3GPP 3D MIMO channel model: a holistic implementation guideline for open source simulation tools
- Fjolla Ademaj^{1}Email author,
- Martin Taranetz^{1} and
- Markus Rupp^{1}
https://doi.org/10.1186/s13638-016-0549-9
© Ademaj et al. 2016
Received: 14 August 2015
Accepted: 4 February 2016
Published: 19 February 2016
Abstract
Massive MIMO and 3D beamforming have been identified as key technologies for future mobile cellular networks. Their investigation requires channel models that consider not only the azimuth- but also the elevation direction. Recently, the 3rd Generation Partnership Project (3GPP) has released a new 3D spatial channel model. It supports planar antenna arrays and enables to scrutinize concepts such as elevation beamforming and full dimension MIMO. A particular challenge is the practical implementation of the model. Dealing with enormous computational complexity requires to design a highly efficient approach. This paper provides a guideline for the practical implementation of the 3GPP 3D model into existing link- and system-level simulation tools. Considering the complexity of the model itself, our main focus is on computational efficiency. We present simulation examples using the proposed procedure with the Vienna LTE-A Downlink System Level Simulator. We measure simulation run times with respect to various network parameters. Our results allow to quantify the increase in complexity, when accounting for the elevation dimension. Moreover, they exhibit general trends when considering a large number of antenna elements per antenna array. We also draw a comparison with the WINNER channel model, which represents the most closely related channel model in 2D.
Keywords
1 Introduction
In the last decades, simulations have become a substantial tool for analyzing and designing wireless cellular communication systems. As the systems themselves are growing in complexity, the effort of simulations becomes tremendous. Thus, the challenge is to keep the computational costs at a minimum while preserving accuracy. A commonly employed solution is to divide the simulations into two stages or levels of abstraction, known as link-level and system-level [1]. Link-level simulations are used to assess the performance of the physical layer and those higher layer aspects directly related to the radio interface. Mostly, only a single radio link is evaluated, rarely some few users. System level simulations, on the other hand, aim to evaluate the performance of a whole network comprising a substantial number of Evolved Node B (eNodeB) sectors and user equipments (UEs) [2, 3]. At the UEs, both the signals received from the serving as well as the interfering eNodeB sectors are modeled, taking into account large- as well as small-scale fading effects. Realistic models for the small-scale effects, also known as channel models, impose a major challenge in describing wireless communications. Broadly speaking, channel models can be divided into two categories, deterministic and stochastic [4]. Deterministic models describe the channel for a specific propagation environment between eNodeB sector and UE. This method can be tedious to evaluate and does not allow for general statements in an ensemble of environments. In stochastic models, the channel characteristics are condensed to a statistical description, e.g., the power delay profile (PDP) [5–7].
In order to close the gap between the two approaches, the 3rd Generation Partnership Project (3GPP) has introduced the Spatial Channel Model SCM [8]. Unlike traditional channel models, it incorporates not only a random PDP but also a random angular profile (AP). The model represents scatterers through statistical parameters without having a real physical location. The SCM belongs to the class of geometric stochastic model and separately defines large-scale parameters (e.g., shadow fading, delay spread, and angular spreads) and small-scale parameters (e.g., delays, cluster powers, and arrival- and departure angles). Both parameter sets are randomly drawn from tabulated distributions. The large-scale parameters encompass the geometric positions of the eNodeB sectors and the UEs, respectively. Moreover, they are used to parameterize the statistics of the small scale parameters. The SCM model in [8] includes six different scenarios, each of them representing a unique environment. Initially, it was targeted for a bandwidth of 5 MHz and a carrier frequency of 2 GHz. Later, it was extended to the Spatial Channel Model Extended (SCME). The SCME follows the same procedure as the SCM, but supports bandwidths of up to 100 MHz and a frequency range of 2−6 GHz. In the course of the Wireless World Initiative New Radio (WINNER) projects, the model was extended for 15 different scenarios [9, 10], including urban-, rural-, and moving environments. The WINNER model is recommended as a baseline for evaluating radio interface technologies in the International Telecommunication Union - Radiocommunication Sector (ITU-R) [11].
The interest in 3-dimensional (3D) beamforming is greatly increasing in industry and standardization consortia, enabling concepts such as full dimension (FD)-multiple input multiple output (MIMO) and vertical sectorization [12, 13]. Consequently, describing channel characteristics in three dimensions, including both azimuth- and elevation angles is becoming indispensable. Recently, 3GPP introduced a new 3D SCM for Long Term Evolution-Advanced (LTE-A) in their recommendation TR 36.873 [14].
