1. Introduction
Three Dimensional MIMO (3D-MIMO) is a type of Massive MIMO Technology which has the ability to move the beam horizontally as well as vertically. In recent years, with the widespread use of smartphones such as mobile phones and tablets, the volume of mobile data services has exploded, and existing wireless communication systems can no longer meet such huge business demands. Therefore, academia and industry have successfully conducted research on 5G mobile communication. Massive MIMO technology is one of the candidate key technologies for 5G. Compared with the existing 4G technologies, it can significantly improve the spectrum efficiency and energy efficiency of the communication system and has become a research hotspot at home and abroad [1]. The combination of Massive Multi-user MIMO (MU-MIMO) systems can further utilize spatial freedom to significantly increase system throughput and spectrum efficiency [2]. As a key technology of the MU-MIMO system, precoding can effectively suppress multi-user interference and improve the Signal-to-Noise Ratio (SNR) [3]. However, to make full use of the role of precoding, the transmitter must obtain enough channel state information (CSI). For Time Division Duplexing (TDD) systems, CSI can be obtained through the reciprocity of uplink and downlink channels, but susceptible to pilot contamination [4]. In a Frequency Division Duplex (FDD) system, CSI acquisition relies on a feedback link. In an actual system, the feedback link bandwidth is limited. Therefore, in FDD massive MU-MIMO systems, codebook-based Multi-user precoding scheme, in which codebook design and multi-user scheduling strategy, are particularly important.
In the traditional MIMO system, the base station adopts a uniform linear array with a fixed down-tilt angle, and the wireless channel exhibits two-dimensional (2D) characteristics, that is, only the horizontal dimension freedom is available, which is called 2D-MIMO. However, in massive MIMO systems, base stations usually use 2D or 3D array antennas, which form the so-called 3D-MIMO technology [5,6]. Due to the expansion of the antenna array structure, 3D-MIMO channels exhibit different spatial correlations [7,8], and they also include horizontal and vertical dimension channel information. Therefore, 3D beamforming techniques can accurately align different levels of the dimensional sum. Thus, reduce the interference between users.
This paper proposes a novel codebook design for 3D based MIMO system in heterogeneous network scenarios. According to the quantization error and statistical characteristics of the random distribution of the system, the influence of feedback overhead and base station density on system performance is analyzed using stochastic geometry. An improved 3D precoding scheme based on horizontal emission angle and vertical down-tilt is proposed. Through simulation analysis, the influence of feedback overhead on system throughput is compared, and the effects of traditional DFT precoding methods in 2D and 3D environments and improved 3D precoding schemes on system BER and throughput are compared. The simulation results show that the feedback overhead will reduce the system throughput and improve the system BER, while the improved precoding scheme due to the joint consideration of the horizontal emission angle and vertical down-tilt, thus effectively improving the system throughput and reducing the system BER, optimized system performance.
The rest of the paper is organized as follows. Section 2 discusses the literature review. Section 3 explains the system model. Section 4 provides system performance analysis based on random geometric finite feedback. Section 5 provides the improved 3D codebook design concepts. Section 6 gives the simulations results and analysis while Section 7 concludes the paper.
