Massive MIMO in real propagation environments

Transcription

1 1 Massive MIMO in real propagation environments Xiang Gao, Ove Edfors, Fredrik Rusek, Fredrik Tufvesson Department of Electrical and Information Technology Lund University, Box 118, SE-22100, Lund, Sweden {xiang.gao, ove.edfors, fredrik.rusek, arxiv: v1 [cs.it] 13 Mar 2014 Abstract Massive MIMO, also known as very-large MIMO or large-scale antenna systems, is a new technique that potentially can offer large network capacities in multi-user scenarios. With a massive MIMO system, we consider the case where a base station is equipped with a large number of antennas and serving multiple single-antenna users in the same time-frequency resource. So far, investigations are mostly based on theoretical channels with independent and identically distributed (i.i.d.) complex Gaussian coefficients. Here, we investigate how massive MIMO performs in real propagation environments. Based on channel measurements at 2.6 GHz using a physically large linear array and a compact cylindrical array, both having 128 antenna elements, we illustrate the channel behavior of massive MIMO in typical propagation conditions, and evaluate the corresponding performance. The investigation shows that the measured channels, for both array types, allow us to achieve performance close to that in ideal i.i.d. channels. Thus, it can be concluded that in real propagation environments, we have characteristics that allow for efficient use of massive MIMO technology. Index Terms Massive MIMO, large antenna array, multi-user MIMO, channel measurement I. INTRODUCTION Massive MIMO systems, also known as very-large MIMO or large-scale antenna systems, is an emerging technology in wireless communications, that has attracted a lot of interest in recent years. With massive MIMO, we consider multiuser MIMO (MU-MIMO) systems [1] where the base stations are equipped with a large number (say, tens to hundreds) of antennas, as compared to conventional MIMO systems. As a comparison, the LTE standard only allows for up to 8 antennas at the base station [2]. Massive MIMO scales up conventional MIMO by an order or two of magnitude. Typically, the base station with a large number of antennas serves several singleantenna users in the same time-frequency resource. It has been shown in theory that such systems have potential to remarkably improve performance in terms of link reliability, data rate and transmit energy efficiency [3] [6]. These promising properties are due to the large number of base station antennas that greatly scales up the benefits of conventional MIMO, such as diversity gain, spatial multiplexing gain and array gain. Another important characteristic of massive MIMO is that it can substantially reduce intra-cell interference between users served in the same time-frequency resource. The fundamental idea is that as the number of base station antennas grows very large, the channel vectors between the users and the base station become very long random vectors, and under favorable propagation conditions, these channel vectors become pairwise orthogonal. In this case, simple precoding/detection schemes, e.g., zero-forcing and matched-filtering, become nearly optimal [3], [4], [7]. These attractive features of massive MIMO are, however, based on crucial but optimistic assumptions about the propagation conditions, hardware implementations and the number of antennas that can be deployed in practice. So far, investigations are mostly based on theoretical independent and identically distributed (i.i.d.) complex Gaussian (Rayleigh fading) channels with unlimited number of antennas. When this new technology is brought from theory to practice, the question is whether the promising results obtained in theoretical i.i.d. channels can also be achieved in real propagation environments using practical large antenna array setups. To answer this question, several measurements were performed to investigate how massive MIMO performs in real channels. The initial results were reported in [7] [11]. In [7], based on measurements at 2.6 GHz with an indoor base station using a 128-port cylindrical patch array, it has been shown that the orthogonality of user channels improves with increasing number of base station antennas. Already at 20 antennas, simple linear precoding schemes can achieve sum-rates very close to the optimal dirty-paper coding (DPC) capacity, for two single-antenna users in the measured channels. In [8] and [9], massive MIMO channel behavior using a 128-element linear array, also in the 2.6 GHz frequency range, were studied. The most important observation is that the propagation channel cannot be seen as wide-sense stationary over this physically large antenna array, as is usually the case for conventional MIMO. Some scatterers are not visible over the whole array, and for scatterers being visible over the whole array, their power contribution may vary considerably. Thus, large-scale/shadow fading can be experienced over physically large arrays. As a comparison, the cylindrical array studied in [7] is relatively compact, but still a similar effect of power variation can be experienced over the array. This is, however, due to its directional patch antenna patterns rather than largescale/shadow fading in the radio channel. In [10], we reported channel measurements using the two types of large arrays mentioned above in the same outdoor base station scenario. In [11], the authors reported another measurement campaign with a scalable antenna array consisting of up to 112 elements. The results in both [10] and [11] show that despite fundamental differences between measured and i.i.d. channels, a large fraction of the theoretical performance gains of large antenna arrays can be achieved in practice. In this paper, we aim for a deeper insight into how massive MIMO performs in reality. The investigations are based on