As of this writing, only a few simulation studies, including reports from the 3GPP TSG RAN WG1 meetings, have been published, claiming the practical implementation of the model [15, 16]. In [17], we have introduced the implementation and validation of the 3GPP 3D channel model in open source simulation tools, considering only the desired signal channels, while the interfering channels are modeled by Rayleigh fading. In this contribution, we extend our approach considering also the interfering links to fade according to the 3GPP 3D channel model. We provide a complete guideline for the practical implementation of the model. The MATLAB source code is openly available for download on our webpage under an academic, non commercial use license [18]. It is provided as a stand-alone package that is directly applicable for system level simulation tools and can straightforwardly be ported to link level. We strongly believe that open access is a key prerequisite for reproducible simulation studies. Moreover, we have made an iteration of the model openly available, with over 100 beta testers and an active online forum. We see it as the only way to ensure the quality of implementation. In this paper, we focus on downlink. According to [14], the channel can be applied for both up- and downlink. For this reason, the notions transmitter and receiver interchangeably refer to the antenna elements of the eNodeB sectors and the UEs, respectively. In practice, eNodeB sectors and UEs will be equipped with antenna arrays, each consisting of one or more antenna elements (conf. Fig. 2). Note that an eNodeB comprises a base band processing unit and can serve multiple sectors or cells.
This contribution outlines as follows. A brief description of the 3GPP 3D channel model is provided in the beginning of Section 2, followed by a guideline for its computationally efficient implementation. In Section 3, the implementation is validated against results from the 3GPP standard with the Vienna LTE-A System Level Simulator. Moreover, simulation run time measurements are provided with respect to various parameters that determine the network complexity. We also compare the 3GPP 3D model with the WINNER channel model. Section 4 outlines challenges and new opportunities for investigations. Section 5 concludes the work.
2 3GPP 3D channel model in system level simulator
2.1 3GPP 3D channel model
The 3GPP 3D channel model characterizes wireless communication channels of typical European cities. It is a 3D geometric stochastic model, describing the scattering environment between eNodeB sector and UE in both azimuth and elevation dimensions. The scatterers are represented by statistical parameters without having a real physical location. In 3GPP TR 36.873 [14], three scenarios, urban macro cell (UMa), urban micro cell (UMi), and UMa-high rise (UMa-H) are specified. They represent typical urban macro-cell and micro-cell environments. Both UMa and UMa-H scenarios, consider an sector antenna height of 25 m, thus surpassing the surrounding buildings. UMa-H also specifies such environments with one high-rise building per eNodeB sector. UMi, considers a sector antenna height of 10 m, lying below the rooftop level. All three environments are assumed to be densely populated with buildings and take into account both indoor- and outdoor UEs.
The 3GPP 3D channel model specifies three propagation conditions, line-of-sight (LOS), non line-of-sight (NLOS) and outdoor-to-indoor (O-to-I). For each of these conditions, it defines different parameters for mean propagation path loss, macroscopic fading, and microscopic fading. All three scenarios in [14], UMa, UMi, and UMa-H, consider 80 % of the UEs to be located indoors. The probability of being in LOS is determined separately for indoor and outdoor UEs and depends on the height of the UE as well as the break point distance. The break point distance characterizes the gap between transmitter and receiver at which the Fresnel zone is barely broken for the first time [19]. For an indoor UE, LOS refers to the signal propagation outside the building in which the UE is located. For each UE location, large-scale parameters are generated according to its geographic position as well as the propagation conditions at this location. The large scale parameters incorporate shadow fading, the Ricean K-factor (only in the LOS case), delay spread, azimuth angle spread of departure- and arrival, as well as zenith angle spread of departure- and arrival.
where p ε P and q ε Q. The terms P and d _{ H } denote the number of antenna elements and the element spacing in the horizontal direction, while Q and d _{ V } are the number of antenna elements and the element spacing in the vertical direction, respectively. The last component of (1), v _{ n,m }, represents the Doppler frequency component of the UE moving at velocity \(\bar {v}\). Further details on the calculation of the variables in (1) can be referred from [14].
