Research Article  Open Access
Limited Feedback for 3D Massive MIMO under 3DUMa and 3DUMi Scenarios
Abstract
For threedimensional (3D) massive MIMO utilizing the uniform rectangular array (URA) in the base station (BS), we propose a limited feedback transmission scheme in which the channel state information (CSI) feedback operations for horizontal domain and vertical domain are separate. Compared to the traditional feedback scheme, the scheme can reduce the feedback overhead, code word index search complexity, and storage requirement. Also, based on the zenith of departure angle (ZoD) distribution in 3DUrban Macro Cell (3DUMa) and 3DUrban Micro Cell (3DUMi) scenarios, we propose the angle quantization codebook for vertical domain, while the codebook of long term evolutionadvanced (LTEAdvanced) is still adopted in horizontal domain to preserve compatibility with the LTEAdvanced. Based on the angle quantization codebook, the subsampled 3bit DFT codebook is designed for vertical domain. The systemlevel simulation results reveal that, to compromise the feedback overhead and system performance, 2bit codebook for 3DUMa scenario and 3bit codebook for 3DUMi scenario can meet requirements in vertical domain. The feedback period for vertical domain can also be extended appropriately to reduce the feedback overhead.
1. Introduction
Multipleinput multipleoutput (MIMO) is a maturing and important technology in the 3rd Generation Partnership Project (3GPP) LTE and LTEAdvanced. Its advantages have been exploited in the past years. Recently, relying on a large excess of antennas in the BS over the terminals, massive MIMO as a promising and fascinating technology to improve energy efficiency and spectrum efficiency of future networks becomes a hot spot in academia and industry [1, 2].
Restricted to the physical space, the URA draws a lot of attention in massive MIMO system. With the use of active antenna systems (AAS), such twodimensional (2D) antenna array can offer more spatial degrees of freedom (DoFs) in both elevation and azimuth domains in contrast to the uniform linear array (ULA). Equipped with the 2D antenna array, the BS can form beams in both elevation and azimuth domains adaptively [3]. Recently, there is a new study item for 3D MIMO which has been approved for the sake of investigation on the benefit of 2D antenna array [4].
In the traditional 2D MIMO system, the users can be just served simultaneously in different horizontal directions. However users located in the same azimuth angle cannot be served at the same time because all beams in vertical domain have the same downtilt [5]. With a 2D active antenna array, 3D MIMO can exploit the elevation dimension as well as the azimuth dimension in MIMO system. It is possible to achieve system performance improvement to meet the increasing capacity demand [6, 7].
Traditional channel models such as 2D spatial channel models (SCMs) just concentrate on the 2D propagation in the horizontal plane. Accordingly, to evaluate the performance of 3D MIMO transmission technique, the 3D channel model considering both the azimuth domain and elevation domain of signal propagation must be proposed [8, 9]. The 3GPP has developed the 3D channel model under 3DUMa and 3DUMi scenarios [10].
To explore the potentials of massive MIMO, downlink transmit precoding is essential. The acquisition of CSI is crucial for the efficient precoding. The time division duplexing (TDD) system can obtain CSI based on channel reciprocity via uplink pilot training [1]. There are also many existing cellular networks based on frequency division duplexing (FDD) which obtains the CSI via uplink feedback from the user. However, the feedback overhead grows inevitably as the number of antennas increases and the code word search requires more computational complexity [11, 12]. The limited feedback is challenging for massive MIMO.