2 2 channel measurements of outdoor base station scenarios using the above mentioned 128-port cylindrical and 128-element linear arrays, as reported in [10]. We study the channel behavior of massive MIMO under three typical propagation conditions, where the users are: 1) closely located with lineof-sight (LOS) conditions, 2) closely located with non-lineof-sight (NLOS) conditions, and 3) well separated with LOS conditions. When the users are closely located, it is implied that the spatial separation of the users is particularly difficult, as compared to the case of the users being well separated. The LOS condition may cause high correlation between the channels to different users, which also represents a difficult situation, as compared to the NLOS case. To provide intuitive understanding of the physical propagation channels in these scenarios, we show and discuss simplified forms of the angular power spectrum at the large arrays. We call these spatial fingerprints of the users, as each fingerprint identifies the spatial property of the channel from a specific user as seen at the base station. By comparing the spatial fingerprints of users served in the same time-frequency resource, we can get a qualitative understanding of the spatial separability of these users. Then we investigate the corresponding performance obtained in these physical channels, as compared to theoretical i.i.d. channels. For this purpose we study the singular value spreads and achieved sum-rates for the measured channels. In the measured channels, especially when users are far apart, large inequality of channel attenuations between users can affect the performance evaluation. For example, in order to maximize the downlink sum-rate capacity in these situations, a large proportion of the transmit power will be allocated to the user channels with lower attenuations, and these users thus have very high date rates, while the users with higher channel attenuations may have very low data rates due to low received power. When this happens, it is difficult to investigate how spatial properties of the propagation channels affect the system performance. To avoid large inequality of channel attenuations, users with similar attenuations, i.e., path losses, should be served on the same time-frequency resource. However, due to limited user positions in the measurements, we do not have such a case when users are far apart. To focus on the influence of spatial properties of the channels on the system performance, we therefore remove the large attenuation inequality between well-separated users, when evaluating their sum-rate capacities. Moreover, we also make a comparison between the two large array structures. As mentioned in previous paragraphs, the cylindrical array is a compact array and relatively small in size, while the linear array is physically large. From a practical point of view, with the same number of antennas, it is preferable to have a physically compact array, since it is easier to deploy. On the other hand, if we make the arrays smaller, it will bring drawbacks such as higher antenna correlation and reduced spatial resolution. Having a large aperture, the linear array can benefit from very high angular resolution in one dimension. The cylindrical array has smaller aperture and thus lower angular resolution, but it exploits both horizontal and vertical dimensions. Which one is superior will depend on propagation scenarios. Therefore, we compare the performance we can achieve with the two types of arrays in the same propagation environment, and investigate what effect the array structure has on the system performance. The rest of the paper is organized as follows. In Sec. II, we describe our massive MIMO channel measurements using the two large antenna arrays, including measurement setups and propagation environments. In Sec. III, we describe the system model and the performance metrics used when evaluating the measured channels, i.e., the singular value spreads and sumrate capacities. Based on the obtained measurement data, the propagation characteristics in the three scenarios above are illustrated and discussed in Sec. IV. Then in Sec. V, we assess the corresponding singular value spreads in the measured channels and the sum-rate capacities that can be achieved, for each propagation scenario. Finally in Sec. VI, we summarize our contributions and draw conclusions. II. CHANNEL MEASUREMENTS In this section, we present the measurement campaigns for massive MIMO channels, based on which we study the propagation characteristics and evaluate the system performance. First we introduce the measurement setups, including the two types of large arrays and the measurement equipment. Then we describe the semi-urban environment where the channel measurements were performed under different propagation conditions. A. Measurement setups Two channel measurement campaigns were performed with two different large antenna arrays at the base station side. Both arrays contain 128 antenna elements and have an adjacent element spacing of half a wavelength at 2.6 GHz. Fig. 1a shows the cylindrical array, having 16 dual-polarized directional patch antennas in each circle and 4 such circles stacked on top of each other, which gives a total of 128 antenna ports. This large antenna array is physically compact with both diameter and height around 30 cm. Fig. 1b shows the virtual linear array with a vertically-polarized omni-directional antenna moving along a rail, in 128 equidistant positions. In comparison, the linear array is physically large and spans 7.4 m in space, which is more than 20 times the size of the cylindrical array. In both measurement campaigns, an omni-directional antenna with vertical polarization was used at the user side, measurement data were recorded at center frequency 2.6 GHz and a signal bandwidth of 50 MHz. With the cylindrical array, measurements were taken with the RUSK LUND channel sounder, while with the linear array, an HP 8720C vector network analyzer was used. With the virtual linear array and vector network analyzer, it takes around half an hour to record one measurement, when the antenna moves from the beginning of the array to the end. In order to keep the channel as static as possible during one measurement, we performed this campaign during the night when there were very few objects, such as people and cars, moving in the measurement area.