2. Related Work
Massive multiple-input multiple-output (MIMO) has become one of the most important technologies in wireless communication in the future [9]. Three-dimensional MIMO (3D-MIMO) is one of the main application scenarios of massive MIMO. Due to the limited space of these base station (BS), 3D-MIMO can use the Uniform Planar Arrays (UPA) to place hundreds of antennas in a relatively small space. In addition, 3D-MIMO can control the beam in the horizontal and vertical directions of the signal. Reasonable transmission and reception techniques can reduce multi-user interference and greatly improve system performance [10]. As the urban environment becomes more and more modern, the number of users in the community is increasing, and users are more and more dispersed in three-dimensional space. Since traditional base station transmitter beam can only be adjusted in the horizontal dimension, the vertical dimension is a fixed down dip for each user. However, the actual signal propagation channel has three-dimensional space characteristics, which can lead to serious inter-cell interference among the users of the cell, which greatly reduces the cell edge user throughput [11]. The 3D-MIMO precoding technique can divide each vertical antenna element into a plurality of elements without changing the size of the existing antenna so that the vertical dimension has a distinguishable pitch angle, which performed in the horizontal and vertical dimensions. Joint beamforming design can make full use of three-dimensional space freedom, bring more power interference control capabilities, and improve system performance [12]. At present, the research on the codebook design scheme for 3D precoding has achieved certain results, but most studies are based on the discrete Fourier transform (DFT) codebook [13,14]. However, since the DFT codebook has strong beam directivity and uniform distribution, it is suitable for horizontal dimension codebooks using a uniform linear array (ULA). However, due to the narrow and nonuniform distribution of the up-and-down inclination of the vertical direction, it is not applicable to the vertical dimension codebook using the uniform planar array (UPA) [15]. The improved codebook study still uses the DFT codebook in the horizontal direction and uses the distribution characteristics of the vertical down tilt in the vertical direction. Several discrete quantization angles are extracted in the vertical down-tilt angle interval and constructed by the corresponding beam steering vectors. The vertical codebook [16], or the codeword phase determined by the specific position of the antenna array element, is used to construct the vertical codebook [17], or on the basis of analyzing the correlation of the 3D-MIMO channel, for the transmit correlation and receive correlation matrix in the decomposition of the horizontal and vertical dimensions, a new 3D codebook is constructed combining the DFT codebook and the Grassmannian codebook in the 2D-MIMO channel [18]. However, these codebook designs do not consider the launch angle in the horizontal direction of the antenna array elements. Although the horizontal launch angle can be adjusted in a small range, if it is regarded as a fixed angle, the accuracy of the beam pointing will be reduced, causing inter-user interference, which seriously affect system performance.
Based on the quantization error and statistical characteristics of the random distribution of 3D-MIMO systems, the impact of stochastic geometry analysis feedback overhead on system performance was studied. Based on the deployment of UPA antenna at the base station, a horizontal launch angle and vertical downcast angle and Kronecker were used. We construct a design scheme for the 3D-MIMO multiuser codebook and simulate and analyze the designed codebook scheme. The proposed scheme has obvious performance enhancement as compared with the traditional schemes.
3. System Model
The traditional base station is equipped with a ULA array. As shown in Figure 1, multiple beams for a terminal cannot be implemented in the vertical plane, so that the base station can form three beams in the horizontal dimension to align users with different angles from the base station, but in the horizontal dimension. Users with the same angle as the base station, such as User Equipment 2 and 3 (UE2 and UE3), whose beams interfere with each other. The 3D-MIMO technology provides vertical plane beamforming. As shown in Figure 2, UE2 and UE3 can be distinguished in the vertical dimension to form the beams that are aligned with them to serve them, thereby controlling the interference of adjacent cells and improving the spectrum efficiency [19].
This paper adopts the space division multiple access (SDMA) heterogeneous network system model composed of the microbase station and macro base station and multiuser. The distribution of micro base station follows the isomorphous Poisson Point Process (PPP) Φ(λ) Φ(λ) , with a density of λ λ . Each micro base station is equipped with an Nt Nt root antenna and the transmission power is P P ; the distribution of macro base station follows the isomorphism PPP Φ(λM) Φ(λM) , where the density is λM λM , each macro base station is equipped with NM NM antennas and the transmission power is nP nP . Each base station serves K K users, K≤Nt K≤Nt and NS≤NM NS≤NM , and it is assumed that the user obeys the independent stable point process and is randomly distributed in a circle whose radius is dmax dmax centered on the serving base station. For the fading model, it is assumed that all point-point channels obey the unitary mean of independent, identically distributed Rayleigh block fading, and the received power varies with distance d d by d−α d−α , where α α is the path loss index and α>2 α>2.
