Spatial Degrees of Freedom in Small Cells ... - IEEE Xplore

Spatial Degrees of Freedom in Small Cells: Measurements with Large Antenna Arrays V. Jungnickel1 , A. Brylka1 , U. Krueger1 , S. Jaeckel1 , M. Narandzic3 , M. Kaeske3 , M. Landmann2 , R. Thomae3 1

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Fraunhofer Heinrich Hertz Institute, Einsteinufer 37, 10587 Berlin, Germany Fraunhofer Institute for Integrated Circuits, Helmholtzplatz 2, 98693 Ilmenau, Germany 3 Technische Universität Ilmenau, FG EMT, PSF 100565, 98684 Ilmenau, Germany

Abstract—In this paper, we study the spatial structure of multiple-input multiple-output (MIMO) links in small urban macro-cells at 2.6 GHz. We resolve the double-directional structure of the radio channel. Also we compute common metrics used to characterize MIMO links, i.e. the structure of singular values and the resulting capacity. In a line-of-sight (LOS) link, we find that local scattering is not enough to create full-rank MIMO channels. Even behind a sector, we observe a low-rank channel. In a non-line-of-sight (NLOS) scenario, although we resolve several multi-paths with individual delay, direction of departure (DoD) and direction of arrival (DoA), the impact of local scattering is limited. Singular values indicate few more degrees of freedom for NLOS channels, but less than for a random matrix. We can model the spatial degrees of freedom in small cells better by assuming a random but small number of nearly specular paths feeding some local scattering widely spread in azimuth and elevation. Based on our results, we discuss modeling aspects and the value of large antenna arrays in mobile networks.

I. I NTRODUCTION In order to satisfy quickly increasing demands for higher data rates in mobile networks, large antenna arrays (massive MIMO) received a lot of attention in research. At the same time, small cells are considered to multiply the spatial reuse of radio resources. LTE-Advanced considers higher frequencies for small cells since more antenna elements can be integrated in the same base station panel [1–3]. But are the spatial degrees of freedom also increased in this way? Small-cells imply reduced distance to the base station. With bases stations above roof-top, a free LOS is more likely [4]. In previous measurements at 5.2 GHz, we classified outdoor MIMO links according to their singular values into 3 scenario groups, i.e. strong LOS, local as well as rich scattering. Strong LOS links serve only 2 spatial degrees of freedom due to crosspolarized antenna elements [5]. Moreover, users are more often alone in small cells, i.e. spatial multiplexing with other users (multiuser MIMO) is less efficient to increase the spatial degrees of freedom. Obviously, the benefit of massive MIMO depends on the cell size. In this paper, we report on channel measurements at 2.6 GHz using large antenna arrays in small urban macrocells. We use high-resolution bi-directional parameter estimation and decompose the measured channel into the dominant propagation paths. We identify main path parameters such as amplitude, delay, DoD and DoA. At the same terminal location, we measure in addition common MIMO metrics such as singular values and information-theoretic capacity.

Figure 1. Antenna arrays for 2.6 GHz cellular measurements. Top left: Cross-polarized 1x8 uniform linear array (ULA) used at the base station (BS). Center: Cross-polarized 2x12 uniform circular array (UCA) used at the terminals side. A cube antenna with 5 cross-polarized elements is used on top as a terminal prototype. Bottom: Calibration of the arrays in the anechoic chamber in Ilmenau. Right: Measured antenna patterns of selected antenna elements (top down) azimuth and elevation at the base station ULA, azimuth and elevation at the terminal UCA.

Since large arrays are not practical at the terminal side, we need to emulate realistic antennas. Traditionally, the channel is decomposed using high-resolution parameter estimation. The impulse responses are then synthesized for desired element patterns [6]. Recently, we proposed a more direct approach combining data from large array measurements using the pattern data of all elements [7]. Here, we introduce a third way, i.e. we measure the channel at the same location simultaneously with a small cube antenna and a large uniform array. The paper is organized as follows. In Section II, we describe our antennas and measurement equipment. In Section III, we describe three exemplary scenarios. Evaluation of measurement data is described in Section IV. Results are compared in Section V. Finally, we derive our conclusions.