3 3 Fig. 1. Two large antenna arrays at the base station side: a) a cylindrical array with 64 dual-polarized patch antenna elements, giving 128 ports in total, and b) a virtual linear array with 128 vertically-polarized omni-directional antennas. B. Measurement environments The channel measurements were carried out outdoors at the E-building of the Faculty of Engineering (LTH), Lund University, Sweden (N , E ). Fig. 2 shows an overview of the semi-urban measurement area. The two base station antenna arrays were placed on the same roof of the E-building during the two measurement campaigns. More precisely, the cylindrical array was positioned on the same line as the linear array, near its beginning, and was for practical reasons mounted about 25 cm higher than the linear array. At the user side, the omni-directional antenna was moved around the E-building at 8 measurement sites (MS) acting as single-antenna users. Among these sites, three (MS 1-3) have LOS conditions, and four (MS 5-8) have NLOS conditions, while one (MS 4) has LOS for the cylindrical array, but the LOS component is blocked by the roof edge for the linear array due to the slightly lower mounting. Despite this, MS 4 still has LOS characteristic for the linear array, where one or two dominating multipath components due to diffraction at the roof edge cause a relatively high Ricean K- factor. At each MS, 40 user positions were measured with the cylindrical array, and 5 positions were measured with the linear array. The reason for measuring fewer positions with the linear array was due to the long measurement time. III. SYSTEM DESCRIPTION The acquired data from the two channel measurement campaigns allows for the study of various aspects of massive MIMO systems. We would like to study the channel behavior with the large arrays in different propagation scenarios, and evaluate the corresponding performance obtained in these channels. Before discussing the channel behavior and evaluating the performance of massive MIMO, we first define our system model. A. Signal model We consider a single-cell multi-user MIMO-OFDM system with N subcarriers in the downlink. The base station is equipped with M antennas, and is simultaneously serving K (K M) single-antenna users. We assume that the base Fig. 2. Overview of the measurement area at the campus of the Faculty of Engineering (LTH), Lund University, Sweden. The two base station antenna arrays were placed on the same roof of the E-building during two measurement campaigns. Eight user sites around the E-building were measured. Base station M z Fig. 3. System model of the downlink of an MU-MIMO system with an M-antenna base station and K single-antenna users. station has perfect channel state information (CSI), and that the channel can be described as narrow-band at each subcarrier. As shown in Fig. 3, the signal model of the considered narrow-band MU-MIMO downlink channel is described as ρk y l = M H lz l +n l, (1) where H l is a K M channel matrix at subcarrier index l. From our measurements, we have channel data obtained with 128 antenna elements at the base station, and at the user side, we select among the measured positions and each position represents one single-antenna user. With the selection of K user positions, we have a measured channel matrix of size K 128, which we denote H raw l, at subcarrier l. The channel matrix H l in (1) is then formed by selecting M columns from a normalized version of H raw l. Two different normalizations of H raw l are used in different investigations. The two channel normalizations are: Normalization 1. The measured channel vectors of each user, i.e., the rows of H raw l, denoted as h raw i,l,i = 1,2,...,K, are normalized such that the average energy over all 128 antennas and all N subcarriers is equal to H... 1 y K

4 4 one. This is achieved through h norm i,l = 128N N l=1 h h raw i,l 2 raw i,l, (2) where the vector h norm i,l is the ith row of the normalized channel matrix H norm l, at subcarrier l. With this normalization, the imbalance of channel attenuations between users is removed, while variations over antenna elements and frequencies remain. Normalization 2. The measured channel matrix is normalized such that the channel coefficients have unit average energy over all 128 antennas, K users and N subcarriers. This is achieved through H norm l = 128KN N l=1 H raw l 2 F H raw l, (3) where F represents the Frobenius-norm of a matrix. Compared with Normalization 1, here we keep the difference in channel attenuation between users, as well as variations over antenna elements and frequencies. Note that both normalizations are done for the originally measured channel matrix with 128 columns, rather than the sub-channel matrix with M columns, obtained by selecting a subset of the 128 antennas. The reason for this is that we would like to maintain the power variations over the antenna arrays due to large-scale fading or directional antenna elements, which can be critical for performance evaluation of massive MIMO. For the investigation of singular value spreads of the measured channels, we use Normalization 1. For the capacity evaluation, Normalization 2 is used in scenarios where users are closely located, while Normalization 1 is used when users are well separated and have large differences in channel attenuation. Now, let us return to (1), where z l is the transmit vector across the M base station antennas and satisfies E { z l 2} = 1, y l is the receive vector at the K users, and n l is a noise vector with unit variance elements. The term ρk/m contains the transmit energy, and the variable ρ relates to the average receive signal-to-noise ratio (SNR) at the users 1. As can be seen from the term ρk/m, we increase the transmit power with the number of users and reduce it as the number of base station antennas grows. As K increases, we keep the same transmit power per user. With increasing M the array gain increases, and we choose to harvest this gain as reduced transmit power instead of increased receive SNR at the users. 1 With the defined signal model, the average receive SNR at the users is smaller or equal to ρ, and different values can be obtained according to different precoding schemes. For example, when user channels are not completely spatially orthogonal and thus user interferences exist, with dirtypaper coding the average receive SNR at the users would be higher than that with zero-forcing precoding. Equality of the average receive SNR and ρ is obtained when the user channels are interference free, i.e., row vectors in the channel matrix H l become orthogonal and thus the Gram matrix H l H H l is diagonal. In this case, the average receive SNR equals ρ both for dirtypaper coding and the simple precoding schemes, such as zero-forcing and matched-filtering, and therefore, these simple precoding schemes can achieve the optimal performance [7]. B. Singular value spread As mentioned in Sec. I, massive MIMO has the potential to eliminate user interference by having a large number of base station antennas. This relies on favorable propagation conditions under which the user channel vectors become pairwise orthogonal. One way to evaluate joint orthogonality of the users is singular