The channel vectors from the micro base station T0 T0 , the mth mth macro base station, and the ith ith macro base station to the user U0(k) U0(k) are represented as h0k∈ℂNS×1 , hmk∈ℂNM×1 , hik∈ℂNS×1 , respectively, which are all composed of independent complex Gaussian random variables with zero mean unit variance. The normalized transmitted signal vectors of the micro base station T0 , the mth macro base station, and the ith micro base station are respectively represented as x0∈ℂNS×1 , xm∈ℂNM×1 , xi∈ℂNS×1 , and the transmitted signal vector x is a linear function x=∑k=1KWk Sk , where Sk is the data symbol of the kth user, Wk is the unit norm beamforming vector for the kthuser.
Because the transmission power of the micro base station is low, the macro cell users far away from the micro base station can only obtain a small gain even if the macro base station and the micro base station cooperatively transmit data under the coordinated multipoint (CoMP) mechanism [20]. Therefore, this article only analyzes downlink information transmission for users in the micro base station. Assuming that the serving base station of each user is the closest base station to it, the micro base station serving the kth specific user U0(k) is represented as T0 . Assuming that it is located at the origin, the distance between U0(k) and T0 is dk . Then the U0(k)received sithe gnal can be expressed as:
y0k=ρ dk−α2 h0kH x0+ρ′ ∑m∈ Φ(λM)lm−α2 hmkH xm+ρ ∑i∈Φ(λ)/T0Di−α2 hikH xi+n0k
where, ρ=P/K , ρ′=nPK, equivalent power allocation is used for analysis, lm is the distance between the user and the mth macro base station in micro base station T0 , Di is the distance between the user and the ith micro base station in the micro base station T0 , n0k is the additive white Gaussian noise with variance σ2.
In this paper, a limited feedback mechanism is adopted, and the base station can only acquire part of the channel state information (CSI) [21]. The micro base station T0 and the user U0(k) keep the same quantization codebook Ck={ck1, ck2, … ckN} , which contains N=2B unit norm vector codewords. The kth user selects the quantization vector (codeword) h^k closest to the channel direction h¯k=hk/hk from the codebook with B=ln(N)bit, and the user selects the optimal codeword from the codework by receiving the SNR maximization criterion:
h^k=argmaxcki∈Ck|h¯kH Cki|2
After searching for the best-quantized codeword, the user feedbacks the index of the codeword to the base station using B bit. After the base station receives the index, the codeword corresponding to the index is found as a beamforming vector in the codebook, and then the related signal processing is made [22].
The received signal interference–noise ratio (SINR) of user U0(k)is given by:
SINR=ρS0k dk−αIr+Ip+Iq+σ2
Ir=∑m∈Φ(λM)ρ′‖hmkH Wm‖lm−α
Ip=∑i∈Φ(λ)/T0ρ‖hikH Wi‖Di−α
Iq=∑j∈K, j≠kρ|hkH Wj|2 dk−α
Among them, W=[w1,w2, …, wK] , Ir is the inter-cell interference from the macro base station Poisson domain Φ(λM) , Ip is the inter-cell interference from the micro base station Poisson domain Φ(λ)/T0 , Iqis the inter-user interference in the cell estimated from the quantized CSI.
The system throughput, that is, the regional spectrum efficiency, is defined as the product of the absolute coverage probability and the maximum sum rate of transmission information per unit area. Let T be the SINRthreshold, then the system throughput can be expressed as:
T=λ∑k=1KP(T,α)ln(1+T)
The flowchart in Figure 3 explains the system procedure.
4. System Performance Analysis Based on Random Geometric Finite Feedback
According to the statistical characteristics of the random distribution of channel gain and Laplace transform, the system outage probability can be obtained [21,23]:
P(T,α)=P(SNR>T)=Lr(nξk)Lp(ξk)Lq(ξk)e−ξk σ2ρ
where, ξk=Tdkα.