2.2 Antenna modeling
The 3GPP 3D channel model enables to scrutinize 2-dimensional (2D) planar antenna arrays, also known as rectangular arrays. The antenna elements can either be linearly polarized (co-pol) or cross prolarized (cross-pol), as shown in Fig. 2. In this regard, the model represents a compromise between practicality and precision as it does not include the mutual coupling effect as well as different propagation effects of horizontally and vertically polarized waves. Our well-structured implementation will substantially facilitate the implementation of further techniques for modeling different polarization modes such as the one proposed in [20].
where \([\mathbf {H}^{\mathrm {c}}_{\textit {i,n}}(t)]_{\textit {a,b}}\) represents the weighted and combined channel coefficients. The index i indicates the eNodeB sectors, where i=0 denotes the serving sectors, while the indices i={1,2,…} refer to the interfering sectors. The terms \({\mathcal {P}}_{a}\) and \({\mathcal {P}}_{b}\) denote the sets of antenna elements that belong to receive antenna port a with a∈{1,…,N _{Rx}} and transmit antenna port b with b∈{1,…,N _{Tx}}, respectively. The terms ω _{ u } and ω _{ s } are complex weights that account for phase shifts as applied for static beamforming (e.g., electrical downtilting), respectively. The relative position of each element in the array is incorporated in the channel coefficients H _{ u,s,n }(t), where n denotes the cluster index, s and u are the eNodeB sector and UE antenna elements, respectively.
In the following, a detailed procedure on the implementation of the model for simulations is provided.
2.3 Implementation in system-level
In this section, we describe the necessary steps to integrate the 3D channel model into an existing simulation tool. The target is to compute a N _{Rx}×N _{Tx} MIMO-channel matrix H(t,f) for each sampling point on the time-frequency grid, where N _{Tx} and N _{Rx} refer to the number of transmit- and receive antenna ports, respectively. On link level, channel realizations are typically calculated per OFDM symbol and LTE-A subcarrier [21]. On system level, they are commonly generated per physical resource block (RB) and transmission time interval (TTI) [22].
where the serving eNodeB sector is denoted by index 0 and the interfering eNodeB sectors are denoted by the indices i={1,…,I}. In case the UE is not in LOS of BS i, δ _{ i,K}=0. These tasks can be performed off-line, i.e., before entering the actual simulation loop. Moreover, they can be carried out simultaneously for serving- and interfering eNodeB tors, allowing to employ, e.g., MATLAB’s parallel computing toolbox. Similar to the generation of the shadow fading, they have to be performed only once per site.
[SSP] _{ i } The next step is to generate small-scale parameters for desired and interfering signals. In the 3GPP 3D channel model, channel coefficients H _{ i,u,s,n }(t) are determined individually for each eNodeB sector i, each cluster n, and each receiver- and transmitter antenna element pair {u,s}, respectively. Similar to the implementation in [17], the calculation of H _{ i,u,s,n }(t) requires to generate delays (Step 5), cluster powers (Step 6) as well as arrival- and departure angles for both azimuth and elevation (Step 7). After coupling the rays within a cluster (Step 8), cross polarization power ratios (XPRs), and random initial phases are drawn (Step 9 and 10). Together with the calculation of the spherical unit vectors and the Doppler frequency component (both Step 11), all parameters mentioned above are commonly applied to each antenna element pair {u,s} and thus have to be determined only once per antenna array and eNodeB sector. The Doppler component accounts for the time variance of the channel. The frequency selectivity is determined by the channel impulse response H _{ i,u,s,n }(t) and the sampling frequency, which is directly related to the system bandwidth.
where, k=0,1,…,N−1. The term N represents the number of FFT samples which is the maximum number of delay taps m. For example, assuming a transmission bandwidth of 10 MHz, according to [23], the sampling interval is T _{ s }=65 ns and the number of FFT samples is N=1024.