Several works have been engaged in this issue. In [11], based on the spatial correlation and channel conditions in massive MIMO systems, the authors suggest two compression methods for channel feedback to reduce the feedback overhead. In [12], a novel noncoherent trelliscoded quantization for massive MIMO is proposed. Its complexity increases linearly with the number of transmit antennas. When supporting a variable number of antennas, it could adjust flexibly the feedback overhead and does not have to change the structure of the quantizer. Literature [13] designs a noniterative twostage precoding method with limited feedback for the interference channel in massive MIMO. The second stage precoders can compress the CSI of interfering links. Based on the compressed CSI, the task of the first stage precoders is to zeroforce the interference. A hybrid limited feedback design is proposed for massive MIMO in [14]. It considers both the quantized feedback and codebook based feedback. Literature [15] proposes a codebook design for port modulation in massive MIMO system. It can offer low average bit error probability without instantaneous CSI at the transmitter, only with low feedback burden. In [16], based on the Kroneckertype approximation of the array correlation structure, the authors propose a codebook for URA deployment and the codebook is suitable for closely spaced antennas of massive MIMO. Literature [17] proposes a limited feedback transmission for 3D MIMO. It utilizes two CSIRS ports to calculate the horizontal CSI and vertical beam gain. In [18], the authors propose a 3D MIMO beamforming scheme. Using the horizontal and vertical PMIs from the user, the scheme can improve the overall system performance relatively to the 2D MIMO system.
In this paper, for the massive MIMO equipped with the URA, we propose the scheme in which the user feeds back the CSI for horizontal domain and vertical domain separately based on the characteristics of 3D MIMO. This can reduce the code word size and search complexity. According to the characteristics of the 3DUMa and 3DUMi scenarios, we design the codebook for the vertical domain and reduce the feedback overhead as much as possible. Also, we propose that the feedback period for vertical domain can be extended, thus leading to the reduction of feedback overhead.
2. System Model
2.1. 3D Antenna Radiation Pattern
Here we incorporate 3D antenna radiation pattern proposed by 3GPP for the antenna elements of the BS array [10].
The horizontal radiation pattern is listed below:
And the vertical radiation pattern iswhere is the azimuth angle between the user and the boresight of the array in horizontal domain. is the elevation angle between the user and the boresight of the array in vertical domain. is the fronttoback attenuation and denotes sidelobe attenuation. and are the halfpower beamwidth (HPBW) in horizontal and vertical domains, respectively.
The 3D antenna pattern is
2.2. 3D Channel Model
To evaluate the massive MIMO, here we introduce the 3D channel model of 3GPP [10]. The 3D channel model considers not only the radio propagation in the horizontal dimension but also the radio propagation in the vertical dimension in contrast to the 2D channel model.
The generation of the 3D channel includes the scenario selection, the determination of user parameters, and the channel coefficients. The channel coefficients consist of the large scale parameters and the small scale parameters. Due to space limitations, for the large scale parameters such as shadow fading and path loss refer to [10]. The generation of the small scale channel coefficients comes from a contribution of several clusters. Also each cluster contains several rays. In Figure 1, we depict a ray labeled as in the coordinate system for 3D MIMO. denotes the th ray in the th cluster. In this figure, is the direction of . and are the spherical basis vectors. In the coordinate system, the zenith angle of departure (arrival) and the azimuth angle of departure (arrival) are defined. points to the zenith direction and points to the horizontal direction.
For the th cluster which is composed of rays, the channel coefficient of the receivetransmit element pair () is modeled as the following.
In the nonlineofsight (NLOS) case,In the lineofsight (LOS) case, let . The channel coefficients include a lineofsight ray and the other channel coefficients generated by (4),where is Diracâ€™s delta function. and are the antenna radiation patterns of transmit antenna in the direction of the spherical basis vectors, and , respectively. and are the antenna radiation patterns of receive element in the direction of the spherical basis vectors, and , respectively. and indicate the location vectors of the receive and transmit elements, respectively;is the spherical unit vector with the elevation departure angle and the azimuth departure angle . Also is the counterpart at the receive side. is the crosspolarization power ratio. means the Doppler frequency component. denotes the Ricean factor. indicates the wavelength of the carrier frequency. are the random initial phases for the th ray of the th cluster and for four different polarizations combinations . Due to space constraint, for more detailed description about the process of the 3D channel generation refer to [10].