According to the probability density function (PDF) and cumulative distribution function (CDF) of the radius` r in the 3D Poisson process, the inter-cell normalization from the Poisson domain Φ(λ) of the microcell can be obtained through the probability generation functional (PGFL). The Laplace transform Lp of the interference I¯pcan be expressed as:
Lp(ξk)=exp{−4πλ∫0∞[∫dk∞(1−e−TdkαSr−α)r2dr]f(s)ds}
By expanding and integration process we get:
=exp{−4πλ∫0∞[∫dk∞r2dr-∫dk∞e−TdkαSr−αr2dr]f(s)ds}
=exp{−4πλ∫0∞[∫dk∞r2dr-e−STdkα∫dk∞e−r−αr2dr]f(s)ds}
Putting limits and rearranging to PGFL form we get:
=exp{4πλdk33−4πλT3/α dk3αES[(S)3/α[Γ(−3α, TS)−Γ(−3α)]]}
where Γ(·) is the PGFL. The Laplace transform Lr of the inter-cell normalized interference I¯r from the macro-cell Poisson domain Φ(λM)can be expressed as:
Lr(nξk)=exp{4πλM dk33−4πλM (nT)3/α dk3αES[(S)3/α[Γ(−3α, nTS)−Γ(−3α)]]}
For the interference term |hkH wj|2=‖hk ‖2 |h¯kH wj|2 . φk represents the quantized distortion angle between hk and h^k , decomposing the normalized channel vector h¯k=(cosφk)h^k+(sinφk)vk , where vk is an isotropic unit norm vector that is distributed in the null space of h^k and is independent of sinφk . Since wj and vk are independent, they are |vkH wj|2~B(1, NS−2) [23] and are independent of the quantization error sinφk. To normalize interference between users, we can write:
I¯q=dk−α‖hk ‖2 sin2 φk∑j∈K,j≠kB(1,Ns−2)
Among them, X=‖hk ‖2 sin2 φk~Γ(Ns−1, δ) , ‖hk ‖2 , φk and B(1,Ns−2) are independent of each other, δ=2− B/(Ns−1) which follows the exponential distribution exp(1/δ) [22]. Let I¯q=dk−αZ , then Z~Γ(K−1, δ) . Therefore, normalize the inter-user interference I¯q~Γ(K−1, δdk− α). The Laplace transformation of I¯qis:
Lq(ξk)=1(1+Tδ)K−1
Putting Equations (12), (13), and (15) into Equation (7), we get:
=λ∑k=1K{1−4πλ3×∫0∞ e−πλx(β1(λ,T,α)+β2(λ,T,α))−Tσ2 xα/3}×ln(1+T)
β1(λ, T, α)=4T3/αα(1+Tδ)K−1×ES[(S)3/α[Γ(−3α, TS)−Γ(−3α)]]
β2(λ, T, α)=4(nT)3/αα(1+Tδ)K−1×ES[(S)3/α[Γ(−3α, nTS)−Γ(−3α)]]
Among them, Γ(x)=∫0∞ tx−1 e−tdtis a gamma function.
From Equations (16)–(18), the throughput is related to the SNR at the base station density and the feedback overhead. The quantization error is reflected by the feedback overhead. The greater the feedback overhead, the greater the amount of information received by the base-stations from the user feedback, the smaller the quantization error, the more accurate the beam vector, the smaller the throughput loss, and the better the system performance. This article studies the improved 3D-MIMO precoding scheme.
5. Improved 3D Codebook Design
As shown in Figure 4, the base station configures the UPA arrays, where the number of horizontal antenna array elements is Nh , the array element spacing is dh , the number of vertical antenna array elements is Nv , and the array element spacing is dv.
The horizontal codebook contains Nh(Nh=2Bh) horizontal codewords, and the vertical codebook contains Nv(Nh=2Bv) vertical codewords. As shown in Figure 5, the base station transmit antenna height is HBS , the mobile subscriber receive antenna height is HUS , Li is the distance between the ith horizontal antenna array element and the base station, i.e., Li=id , i=1, 2, … , Nh, Sm is the horizontal distance from the base station antenna for the beam alignment position formed by the mthhorizontal codeword.
The horizontal emission angle θm of the beamforming the mthcodeword is:
θm=arctan(HBS−HUS)2+S2 mLi
The base station antenna array phase difference is given by:
Δφm=2πdhcosθmλ
The mthhorizontal codeword can be expressed as:
cm(h)=1Nh[1 ej2πdhcosθmλ … ej2π(Nh−1)dhcosθmλ ]m=0, 1, … , Nh−1
where λis the signal wavelength and the phase of the first antenna element is assumed to the reference phase 0.