value spread of the normalized propagation matrix. The propagation matrix H l, with Normalization 1, has a singular value decomposition (SVD) [12] H l = U l Σ l V H l, (4) where U l and V l are unitary matrices, and the K M diagonal matrix Σ l = diag{σ l,1,σ l,2,...,σ l,k } contains the singular values of the channel, at subcarrier l. The singular value spread, also called condition number, is defined as the ratio κ l = σ l,max σ l,min, (5) of the largest and smallest singular values of the channel. With Normalization 1, since the imbalance of channel attenuations between the users is removed, the singular value spread shows the spatial separability of the users. A large singular value spread κ l indicates that at least two rows of H l, i.e., two user channel vectors, are close to parallel and thus are relatively difficult to separate, while κ l = 1 (0 db) implies the best situation that all rows are pairwise orthogonal. The singular value spread can be an indicator whether the users should be served in the same time-frequency resource or not. It has also been shown to have close connection with the performance of MIMO precoders/detectors [13] [15]. With massive MIMO, as the number of base station antennas grows large, we expect better orthogonality between the user channels and thus a smaller singular value spread, as compared to conventional MIMO. While this is true for theoretical i.i.d. channels, we need to know whether real propagation channels and practical large arrays can provide enough spatial separation of the users. Therefore, in Sec. V, singular value spreads of the measured channels are evaluated and compared with those of i.i.d. channels. C. Dirty-paper coding capacity In addition to the singular value spread, which measures the joint orthogonality of the users, it is also interesting to know the overall performance of a massive MIMO system, i.e., the sum-rate capacity that can be achieved in the channel. The singular value spread offers some indication of the channel capacity. A small singular value spread leads to a high channel capacity, as the interference among the users is low. However, a very large singular value spread does not imply a very low channel capacity. For example, in a rank-deficient channel with one singular value being zero, the singular value spread goes to infinity, but the channel capacity can still be relatively high, depending on the remaining singular values. The sum-rate capacity in the narrow-band MU-MIMO downlink channel is given as [16], C DPC,l = max P l log 2 det (I + ρkm HHl P lh l ), (6)

5 5 which can be achieved using non-linear DPC [17]. The diagonal matrix P l with P l,i,i = 1,2,...,K, on its diagonal allocates the power among the user channels. The capacity is found by optimizing over P l under the total power constraint K i=1 P l,i = 1. This optimization can be done by the sumpower iterative waterfilling algorithm in [18]. In scenarios where users are well separated, the imbalance of channel attenuations between users can be quite large due to different path losses. In order to achieve higher capacity for each user in these situations, user scheduling should be considered, i.e., users having similar path losses should be served in the same time-frequency resource. This is, however, not covered in this paper. When evaluating channel capacities in scenarios where users are far apart, we thus normalize the attenuation imbalance among the users as described in Normalization 1, which maintains the spatial property of the channels from each user to the base station. In scenarios where users are closely located, the path loss can be expected to be similar for all users and any attenuation imbalance is mainly due to small-scale and large-scale fading. From our measurements, we observe that the attenuation imbalance between co-located users is very small. Thus, in this case, we apply Normalization 2 on the measured channels and keep the small attenuation imbalance among the users for capacity evaluation, as is the case in i.i.d. Gaussian channels where the users have attenuation imbalance due to Rayleigh fading. Ideally in massive MIMO, as the number of base station antennas goes to infinity in favorable propagation conditions, the channels to different users become interference free (IF) [4] with per-user receive SNRs ρ. This leads to the asymptotic sum-rate capacity C IF = Klog 2 (1+ρ), (7) to which i.i.d. channels converge, as the number of antennas grows. However, in the measured channels we would like to know how much can be achieved, compared to this asymptotic capacity, at a limited number of antennas. This is shown and discussed in Sec. V. IV. PROPAGATION CHARACTERISTICS With the available measurements, we can study many different scenarios with various numbers of users and combinations of user positions. Of these we have chosen three representative propagation scenarios, briefly outlined in Sec. I, which we present performance evaluation results for and make comparisons between. In this section, we focus on propagation characteristics in these three scenarios, which helps us understand the evaluation results of singular value spreads and sum-rate capacities presented later in Sec. V. Each of the three scenarios has the same number of users, i.e., four users (K = 4), to allow direct comparisons. In two of the scenarios, the four users are placed close to each other (1.5-2 m spacing), representing situations where the spatial separation of users is particularly difficult. In the third scenario, on the contrary, the four users are well separated from each other (> 10 m spacing), representing situations where users are distributed around the base station. Combining the user positions with the LOS condition, the three scenarios are as follows, 1) the four users are close to each other at MS 2, having LOS conditions to the base station, 2) the four users are close to each other at MS 7, with NLOS conditions, 3) the four user are well separated, at MS 1-4, respectively, all having channels with LOS characteristics. For better understanding of the physical propagation channels in the three scenarios, we estimate the angular power spectra at the base station. The directional estimates for the linear array are obtained through the space-alternating generalized expectation maximization (SAGE) algorithm [19], which jointly estimates the delay, incidence azimuth and complex amplitude of multipath components (MPCs) in radio channels. More precisely, we apply a sliding window with 10 neighboring antenna elements on the linear array. For the measured channel data within each window, 200 MPCs are estimated through the frequency-dependent SAGE algorithm. The reason for estimating the MPC parameters based on 10- antenna windows is that the channel can be considered as wide-sense stationary within such a small window. Furthermore, when the SAGE algorithm estimates the directional information, 10 antennas can provide relatively high angular resolution. Note that the range of directional estimation is degrees for the linear array, which is due to the directional ambiguity problem inherent in this type of array structure [20]. Based on the estimates from the SAGE algorithm, we can obtain