), the embeddedrealized gain goes to zero. These directions are called scanblindness angles (SBAs). Note that in practice, the reflectionat SBA can be smaller than 1 due to the losses in dielectric andmetal of the antenna elements. The far-field components can beobtained by analyzing the transmission from the antenna portto the main Floquet harmonic. One of the obvious conclusionsof this paper is that a strong mutual coupling between elementscan completely destroy the omnidirectional pattern of thedipole.In a finite array, the situation is quite different. There,because of the edge effect, i.e., the fact that the elements at theedges see a different environment compared with the elementsin the middle, the embedded gains of the elements are notidentical. In this paper, the maximum gain variation over theelements was obtained in three steps. First, for each directionof incidence (θ k , φ k ) , the embedded gains of all elements g fk are calculated, where the superscript f stands for finitearray. Second, for a given θ k and φ k , the maximum differencebetween two embedded element realized gains is calculatedover the whole array max m , n ( g fm , k (θ k , φ k ) − g fn , k (θ k , φ k )) . Finally,this maximum difference can be studied as a function of direc-tion as depicted in Fig. 5. Two very important observationscan be made. First, the maximum gain variation increases All simulated results are perfectly symmetrical because the simulatedtopology is symmetrical, and thus it is convenient to show only half of thescan range. Fig. 4. Reflection coefficient for elements in an infinite phased array at2.6 GHz.Fig. 5. Maximal gain variation between two elements in terms of directionof incidence in the azimuthal plane of the 32-element finite array at 2.6 GHz. considerably when the angle θ k approaches the SBA. Second,the patch array shows a lower gain variation between elementsat angles closer to the direction normal to the array. This meansthat, counter-intuitively, the more directive patch elements arethe better choice from the point of view of gain variation.In order to study the dynamic range of the array, for eachangle θ k , we plotted max m ,φ k ( g fm , k (θ k , φ k )) , min m ,φ k ( g fm , k (θ k , φ k )) ,and mean m ,φ k ( g fm , k (θ k , φ k )) of the embedded gains in Fig. 6. Itis clearly proven that the role of mutual coupling is verydestructive: elements that are intrinsically omnidirectionalwhen isolated do not provide an omnidirectional coverage anymore in the finite array environment. As long as θ k is less than60°, the dynamic range of the patch element is around 5 dB,which is 5 dB less than that of the dipole array.IV. M EASURED A CTIVE G AIN P ATTERNS
In order to validate the active gain variations predicted bythe simulations, measurements were performed on the finite32-element patch array in receive. The operating frequencywas 2 .
716 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 65, NO. 12, DECEMBER 2017
Fig. 6. Embedded realized gain variation for a 32-element finite array. Thereis a higher gain variation for the dipole array even at angles θ k close to thedirection normal to the array at 2 . plane. Each patch was connected via 18 m RF cables to MIMOtest bed outputs. The dimension of the patch array is about 44 ×
44 cm.Following the horn specification, the 3-D beamwidth in theE-plane is of 53° and 48° in the H-plane. So the arrayillumination should remain relatively uniform and the incidentfield variation is considerably smaller in comparison withthe variation of measured power levels between elements. Soall observed variations in the received power levels can beattributed to mutual coupling between antenna elements. Thedependence of the gain variation on the angle was validatedby performing measurements in the following zenith angles − : :
75° (31 discrete angles in the y –z plane) whilefixing the azimuth angle φ k to 90°. Note that, while assuminga thermal noise level of −
