- Open Access
Performance of a dense urban massive MIMO network from a simulated ray-based channel
© The Author(s) 2019
- Received: 7 March 2019
- Accepted: 10 April 2019
- Published: 2 May 2019
Massive MIMO network deployments are expected to be a key feature of the upcoming 5G communication systems. Such networks are able to achieve a high level of channel quality and can simultaneously serve multiple users with the same resources. In this paper, realistic massive MIMO channels are evaluated both in single and multi-cell environments. The favorable propagation property is evaluated in the single-cell scenario and provides perspectives on the minimal criteria required to achieve such conditions. The dense multi-cell urban scenario provides a comparison between linear, planar, circular, and cylindrical arrays to evaluate a large-scale multi-cell massive MIMO network. The system-level performance is predicted using two different kinds of channel models. First, a ray-based deterministic tool is utilized in a real North American city environment. Second, an independent and identically distributed (i.i.d.) Rayleigh fading channel model is considered, as often used in previously published massive MIMO studies. The analysis is conducted in a 16-macro-cell network with both randomly distributed outdoor and indoor users. It is shown that the physical array properties like the shape and configuration have a large impact on the throughput statistics. Although the system-level performance with i.i.d. Rayleigh fading can be close to the deterministic prediction in some situations (e.g., with large linear arrays), significant differences are noticed when considering other types of arrays. The differences in the performance of the various arrays utilizing the exact same network parameters and the same number of total antenna elements provide insights into the selection of these physical parameters for upcoming 5G networks.
- Massive MIMO
- Channel modeling
- Ray-based model
- Performance evaluation
Massive MIMO (maMIMO) technology has been shown to provide the requirements set by the 5G standard in various studies and the literature. It helps to improve the spectral efficiency and utilize the available channel resources more efficiently. Although many operators and equipment manufacturers have today conducted controlled experiments to demonstrate the possible gains of this technology, large-scale deployments of the technology and its network-level performance in real scenarios is yet to be seen.
In this paper, a realistic ray-based propagation channel has been utilized to predict the performance of a dense urban maMIMO network with different settings. Such a study makes it possible to better understand and apply the technology in realistic environments, which can significantly differ from theoretical analysis. It also permits to properly anticipate the possible applications and gains, refine the systems, and prepare the deployment strategies. Single-cell analysis considering multiple simultaneous users [1, 2] in realistic environments only provides a partial perspective of the network performance. In this paper, a multi-cell network is deployed in a real and complex environment, which is precisely represented into 3D geographical data. A combination of both outdoor and indoor users is considered to best reflect realistic conditions, with indoor users distributed in different building floors. The obtained physical channels are then utilized to perform precise system-level simulations  leading to the assessment of the user throughput. The simulator implements state-of-the-art signal processing schemes, including transmit precoding and power allocation techniques. It supports multi-cell multi-user scenarios and computes inter- and intra-cell interferences. It can take any kind of MIMO channel data as an input, which made the interface with the ray-based channel model straightforward.
Similar to the current 4G macro base station (BS) sites, the maMIMO base stations are considered to be located on the rooftops of dominant buildings with roughly constant inter-site distance. In maMIMO systems, the number of antenna elements can be large as compared to the existing systems, and this permits the possibility of utilizing different antenna shapes like linear, planar, circular, and cylindrical arrays. Those different shapes are considered in this study to evaluate how the performance of the network changes while all other inputs are constant. The same approach can further be applied to different complex networks with varying inter-site distances (ISD), sectorization, and even complemented with a dense small-cell network, in order to determine the best deployment strategy for given objectives into a particular environment. These complex network changes are out of scope of the presented study. The paper also explores how the chosen channel model impacts the estimated maMIMO performance. The throughputs that have derived from the ray-based channel environments are drawn against those of a basic statistical model, as often used in the evaluation studies.
The large number of BS antennas of a maMIMO system allows for large spatial degrees of freedom to serve multiple users in the same time-frequency resource. It actually contributes towards two key maMIMO physical properties known as favorable propagation and channel hardening as described in  and , respectively. Together, these properties should enable a maMIMO system to spatially separate all the simultaneous users  (even if closely located) and provide stable stationary channel conditions, even with small user movements. These conditions are satisfied when very large arrays are considered. But in reality, the array size of a maMIMO system is limited, although large. Especially, when considering 3D arrays like cylindrical arrays, the aperture of the antenna array is limited as compared to a linear array. With these physical limitations, it is important to assess and demonstrate the performance of practical maMIMO systems in real propagation conditions.