the angular power spectra in azimuth at each position along the linear array. In each scenario, we compare the angular power spectra from different users as seen at the base station. For the convenience of comparison, we simplify the angular power spectrum from each user. Instead of showing the estimated power levels from all the azimuth directions, we show the directional information from which the incoming energy are the strongest and all together contribute 90% of the total energy in the channel across the whole array. This simplified form of angular power spectrum illustrates the directional pattern of the incoming energy at the base station from a specific user. Since it identifies the spatial property of the channel from a specific user, we name it the spatial fingerprint of that user. In Fig. 4, for each scenario, we plot the spatial fingerprints of the four users on top of each other. The four colors in each plot represent the spatial fingerprints of the four different users, rather than the strength of the estimated power levels. The spatial fingerprints show the spatial properties of the channels with the linear array. For the cylindrical array, since it was positioned at the beginning of the linear array, as indicated by the dashed lines in Fig. 4, we consider that it experiences the propagation channels at that part of the linear array, but with directional antenna elements. These spatial fingerprints provide us an intuitive understanding about the real propagation channels. By comparing the spatial fingerprints of the four users in each scenario, we can acquire some information about the spatial separability of the users by using the large arrays. When the spatial fingerprints of the users are distinct, it indicates relatively good spatial

6 6 (a) (b) (c) Fig. 4. Spatial fingerprints (simplified forms of angular power spectra along the 128-element linear array), in (a) a LOS scenario where the four users are co-located at MS 2, (b) an NLOS scenario where the four users are co-located at MS 7, (c) a LOS scenario where the four users are well separated at MS 1-4, respectively. The four colors in each plot represent the spatial fingerprints of the four different users. The dashed lines indicate the position of the cylindrical array, which is considered to experience the propagation channels at that part of the linear array. Distinct spatial fingerprints indicate relatively low spatial correlation between user channels, which is the situation in (b) and (c), while similar spatial fingerprint patterns implies relatively high spatial correlation between user channels, which is the case in (a). orthogonality of the user channels, where we expect that the users can be spatially separated. In this case, therefore, the channels may have relatively small singular value spreads, and relatively high channel capacities could be achieved. When spatial fingerprints are similar and overlapping each other, it represents a difficult situation to separate the users as the user channels may have relatively high spatial correlation 2. However, since only the amplitude information is visible in these fingerprints, the phase may still provide a good decorrelation which is not immediately apparent in the figures. Now we turn our attention to the situations in the three scenarios with different propagation conditions. In Fig. 4a, we can see that in the LOS scenario where the four users are colocated, the incoming energy from all the users concentrate around 160 degrees, which is the LOS direction. For some users, a significant amount of energy also come from some scatterers at around 20 degrees at the end of the linear array. The overlap of the four users spatial fingerprints indicates relatively high correlation between their channels, which reveals that it is particularly difficult for the large arrays to spatially decorrelate the users in this scenario. A totally different situation is shown Fig. 4b, where the four users are still located close to each other but in an NLOS scenario with rich scattering. We can see that the incoming energies from the four users are much more well spread over a large angle across the array, which reflects the rich scattering environment. The spatial fingerprints of the four users are very complex and are quite different from each other, as compared to the case in Fig. 4a. This indicates that the spatial correlation between the user channels is relatively low, which allows a better separation of the users, even though they are closely located. Fig. 4c shows the scenario where the four users are well separated from each other, all having LOS characteristics. The users at MS 2 and 3, whose spatial fingerprints are in blue and green, respectively, have stronger LOS characteristics. 2 The spatial correlation we talk about here is an instantaneous property between the users, rather than an average property, e.g., over time realizations of the channels. We can see that the incoming energy from the two users are more concentrated, as compared to the energy from the users at MS 1 and 4, whose spatial fingerprints are in red and yellow. Since the four users are located at different sites, their fingerprints are very different from each other, which again indicates relatively low spatial correlation between the user channels. Thus, a good spatial separation of the users can also be expected in this scenario. From these plots, we can see that the physically large linear array potentially experiences channels with much more spatial variations, as compared to conventional small arrays which span only a few wavelengths in space. The large spatial variations can help decorrelate the users even when they are closely located, as in the scenario shown in Fig. 4b, where spatial fingerprints of users may overlap locally on the array, but over longer distances their fingerprints are quite different. That is to say, with small arrays, the users may have relatively low spatial correlation on average, e.g., over time, while with the physically large linear array, decorrelation is instantaneous when observing the entire array. However, strong LOS may kill the ability of the linear array to separate co-located users, such as the situation shown in Fig. 4a. Since we do not know the phase information over the array when only observing the spatial fingerprints, we investigate this situation in more detail by evaluating the singular value spreads of the channels and the achieved sum-rate capacities, as compared to the case in i.i.d. Gaussian channels. For the compact cylindrical array, since it experiences only a small part of channels seen by the linear array, the channels may provide less spatial separation of the users. Especially when users are closely located and strong incoming energy are likely from similar directions, the directional antenna elements pointing in the wrong directions may contribute little to separate the users. Despite this, the cylindrical array may still gain from its directional antenna patterns and provide good decorrelation between users, when they are well separated and distributed around the base station, and thus strong incoming energy are from different directions, as the case shown in Fig. 4c.