174 dBm/Hz, the SNR of thismeasurement was above 50 dB. Details of the RF settingsare given in Table I.The synchronized power measurement from 32 antennaswas accomplished by a massive MIMO system termed MIMOframework [16] running in the KU Leuven (KUL) MaMi test The anechoic chamber has an asymmetrical opening for RF cables andthe positions of the RF cables are also not ideally symmetrical. Thus the realsetup is a little asymmetrical due to several supporting elements leading to aslightly asymmetrical response. It is also important to remember that the radiation pattern of a patchelement in the E-plane is not symmetrical. As a consequence, we do notexpect any symmetrical gain measurements in the vertical set of elements forany incident angle. Fig. 7. Measurement setup. (a) 32-element patch array on a round tablerotating in the range θ k = − : : θ k equals 0°.Fig. 8. Measurement setup: power gain variations across the array werecalculated from LTE-like uplink data symbols in the KUL massive MIMOtest bed. 32 antennas were used in this measurement. bed. From which 16 (2 RF ports each) universal software radioperipherals (USRPs) jointed together as a BS as shown inFig. 8.For the user side, a single USRP was connected to thehorn antenna as a transmitter. The received power strength ofthe 32-element was calculated from the uplink data symbolssynchronized by an LTE-like frame structure.At each θ k , 30 s of signal strength were recorded and thestatistics of maximum, minimum, and mean from 32 antennaswere plotted in Fig. 9. We observe that there is a high powergain variation among the antenna array while the zenith angledeviates from 0°. In addition, the measurements agree withthe CST simulation in several aspects. First, the received gainis quite flat when | θ k | ≤ ±
20° and within this region, thereis a low variation of around 3 dB. Second, the maximum
HEN et al. : FINITE LARGE ANTENNA ARRAYS FOR MASSIVE MIMO: CHARACTERIZATION AND SYSTEM IMPACT 6717
Fig. 9. Measured gain variation by a 32-element rectangular antenna array.The array has a lot of variation at high zenith angles (large difference betweenmax and min).Fig. 10. Maximal measured and simulated gain variation between twoelements in terms of direction of incidence in the azimuthal plane at 2.6 GHz. received gain decreases noticeably for larger zenith angleswhile the gain variation is increasing. The measured gainrange at each incident angle is summarized in Fig. 10, whichfollows the simulation trend with a higher level of about1 dB. The higher level can be explained by the presence ofvarious supporting elements located in the array environmentthat were not taken into account during the simulation. To seehow the gain variation distributed along the panel with relatedto different angle of arrivals, we further map the measuredgain of each element with its position on the panel at zenithangles 40° and −
40° for both simulation and measurement.The received power were normalized to the mean power andshown in Fig. 11. Again, the simulation results are perfectlysymmetric for both angles. In addition, the measurement resultat θ k =
40° matches the simulation quite well over thewhole map. For the angle at θ k = − TABLE IRF P
OWER S ETTINGS FOR A RRAY G AIN M EASUREMENT
Fig. 11. Illustration of the simulated and measured power when the signalarrives from different angles. It is quite clear to see that received powerstrength depends on the incident angle. In LoS scenarios, the power receivedfrom different users might have different levels of power distribution amongthe antenna elements. (a) θ k = θ k = − different directions, i.e., there is a severe gain variation thatvaries with incident angle. In any case, when the signal comesfrom different angles, an antenna element that receives ahigher power in one direction does not always receive a higherpower from the other direction. We should point out that gainvariation also increases the required dynamic range for a fixed-point system implementation, as the automatic gain control inthe receiver is not capable of jointly optimizing the receivedpower levels from different directions.V. G AIN V ARIATION AND S PECTRAL E FFICIENCY
We have seen that there is a considerable gain variation overthe array. Also, there is a different level of gain variation forpatch and dipole antenna arrays. In this section, we compare
718 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 65, NO. 12, DECEMBER 2017 the impact on single user achievable rate in a massive MIMOsystem. First, to theoretically show how the gain variationaffects the single user achievable rate, we introduce the SEmetric for both linear maximum ratio combining (MRC) andzero-forcing (ZF) detectors. Then, we apply the measured gainvariation from the patch array and the CST simulated gainfrom the dipole array, respectively, to examine the impact ofarray pattern variation on a massive MIMO system.