978-1-4673-6337-2/13/$31.00 ©2013 IEEE

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Antenna arrays consist of the same quadratic patch element fed from two different points so that horizontally and vertically polarized signals are transmitted from the same patch, see [5]. The design was made so that radiation efficiency was maximal in a 3 dB bandwidth of 100 MHz around 2.53 GHz. Our base station array (Fig. 1 top left) consists of a 10x4 matrix of patches at λ2 spacing in vacuum. Always 4 elements in 8 central columns are co-phased using a 1x4 power divider, yielding more directive vertical characteristics. Horizontal characteristics has half-power beam width (HPBW) around 90◦ , see Fig. 1 right. Elements in the two outer columns are connected to ground via 50 Ω. Coupling between the elements is -18 dB in E-plane and -24 dB in H-plane. Antenna ports can be switched onto the transmitter output using a custommade high-power 1x16 pin-diode switch passing through up to 10 W power to the active antenna port. All antenna ports are connected to ground via 50 Ω in receive direction using a circulator. Altogether, our base station array can be considered as a cross-polarized 8x1 uniform linear array (ULA) with a typical radiation characteristics of a small-cell sector antenna. Our mobile terminal antenna (Fig. 1 top center) consists of two parts. In the lower part, there is a large cross-polarized 2x12 uniform circular array (UCA) with 48 antenna ports. On top, we placed a smaller cube with with 5 cross-polarized patch elements, i.e. 10 antenna ports. The two rings in the UCA enable estimation of the DoA both in azimuth and elevation. All antenna ports can be switched onto the receiver path using a low-power 1x64 pin-diode switch. If we ignore the minor difference in height, the same channel is tested twice at the same location and in the same switching sequence using the large antenna array and the small cube. In this way, double-directional channel parameters and MIMO properties representing a small mobile terminal can be tested jointly. The terminal is moved on two rails at low speed of 6 cm/s due the 16·58=928 possible antenna port combinations 1 . Low speed is required for phase correction and noise reduction by averaging over multiple snapshots, see [5]. Our test signal has 6.4 μs duration followed by a pause of same length used for switching between antenna ports. A chirp sequence is formed with nearly constant envelope using 129 sub-carriers in 20 MHz bandwidth, see Fig. 2. It enables us to drive the power amplifier 2 dB below the point with is checked using correlation between consecutive snapshots.

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negligible distortion (1 dB compression). We measured the complex-valued azimuth and elevation patterns of all transmit and receive elements in an anechoic chamber (Fig. 1, bottom) needed for high-resolution parameter extraction. Position and orientation of antennas during field measurements were noted to identify major propagation paths in the scenarios. Terminal position on rails was recorded using a distometer. III. S CENARIOS Since mobility was limited, we focused on two specific case studies in a dense urban environment representing exemplary LOS and NLOS scenarios. Local small-scale fading statistics were captured by moving the terminal along the rails. In the LOS scenario in Fig. 4, the base station antenna was placed on top of the Telefunken Tower at Ernst-ReuterPlatz in Berlin at 83 m height. The array was placed near the rooftop edge facing Strasse des 17. Juni and rotated by ±60◦ emulating the forward sectors. Azimuth of departure is measured with respect to the main lobe direction of the antenna. The reverse sector antenna was directed to 270◦ at the other side of the building. Downtilt was not used. The terminal was placed on Strasse des 17. Juni moving perpendicular to the LOS. The reference direction of the terminal antenna is indicated by 01 and a green arrow in Fig. 4. In this way, DoDs and DoAs of multi-path components can be embedded into the scenarios. In the NLOS scenario, the base station antenna was placed on the rooftop of the HHI tower at 63 m height pointing to 120◦ with respect to the north direction. The terminal was moved perpendicular to a campus road between the high-rise E and EN buildings of the Elektrotechnik department. The LOS was blocked at any point on the track. The reference direction of the terminal antenna is indicated in Fig. 4, right. IV. E VALUATION A. Parameter Estimation using RIMAX For estimating the physical propagation parameters, we used a maximum-likelihood based approach. A common technique is the SAGE algorithm adapted to radio channels in [8]. A generic model of multi-path propagation is used, for which the routine estimates all parameters of each multi-path component by minimizing the mean-square error between the model and the measured data. The approach was further developed in [9–12] where computational complexity was reduced and a