7 7 V. PERFORMANCE EVALUATION In this section, we evaluate the corresponding performance of massive MIMO in the above scenarios. In all three scenarios, over N=161 subcarriers and 2000 random selections of antenna subsets, i.e., selections of M antennas out of the 128, we show a) the cumulative distribution functions (CDFs) of the singular value spreads in the channels, when using 4, 32 and 128 base station antennas, and b) the average DPC capacities including their 90% confidence intervals, as the number of base station antennas M grows from 4 to 128. Note that for M = 128 there is only a single choice of selecting the antenna subset, and the CDFs of the singular value spreads and the capacity confidence intervals are therefore computed over frequencies only. For M < 128, we randomly select 2000 antenna subsets, and let the CDFs of the singular value spreads and the capacity confidence intervals also take the random antenna selections into account. As a reference, we also show simulated results for ideal i.i.d. channels, often used in theoretical studies. We select the interference-free SNR ρ = 10 db, therefore, with four users the asymptotic capacity given in (7) is 4log 2 (1+10)=13.8 bps/hz. In the following we discuss the singular value spreads and DPC capacities in the three scenarios separately. 1) Four users co-located with LOS: As discussed in Sec. IV, this scenario represents a particularly difficult situation in terms of separating the users, which can be seen from the similar patterns of the spatial fingerprints of the four users in Fig. 4a. We need to investigate whether the propagation channels and our large arrays in this situation can provide enough decorrelation between the users, so that the intracell interference can be reduced. First we study the CDFs of singular value spreads when using 4, 32 and 128 antennas, as shown in Fig. 5. We observe that for ideal i.i.d. channels, the median of the singular value spread significantly reduces from 17 db to below 4 db, as the number of base station antennas increases from 4 to 32 and 128. It should also be noticed that the singular value spreads become much more stable around the small values, as the CDF curves have no substantial upper tails, when using 32 and 128 antennas, as compared to the case of using 4 antennas. For the measured channels using the linear and cylindrical arrays, the singular value spreads are significantly larger than those of i.i.d. channels, for all three numbers of antennas. It indicates a much worse orthogonality of the users in the measured channels than in i.i.d. channels, due to the strong LOS conditions in this scenario. Still, trends similar to those seen in i.i.d. channels can be observed in the measured channels. The median of the singular value spread significantly decreases by 14 db with the linear array and 12 db with the cylindrical array, as the number of antennas increases from 4 to 128. Meanwhile, when using a large number of antennas, the substantial upper tails of the CDF curves reduce a lot, and almost disappear in the case of 128 antennas, as observed in i.i.d. channels. When using only 4 antennas, the selections of antenna subsets and subcarriers can make a big difference on the orthogonality of the user channels. It means that with small antenna arrays we may encounter propagation channels CDF I.i.d. channels Linear array Cylindrical array # of BS antennas Singular value spread [db] Fig. 5. CDFs of the singular value spreads when using 4, 32 and 128 antennas, in the scenario where the four users are closely located at MS 2, all having LOS to the base station antenna arrays. with very good channel conditions as well as very bad channel conditions, depending on the choice of antenna positions and subcarriers. When increasing the number of antennas to 32, we can see that user orthogonality improves and becomes much more stable over the antenna selections and subcarriers. Thus, those very bad channel conditions can be avoided by adding more antennas at the base station. When using all the 128 antennas, the user orthogonality improves further and becomes more stable over subcarriers. The above observations tell us that despite a significant gap between the measured channels and i.i.d. channels due to the strong LOS conditions, the spatial separation of the co-located users can be greatly improved in the measured channels by using a large number of antennas, and more importantly, the improved results are quite stable over subcarriers and different random antenna selections. We now move to the DPC capacities shown in Fig. 6. As a reference, the average capacity in i.i.d. channels converges to the asymptotic capacity of 13.8 bps/hz, and the capacity variation becomes smaller as the number of antennas increases. In the measured channels, however, the averages are significantly lower, and the variations are also larger. Here we focus on the average capacities first, and discuss the capacity variations later in the paper. The drops of the average capacities in the measured channels coincide with the larger singular value spreads, as compared to i.i.d. channels. Despite all this, in this potentially difficult spatial separation situation, the linear and cylindrical arrays perform at 90% and 75% of the asymptotic capacity achieved in i.i.d. channels, respectively, when the number of antennas is above 40, i.e., when the number of antennas is 10 times the number of users. 2) Four users co-located with NLOS: In this scenario we still have the users closely spaced but with NLOS to the base station antenna arrays. The NLOS condition with rich scattering, as illustrated in Fig. 4b, where the spatial fingerprints of the four users are complex and distinct, should improve the situation by providing more favorable propagation and thus allowing better spatial separation of the users. The benefits