A. Spectral Efficiency of MIMO Detectors
Under the assumption that the BS has perfect channel stateinformation and the channel is ergodic, the uplink ergodicachievable rate from MRC and ZF detector can be representedas [17] R mrck = E (cid:3) log (cid:8) + x k (cid:9) d k (cid:9) x k (cid:9) Ki = , i (cid:10)= k (cid:10)(cid:10) d Hk d i (cid:10)(cid:10) + (cid:9) d k (cid:9) (cid:11)(cid:12) (7)and R z fk = E (cid:4) log (cid:13) + x k (cid:9)[ ( D H D ) − ] k , k (cid:9) (cid:14)(cid:15) . (8)The MRC per user rate R mrck in (7) illustrates the two maineffects that determine the SE of massive MIMO.1) Due to the array gain, the SNR without consideringinteruser-interference (IUI) increases linearly with theantenna array size. In our system model, we giventhe noise power σ w =
1, so SNR = x k (cid:9) d k (cid:9) / (cid:9) d k (cid:9) ,meaning that is best to have a maximal number ofantennas. Antennas with a low gain, do not contributeand reduce the effective number of antennas seen.2) The user separation enables to spatially multiplex multi-ple users based on their unique signature at the antennaarray. The interuser correlation term (cid:9) d Hk d i (cid:9) in thedenominator of (7), when considering only two usersfor simplicity, the IUI term can be represented as (cid:10)(cid:10) d Hk d i (cid:10)(cid:10) = (cid:9) d k (cid:9) (cid:9) d i (cid:9) (cid:9) cos θ ki (cid:9) (9)where cos θ ki is the angle between d k and d i . Supposedue to gain pattern variation, user k has a higher channelvector two-norm than user i . We then obtain the signalto interference ratio (SIR) relationship between user k and i asSIR i ≤ SIR k ⇐⇒ (cid:9) d i (cid:9) (cid:9) d k (cid:9) ≤ (cid:9) d k (cid:9) (cid:9) d i (cid:9) . (10)We call this user unfairness caused by antenna gainpattern variation.On the other hand, the performance of the ZF detector canbe understood by looking into (cid:9)[ ( D H D ) − ] k , k (cid:9) − = (cid:9) det ( D H D ) (cid:9) cofactor ( D H D ) k , k (cid:13) (cid:9) d k (cid:9) . (11)Here, the Hadamard inequality is applied in the approximation.Hence, we can observe that the achievable rate is directlyproportional to the two-norm of the channel vector, includingthe antenna gain pattern. Fig. 12. There are 31 measured locations, where the good user (user one)locates in the region with high power and low gain variation (15 discretelocations), while the bad user (user two) is placed outside this region(16 discrete locations).
B. Simulated Gain Variation Impact
To simulate the impact of measured antenna gain variationon system SE, we consider a LoS scenario with M = K =
2. The two users are assumed to have equaldistance to the BS, so we say they share a common large-scale fading α k =
1. Moreover, good user (user one) locatesin a higher power and less gain variation region, i.e., in thezenith angles | θ k | ≤
35° (15 discrete locations). While asecond bad user locates outside this region, i.e., in zenithangles 35° < | θ k | ≤
75° (16 discrete locations), as illustratedin Fig. 12. Both of their azimuth angles are distributed at avery limited region φ k = : : x k is assumed to be equal for both users.We compare the single user achievable rate of both users forthe measured patch array and the simulated dipole array. As apatch antenna has higher embedded gain and can be referencedfrom Fig. 6, the peak power of patch and dipole arrays arenormalized to 0 and − =
25 dB. Second,the ZF achievable rate is shown in Fig. 14. From (11), wesee the achievable rate is directly proportional to the receiveduser power and this matches the result that achievable rate ofpatch is in general higher than that of dipole. If we comparethe reference with the bad-power user of dipole array, there isa huge SNR loss by 10 dB and can be improved by 3 dB ifinstead applying the patch array.Figs. 13 and 14 are obtained under the assumption that thereare always two users actively communicating in the system.The conclusion of the MRC method is that the achievablerates of both users are coupled. The good user causes a larger
HEN et al. : FINITE LARGE ANTENNA ARRAYS FOR MASSIVE MIMO: CHARACTERIZATION AND SYSTEM IMPACT 6719
Fig. 13. MRC per user rate. Performance of dipoles exhibits a higher levelof user unfairness.Fig. 14. ZF per user rate. Dipoles counter-intuitively is less omnidirectional.The bad-gain user suffers from lower level of received power hence gets thelowest achievable user rate.
