Massive multiinput multioutput (MIMO) is a promising technique for the next generation of wireless communication networks. In this paper, we focus on using the raylaunching based channel simulation to model massive MIMO channels. We propose one deterministic model and one statistical model for indoor massive MIMO channels, both based on raylaunching simulation. We further propose a simplified version for each model to improve computational efficiency. We simulate the models in indoor wireless network deployment environments and compare the simulation results with measurements. Analysis and comparison show that these raylaunching based simulation models are efficient and accurate for massive MIMO channel modelling, especially with application to indoor network planning and optimisation.
Massive MIMO is to equip a large number of antennas at both the transmitter and the receiver in a wireless communication system. It is also known as large array system. Massive MIMO has the advantage of providing both higher spectral efficiency and power efficiency. Recently, massive MIMO has been widely accepted as a promising technique for the next generation of wireless communication system [
Sitespecific channel modelling is to model the channel using the environment information and physical radio propagation model to obtain the channel information for specific scenarios. Popular sitespecific channel models are electromagnetic propagation based methods such as finitedifference timedomain (FDTD) and raybased methods. One of the major applications for the sitespecific channel models is wireless network deployment. The raylaunching algorithm is especially suitable for this application purpose due to the modelling efficiency [
Wireless network planning and optimisation is the one of the major applications of the sitespecific channel models. Figure
An example of channel map for indoor network planning.
There have been research works applying the raybased models to model MIMO channels. The work of [
The aforementioned research works of raybased MIMO channel modelling have all focused on modelling the conventional MIMO system with a small number of antennas. A raybased model specifically for massive MIMO system is still missing. Although some of the models can be applied to model massive MIMO channel, the performance, especially the computational efficiency, is unsatisfying to the demand of network planning and optimisation purpose. The primary challenge of modelling massive MIMO channel using raybased sitespecific models, especially for applications in wireless network deployment, is the high computational cost, caused by the large number of antennas.
Another popular sitespecific channel modelling tool for network planning is FDTD method and related models [
To address the computational efficiency challenge of modelling massive MIMO channel for wireless network deployment application, we propose to apply a computationally efficient intelligent raylaunching algorithm (IRLA) [
The purpose of the paper is to propose 2 raylaunching based models in massive MIMO channel modelling for indoor wireless network deployment application. The first raylaunching model is a direct application of raylaunching to massive MIMO modelling. Based on the first model, we further simplified the model by using a reference point. Later we proposed the second model based on probabilistic principle. We also gave a simplified model based on a reference point. These simplified models have the advantage of computational efficiency in massive MIMO modelling. Furthermore, the comparison between the model simulation results and channel measurements shows good agreements.
The organisation of the paper is as follows. In Section
The MIMO system is to equip multiple antennas both at the transmitter and the receiver. Figure
MIMO transmitter and receiver scheme.
According to multipath propagation, the narrow band MIMO channel matrix elements can be written as
This equation gives the channel frequency response as a result of summation of the rays or multipath components. It is the mathematical relationship we use to obtain the channel from the raylaunching model.
By applying this relationship, the raylaunching model can be used to predict the set of MIMO channel matrices over the targeted network deployment site. We can write the channel frequency response as
The channel parameters, the amplitude
Raylaunching in an indoor environment.
We name the above model as the deterministic model. To further improve computational efficiency, we propose a simplified model based on this model.
Deterministic Phaseshift model is a model based on modelling the MIMO channel through the array response of the receiver antenna array. The transmitter array and propagation mechanism are modelled by the raylaunching model. For a receiver array, we can write the channel output in time domain as
The array response can be written in a row vector form as
An illustration of the phaseshift model in a linear array.
On the other hand, the arriving group of rays can be written as
The matrix elements in
Here we derive the model for the receiver array used in the measurement using the above phaseshift model. Figure
A cylindrical antenna array.
We can identify the distance differences by the geometric relationship. The distance difference has four possible values as in (
Thus, the array response vector is written as (
A similar phaseshift model has also been used in MIMO channel modelling in [
In this case, the distance difference is given as
