The exponential traffic growth of wireless communication networks gives rise to both the insufficient network capacity and excessive carbon emissions. Massive multipleinput multipleoutput (MIMO) can improve the spectrum efficiency (SE) together with the energy efficiency (EE) and has been regarded as a promising technique for the next generation wireless communication networks. Channel model reflects the propagation characteristics of signals in radio environments and is very essential for evaluating the performances of wireless communication systems. The purpose of this paper is to investigate the state of the art in channel models of massive MIMO. First, the antenna array configurations are presented and classified, which directly affect the channel models and system performance. Then, measurement results are given in order to reflect the main properties of massive MIMO channels. Based on these properties, the channel models of massive MIMO are studied with different antenna array configurations, which can be used for both theoretical analysis and practical evaluation.
The requirements for high rate of wireless communication networks grow exponentially with the applications of smart terminals. Thus, the capacity of the networks has to be increased in order to guarantee the quality of service (QoS) of mobile applications. Improving the spectrum efficiency (SE) is one of the feasible ways to achieve the better network capacity. Besides it, with the excessive power consumption of wireless communication networks, both the carbon emissions and operator expenditure increase every year [
Multipleinput multipleoutput (MIMO) technique has attracted much attention in wireless communications for more than ten years because it can offer significant increases in data throughput and link reliability without extra bandwidth or boosting transmission power. Nowadays, MIMO together with orthogonal frequency division multiplexing (OFDM) has been accepted as key techniques in the third generation (3G) longterm evolution (LTE) cellular networks and its advancement (Adv.). The evolved Node B (eNB) equipped with multiple antennas communicates with several types of user equipment (UE); at the same time frequency resources, named as multiuser MIMO (MU MIMO), can improve the spectrum efficiency, link reliability, and system energy efficiency [
Features of massive MIMO.
Feature  Main reason  

Advantages  High spectrum efficiency [ 
Large multiplexing gain and array gain 
High energy efficiency [ 
Radiated energy can be concentrated on UE  
High reliability [ 
Large diversity gain  
Efficient linear precoder/detector [ 
Favorable propagation condition for i.i.d. Rayleigh channel  
Weak interuser interference and enhanced physical security [ 
Orthogonal UE channels and extremely narrow beam  
Simple scheduling scheme [ 
Channel harden phenomenon averages out the fast fading  
Robust to individual element failure [ 
Large number of antenna array elements  


Disadvantages  Pilot contamination [ 
Limited orthogonal pilots as of bounded coherent interval and bandwidth 
High signal processing complexity [ 
Large number of antennas and multiplexing UE  
Sensitive to beam alignment [ 
Extremely narrow beam is sensitive to UE moving or antenna array swaying  
Poor broadcast channel [ 
Be blind to UE positions 
In Release 11 (R11) specified by the 3rd generation partnership project (3GPP), the MIMO technique can only radiate the beam in horizontal dimension as of the fixed down tilt of antenna array. In order to well exploit the vertical angular resolution of signal propagation, different kinds of the antenna array configurations, such as the rectangular, spherical, and cylindrical antenna array deployments, have been studied in 3GPP [
Up to now, massive MIMO has been paid much attention to by both academic and industry organizations. There are lots of works done for massive MIMO, such as performance analysis, remedies for alleviating pilot contamination, and channel estimation. The channel model is fundamental for theoretical analysis as well as for performance evaluation of massive MIMO system. Therefore, this paper mainly investigates the state of the art of the channel models for the massive MIMO system. The configuration of antenna array as the critical factor deciding the characteristics of massive MIMO channels is first presented briefly. Based on the given antenna array configurations, the current measured activities of massive MIMO channels are studied for working out the main properties of massive MIMO channels, which are the basis for the precise channel models. With the new properties, two kinds of channel models, namely, correlationbased stochastic models (CBSMs) and geometrybased stochastic models (GBSMs), are presented for the massive MIMO in consideration of both the theoretical analysis and realistic system evaluation.
The remainder of this paper is organized as follows. Section
The antenna array structures roughly undergo three phases with the development of technique in manufacturing. In the traditional passive antenna array, the radiofrequency circuit is usually connected to the physical antennas through the radiofrequency cable. Subsequently, in order to reduce the loss induced by the radiofrequency cable and save the cost of installation and maintenance, the remote radio unit (RRU) separated from the baseband unit (BBU) has been widely adopted [
As shown in Figure
Antenna array configuration [
The configurations of antenna array directly affect the channel properties, furthering the performance of massive MIMO system. Taking the antenna space as an example, it decides the mutual coupling and correlation matrix, furthering the capacity of massive MIMO. However, the spaces between adjacent antennas in current antenna array are usually set as equal. Therefore, the study of the antenna array configuration on a constraint or unconstraint area is valuable for the development of massive MIMO, such as the design of sparse antenna array.
Lots of channel measurements have been carried out in order to discriminate the main properties of massive MIMO channel. Typical measurements are summarized in Table
Channel measurement.
Scenario  Antenna configuration  Antenna space  Bandwidth/carrier  Measured metric 