IUI to the bad user which results in a big impact on theachievable rate of the bad user. On the other hand, the baduser induces less IUI, and that is why the achievable rateof the good user is higher than the achievable rate of nogain variation case. We should notice that when there is nogain variation, the two users receive the same peak powerfrom all directions. Moreover, we should highlight that for afair communication system, all users should receive similarachievable rate instead of some benefits more if the userreceives a better channel condition. The performance of eachmethod should be evaluated by the performance of the baduser. VI. C
ONCLUSION
It has often been assumed in theoretical studies on massiveMIMO that all antennas contribute equally in a massive MIMOsystem. In this paper, we experimentally verify that in afinite array, there is a strong variation in the gain pattern ofthe different antenna elements. This gain pattern variation iscaused by mutual coupling and the edge effect, and stronglydepends on the angle of arrival. Remarkably, the gain variationis larger in a dipole array, because of stronger mutual couplingin such a system. This makes the array, consisting of omni-directional elements, more sensitive to angle of arrival than a patch array consisting of directional elements. Because of thisangle of arrival-dependent gain variation, the received powerover the array is not the same for all the users. While gainvariation is potentially beneficial for user separation, the maineffect is that the received power from each user is decreasedbecause of suboptimal antenna gains. For the MRC detector,the system-level impact leads to user unfairness as this detectorexploits the decreased correlation of the users maximally whiledisadvantaging the user in a suboptimal angle. For ZF, ourassessment shows that all users are disadvantaged by theantenna gain variation, and see a lower rate than a systemwith ideal identical antennas. Our future work is to investigateappropriate topologies and configurations of the antenna arrayto reduce the impact of such large gain variation effects.A
CKNOWLEDGMENT
The authors would like to thank NI Engineer Dr. A. NasserAli Gaber for his technical support of the massive MIMOframework. R
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Cheng-Ming Chen (S’16) received the M.S. degreefrom the Graduate Institute of Communication Engi-neering, National Taiwan University, Taipei, Taiwan,in 2006. He is currently pursuing the Ph.D. degreewith the Katholieke Universiteit Leuven, Leuven,Belgium, investigating distributed massive MIMOsystem with software defined radio.From 2006 to 2011, he was with the IndustrialTechnology of Research Institute (ITRI), Hsinchu,Taiwan, where he was involved in the basebanddesign of WiMAX and LTE. He also involved inthe 802.16m standardization with ITRI. From 2011 to 2015, he was withBroadcom Corporation, Irvine, CA, USA, as a Senior System Design Engi-neer, mainly focused on WiFi receiver performance verification, which includereceived signal strength indication, sensitivity, IQ imbalance, and adjacentchannel interference. His research interests include signal processing, MIMO,coding theory, and optimization.
Vladimir Volski (M’00) graduated from and thenreceived the Ph.D. degree from the Moscow PowerEngineering Institute, Moscow, Russia, in 1987 and1993, respectively.In 1987, he joined the Division Antennas andPropagation of Radio waves, Moscow Power Engi-neering Institute, as a Researcher. Since 1996 hehas been a Researcher with the ESAT-TELEMICDivision, Katholieke Universiteit Leuven, Leuven,Belgium. His current research interests include elec-tromagnetic theory, computational electromagnetics,antenna design, and measuring of electromagnetic radiation.
Liesbet Van der Perre (M’02) received the Ph.D.degree from the Katholieke Universiteit Leuven,Leuven, Belgium, in 1997.She was with the Nano-Electronics Research Insti-tute, imec, Leuven, from 1997 to 2015, where shetook on responsibilities as a Senior Researcher,a System Architect, Project Leader, and ProgramDirector. She was appointed Honorary Doctor withLund University, Sweden, in 2015. She was the Sci-entific Leader of the EU-FP7 Project MAMMOETon Massive MIMO. She is currently a Professor withthe Department of Electrical Engineering, Katholieke Universiteit Leuven, anda Guest Professor with the Electrical and Information Technology Department,Lund University, Lund, Sweden. She has been a member of the Board ofDirectors of Zenitel, Belgium, since 2015. She has authored or co-authoredover 300 scientific publications. Her current research interests include wirelesscommunication, with a focus on physical layer and energy efficiency.
Guy A. E. Vandenbosch (F’13) received the M.S.and Ph.D. degrees in electrical engineering from theKatholieke Universiteit Leuven, Leuven, Belgium, in1985 and 1991, respectively.Since 2005, he has been a Full Professor with theKatholieke Universiteit Leuven. In 2014, he was aVisiting Professor with Tsinghua University, Beijing,China. He has taught courses on electromagneticwaves, antennas, electromagnetic compatibility, fun-damentals of communication and information theory,electrical engineering and electrical energy, and dig-ital steer and measuring techniques in physics. His work has been published inca. 250 papers in international journals and has led to ca. 350 presentations atinternational conferences. His current research interests include electromag-netic theory, computational electromagnetics, planar antennas and circuits,nano-electromagnetics, EM radiation, EMC, and bioelectromagnetics.Dr. Vandenbosch was a member of the Board of FITCE Belgium, theBelgian branch of the Federation of Telecommunications Engineers ofthe European Union, from 2008 to 2014. From 2001 to 2007, he was thePresident of SITEL, the Belgian Society of Engineers in Telecommunicationand Electronics. From 1999 to 2004, he was the Vice-Chairman, and from2005 to 2009, he was the Secretary of the IEEE Benelux Chapter on Antennasen Propagation. He holds the position of the Chairman of this Chapter. From2002 to 2004, he was the Secretary of the IEEE Benelux Chapter on EMC.From 2012 to 2014, he was the Secretary of the Belgian National Committeefor Radio-electricity, where he is in charge of Commission E.