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 [3] 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 [3] 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.

In Fig. 10, the cumulative distributive function (CDF) of the downlink (DL) throughput/rate per UE [3] is given for different antenna array configurations. In each simulation, outdoor users are randomly dropped in the considered area. At the median percentile, the linear array performs the best with a throughput per UE of 76 Mbit/s. The cylindrical array performs the worst with a throughput per UE of 52 Mbit/s. This difference can be explained by the spatial aperture of each antenna array. The cylindrical array containing 192 antennas (24 × 8) has the smallest radius (dimension) of all the selected configurations. This is followed by the planar, circular, and linear arrays, which have similar median performance. At the highest percentiles, however, the performance of all different array configurations converges when the users all have good/favorable channel conditions in the outdoor scenario.

In Fig. 11, the i.i.d. Rayleigh fading channel is considered with the same multi-cell system-level simulator from [3]. The channel is defined only by the number of antenna elements for each user position and no correlation along the antenna coefficients or between user positions are considered. This model has the advantage of being easily implemented and analyzed, since there are closed-form rate expressions available in the literature [3], but the accuracy of the results is limited. In order to fairly compare the i.i.d. Rayleigh fading results with the deterministic setup, the path losses obtained from the deterministic setup are also used in the i.i.d. Rayleigh fading setup. This process makes sure that the path losses between the two different channel models are the same, and therefore, we are able to compare the impact of the two channel models in terms of angular diversity and cross-link correlation. It can be seen from Fig. 11 that the performance of the normalized i.i.d. Rayleigh channel is similar to that of the deterministic channel in case of the linear array. At the median percentile, both the i.i.d. Rayleigh fading channel and the deterministic channel give a throughput of 80 Mbit/s per UE. However, if we consider the planar array, a significant loss in throughput can be observed. When considering the deterministic model, a DL throughput/rate per UE of 60 Mbit/s is obtained at the median value for the planar array. This difference of 20 Mbit/s between the planar and linear arrays is not seen in the i.i.d. Rayleigh model. The difference that is not captured by the i.i.d. Rayleigh model is due to the smaller aperture in the horizontal direction of the planar array.

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.

Both user distributions (outdoor only, or mixed) are considered in Fig. 12. The linear antenna array performs the best in both the user distributions as compared to the planar array. Although the indoor users provide better separability to the BS, the attenuation caused due to the outdoor-to-indoor propagation loss results in lower values of the data throughput. The linear array performance is expected to be better in the outdoor scenario as discussed in relation to Fig. 10; however, similar performance is noticed in the scenario with indoor users as well. This is due to the fact that the horizontal dimension is significantly dominant as compared to the vertical dimension, even when multi-floor users are simulated. At each simultaneous time-frequency slot, each BS is connected to a maximum of ten users. These users are located at different locations of the macro-cell, and although they are located at different heights, the horizontal spread of the users is greater. Indeed, if all the simultaneous users are located in the same building, this could be different. As shown in Section 5, the minimum distance or angle between two closely spaced users can be significantly small to achieve FP-like conditions, and the minimum separation of 3 m between different floors of a building may be sufficient to separate users in the vertical direction. Therefore, the worst case scenario would be when all the users are located in the same building present at the cell edge. However, since the probability of such an event is very small, we can conclude that the horizontal dimension still retains the significant role in macro-cell scenarios.

In Fig. 13, the impact of decreasing the horizontal dimension of the antenna array while maintaining the same number of total antenna elements is illustrated. Clearly, the linear array performs significantly better than the planar arrays due to its large horizontal aperture. The planar array with the smallest horizontal aperture with 24 horizontal elements has the lowest throughput performance with the other intermediate arrays in between. However, this does not mean that there is no impact of the vertical dimension and it must also be considered. In Fig. 14, 2 different types of individual antenna elements used in the arrays have been compared. The first element is the same as used in the rest of the study with a beamwidth of 90^{∘} in the horizontal direction and 20^{∘} in the vertical direction. The second element has a larger vertical beamwidth of 60^{∘} and the same horizontal beamwidth. At the 40th percentile, when all the elements of the planar array are considered with the larger vertical beamwidth, a throughput of 20.5 Mbit/s is achieved whereas the smaller vertical beamwidth provides a throughput of 24 Mbit/s. It is interesting to note that the signal processing provides digital beamforming as well, and the impact of the antenna element beamwidth is limited. However, these results provide an insight into the careful selection of the physical parameters of the antenna arrays to provide the best possible performance. Such information about the physical parameters of the antenna arrays can also be useful in designing future hybrid antenna arrays that utilize fewer radio-frequency chains as well.