Assuming that the horizontal distance of the beam alignment position formed by the nth vertical codeword from the base station antenna is Sn and the height of the first vertical antenna element is Hl , the vertical downtilt angle of the beam formed by the nthcodeword is:
βn=arctan(Hl−HUSSn) l=1,2, … , Nv
The base station antenna array phase difference is given by:
Δφn=2πdvcosβnλ
Then the nthvertical codeword can be expressed as:
cn(v)=1Nv[1 ej2πdvcosβnλ… ej2π(Nv−1)dvcosβnλ]n=0, 1, … , Nv−1
Combining horizontal and vertical codebook design, the Kronecker product codebook for improved 3D-MIMO can be expressed as:
c=cm(h)⨂cn(v)
Substituting the codebook cinto the system model to guide beamforming can optimize the system performance.
Since each array element has its own specific location in both horizontal and vertical directions, if the UPA array developed by the base station is regarded as a whole, the beam will be too divergent. In order to make the beam pointing more accurate, it is necessary to consider the position of the array element in the horizontal and vertical directions at the same time. Based on previous studies, this paper considers the influence of the adjustable range of the horizontal launch angle on beamforming accuracy. Using the phase of the antenna array element and the phase difference between the array elements, an improved horizontal and vertical codeword is proposed and used the Kronecker product to get the improved precoding codebook.
6. Simulation Results
Consider a two-layer 3D-MIMO heterogeneous network consisting of the macrobase station, a micro base station, and multiple users, where the serving base station is a micro base station. Let the serving base station is T0 collaborate with other micro base stations and macro base stations that greatly interfere with user terminals. At this time, the interference of the user terminal can be eliminated as much as possible. This heterogenous network simulation environment is built by MATLAB, and the improved 3D codebook is brought into the process of system performance analysis. The simulation curve of the closed-form solution of the system performance analysis illustrates the impact of various performance parameters and the improved 3D precoding scheme on system performance. The main simulation parameters are shown in Table 1.
[ Table omitted. See PDF. ]
Figure 6 shows how the network throughput varies with the base station density. The proposed 3D MIMO codebook scheme is compared with perfect CSI condition for feedback bits of 4 and 6 respectively. The simulation results are consistent with the analysis results. As the base station density increases, the throughput gradually increases. It can be seen that proper adjustment of the base station density can increase system throughput and optimize system performance. Moreover, as the base station density increases, the impact of system performance caused by incomplete CSI becomes more serious. Furthermore, the system throughput curve when the base station receives perfect CSI is plotted as a comparison, indicating that the more feedback bits, the better the system performance. Figure 7 compares 3D DFT precoding scheme when the number of feedback bits is 4 bits and 6 bits, respectively, and perfect CSI, the BER of the system varies with the SNR of the base station transmitter. Simulation results show that as the number of feedback bits increases, the system’s BER decreases.
Enlarge this image.Figure 6. Throughput comparison of the proposed 3D MIMO codebook scheme for feedback bits of B = 4, 6 bits with perfect CSI conditions.
Enlarge this image.Figure 7. The relationship between the BER and SNR for the proposed 3D DFT Scheme for a different number of feedback bits.
Figure 8 compares the use of DFT precoding schemes in 2D and 3D environments, respectively, under the BER, and in the 3D-MIMO channel model, the performance difference between the improved precoding scheme and the DFT precoding scheme proposed in this paper in terms of system BET. The traditional DFT precoding scheme is not suitable for vertical dimension codebooks in a 3D environment in which the base station employs both planar and planar antenna arrays due to the problem of adjustable dynamic range and vertical distribution of the vertical dip and tilt angle, and this paper considers horizontal emission jointly. The 3D codebook is constructed by angle and vertical down-tilt, so the performance of the improved precoding scheme proposed in this paper is better.