2.3. Received Signal Model
Figure 2 depicts the multicell layout. Each hexagonal site is split into 3 cells. The BS in each cell is equipped with the URA. As depicted in Figure 1, the antenna array configuration comprises antenna elements in the vertical direction and antenna elements in the horizontal direction. So the total number of antennas is . Each user has receiving antennas.
Here we just consider that the number of transmission spatial layers to each user is 1. The received signal vector of the coscheduled users in cell can be expressed aswhere is the vector of the transmitted signal. is the channel matrix from the BS in cell to the coscheduled users in cell . is the average transmit power. The second term denotes the interference from the neighboring cells. is the precoding matrix for the coscheduled users. is the noise.
3. 3D CSI Feedback Scheme
Based on the characteristics of URA, here we propose that the CSI for horizontal dimension and the CSI for vertical dimension are fed back separately. Assume that, based on the downlink pilot, each user achieves the perfect channel matrix. Then the user selects the appropriate precoding code words from the codebook for the horizontal and vertical domains, respectively.
Figure 3 depicts the cumulative distribution function (CDF) of zenith spread of departure angle (ZSD) and azimuth spread of departure angle (ASD) in 3DUMa and 3DUMi scenarios. In vertical plane, the angle spread (AS) is relatively smaller than that in horizontal plane in both scenarios.
Figure 4 shows the limited feedback model of 3D MIMO. Here we describe the limited feedback scheme for user in cell . The procedure of the code word selection for user is as follows.
Step 1. Assume the transmitted antenna elements in the BS are rowwise indexed; the channel matrix from user to the BS is . () is the channel matrix between the th row transmit antenna elements and user . For convenience, here is called the horizontal channel. Calculate the average correlation matrix for the horizontal channelsAssume that the set of codebook for horizontal domain is , . So the optimal code word for the horizontal dimension can be selected as
Step 2. When the antenna elements in the BS are columnwise indexed, the channel matrix between user and the BS is . () is the channel matrix from the th column of antenna elements to user . We call the vertical channel. So the average correlation matrix for vertical domain is calculated asAssume that the set of codebook for vertical domain is , (). So the optimal code word for the vertical dimension is
Step 3. The user feeds back the code word indexes for horizontal and vertical domains separately to BS in cell . In the BS, the 3D precoding vector for channel matrix is calculated as follows:where denotes the Kronecker product.
For MUMIMO, assume that the set of the scheduled users is in the BS. Based on the principle of maximizing the total capacity of the users, the BS selects the paired users from the set . In order to eliminate the interference of coscheduled users, the operation of zero forcing (ZF) is brought in to form the precoding matrix. The precoding matrix in (7) can be expressed aswhere is the normalization factor. is the number of coscheduled users.
4. Proposed Codebook Design
The CSI can be fed back separately for the horizontal and vertical domains. In this paper, for a backward compatibility, we still exploit the existing codebook of LTEAdvanced for horizontal domain. Based on the ZoD distribution in 3DUMa and 3DUMi scenarios, we focus on the codebook design for the vertical dimension to balance the feedback overhead and the system performance.
4.1. ZoD Angle Quantization Codebook
Figure 5 depicts the ZoD of the user. ZoD is the angle measured between the zenith direction and the line connecting the user to the respective BS. Figure 6 presents the CDF of ZoD of all users in the cellular network under 3DUMa and 3DUMi scenarios, respectively.
We can see that the distribution range of ZoD mainly concentrates on ~ in 3DUMa scenario and ~ in 3DUMi scenario. Based on the distribution of the ZoD, we propose angle quantization codebook set () for the vertical domain. The code word in is expressed aswhere is the index of the code word. is the number of antennas in vertical direction. is the quantized angle value. is the codebook size (in bits). is the space between the vertical antenna elements. is the carrier wavelength.
For small ZSD in the vertical domain, increasing the codebook size of the angle quantization codebook can improve the system performance; while the AS or the codebook size is large enough, increasing the codebook size does not work. This will be proved in Appendix.