3 Simulation run times and throughput performance evaluation
3.1 Calibration
Simulation parameters for calibration as referred from [14]
Parameter | Value |
---|---|
Carrier frequency | 2 GHz |
LTE bandwidth | 10 MHz |
Macro-site deployment | Hexagonal grid |
Scenarios | 3D-UMa, 3D-UMi |
Sector antenna height (UMa) | 25 m |
Sector antenna height (UMi) | 10 m |
Sector antenna configuration | N _{Tx}=4 |
UE antenna configuration | N _{Rx}=2 |
Polarized antenna modeling | Model 2 [14] |
Sector antenna polarization | X-pol (+/−45°) |
UE antenna polarization | X-pol (0/+90°) |
Antenna elements per port | M=10 |
Vertical antenna element spacing | 0.5λ |
Horizontal antenna element spacing | 0.5λ |
Maximum antenna element gain | 8 dBi |
UE antenna pattern | Isotropic antenna gain |
Electrical downtilt | 12° |
UE distribution | Uniform in cell ([14] Tab. 6-1) |
3.2 Simulation run times
In this section, we measure the simulation run times of the 3GPP 3D channel model in the Vienna LTE-A Downlink System Level Simulator. The goal is to observe how the 3GPP 3D channel model affects the simulation run time. Note that applying this model does not alter the signal processing part of the simulation tool. For a fair comparison, all simulations were carried out on the same hardware, an Intel(R) Core(TM) i7-3930K CPU@3.20 GHz, equipped with 32 GB of DDR3 1333 quad-channel RAM.
Simulation setup
Parameter | Value |
---|---|
Carrier frequency | 2 GHz |
LTE bandwidth | 10 MHz |
Macro-site deployment | hexagonal grid, one tier |
Interfering eNodeB sectors | N _{sector}={2,8,14,20} |
Number of UEs per cell | K={2,20,50} |
Antenna elements per antenna array | M={8,24,40,80} |
Antenna elements per antenna port | Q={2,6,10,20} |
3GPP scenario | 3D-UMa |
Inter-site distance | 500 m |
eNodeB transmit power | 46 dBm |
Antenna element gain pattern | 3D pattern ([14] Tab. 7.1-1) |
Antenna polarization | co-pol |
Polarized antenna modeling | model 2 ([14] Sec. 7.1.1) |
Maximum antenna element gain | 8 dBi |
Vertical antenna element spacing | λ/2 |
Horizontal antenna element spacing | λ/2 |
UE distribution | uniform |
UE speed | 3 km/h |
UE antenna gain pattern | omni-directional |
UE antenna array polarization | co-pol |
Wrapping method | center UEs evaluated |
Receiver type | zero forcing |
Channel knowledge | perfect |
Feedback delay | 3 TTI |
Noise power density | −174 dBm/Hz |
LTE transmission mode | 4 |
Scheduler | proportional fair |
Traffic model | full buffer |
Simulation length | N _{TTI}={10,50,100} |
3.3 Throughput performance evaluation
In this section, the impact of modeling both the desired as well as the interfering channels with the 3GPP 3D channel model is scrutinized. We consider a network with seven macro-sites, each employing three eNodeB sectors, and simulate 50 randomly distributed UEs per eNodeB sector. The simulation parameters are summarized in Table 2.
3.3.1 Rayleigh versus 3GPP 3D model
3.3.2 2D- versus 3D channel modeling
4 New opportunities and challenges
The integration of the 3D channel model into existing link- and system-level simulation tools paves the way for more advanced studies on the performance of a mobile cellular system in realistic environments. Existing channel models only support linear antenna arrays in the azimuth. With the introduction of the third dimension, not only higher-order MIMO schemes, but also a higher number of antenna elements per antenna array can be investigated. Currently, the 3GPP LTE-A standard supports up to eight antenna ports. However, recent trends aim at 100 and more antenna ports per eNodeB sector [31]. A main enabler for this so called massive MIMO approach will be the adoption of higher carrier frequencies, also termed millimeter-wave communication, as it enables to considerably decrease the size of the antenna arrays. On the one hand, this may lead to higher complexity of the hardware, larger energy consumption and a greater demand for signal processing capabilities. On the other hand, it will enable a much more accurate bundling of energy towards the intended receiver, which is a key prerequisite for aggressive frequency reuse. In dense urban environments, where UEs move in three dimension (consider, e.g., shopping malls, skyscrapers, and more), it is conceivable that the spectral efficiency per unit sphere might replace the area spectral efficiency as a figure of merit. Other important use cases are scenarios with high user mobility, as the number of commuters is expected to increase substantially. People have become used to services following them wherever they travel. Mobile cellular access has even become a key argument to choose the means of transportation. Sharp, steerable beams might be an expedient solution to this issue, as they could follow a vehicle along its path.
Improvements targeting planar antenna arrays are to be further investigated. New virtualization models of antenna arrays, considering a full-connection between antenna elements, weighted in both horizontal-and vertical directions will lead to a better understanding of the 3D beamforming. Moreover, new two-dimensional codebook designs are necessary for the evaluation of FD-MIMO.