Enlarge this image.Figure 8. The relationship between the BER and SNR for the proposed precoding scheme and other schemes.
Figure 9 shows the Cumulative Distribution Function (CDF) curves for different codebook schemes. It can be seen from the simulation results that the 3D DFT precoding scheme can effectively improve the system throughput compared to the 2D DFT precoding scheme because it fully utilizes the vertical dimension of the UPA array. The improved 3D precoding scheme proposed in this paper jointly considers the horizontal adjustable range and the vertical down-tilt adjustable range, and considers the specific location of the antenna array elements rather than the UPA array as a whole, so it is more effective. The proposed codebook scheme controls inter-user interference at the edge of the cell to significantly increase system throughput.
Figure 10 compares the spectral efficiency (SE) versus SNR of the proposed 3D codebook scheme with other state-of-the-art codebook schemes. As can be seen from Figure 10 that the proposed 3D codebook scheme outperforms the other codebook schemes which show its superior performance over other codebooks schemes. Moreover, the rate gap between the proposed scheme and other schemes increases with increasing SNR which means that the proposed 3D codebook scheme shows better SE performance in low as well as high SNR level. Such results cover the real-world aspect of the MIMO system deployment where the SNR changes due to certain channel impairments and there is a need for a flexible and robust codebook scheme which should provide better service in wireless communications systems.
Enlarge this image.Figure 10. Spectral efficiency comparison versus SNR for the proposed 3D codebook scheme with other state-of-the-art schemes.
Figure 11 shows the impact of the inter-cell interference on the system using different codebook schemes. As can be seen from the Figure 11, when the number of users increases, the interference from different cells increases which causes communication interruption. Moreover, the proposed 3D codebook scheme shows have lowest Inter-Cell Interference (ICI) level which is much better as compared with those of previous papers [24,25] and 2D DFT schemes. Therefore, the proposed 3D codebook scheme also shows better ICI performance which obviously makes it an attractive candidate to deploy in real-world application scenarios.
Enlarge this image.Figure 11. Comparison of the inter-cell interference versus a number of users for the proposed 3D codebook and other state-of-the-art schemes.
Figure 12 compares a number of feedback bits required versus the number of users for the proposed 3D MIMO codebook and other state-of-the-art schemes. It is clear from the results that the proposed scheme shows efficient performance as it requires a smaller number of feedback bits for channel estimation whereas the other codebook schemes require large number feedback bits which indicates that such schemes have large feedback overhead. Therefore, such comparison proves that the proposed 3D MIMO codebook scheme is also cost-effective as we know that feedback bits directly impact the system implementation cost, thus the proposed scheme is time-efficient and cost-efficient.
Enlarge this image.Figure 12. Comparison of feedback bits versus the number of users for the proposed 3D codebook scheme and other state-of-the-art schemes.
Figure 13 compares the spectral efficiency of the proposed 3D MIMO codebook scheme against the number antennas (Nv) and compares it with other schemes. As can be seen from Figure 13, when the number of antennas increases, the spectral efficiency increases for all codebook schemes. Furthermore, the proposed 3D DFT codebook scheme shows better performance than 2D and 3D DFT [11] codebook schemes. It is worth notable from the results that the proposed codebook scheme shows nearly optimal SE performance as its curve is closer to the ideal CSI performance. Therefore, such results show that the proposed codebook scheme have efficient performance in case of a large number of antennas.
Enlarge this image.Figure 13. Spectral efficiency comparison against the number of antennas for the proposed 3D MIMO codebook scheme with other schemes.