Considering the feedback overhead and system performance, we assign to 4, 3, 2, and 1 to evaluate the system performance. The details of the codebook design are listed as follows.
4.1.1. Codebook for 3DUMa Scenario
Codebook 14. Consider and uniform quantization in the angle range ~.
Codebook 13a. Consider and uniform quantization in the angle range ~.
The uniform quantization can be calculated as
Also we can select the angles nonuniformly based on the CDF of the usersâ€™ ZoD. Codebooks 13b, 12, 11a, 11b, and 11c select the angles which account for a large percentage of the ZoD distribution under 3DUMa scenario in Figure 6 to construct the angle set.
Codebook 13b. Consider and .
Codebook 12. Consider and .
Codebook 11a. Consider and .
Codebook 11b. Consider and .
Codebook 11c. Consider and .
4.1.2. Codebook for 3DUMi Scenario
Codebook 24. Consider and uniform quantization in the angle range ~.
Codebook 23a. Consider and uniform quantization in the angle range ~.
The uniform quantization of can be calculated as
Codebook 23b. Consider and .
Codebook 22a. Consider and .
Codebook 22b. Consider and .
Codebook 21a. Consider and .
Codebook 21b. Consider and .
Codebook 21c. Consider and .
Also, in codebooks 23b, 22a, 22b, 21a, 21b, and 21c, the angle set is made up of the angles which account for a large percentage of the ZoD distribution under 3DUMi scenario in Figure 6.
4.2. Sampling DFT Codebook
Discrete Fourier Transform (DFT) based codebook is favored by LTE for its simplicity. And in [19], it reveals that DFTbased codebook is effective for small AS. The simulation results in Section 5 reveal that 3bit angle quantization codebook for 3DUMa and 3DUMi scenarios can guarantee the system performance. To make full use of the orthogonality of the DFTbased codebook, here we select code words from 5bit 32DFT codebook to construct 3bit codebook set for vertical domain.
The code word of the 5bit 32DFT codebook set is expressed aswhere . is the index of code word.
To select 8 code words from and construct 3bit codebook, we need to calculate the corresponding beam directions of 32DFT codebook through the expression
Here we just cope with the condition in which . Calculated by (18), the set of the beam direction corresponding to the code word in sorted by from 0 to 31 is
4.2.1. DFTBased Codebook for 3DUMa Scenario
Here we utilize the construction of codebook 13c as an example to show how to select code word elements from to generate the 3bit 32DFT codebook. The angle set corresponding to codebook 13a is . Based on the angle set , we select angle elements from to construct angle set . The angle element selection from follows the principles as below:(1)The elements in are approximately equal to the elements in set .(2)The elements in are sorted in ascending order. So the element values in corresponding to the elements in are also sorted in ascending order. Also for 3DUMa scenario, the range of angle values is restricted to ~.So following the principles, corresponding to the set , we can get , from . The index set corresponding to the angle elements of in is . So based on the index set, we select code words from to construct the codebook 13c:
Via the same method, we can construct the codebook based on codebook 13b. According to the angle set of codebook 13b, the angle set is . Through the index set corresponding to the angle elements of from , we can get the code words in . So codebook 13d can be expressed as
Because the range of ZoD under 3DUMa scenario is small, the 3bit DFT codebook 13c corresponding to codebook 13a and codebook 13d corresponding to codebook 13b are the same.
4.2.2. DFTBased Codebook for 3DUMi Scenario
Here we will adopt the same method above to design the 3bit 32DFT codebook for 3DUMi scenario.