5 Conclusions
This work presented a guideline for the practical implementation of the 3GPP 3D channel model into existing link-and system level simulation tools. In comparison to previous work in [17], we faced the challenge of calculating the channel coefficients at simulation runtime for both desired- and interfering channels by carefully partitioning the step-wise procedure as proposed by 3GPP. We demonstrated the behaviour of the 3GPP 3D model in terms of simulation run time. A comparison against the WINNER channel model indicates that the incorporation of the elevation dimension increases the computational complexity by more than three times. Furthermore, we observed that the complexity grows roughly linearly with the number of antenna elements per antenna array. Hence, it may become one of the dominant factors that affects the simulation run time in future massive MIMO scenarios. We showed that, compared to Rayleigh fading interference channels, as applied in [17], when the interfering channels are abstracted by the 3GPP 3D channel model, a more optimistic view on the performance is obtained. This result indicates that more simple channel models may underestimate the achievable performance. Next, we compared linear against planar antenna arrays. Remarkably, taking into account a planar antenna array results in performance degradation. This result indicates, that the beams might not be as sharp as largely envisioned. A systematic evaluation of this behavior is left for further work. The paper is completed by an elaboration on new opportunities that became possible with the 3D channel model, and the challenges ahead to realize the full potential of the upcoming new technologies. Our implementation approach is openly accessible, and our hope is to inspire researches and developers of link- and system level simulation tools to further elaborate and develop these topics by applying it.
Declarations
Acknowledgments
This work has been funded by A1 Telekom Austria AG, and the KATHREIN-Werke KG. The financial support by the Federal Ministry of Economy, Family and Youth and the National Foundation for Research, Technology and Development is gratefully acknowledged.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
- S Ahmadi, LTE-Advanced: a practical systems approach to understanding 3GPP LTE releases 10 and 11 radio access technologies (ITPro collection, Elsevier Science, 2013).Google Scholar
- J Ikuno, M Wrulich, M Rupp, in Vehicular Technology Conference (VTC 2010-Spring). System level simulation of LTE networks, (2010), pp. 1–5. doi:n10.1109/VETECS.2010.5494007.View ArticleGoogle Scholar
- A Rodriguez-Herrera, S Mcbeath, D Pinckley, D Reed, in IEEE 62nd Vehicular Technology Conference, VTC-2005-Fall, 3. Link-to-system mapping techniques using a spatial channel model, (2005), pp. 1868–1871. doi:10.1109/VETECF.2005.1558430.Google Scholar
- P Matthias, Mobile fading channels (John Wiley and Sons, Inc., New York, NY, USA, 2002).Google Scholar
- J Parsons, The mobile radio propagation channel, 2nd edn. (John Wiley and Sons, Inc., New York, NY, USA, 2000).View ArticleGoogle Scholar
- P Almers, E Bonek, A Burr, N Czink, M Debbah, V Degli-Esposti, H Hofstetter, P Kyosti, D Laurenson, G Matz, A Molisch, C Oesteges, H Ozcelik, Survey of channel and radio propagation models for wireless MIMO systems. EURASIP J. Wireless Commun. Networks (2007). doi:10.1155/2007/19070.
- A Paulraj, R Nabar, D Gore, Introduction to space-time wireless communications (Cambridge University Press, 2003).Google Scholar
- 3GPP TR36.996, Spatial channel model for multiple input multiple output (MIMO) simulations (3rd Generation Partnership Project (3GPP), 2003).Google Scholar
- WINNER I WP5, Final report on link level and system level channel models. IST-2003-507581 WINNER I Deliverable D5.4 (2005). http://www.ist-winner.org/phase_model.html.
- WINNER II WP1, WINNER II channel models. IST-4-027756 WINNER II Deliverable D1.1.2 (2007) http://www.ist-winner.org/phase_2_model.html.
- ITU-R and M.2135, Guidelines for evaluation of radio interface technologies for IMT-Advanced. Report (2009). https://www.itu.int/dms_pub/itu-r/opb/rep/R-REP-M.2135-1-2009-PDF-E.pdf.