7. Conclusions
This paper constructs a multi-user 3D-MIMO heterogeneous network system model. Through finite feedback quantization error analysis, according to the quantization error and statistical characteristics of the random distribution of the system, the influence of feedback overhead and base station density on system performance is analyzed using stochastic geometry technology. Based on the traditional precoding scheme, an improved 3D precoding scheme based on horizontal emission angle and vertical down-tilt is proposed. Through simulation analysis, the influence of feedback overhead on system throughput was compared, and the effects of traditional DFT precoding methods in 2D and 3D environments and improved 3D precoding schemes on system BER and throughput were compared. The simulation results show that the feedback overhead will reduce the system throughput and improve the system BER, while the improved precoding scheme due to the joint consideration of the horizontal emission angle and vertical down-tilt, thus effectively improving the system throughput and reducing the system BER, optimized system performance. Future work in this research is to incorporate mmWave with 3D-MIMO in order to utilize it underutilized bandwidth which ranges from 30–300 GHz. Also, various other important parameters such as Energy Efficiency and Normalized Mean Square Error (NMSE) can be analyzed in different deployment scenarios.
Author Contributions
M.A. provides extensive support in the overall research; I.K. conceived and designed the presented idea and developed the theory, performed the simulations, and wrote the paper; J.L. verified the analytical methods and encouraged to investigate various relevant aspects of the proposed research; I.B. provided critical feedback and helped shape the research, analysis, and manuscript. All authors discussed the results and contributed to the final manuscript.
Acknowledgments
This work has been partially supported by the “Ministerio de Economía y Competitividad” in the “Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia, Subprograma Estatal de Generación de Conocimiento” within the project under Grant BIA2017-87573-C2-2-P.
Conflicts of Interest
The authors declare no conflicts of interest.
1. Khan, I. A Robust Signal Detection Scheme for 5G Massive Multiuser MIMO Systems. IEEE Trans. Veh. Technol. 2018.
2. Gesbert, D.; Kountouris, M.; Heath, R.W. Shifting the MIMO Paradigm: From Single User to Multiuser Communications. IEEE Signal. Process. Mag. 2007, 24, 36–46.
3. Liu, G.; Hou, X.; Wang, F.; Jin, J.; Tong, H.; Huang, Y. Achieving 3D-MIMO With Massive Antennas from Theory to Practice With Evaluation and Field Trial Results. IEEE Syst. J. 2016, 11, 62–71.
4. Ngo, H.Q.; Marzetta, T.L.; Larsson, E.G. Analysis of the Pilot Contamination Effect in Very Large Multicell Multiuser MIMO Systems for Physical Channel Models. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Prague, Czech Republic, 22–27 May 2011; pp. 3464–3467.
5. Lu, X.; Tolli, A.; Piirainen, O.; Juntti, M.; Li, W. Comparison of Antenna Arrays in a 3-D Multiuser Multicell Network. In Proceedings of the 2011 IEEE International Conference on Communications, Kyoto, Japan, 5–9 June 2011; pp. 1–6.
6. Ng, B.L.; Kim, Y.; Lee, J.; Li, Y.; Nam, Y.-H.; Zhang, J.; Sayana, K. Fulfilling the Promise of Massive MIMO with 2D Active Antenna Array. In Proceedings of the 2012 IEEE Globecom Workshops, Anaheim, CA, USA, 3–7 December 2012; pp. 691–696.
7. Nadeem, Q.-U.-A.; Kammoun, A.; Debbah, M.; Alouini, M.-S. 3D Massive MIMO Systems: Modeling and Performance Analysis. IEEE Trans. Wirel. Commun. 2015, 14, 6926–6939.
8. Li, X.; Jin, S.; Suraweera, H.A.; Hou, J.; Gao, X. Statistical 3-D Beamforming for Large-Scale MIMO Downlink Systems Over Rician Fading Channels. IEEE Trans. Commun. 2016, 64, 1529–1543.
9. Khan, I.; Zafar, M.H.; Jan, M.T.; Lloret, J.; Basheri, M.; Singh, D. Spectral and Energy Efficient Low-Overhead Uplink and Downlink Channel Estimation for 5G Massive MIMO Systems. Entropy 2018, 20, 92.
10. Khan, I.; Singh, D. Efficient Compressive Sensing Based Sparse Channel Estimation for 5G Massive MIMO Systems. AEUE Int. J. Electron. Commun. 2018, 89, 181–190.