8 Average and 90% confidence intervals Linear array Fig. 6. Sum-rate capacity in the downlink, achieved by DPC, in the scenario where the four users are close to each other at MS 2, all having LOS to the base station antenna arrays. Fig. 8. Sum-rate capacity in the downlink, achieved by DPC, in the scenario where the four users are close to each other at MS 7, with NLOS to the base station antenna arrays. CDF Singular value spread [db] I.i.d. channels Linear array Cylindrical array # of BS antennas Fig. 7. CDFs of the singular value spreads when using 4, 32 and 128 antennas, in the scenario where the four users are closely located at MS 7, with NLOS to the base station antenna arrays. can be clearly seen in the CDFs of the singular value spreads shown in Fig. 7. The singular value spreads in the measured channels become significantly smaller, as compared to those in the previous scenario. Especially for the linear array, the CDF curves are very close to those of i.i.d. channels. We can also see that the substantial upper tails of the CDF curves observed when using a small number of antennas disappear when using all the 128 antennas in the measured channels, similar to the situation in i.i.d. channels. This means that over the measured bandwidth the probability of seeing a singular value spread much larger than 2 db for the linear array, and 7 db for the cylindrical array, is very low. The stability of the singular value spreads indicates the stability of the real propagation channels, as well as the stability of the performance of MIMO precoders/detectors, when using the large arrays. Correspondingly, the benefits brought by the NLOS condition with rich scattering can also be observed in the DPC capacities, as shown in Fig. 8. Despite the closely spaced users, the linear array here provides average performance very close to the asymptotic capacity achieved in i.i.d. channels, while the cylindrical array reaches more than 90%, when the number of antennas is above 40. 3) Four users well separated with LOS: In this scenario, despite the LOS characteristics, the increased separation of users should help to improve the performance. As can be seen in Fig. 4c, the spatial fingerprints of the four users are significantly different, which indicates a favorable user decorrelation situation for the large arrays. In the CDFs of the singular value spreads shown in Fig. 9, we can see that the linear array again performs very close to i.i.d. channels. The cylindrical array has a significant improvement as compared to the previous scenarios: the median of the singular value spread reduces to below 5 db when using 128 antennas, which is quite close to that of i.i.d. channels using 32 antennas. The singular value spreads in the measured channels again become quite stable when using a large number of antennas. For the DPC capacities in this scenario, as can be seen in Fig. 10, both the linear and cylindrical arrays perform very close to that of the asymptotic capacity achieved in i.i.d. channels, when having more than 40 antennas. The cylindrical array shows slightly lower performance than the linear array. Throughout the three scenarios discussed above and whose performances are shown in Fig. 5 - Fig. 10, we observe that the linear array performs better than the cylindrical array. Due to its large aperture, the linear array experiences larger spatial variations in the channels over the array, which provide more distinctions between the user channels and thus better spatial separation of the users. In other words, the linear array has a very high angular resolution due to its large aperture, which helps to resolve the scatterers better than the compact cylindrical array with the same number of antennas. The small aperture of the cylindrical array and its patch antenna elements pointing in different directions make it difficult to resolve the scatterers at similar azimuth angles, which is usually

9 9 CDF Singular value spread [db] I.i.d. channels Linear array Cylindrical array # of BS antennas Fig. 9. CDFs of the singular value spreads when using 4, 32 and 128 antennas, in the scenario where the four users are well separated at MS 1-4, respectively, each having LOS characteristics. the case when users are closely spaced. When the users are distributed far apart around the base station, the cylindrical array can separate the scatterers at different azimuth angles, thus achieves better performance which is quite close to that in i.i.d. channels. For the DPC capacities, we focus on the average capacities in the previous discussions, now we turn our attention to the capacity variations over frequencies and random antenna selections. Comparing with i.i.d. channels, we notice that the capacity variations in the measured channels are much larger, and decrease much slower as the number of antennas increases. This is due to larger power variations over antenna elements and over frequencies in the measured channels, as compared to those in i.i.d. channels. For the linear array, the power variation over its antenna elements is due to the largescale/shadow fading experienced over the array, as reported in [8], [9], while for the cylindrical array, it is due to the directivity and polarization of its antenna elements. With omnidirectional antenna elements, the linear array has larger power variations over the measured bandwidth, as compared to the cylindrical array with directional antenna elements. This gives the linear array larger capacity variations than the cylindrical array, especially for the case of 128 antennas when the capacity variations are only across frequencies. It should be mentioned that the capacity with a small number of antennas can be higher than that with a large number of antennas, as can be clearly observed from the upper part of the 90% confidence intervals of the cylindrical array in Fig. 8. This is mainly because we reduce the transmit power as the number of antennas increases, in our signal model, while some antennas contribute more to the capacity than the others. It implies that we may gain by selecting the right antennas, as discussed in [21]. It should also be remarked that in all three scenarios, using the linear array, as few as 20 antennas gives very competitive performance for the case of four users, while slightly higher numbers are required for the cylindrical array. However, when using precoding schemes that are simpler and more practical than DPC, such as zero-forcing (ZF) and matched-filtering (MF) precoding, the sum-rate performance converges slower, which means that more antennas are needed to achieve the required performance. This