distinction between specular and dense (i.e. diffusely scattered) multi-path components was made. Insights into the physical nature of multi-path propagation in our scenarios rely on the implementation of the RIMAX algorithm used by MEDAV GmbH and TU Ilmenau in the project EASY-C [13] yielding a path-wise representation of our measurement data. For each multi-path, four complexvalued path gains γhh , γhv , γvh and γvv between vertically and horizontally oriented antennas, delay, azimuth angle of departure φT and azimuth and co-elevation angles of arrival φR and θR were estimated for 100 consecutive snapshots in each scenario, see Fig. 3. B. Singular values and MIMO capacity MIMO channel properties are measured for the link between the cross-polarized 1x8 ULA and the small additional cube antenna with 5 patches yielding a 10x16 MIMO channel. Evaluation of singular values and MIMO capacity follows the detailed description available in [5]. We considered the same 100 snapshots plus 100 each before and after the snapshots used by RIMAX for estimating the path parameters. Due to slow motion on the rails, the long coherence time enabled averaging the channel over 20 snapshots before computing singular values and capacity. In this way, we reached signal to noise ratio (SNR) gains up to 13 dB after phase correction, see [5]. Next we perform a singular value decomposition (SVD) [14] on each frequency bin n as Hn = Un Dn VnH

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where Un and Vn are unitary transform matrices and the matrix Dn contains the singular values λn,i > 0 on the main diagonal where i = 1...min(nr , nt ) and nr and nt are the numbers of receivers and transmitters, respectively. The statistics of singular values cover 129 frequency bins and 30 averaged channels recorded in time. Next we used N min(n r,  1  C= N n=1 i=1

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Our objective is to highlight the relation between the multipath structure of the mobile radio channel and the achievable capacity when using multiple transmit and multiple receive antennas. Due to the complex processing when using the RIMAX algorithm and since averaging is needed to reduce noise and the capacity error likewise, our comparison is conducted for a local set of channels, i.e. results do not cover a full channel statistics.

V. R ESULTS A. Identification of multi-path components In a first step, we estimated the major multi-path components by using the RIMAX algorithm. Great care was taken to reconstruct the geometry of the most important paths based on the underlying propagation environment, see Fig. 4. Multipaths have been marked by arrows in the campus map and and the numbers correspond to their relevance. 1) BS2 Sector 1 LOS: At first, we considered a strong LOS scenario where the base station antenna was fixed on the high-rise Telefunken building. The terminal was placed near a parking lot north from a six-lane road in the metropolitan area of Berlin surrounded by buildings of the Technical University with rooftop heights between 35 and 50 m. The terminal was moved perpendicular to the LOS to capture the local fading statistics. Dominant multi-paths are estimated with respect to power, azimuth of departure as well as azimuth and elevation of arrival in Fig. 5. We resolve the LOS path denoted as 1 in Fig. 5 left having shortest delay and around 20 dB more power than other signals. Note that RIMAX assigns around 10 sub-paths with path gain between -100 and -115 dB to the LOS, which altogether are more intense than all other scattering signals identified. At the terminal, these signals are received at an azimuth around 0◦ (pointing to the west) and from two elevations around 90◦ (corresponding to horizontal) attributed to direct and ground wave reflected from the street. At significantly lower power level and roughly at the same delay as for the LOS, we observe local scattering due to other antenna poles and the balustrade on the rooftop being one story below the transmitter in the field of view (FOV) of the base station antenna. Around the receiver, there is almost isotropic local scattering. The paths group 2 in Fig. 5 left is due to cars on the parking lot. More contributions come from cars in the back of the antenna around 180◦ . There is a wide spread of elevation of arrival, probably due to the more than 2 m antenna height and an array of bicycle stands nearby the receiver. Further multi-paths 3−6 in Fig. 5 are identified more than 30 dB below the LOS signal. 2) BS2 Sector 2 LOS: This is a rather unusual scenario in the back of a sector. It is included here since it illuminates what can happen on real base station sites. While there is minor signal at 0◦ azimuth, i.e. in opposite direction to the receiver, two strong paths around 70◦ and 75◦ azimuth are denoted as 1 in Fig. 5 center. Our sector antenna was located close to rooftop edge where two antenna poles at the same height were fixed acting as backscatters here. Moreover, there is an isotropic scattering floor at the transmitter denoted as 2 in Fig. 5 center similarly as in the previous scenario. The receiver observes the two dominant signals 1 at the same azimuth indicating that scattering is localized few meters around the transmitter also confirmed by the short delay. In elevation, the signal is split into direct and ground wave. RIMAX detects further multi-path groups 3 − 4 in Fig. 5 center at more delay and less power.