The performance of the maMIMO system depends on the cross-correlation between channels, either the multiple channels from all array elements to a single user or the channels from one base station to the simultaneous users (that may cause mutual interference) . For accurate predictions, this requires the channel models to be spatially consistent, i.e., to be able to reproduce variations and correlations between two antenna positions. Independent and identically distributed (i.i.d.) channel models do not support such spatial correlation and can therefore not accurately predict maMIMO channels. Some other models like geometry-based stochastic channel models (GSCM) create spatially correlated channels, thus might be appropriate; however, they are not able to manage the specificities of a particular physical environment . The ray-based deterministic channels also provide inherent correlation, due to the computation of the physical wave propagation and interactions, but have the additional advantage that they can be run in real environments, using geographical map data. Therefore, they are relevant to assess various kinds of network topologies in a very accurate manner.
Section 2 describes briefly the system-level maMIMO simulator and its usage to obtain the rates that are achievable by the maMIMO system. Section 3 details the single-cell and multi-cell multi-user scenarios and setup, located in a North American dense urban area. Section 4 studies the multi-cell maMIMO channel characteristics. Section 5 presents the evaluation of the single-cell study with regard to favorable propagation. Section 6 discusses the system-level maMIMO performance for different antenna array shapes and configurations along with different channel models. Finally, Section 7 provides some conclusions, perspectives, and future work to be conducted on maMIMO system-level studies, with 5G radio planning as an objective.
The first open-source system-level simulator for maMIMO systems was delivered as supplementary material to the book . This MATLAB simulator supports the state-of-the-art methods for channel estimation, receive combining, transmit precoding, and power allocation, as well as quantifying the corresponding achievable rates. While some of these methods are tailored for statistical channel models, with known first- and second-order moments, in this paper, we use methods that support any channel model. More precisely, we consider least-square channel estimation (under the presence of pilot contamination) and regularized zero-forcing (RZF) precoding. The power allocation is selected to maximize the product of the users’ effective SINRs, which is essentially the same as maximizing the sum rate, except that there is a “bias” towards giving higher rates to the most unfortunate users than they would get with pure sum-rate maximization (which could lead to zero rate for the weakest users). The rates presented in this paper are obtained for full-buffer transmission. We have modified the original simulator from  to support our setup, for example, by including BS user association.
In a maMIMO system, the number of simultaneous users is typically much smaller than the number of BS antennas, because there is a limited number of pilot sequences available for channel estimation. In this paper, we have considered a maximum of 20 active users that can be connected to any single BS simultaneously. If there are more users, then the system has the possibility to select and allocate some of them on different time slots or frequency sub-bands (maMIMO scheduling). Once a set of users is selected for simultaneous allocation, i.e., at the same time and frequency, the BS allocates 1 of the 20 pilots uniformly at random to the users. Each pilot is only used once per cell, but will be reused across cells, which leads to pilot contamination. The different propagation and interference conditions experienced by the users are partly mitigated by carefully attributing the powers.
To evaluate the performance of a maMIMO system, two different scenarios have been considered. A single-cell multiple simultaneous user environment is first evaluated for the minimum conditions similar to favorable propagation (FP) that can be achieved. Then, a multi-cell network of maMIMO macro BS is considered to evaluate the performance of the network considering signal processing schemes for different antenna array shapes. The first scenario provides insights into the minimum horizontal separation required for a maMIMO BS to be successfully able to differentiate between users. Whereas, the second scenario evaluates these results in a large-scale realistic maMIMO environment with 3D spatial distributions of the users.
The selected scenarios utilizes 3D geographic map data from New York City, which includes buildings of varying heights. The selected area contains various different geographic features like narrow and wide streets, open squares, and cross sections. This map data makes it possible to obtain realistic and highly variable channel predictions for the considered scenarios.