The angle set of codebook 23a is . So the corresponding angle subset from the set is , . Based on the indexes of the angle elements of in , we can select code words from to construct codebook 23c:
is the angle set of codebook 23b. The corresponding angle set from is . So we obtain codebook 23d:
5. Numerical Results
To evaluate the proposed scheme and codebook design, the systemlevel simulation is performed. In the simulation, the cellular network layout adopts wrapround technique. As depicted in Figure 2, there are 19 hexagonal sites each with 3 cells in horizontal domain. So the cellular network consists of 57 cells. And each cell accommodates 10 active users. For the generation of 3D channel model refer to [10]. For simplicity, detailed simulation parameters are listed in Table 1. The configuration of the 2D planar uniformly spaced antenna array in the BS can be represented by (). is the number of antenna elements with the same polarization in each column. is the number of columns. is number of polarization dimensions. Each user is equipped with 2 antennas; namely, .

5.1. Separate CSI Feedback for Horizontal and Vertical Domains
To make a comparison with the proposed scheme, we introduce the method in [18] as the benchmark scheme which also proposes a separation of the vertical and horizontal domains. In this subsection, the antennas array configuration is (); namely, , and we adopt the copolarized antenna array. The proposed scheme utilizes the same 5bit 32DFT codebook for horizontal and vertical dimensions, respectively. In the benchmark scheme, assume that it transmits one stream in horizontal domain and one stream in vertical domain, respectively. Here the code word for the benchmark scheme in two domains is the vector. We adopt the method in [16] to generate the codebook for the benchmark scheme. It utilizes two 5bit 32DFT codebooks to generate the 10bit codebook by the Kronecker product. Each code word is a vector.
Figure 7 shows the simulation results of the two schemes in singleuser MIMO system under 3DUMa and 3DUMi scenarios. We can see that the performance of the proposed scheme has a slight decrease compared to the benchmark scheme. When the horizontal and vertical domains utilize the same codebook set, the benchmark scheme needs to store code words and the feedback overhead for each domain is 10 bits while the proposed scheme just needs to store code words and the feedback overhead for each domain is 5 bits. What is more, quantizing the vector in the proposed scheme has a lower complexity relative to quantizing the vector in the benchmark scheme. Though there is a slight performance degradation, the proposed scheme reduced the storage requirement, feedback overhead, and search complexity compared to the benchmark scheme.
5.2. Codebook Design for the Vertical Domain
Dual polarization can not only save antenna space but also provide diversity gain and rich scattering for more degrees of freedom. In this subsection, the crosspolarized antenna array is adopted. The antenna array configuration is (10, 4, 2); namely, and . And we adopt crosspolarized antennas. In the horizontal domain, the 8Tx codebook of LTEAdvanced which is a double codebook design and is appropriate for crosspolarized array is utilized [20]. In the vertical domain, the proposed codebooks in Section 4 are evaluated. Figures 8 and 9 show the simulation results in MUMIMO system under 3DUMa and 3DUMi scenarios. The maximal number of coscheduled users is 4.
For 3DUMa scenario, relative to the performance of the 5bit 32DFT codebook in vertical domain, the performances of codebooks 14, 13a, 13b, 13c, and 13d decline slightly as shown in Figure 8. The cell average spectrum efficiency of the 2bit codebook 12 goes down by 6.70% and the cell edge spectrum efficiency decreases by 6.95%. The feedback overhead reduces 3 bits from 5 bits to 2 bits and the loss of the system performance is acceptable. However, the performance of 1bit codebook such as 11a, 11b, and 11c has a sharp degradation.
For 3DUMi scenario, Figure 9 shows that, considering the feedback overhead and the performance, 3bit codebooks including codebooks 23a, 23b, 23c, and 23d are appropriate and acceptable relative to 5bit 32DFT codebook. But the 2bit codebooks perform poorly. Relative to the 5bit 32DFT codebook, the cell average spectrum efficiency of codebooks 22a and 22b decreases by about 12% and the cell edge spectrum efficiency decreases by about 18%. The performance of the 1bit codebooks including codebooks 21a, 21b, and 21c drops drastically.