Figure 4. Scenarios and identified multi-path signals. Left top: LOS BS2 Sector 1, Left bottom: LOS BS2 Sector 2, Right: NLOS BS1 Sector 3. Numbers for each signal correspond to those marked in the RIMAX result in Fig. 5. Small blue arrows indicate the move of the terminal. The green arrow points to zero degrees azimuth of arrival.

Figure 5. Parameters estimated for each multi-path component. Left: LOS BS2 Sector 1, Center: LOS BS2 Sector 2, Right: NLOS BS1 Sector 3. Note that RIMAX extracts co-elevation at the terminal, i.e. we need to subtract the results in the graph from 90◦ to obtain elevation. Fore example, 90◦ co-elevation given in the figures corresponds to 0◦ elevation.

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Figure 6. Distributions of ordered singular values for measured 10x16 MIMO channels (using linear units) for the same scenarios investigated in Figs. 4 and 5. The dashed curves in the NLOS scenario are the statistics of singular values of the i.i.d. Rayleigh fading channel with the same numbers of antennas.

3) BS1 Sector 3 NLOS: For the NLOS scenario, we had to select another base station site since the power supply of a receiver switch was disconnected after moving the position. This was identified by the preprocessing. In the NLOS scenario, we observe three strong groups of multi-path separated by their delay denoted as 1 to 3 in Fig. 5 right. While the 1 is the direct signal bounced once at the EN building, 2 and 3 are assigned to a back-bounce at the main building of the TU Berlin and a second forward-bounce at the EN building yielding 2. A third back-bounce at the bridge between the EN and E buildings yields 3. This assignment becomes clear from the receiver azimuth and delays, where both signals are separated by around 180◦ while 3 arrives little later. Notice that these feeder bounces create diffuse scattering between the E and EN buildings having significant spread in the delay, azimuth and elevation domains. The power of diffuse multi-paths is substantially lower compared to the feeder bounces 1 to 3 in Fig. 5 right. In the NLOS scenario, we resolve few strong multi-paths. But since the terminal is placed in the corridor between two high-rise buildings, the number of paths actually reaching the shaded terminal location with enough power is rather limited. Therefore, few specular paths are dominant in the scenario and have well-distinguished delay, DoD and DoA parameters. Clearly, our NLOS scenario is characterized by limited specular scattering. B. Singular values and capacities In Fig. 6, we show the statistics of the 10 singular values of the 10x16 MIMO link for all scenarios. In both LOS scenarios, we observe two dominant singular values attributed to polarization, see [5]. Results from sector 3 not reproduced here confirm that a fundamental model assumption made in [16] were correct, i.e. that main path parameters in adjacent sectors are related to each other, see also [17]. The interesting observation is that, even in the back of a sector, the link is rank-deficient. This is explained by the observations noted above that the angular spread at the receiver is very small, despite backscattering by other equipment on the same rooftop. Our NLOS scenario has a wider spread of singular values typical for increased scattering. For comparison, we plotted the singular value statistics of a random i.i.d. 10x16 MIMO