- E Larsson, O Edfors, F Tufvesson, T Marzetta, Massive MIMO for next generation wireless systems. IEEE Commun. Mag. 52(2), 186–195 (2014). doi:10.1109/MCOM.2014.6736761.View ArticleGoogle Scholar
- Y Song, X Yun, S Nagata, L Chen, in IEEE International Conference on Communications Workshops (ICC). Investigation on elevation beamforming for future LTE-Advanced, (2013), pp. 106–110. doi:10.1109/ICCW.2013.6649210.Google Scholar
- 3GPP TR36.873, Study on 3D channel model for LTE, v12.2.0 (3rd Generation Partnership Project (3GPP), 2014).Google Scholar
- A Kammoun, H Khanfir, Z Altman, M Debbah, M Kamoun, Preliminary results on 3D channel modeling: From theory to standardization. IEEE J. Selected Areas Commun.32(6), 1219–1229 (2014). doi:10.1109/JSAC.2014.2328152.View ArticleGoogle Scholar
- Z Hu, R Liu, S Kang, X Su, J Xu, in International Conference on Communications and Networking in China (CHINACOM). Work in progress: 3D beamforming methods with user-specific elevation beamfoming, (2014), pp. 383–386. doi:10.1109/CHINACOM.2014.7054323.Google Scholar
- F Ademaj, M Taranetz, M Rupp, Implementation, Validation and Application of the 3GPP 3D MIMO Channel Model in Open Source Simulation Tools. Paper presented at the Twelfth International Symposium on Wireless Communication Systems, ISWCS, 25-28 August 2015.Google Scholar
- Vienna LTE-A Simulators. http://www.nt.tuwien.ac.at/research/mobile-communications/vienna-lte-a-simulators/. Accessed 14 Aug 2015.
- H Masui, T Kobayashi, M Akaike, Microwave path-loss modeling in urban line-of-sight environments. IEEE J. Selected Areas Commun.20(6), 1151–1155 (2002). doi:10.1109/JSAC.2002.801215.View ArticleGoogle Scholar
- A Weber, A Bestard, in 8th International Symposium on Wireless Communication Systems (ISWCS), 2011. Modeling of X-pol antennas for LTE system simulation, (2011), pp. 221–225. doi:10.1109/ISWCS.2011.6125342.View ArticleGoogle Scholar
- S Schwarz, J Ikuno, M Simko, M Taranetz, Q Wang, M Rupp, Pushing the limits of LTE: A survey on research enhancing the standard. IEEE Access. 1:, 51–62 (2013). doi:10.1109/ACCESS.2013.2260371.View ArticleGoogle Scholar
- M Taranetz, T Blazek, T Kropfreiter, MK Müller, S Schwarz, M Rupp, Runtime precoding: enabling multipoint transmission in LTE-Advanced system-level simulations. IEEE Access. 3:, 725–736 (2015). doi:10.1109/ACCESS.2015.2437903.View ArticleGoogle Scholar
- 3GPP TS 36.201, LTE Physical Layer - General Description, v9.0.0 (3rd Generation Partnership Project (3GPP), 2009).Google Scholar
- Y Wang, J Xu, L Jiang, Challenges of system-level simulations and performance evaluation for 5G wireless networks. IEEE Access. 2:, 1553–1561 (2014). doi:10.1109/ACCESS.2014.2383833.View ArticleGoogle Scholar
- 3GPP 325.996, Spatial channel model for Multiple Input Multiple Output (MIMO) simulations, v12.0.0 (3rd Generation Partnership Project (3GPP), 2012).Google Scholar
- 3GPP TSG RAN WG-1 R1-140048, Phase 2 calibration results for 3D channel model. Meeting report, (2014).Google Scholar
- 3GPP TSG RAN WG-1 R1-143469, Summary of 3D-channel model calibration results. Meeting report, (2014).Google Scholar
- 3GPP TR36.897, Elevation Beamforming/Full-Dimension MIMO for LTE, v0.3.1 (3rd Generation Partnership Project (3GPP), 2015).Google Scholar
- L Hentila, P Kyosti, M Kaske, M Narandzic, M Alatossava, Matlab implementation of the winner phase II channel model ver1.1 (2007). http://projects.celtic-initiative.org/winner+/phase_2_model.html. Accessed Sep. 2008.
- O Bakr, M Johnson, R Mudumbai, U Madhow, in 47th Annual Allerton Conference on Communication, Control, and Computing Allerton. Interference suppression in the presence of quantization errors, (2009), pp. 1161–1168.Google Scholar
- F Rusek, D Persson, BK Lau, E Larsson, T Marzetta, O Edfors, F Tufvesson, Scaling up MIMO: Opportunities and challenges with very large arrays. IEEE Signal Process. Mag. 30(1), 40–60 (2013). doi:10.1109/MSP.2011.2178495.View ArticleGoogle Scholar