Modelling the wireless channel as a probabilistic fading channel is another category of channel models in contrast to the deterministic channel models. It has the advantage of simplicity and efficiency when physical model is prohibitively complex. In this part, we propose a probabilistic channel model for massive MIMO based on the raylaunching model. Considering that the model is specifically for indoor scenario, we model the fading channel as Rician distribution. The choice of Rician distribution is because it comprises a rich group of probability distributions: by determining various values for the Rician
A single antenna Rician distributed channel can be written as
We model the channel matrix element
The raylaunching model traces a group of rays equivalent to the multipath components. This multipath information can be used to estimate the parameters of the Rician distribution. Below we adopt the method from the work of [
The rays are modelled as equivalent to the multipath components in (
According to [
The quantity
After obtaining the
Then we can write the MIMO channel matrix as
where
This probabilistic MIMO model requires the calculation of
Similar to the simplified deterministic model for massive MIMO channel, we can choose one representative point to approximate the whole antenna array. Although such an approximation sacrifices certain accuracy, it significantly reduces the computational cost by decreasing the repetition of raylaunching model simulation to only once.
Here again we choose the array center as the representative point to calculate the probability distribution parameters
where
Small cell and heterogeneous wireless networks, such as femtocell and wireless local area network (WLAN), are the major networks to be deployed for the next generation of wireless networks. These small networks are mainly deployed in indoor environments as a complement to the larger cell networks, to deploy heterogeneous networks. The measurements are carried out in indoor environments. They are typical small cell wireless network deployment scenarios. Equipped with massive MIMO antenna arrays, they are interesting scenarios for studying the performance of next generation wireless networks with massive MIMO channels.
We have carried out two measurement campaigns for the indoor cellular networks: downlink and uplink scenarios. We give the details of the channel measurements in the following part of this section. As our primary concern is network planning for indoor networks, the measurement in the uplink scenario was carried out with the receiver at a fixed location. In the downlink scenario, the transmitter stayed in a fixed location.
For channel modelling, such 2 scenarios have little difference on the channel modelling. However, for measurement, we intended to measure the channel with accuracy in real network applications. Furthermore, due to the limitation of mobility of the equipment, the measurements in these 2 environments fall into the network application scenarios of downlink and uplink. Moreover, the two environments have different characteristics. The uplink scenario contains complex walls and windows structure. The downlink scenario is relatively simple environment. The two different scenarios also showed the flexibility and adaptability of the IRLA model.
The downlink channel is measured in an indoor office environment. The measurement site is in the Electrical Engineering Department at Lund University, Sweden. Figure
Building floor map of the downlink scenario.
The antenna array equipped at the transmitter is a flat panel antenna array with 64 dualpolarised patch antenna elements. Figure
The measurement has been carried out in the rooms shown in Figure
The channel measurement for uplink scenario is carried out in the Department of Engineering and Computing Science, Durham University, UK. The measurement environment and the channel sounder have also been used to measure MIMO channel with small number of antennas in the work of [
Building floor map of the uplink scenario.
Transmitter antenna array and receiver antenna array.
The transmitter antenna array is a 32element antenna array with 4 layers of 8element uniform linear arrays. Each antenna element has an omnidirectional radiation pattern. The receiver antenna array has a similar structure with 4 layers of 6element uniform linear arrays.
The measurement scenario is shown as the building map in Figure
The prediction of the channel is based on the simulation of the IRLA. It has shown to achieve accuracy close to FDTD like models in indoor environment [
For outdoor MIMO channel modelling, the work of [
The IRLA simulation requires the detailed information of the environment. The environmental information includes the structures and materials of the environments. The structure of the building is imported through the construction map of the buildings. The walls, doors, and windows structures are all included in the simulation model. The construction material information is provided. It is matched with a material database supported by the IRLA. Figure
Simulation settings.
Number of reflections  5 
Number of horizontal diffractions  5 
Number of vertical diffractions  Unlimited^{1} 
Number of transmissions  Unlimited^{1} 
3D view of the simulation environment of the downlink scenario.
Although the details of the environments are included in the model, there are other factors influencing the modelling accuracy. To further improve the accuracy of the simulation, a model parameter calibration process is adopted to tune the parameters. The calibration process further optimises the accuracy by minimising the errors between the prediction and the measurement. The candidate values of the parameters were written in a vector form. The root mean square (RMS) error between the prediction using the parameters
In this section, we first present the computation time of the 4 models, using them to simulate the downlink and uplink scenarios. Table
Computation time of the models.
Downlink  Uplink  