channel as dashed lines. We can clearly observe that the limited specular scattering in our NLOS scenario implies significant deviations from the i.i.d. model. In particular, the largest singular value is higher and the smallest four values are smaller than expected and they may be due to the noise. Counting the spatial degrees of freedom in this way, up to 6 data channels of different quality may be transmitted in parallel over our NLOS link. They are attributed to the 3 specular multi-paths identified by RIMAX each carrying horizontal and vertical polarization. Obviously, specular bounces are most relevant for the degrees of freedom if they hit the receiver while diffuse scattering is not contributing as much. The limited number of multi-path in our LOS and NLOS scenarios are also reflected in the resulting capacities shown in Fig. 7, which are significantly reduced compared to the i.i.d. Rayleigh fading model. C. Discussion Earlier findings indicate that small urban macro-cells have an increased probability that the LOS is free [4]. This implies reduced degrees of freedom for MIMO observed in [5]. The comparison between the double-directional channel parameter estimation and the analysis of the corresponding MIMO properties in the present paper provide more insights into the origins of the achievable capacities in small urban macrocells. Our results suggest that in small urban macro-cells, besides polarization of the LOS [18], a very limited number of specular multi-paths are most relevant. These are the few specular feeder paths resolved separately as dominant paths by RIMAX. In addition, each such feeder path is likely to create diffuse isotropic scattering around the terminal resolved by RIMAX as a large number of weak specular components arriving little later at significantly less power. The distinction between specular and diffuse scattering is common practice in the literature about double-directional channel parameter estimation [11–13]. However, in the spatial channel model [19], scattering is modeled by splitting a major reflected path into several sub-paths, having equal amplitudes but slightly different DoAs, while the isotopic diffuse scattering is not considered so far. We believe that by modeling our observations in an appropriate manner, we can reproduce rank-deficient MIMO channels often observed in small cell scenarios more precisely.

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scenario, we observed that few specular paths are important, besides diffuse local scattering. We discussed implications on the channel model and that large arrays may be more efficient in large cells. Massive MIMO might be useful to unlock the potential of higher carrier frequencies in future mobile networks beyond 2020.

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ACKNOWLEDGMENTS This research was supported by German Federal Ministry for Education and Research in the collaborative research project EASY-C under grant No. 01BU0631.

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Figure 7. Comparison of 10x16 MIMO capacity statistics measured in the same scenarios investigated in Figs. 4, 5 and 6 compared to the i.i.d. Rayleigh fading channel.

Our observations can be implemented in the spatial channel model as follows. At first, we model the number of clusters yielding nearly specular paths as a small random number L following a distance-dependent statistics so that there is only one specular path if d → 0 and few more at larger distance. Empirical results on that statistics can be obtained from available data if we investigate the average number of relevant specular paths as a function of distance. This remains as an open issue for future research. Moreover, we propose that the distinction between specular and diffuse scattering is also made in the spatial channel model. Now we come back to the application of large antenna arrays in future mobile networks. Large arrays are identified as promising tools for increasing the capacity of mobile networks by orders of magnitude during the next decade [1–3]. The smaller the cells are, however, the more likely users are alone, i.e. spatial multiplexing with other users (multiuser MIMO) is less effective. Moreover, spatial degrees of freedom become limited due to more specular scattering. More antenna elements may not add more spatial degrees of freedom in small cells. More transmission points placed around the terminal (i.e. other small cells) may be better than one big array. On the other hand, at higher carrier frequency, more antenna elements can be hosted in the same panel size also in wide-area macro-cells. If we assume that more antenna elements occupy the same area at higher frequencies compared to fewer antenna elements at lower frequencies, the overall path loss in the up-link becomes fairly independent on the carrier frequency. Hence, by coherently combining the received signals at the large antenna array, we can unlock the potential of higher carrier frequencies for mobile communications. C ONCLUSIONS In this paper, we compared the double-directional structure of the wireless channel and its potential for spatial multiplexing. We confirmed that the contribution of local scattering is negligible in LOS links and that not more than two degrees of freedom are available due to polarization. In a NLOS

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