Outdoor [ 
128antenna linear array  Half wavelength  50 MHz/2.6 GHz  Channel gain, 
Indoortooutdoor [ 
32antenna rectangular to 128antenna cylindrical array  Half wavelength  50 MHz/2.6 GHz  Correlation 
Outdoor [ 
Cylindrical and linear array with 128antenna  Half wavelength  50 MHz/2.6 GHz  Largescale fading and angular resolution 
Outdoor [ 
112antenna virtual array  —  20 MHz/2.6 GHz  Correlation, inverse condition number 
The channel characteristics, such as channel gain,
Illustration of nonstationary phenomenon and nearfield effect [
When the eNB employed a 32antenna rectangular array with half a wavelength between the adjacent antennas, the indoortooutdoor channels were measured with a bandwidth of 50 MHz [
Channel measurements for both the cylindrical and linear antenna array with 128antenna were implemented, when the space of adjacent antennas is half a wavelength and the bandwidth is 50 MHz [
A scalable virtual antenna array with 112antenna was employed at the eNB in order to investigate the channel characteristics for massive MIMO in [
The measurements for the characteristics of elevation angles are extensive for 3
Two kinds of channel models, namely, correlationbased stochastic models (CBSMs) and geometrybased stochastic models (GBSMs), are widely used to evaluate the performances of the wireless communication systems. The complexity of the former is lower and is mainly used for analyzing the theoretical performance of MIMO systems. However, the accuracy is limited for the realistic MIMO system, and it is difficult to model wireless channels considering the nonstationary phenomenon and spherical wave effects. In contrast, the latter can accurately reflect the realistic channel properties and is more suitable for massive MIMO channel even with the higher computation complexity. The current channel models have been summarized in Table
Channel models of massive MIMO.
Modeling method  Category  Property 

CBSM  i.i.d. Rayleigh channel model  Elements of fast fading are i.i.d. complex Gaussian variables 
Correlation channel model  Contain correlation between transmit antennas or/and receive antennas  
Mutual coupling channel model  Consider antenna impedance, load impedance, and mutual impedance  