Deterministic model computation time  302 minutes 56 seconds  278 minutes 24 seconds 
Simplified deterministic model computation time  36 minutes 27 seconds  32 minutes 28 seconds 
Statistical model computation time  308 minutes 43 seconds  281 minutes 25 seconds 
Simplified statistical model computation time  9 minutes 29 seconds  8 minutes 30 seconds 
This result suggests that, for time demanding tasks in network planning and optimisation applications, both the simplified models, Model 2 and Model 4, are better choices.
The received signal power is one of the most important parameters in network deployment and optimisation. It is closely related to the performance of the wireless networks. According to (
Figure
Average received power in downlink.
Average received power in uplink.
According to (
Received signal power RMS error in downlink scenario.
Location  1  2  3  4  5  6  7  8  9 

Deterministic model  3.2301 dB  3.0285 dB  3.4619 dB  2.7061 dB  3.1657 dB  5.3280 dB  2.3195 dB  4.7964 dB  3.3340 dB 
RMS error  


Simplified deterministic  3.7594 dB  5.4562 dB  5.4561 dB  5.0356 dB  5.8612 dB  5.7495 dB  5.8634 dB  5.6547 dB  5.5598 dB 
model RMS error  


Statistical model  4.7565 dB  4.9863 dB  4.8322 dB  4.9879 dB  4.1897 dB  5.7882 dB  4.6671 dB  4.9882 dB  4.3375 dB 
RMS error  


Simplified statistical  5.9781 dB  5.3245 dB  5.4215 dB  5.7145 dB  5.8771 dB  5.8873 dB  5.3227 dB  5.9551 dB  5.7723 dB 
model RMS error 
Received signal power RMS error in uplink scenario.
Location  1  2  3  4  5  6  7  8 

Deterministic model  2.9568 dB  2.2584 dB  3.6514 dB  3.9184 dB  2.3808 dB  2.3101 dB  2.8085 dB  2.2751 dB 
RMS error  


Simplified deterministic  5.8631 dB  5.7761 dB  4.3343 dB  5.4475 dB  5.2403 dB  5.9712 dB  5.3315 dB  5.9882 dB 
model RMS error  


Statistical model  4.7701 dB  4.2321 dB  4.5642 dB  5.4241 dB  4.0214 dB  4.0859 dB  4.8794 dB  4.9583 dB 
RMS error  


Simplified statistical  5.4578 dB  5.3762 dB  5.4772 dB  5.6549 dB  5.6873 dB  5.0857 dB  5.7544 dB  5.7563 dB 
model RMS error 
The results show that the RMS errors of Model 1 and Model 3 are smaller. The RMS errors of Model 2 and Model 4 are higher but still mostly under 6 dB. This shows that the accuracy of Model 1 and Model 3 is higher than that of Model 2 and Model 4. This is because both Model 2 and Model 4 simplify the computation by using a single ray to represent the whole array. The two simplified models trade certain degree of accuracy for computational efficiency. However, the result shows that the overall accuracy of the raylaunching models for massive MIMO systems is satisfying for the network planning and optimisation purpose.
Massive MIMO channels are in a form of large channel matrix. The primary modelling target for massive MIMO is to model the large channel matrices. We have 4 models to generate the channel matrices according to (
In Figure
Distribution of received power of channel elements in downlink.
The uplink scenario result in Figure
Distribution of received power of channel elements in uplink.
Channel capacity gain is one of the most attractive features of the massive MIMO channel promised to the future wireless networks. In this part of the result, we present the channel capacity comparison between the simulated channels and the measurement.
The MIMO channel capacity is calculated according to the equation given in [
We apply the above MIMO channel capacity formula to calculate the MIMO channel capacity from both the simulated channel matrices and the measured channel matrices. Figure
Channel capacity in downlink.
Channel capacity in uplink.
In this work, we first propose 2 raylaunching based simulation models for modelling massive MIMO channel. One is deterministic model and the other is a probabilistic model. We further simplified the 2 models using a phaseshift method. The primary application of these models is network planning and optimisation. We compare the simulation models with the measurement in two real small cell network deployment environments. The comparison results show that the models have good agreements with the measurement. This demonstrates that these raylaunching based simulation models are efficient and accurate models, for planning and optimising indoor networks equipped with massive MIMO arrays.
The authors declare that they have no conflict of interests regarding to the publication of this paper.
The first author would like to thank Mr. Cheng Fang, Dr. Andres Alayon Glasunov, and Professor Fredrik Tufvesson for the measurement campaign carried out in Lund University and Mr. Nasoruddin Mohamad and Mr. Adnan Cheema for the measurement campaign carried out in Durham University. The work was supported by the EU FP7 Project WiNDOW.