The 4bit codebooks, such as codebooks 14 and 24, behave well for 3DUMa and 3DUMi scenarios. To reduce the feedback overhead, the 3bit codebook is viable and worth recommending for 3DUMi scenario while for 3DUMa scenario 2bit codebook tends to be attractive. The reason is that the distribution range of ZoD in 3DUMi scenario is larger than that in 3DUMa scenario.
Also we can see the nonuniform quantization angle codebook outperforms slightly the uniform quantization angle codebook. Because the ZoD distribution range is small in both scenarios, the performances of the two types of codebooks are close.
Relative to the corresponding angle quantization codebooks, the 3bit DFTbased codebooks achieve a slight improvement in performance. In general, the performances of the 3bit DFTbased codebook and the corresponding angle quantization codebook are also close because of the small ZoD distribution range.
5.3. The Extension of Feedback Period for Vertical Domain
In the simulations above, the feedback periods for the horizontal and vertical domains are both 5â€‰ms. In practice, the CSI feedback for horizontal domain and vertical domain can be operated separately. So in this subsection, we study the situation of different feedback periods for the two domains. Here we let the feedback period for horizontal domain remain 5â€‰ms and let the feedback period for vertical domain vary from 5â€‰ms to 20â€‰ms, 100â€‰ms, and 200â€‰ms. In the simulation, codebook 13a is used for 3DUMa scenario and codebook 23a is used for 3DUMi scenario for the vertical domain. The antenna array configuration is the same to the configuration in Section 5.2.
From Figures 10 and 11, we can see that, relative to the performance of the feedback period 5â€‰ms, the cell average spectrum efficiency and cell edge spectrum efficiency decline slightly as the feedback period for vertical domain extends. This is because the ZSD is small in vertical domain as depicted in Figure 3 and the speed of users in vertical direction is very slow. This means that the feedback period for the vertical domain can be extended appropriately to decrease the feedback overhead.
6. Conclusion
In this paper, we study the separate feedback scheme for 3D massive MIMO. It can reduce the feedback overhead, search complexity, and the storage of the code words. Based on the feature of 3DUMa scenario and 3DUMi scenario, the angle quantization codebooks for vertical domain are proposed. Also the 3bit DFTbased codebook selected from 32DFT codebook is recommended. In the end, corresponding to the feedback separation for 3D MIMO in the two domains, we reveal that the feedback period for vertical domain can be extended more in order to decrease the feedback overhead.
Appendix
In [21], the authors analyse the per user rate loss led by utilizing DFT codebook. Here based on the method we investigate the per user rate loss led by angle quantization codebook in vertical domain. Because the angle quantization codebook is designed for vertical domain, for simplicity, we just consider the channel model for ULA which is vertically positioned. Figure 12 presents the channel vector of user consisting of uncorrelated subpaths. The channel can be expressed aswhere is the subpaths gain. is the steering vector. is the number of antenna elements. One has and . is independent of . is antenna spacing distance in vertical direction. is the wavelength. is the angle of subpath with respect to the zenith direction. is the direction matrix. is the gain vector. Assume that .
For simplicity, here we just analyse the uniform quantization angle codebook. The th code word in a bit codebook iswhere is the distribution range of the usersâ€™ ZoD.
Because formula (A.2) is the same to formula (4) in [21] in form, the conclusion of DFT codebook can be applicable to the angle quantization codebook. So we can get the conclusions from [21] as follows.
Define . When the AS in elevation domain is small, can be satisfied. The gap between the rate with perfect CSI and the rate with limited feedbackwhere and are constants. is transmit power of the BS.
This means that we can increase the codebook size to improve the system performance when AS is small. When goes to infinity, approaches a continuous value; the rate loss is more tightly upper bounded by where and .
This means that increasing the codebook size cannot improve the sum rate in this situation.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgments
This research has been supported by 863 Project of China (no. 2014AA01A705) and the State Key Laboratory of Wireless Mobile Communication of China Academy of Telecommunication Technology (no. 2007DQ305156).
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Copyright
Copyright © 2015 Zheng Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.