is shown in [5] and [10]. More antennas are also needed, if we want to have more users served in the same time-frequency resource. In our experience, ten times more antennas than the number of served users let us achieve quite a substantial part of the asymptotic capacity. Fig. 10. Sum-rate capacity in the downlink, achieved by DPC, in the scenario where the four users are well separated at MS 1-4, respectively, each having LOS characteristics. VI. SUMMARY AND CONCLUSIONS The presented investigation shows that in the studied real propagation environments we have characteristics that allow for efficient use of massive MIMO technology. We have illustrated the channel behavior of massive MIMO in three typical propagation scenarios, then discussed the corresponding singular value spreads of the channels and the sum-rate capacities that can be achieved, using two types of large arrays for the case of four users, in these scenarios. In all scenarios, the singular value spread decreases considerably and becomes more stable around a small value over the measured bandwidth, when using a large number of antennas. It indicates that massive MIMO provides better orthogonality between the user channels, as well as better stability of the propagation channels, as compared to conventional MIMO. In the most difficult situation studied, closely spaced users with strong LOS to the base station, the singular value spread is significantly larger than that in theoretical i.i.d. channels, which indicates worse user orthogonality in the measured channels. Despite a gap between the measured channels and i.i.d. channels in this case, a large fraction of the asymptotic capacity achieved in i.i.d. channels can be still obtained in the measured channels, when using a large enough number of antennas. In the other studied scenarios, the NLOS condition with rich scattering provides more favorable propagation and allows better spatial separation of the users, even though they are closely located, while wide separation of the distributed users also helps to improve the performance. Therefore, the

10 10 measured channels with the linear and cylindrical arrays achieve performance very close to that obtained in theoretical i.i.d. channels, which indicates that massive MIMO works well in these propagation conditions. ACKNOWLEDGEMENT The authors would like to acknowledge the support from ELLIIT - an Excellence Center at Linköping-Lund in Information Technology, and also the Swedish Foundation for Strategic Research (SSF). [20] A. Manikas and C. Proukakis, Modeling and estimation of ambiguities in linear arrays, IEEE Transactions on Signal Processing, vol. 46, no. 8, pp , [21] X. Gao, O. Edfors, J. Liu, and F. Tufvesson, Antenna selection in measured massive MIMO channels using convex optimization, in IEEE Global Telecommunications Conference (GlobeCom) 2013 Workshop on Emerging Technologies for LTE-Advanced and Beyond-4G, Atlanta, Georgia, U.S.A., Dec REFERENCES [1] D. Gesbert, M. Kountouris, R. Heath, C.-B. Chae, and T. Salzer, Shifting the MIMO paradigm, IEEE Signal Processing Magazine, vol. 24, no. 5, pp , [2] Requirements for Further Advancements for Evolved Universal Terrestrial Radio Access (EUTRA) (LTE-Advanced), Mar [3] T. L. Marzetta, Noncooperative cellular wireless with unlimited numbers of base station antennas, IEEE Transactions on Wireless Communications, vol. 9, no. 11, pp , Nov [4] F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta, O. Edfors, and F. Tufvesson, Scaling up MIMO: Opportunities and challenges with very large arrays, IEEE Signal Processing Magazine, Jan [5] E. G. Larsson, F. Tufvesson, O. Edfors, and T. L. Marzetta, Massive MIMO for next generation wireless systems, CoRR, vol. abs/ , [6] H. Q. Ngo, E. G. Larsson, and T. L. Marzetta, Energy and spectral efficiency of very large multiuser MIMO systems, IEEE Transactions on Communications, vol. 61, no. 4, pp , [7] X. Gao, O. Edfors, F. Rusek, and F. Tufvesson, Linear pre-coding performance in measured very-large MIMO channels, in 2011 IEEE Vehicular Technology Conference (VTC Fall), Sep. 2011, pp [8] S. Payami and F. Tufvesson, Channel measurements and analysis for very large array systems at 2.6 GHz, in th European Conference on Antennas and Propagation (EUCAP), Mar. 2012, pp [9] X. Gao, F. Tufvesson, O. Edfors, and F. Rusek, Channel behavior for very-large MIMO systems - initial characterization, in COST IC1004, Bristol, UK, Sep [10], Measured propagation characteristics for very-large MIMO at 2.6 Ghz, in 2012 Conference Record of the 46th Asilomar Conference on Signals, Systems and Computers (ASILOMAR), 2012, pp [11] J. Hoydis, C. Hoek, T. Wild, and S. ten Brink, Channel measurements for large antenna arrays, in 2012 International Symposium on Wireless Communication Systems (ISWCS), Aug. 2012, pp [12] A. Paulraj, R. Nabar, and D. Gore, Introduction to Space-Time Wireless Communications. Cambridge University Press, [13] H. Artes, D. Seethaler, and F. Hlawatsch, Efficient detection algorithms for MIMO channels: a geometrical approach to approximate ML detection, IEEE Transactions on Signal Processing, vol. 51, no. 11, pp , [14] J. Maurer, G. Matz, and D. Seethaler, Low-complexity and full-diversity MIMO detection based on condition number thresholding, in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2007, vol. 3, 2007, pp. III 61 III 64. [15] S. Mohammed, E. Viterbo, Y. Hong, and A. Chockalingam, MIMO precoding with X- and Y-codes, IEEE Transactions on Information Theory, vol. 57, no. 6, pp , [16] S. Vishwanath, N. Jindal, and A. Goldsmith, Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels, IEEE Transactions on Information Theory, vol. 49, no. 10, pp , Oct [17] M. Costa, Writing on dirty paper, IEEE Transactions on Information Theory, vol. 29, no. 3, pp , [18] N. Jindal, W. Rhee, S. Vishwanath, S. Jafar, and A. Goldsmith, Sum power iterative water-filling for multi-antenna Gaussian broadcast channels, IEEE Transactions on Information Theory, vol. 51, no. 4, pp , Apr [19] B. Fleury, M. Tschudin, R. Heddergott, D. Dahlhaus, and K. Ingeman Pedersen, Channel parameter estimation in mobile radio environments using the SAGE algorithm, Selected Areas in Communications, IEEE Journal on, vol. 17, no. 3, pp , 1999.