The objective of evaluating the network-level performance of a maMIMO system in real environments is to predict the maMIMO gains as accurately as possible. Such an approach also enables the comparison of physical parameters like different antenna shapes and their corresponding performance in the same network. Results in  and  suggest that the rate performance in many real propagation environments is comparable to the i.i.d. Rayleigh fading. Some explanations of the reason for this is given in . This is due to the favorable propagation and channel hardening properties of maMIMO, which appear as the number of antennas at the BS increase. In reality, the number of BS antennas are limited (far from infinity) and deployed in a limited amount of space, depending on the antenna configuration. This limits the ability of large antenna arrays to observe various channel components. This is demonstrated in this work by comparing several antenna sizes containing the same number of elements using a ray-based deterministic model.
The complex propagation environment creates rich multi-path components, which are predicted by the physical volcano urban ray-based model . These multi-paths affect the maMIMO performance, either by creating spatial separability of users located close to each other or, on the contrary, by producing cross-correlation between users reached by the same canyoning or diffracting phenomenon. The use of a physical channel model does intrinsically bring all correlation factors, between cells and users, which are required for accurate maMIMO assessment.
The channel model produces multi-paths from reflections and diffractions on the building facade, as well as rooftop diffraction. Channel properties, in particular, the departure angles, are depending on the specific physical situation of each BS-user link. The channel properties are predicted from an antenna element at the center of the BS array and then extrapolated to the whole array, by assuming the multi-paths are stationary (i.e., persistent along with constant amplitude).
Here, hi and hk represent the different channel vectors obtained from the two simultaneous closely spaced users. The FPmetric verifies the correlation between the channels of the two closely spaced users such that a lower value of the FPmetric relates to better FP-like conditions. Further details on the equation and favorable propagation can be found in [2–4].
When the geometric distance between the two users is considered, the propagation channels cannot be distinguished until a distance of 20 wavelengths (corresponding to 3 m for a frequency of 2 GHz). For the given scenarios, as the minimum distance between the two users increases to 20 wavelengths, FP-like conditions can be observed.
The distance between the BS and the user is also important to be able to differentiate the user channels, as observed from the BS. Two simultaneous users at different distances from the BS may experience different FP-like conditions. For this, the angle between the two users as observed from the BS provides a better perspective of the FP-like conditions. In Fig. 1, the users located at site 2 achieve FP-like conditions at the smallest angle. This is due to the distance between the BS and the users which is the largest in this location. In all three locations, FP-like conditions are achieved for an angular separation of 2.5∘, between the users.
The performance statistics are obtained from a Monte-Carlo procedure. For the area covered by the 16 cells, 150 users are randomly dropped at each iteration. These user positions are a subset of 320 random user positions that are uniformly distributed in the entire computation area. The maMIMO propagation from all BSs to all 320 user positions are pre-computed. Then, each iteration is conducted in two successive steps; first, the maMIMO channel matrices are created for all BS-user combinations (based on pre-computed data); then, the system-level simulation is run as described in Section 2, including cell selection, precoding, power allocation optimization, and computation of achievable rates.
The system-level simulator presented in  is applied to the multi-cell maMIMO scenario described in Section 2. The channel data is obtained either from the statistical model (i.i.d. Rayleigh) or from importing the channel realizations created by the ray-based model. Several antenna array configurations are implemented and tested: linear, planar, circular, and cylindrical. Communication-theoretic data rate expressions given in  are used to evaluate the maMIMO performance.
All the considered arrays are uniform, and the adjacent antenna elements are separated by half wavelength. The linear array is a single row of 192 antenna elements that are all directed in the same direction. It is more than 8 m long at 3.5 GHz. Due to this size, the practical installation of a 3.5-GHz linear array is unlikely, but this configuration is a particular case for which it is important to assess and compare the performance; that is why it is included in our study. The circular array is a single circular row of 192 antennas that face outwards from the circle with different but uniform orientations around the circle. Its physical diameter is 2.6 m, which remains quite large even for a macro base station. The planar array consists of 24 antenna elements in each of the 8 rows for a total of 192 antenna elements. Its dimensions are obviously reasonable for a practical deployment, with a length of 1 m and a height of 0.34 m. The cylindrical array is obtained similarly by considering a 24 × 8 setup with circular shape. The cylindrical antenna has the smallest dimensions among all the considered antennas; its diameter is less than 0.3 m. It is interesting to note that although the physical number of antenna elements is the same for the different array shapes, the dimensions can vary. These changes can significantly impact the performance of the network and have to be considered for accurate evaluations.