GBSM  2 
Propagate beam on 2 
3 
Propagate beam on 3 
The CBSMs are mainly used as the theoretical model to evaluate the performance of massive MIMO system. The current analysis generally assumes that the UEs employ single antenna in consideration of the complexity and spaces for the terminal equipment with low carrier frequency. Therefore, the following CBSMs are discussed when the UE employs single antenna, which are easy to be extended to the cases that the UE with multiple antennas works at the millimeter wave. Moreover, massive MIMO is more likely to be used in time division duplex (TDD) system at present, since the downlink channel state information (CSI) can be acquired from the uplink due to TDD reciprocity feature. Therefore, only the uplink channel is taken as an example for study in this section.
Let us consider an uplink MIMO system that
According to the fast fading matrix, the CBSMs can be further simplified into three kinds of channels, namely, i.i.d. Rayleigh fading model, correlation channel model, and mutual coupling channel model. We discuss these three kinds of models as follows in detail.
The i.i.d. Rayleigh fading channel model is widely adopted for the theoretical analysis of the massive MIMO system, which assumes there is no correlation and mutual coupling between transmit antennas or receiver antennas. The elements of the fast fading matrix
The favorable propagation is the most important property of the i.i.d. Rayleigh fading channel in the massive MIMO system [
The favorable propagation can not only better the performance but also simplify the algorithm design of massive MIMO system. The orthogonality can alleviate the interuser/intercell interference, which is helpful to improve the system capacity. Channel harden phenomenon can mitigate the impact of fast fading on the scheduling gain, which simplifies the complexity of scheduling scheme [
In order to reflect the antenna correlation caused by the insufficient antenna space and the scattering environments, the correlation channel model is established to evaluate the performance of the massive MIMO system [
When the linear antenna array is assumed at the eNB, the steering matrix
For the rectangle antenna array, the steering vector can be attained by the steering matrix; namely,
This correlation channel model introduces the AoAs, which can be utilized to distinguish the UE and improve the accuracy of channel estimation [
Since the number of antennas increases sharply in the massive MIMO system, the mutual impedance has to be considered as of the limited space for antenna array. Moreover, the load impedance and antenna impedance should also be characterized in order to reflect the realistic channel model.
The channel vector of the
Mutual coupling channel model is more practical for massive MIMO. It is helpful to analyze the effects of antenna space on the performance of massive MIMO, which is significant for designing the antenna array configuration, especially the sparse antenna array.
GBSMs are mainly used for evaluating the performance of practical wireless communication systems, which accurately comprise the channel properties. Considering the elevation or not, the GBSMs of massive MIMO can be classified into two kinds, namely, 2
Employing the linear antenna array, the nonstationary phenomenon and spherical wavefront have been discriminated as the main properties for the massive MIMO channel through channel measurements [
Similar to [
In consideration of both the nonstationary phenomenon and spherical waveform effect, an elliptical GBSM was given for massive MIMO with linear antenna array [
The 3
In WINNER + projects, the main procedures of 3
The procedure of 3
The largescale propagation of the 3
Illustration of path loss [
Generally, the propagation channel contains several clusters (
When the double polarization array is adopted at the eNB, as shown in Figure
Illustration of coordinate [
As for the LoS scenario, the fast fading with a main path can be written as follows [
If only the vertical polarization is adopted in LoS or NLoS scenarios, the
According to the above procedures of channel modeling, we can generate the realistic channel coefficients to evaluate the three aforementioned scenarios. However, the channel model is not precise for simulations, since the nonstationary phenomenon has not been reflected [
Massive MIMO has been regarded as one of efficient ways to improve both spectrum efficiency and energy efficiency for the broadband wireless communication systems. As the first step to evaluate the performance of any communication systems, the channel models for massive MIMO are necessary to be investigated, which is the main concern of this paper. According to the ability of array to radiate the signals, the antenna array configurations are classified into 2
At present, CBSMs are mainly used to analyze the theoretical performance of massive MIMO due to its simplification. There are three kinds of simplified CBSMs widely used for different objectives, namely, i.i.d. Rayleigh channel model, correlation channel model, and mutual coupling channel model. The channel model reflecting both the nonstationary phenomenon and spherical wave effect has been established for the linear antenna array based on the cluster model. The improved 3
The authors declare that there is no conflict of interests regarding the publication of this paper.
The work was supported by the China Natural Science Funding (61271183), Program for New Century Excellent Talents in University (NCET110600), National Key Technology R&D Program of China under Grant 2013ZX03003005, and National High Technology Research and Development Program of China (2014AA01A705).