11. Xie, Y.; Jin, S.; Wang, J.; Zhu, Y.; Gao, X.; Huang, Y. A Limited Feedback Scheme for 3D Multiuser MIMO Based on Kronecker Product Codebook. In Proceedings of the IEEE 24th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications, London, UK, 8−11 September 2013; pp. 1130–1135.
12. Khan, I.; Singh, M.; Singh, D. Compressive Sensing Based Sparsity Adaptive Channel Estimation for 5G Massive MIMO Systems. Appl. Sci. 2018, 8, 754.
13. Halbauer, H.; Saur, S.; Koppenborg, J.; Hoek, C. 3D Beamforming: Performance Improvement for Cellular Networks. Bell Lab. Tech. J. 2013, 18, 37–56.
14. Ogawa, S.; Nishimori, K.; Taniguchi, R.; Mitsui, T.; Hiraguri, T. Performance Evaluation of Downlink Multi-Beam Massive MIMO with Simple Transmission Scheme at Both Base and Terminal Stations. Electronics 2017, 6, 100.
15. Han, Y.; Jin, X.; Huang, Y.; Jiang, L.; Wang, G. Design of double codebook based on 3D dual-polarized channel for multiuser MIMO system. EURASIP J. Adv. Signal. Process. 2014.
16. Xu, Y.; Xia, X.; Xu, K.; Wang, Y. Three-Dimension Massive MIMO for Air-to-Ground Transmission: Location-Assisted Precoding and Impact of AoD Uncertainty. IEEE Access. 2017, 5, 15582–15596.
17. Cheng, X.; Yu, B.; Yang, L.; Zhang, J.; Liu, G.; Wu, Y.; Wan, L. Communicating in the real world: 3D MIMO. IEEE Wirel. Commun. 2014, 21, 136–144.
18. Xu, Z.; Yang, C.; Li, G.Y.; Liu, Y.; Xu, S. Energy-efficient CoMP Precoding in Heterogeneous Networks. IEEE Trans. Signal. Process. 2014, 62, 1005–1017.
19. Kountours, M.; Andrews, J.G. Downlink SDMA with Limited Feedback in Interference-limited Wireless Networks. IEEE Trans. Wirel. Commun. 2012, 11, 2730–2741.
20. Love, D.J.; Heath, R.W.; Lau, V.K.N.; Gesbert, D.; Rao, B.D.; Andrews, M. An overview of limited feedback in wireless communication systems. IEEE J. Sel. Areas Commun. 2008, 26.
21. Zhong, Z.; Peng, J.; Luo, W.; Huang, K. A Tractable Approach to Analyzing the Physical-layer Security in K-tier Heterogeneous Cellular Networks. China Commun. 2015, 12, 166–173.
22. Li, W.; Wang, T.; Lan, X. Codebook Based Beamforming in MIMO Broadcast Channels with Finite Rate Feedback. In Proceedings of the 1st International Conference on Information Science and Engineering, New York, NY, USA, 26–28 December 2009; pp. 2582–2585.
23. Zhang, J.; Heath, R.W.; Kountouris, M.; Andrews, J.F. Mode Switching for the multi-antenna Broadcast Channel Based on Delay and Channel Quantization. EURASIP J. Adv. Signal. Process. 2009, 1, 1–15.
24. Wang, Z.; Liu, W.; Qian, C.; Chen, S.; Hanzo, L. Two-Dimensional Precoding for 3-D Massive MIMO. IEEE Trans. Veh. Technol. 2016, 66, 5485–5490.
25. Li, X.; Zhao, H.; Zhao, L.; Zhao, W.; Zheng, S. Transmission Scheme with Limited Channel State Information Feedback for 3D MIMO System. Int. J. Antennas Propag. 2015, 15, 1–12.
1Department of Industrial Engineering, University of Engineering & Technology, Peshawar 814 KPK, Pakistan
2Department of Electrical Engineering, University of Engineering & Technology, Peshawar 814 KPK, Pakistan
3Integrated Management Coastal Research and Telecommunications and Multimedia Applications (iTEAM) Institutes, Universitat Politècnica de València, 46022 Camino de Vera, Spain
*Author to whom correspondence should be addressed.
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