For the sake of a comprehensible comparison, we were able to set the path losses in both deterministic and i.i.d. Rayleigh models to be the same. However, in reality, if we only consider i.i.d. Rayleigh fading channels, we normally do not have access to accurate models and the path loss information is obtained from more simple approaches (empirical models) which has to be chosen very carefully as small variations in the selection of the model can lead to very different results.
The largest throughput per UE utilizing the deterministic channels corresponds to the linear array followed by the arrays with the largest horizontal dimension. This can be explained as all the users considered are distributed in the horizontal plane (only located outdoors) and the vertical angle of the propagation paths does not vary much from one user to another. Therefore, the BS is mainly required to serve users by separating them in the horizontal direction. The addition of vertical antenna elements then does not contribute as much to the throughput.
In the last stage of our study, we considered a 3D user distribution, with 75% indoor users located at a random floor inside the buildings. The varying building heights are properly considered, so the highest buildings have more users, being uniformly distributed from the ground to the top floor. Due to the height dimension, even two users located at the same 2D location can be separated, as the minimum distance between two floors (3 m) could be sufficient to separate the users. This provides an additional degree of freedom to the BS to separate closely spaced users and provide higher throughput.
This new scenario, where only the ray-based model is involved, investigates how the insertion of the vertical dimension in the user distribution affects the estimated maMIMO performance.
Practical maMIMO systems will have a large but limited number of antennas, which corresponds to limited spatial degrees of freedom and dimensions for the antenna array. The performance of the maMIMO system at the cell and system levels depends on the array structure but also on the propagation characteristics. This paper explored a mechanism to evaluate the favorable propagation conditions in a maMIMO channel utilizing deterministic ray-based channels along with new simulation procedures to reach accurate prediction of a maMIMO network considering highly realistic user distributions in real environments.
The maMIMO channel responses from a ray-based deterministic tool were obtained and used for system-level simulations that include precoding and multi-user power allocation. A multi-cell macro deployment of 16 maMIMO BSs in a dense urban environment was evaluated. At the median percentile, the antenna array with the largest spatial aperture (linear) has the best performance as compared with the cylindrical array (smallest extent) which has the worst performance.
It is shown that at i.i.d. Rayleigh fading channels whose path losses have been set to the same values as those considered in the deterministic model provide rather similar throughput as the deterministic channel when considering the linear array. This can be explained by the fact that the large size of the linear array is able to see various different channel components that is closer to the uncorrelated channels represented by the i.i.d. channels. In the case of the planar array, the impact due to the limited horizontal dimension of the array is not captured by the i.i.d. Rayleigh model and leads to significantly different results.
Finally, the performance of a realistic maMIMO network considering 3D user distributions was provided. The performance of the maMIMO network for different configurations considering the layout of antenna array and also for different physical antenna patterns is provided. The results show that even when considering users located vertically on different floors, the linear array with large horizontal aperture performs better than the planar array. The reason for such performance is due to the physical locations of the simultaneous users in macro-cells. Even when located at different heights, the number of simultaneous users is larger in the horizontal direction as compared to the vertical direction. Indeed, this could be different when considering small cells or a BS providing access to a fixed group of users like in a single large building. All the network parameters for these different results remain identical however just based on the selection of the antenna shape, layout of the array, and even the type of the beam pattern; differences can be observed in the overall performance of the network. A very large antenna array consisting of 192 elements has been considered, and these differences are expected to be larger when considering arrays with smaller dimensions. During the deployments of real maMIMO networks, such physical parameters must also be considered along with optimal signal processing schemes to obtain the best possible network performance. Another perspective of this work is also to predict deterministic maMIMO performance heatmaps, as will be required in 5G radio planning.
This work was supported in part by the European Commission through the H2020-MSCA ETN-5Gwireless project under Grant Agreement 641985.
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All of the authors participated in the proposal and conception of the current study; they all read and approved the final manuscript.
The authors declare that they have no competing interests.
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