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For three-dimensional (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 3D-Urban Macro Cell (3D-UMa) and 3D-Urban Micro Cell (3D-UMi) scenarios, we propose the angle quantization codebook for vertical domain, while the codebook of long term evolution-advanced (LTE-Advanced) is still adopted in horizontal domain to preserve compatibility with the LTE-Advanced. Based on the angle quantization codebook, the subsampled 3-bit DFT codebook is designed for vertical domain. The system-level simulation results reveal that, to compromise the feedback overhead and system performance, 2-bit codebook for 3D-UMa scenario and 3-bit codebook for 3D-UMi scenario can meet requirements in vertical domain. The feedback period for vertical domain can also be extended appropriately to reduce the feedback overhead.

Multiple-input multiple-output (MIMO) is a maturing and important technology in the 3rd Generation Partnership Project (3GPP) LTE and LTE-Advanced. 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 [

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 two-dimensional (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 [

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 [

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 [

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 [

Several works have been engaged in this issue. In [

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 3D-UMa and 3D-UMi 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.

Here we incorporate 3D antenna radiation pattern proposed by 3GPP for the antenna elements of the BS array [

The horizontal radiation pattern is listed below:

And the vertical radiation pattern is

The 3D antenna pattern is

To evaluate the massive MIMO, here we introduce the 3D channel model of 3GPP [

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 [

The coordinate system of 3D MIMO and the antenna configuration in the BS.

For the

In the non-line-of-sight (NLOS) case,

Figure

The cellular network of the downlink system.

Here we just consider that the number of transmission spatial layers to each user is 1. The received signal vector

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

The CDF of ZSD in 3D-UMa and 3D-UMi scenarios.

Figure

Limited feedback model of 3D MIMO.

Assume the transmitted antenna elements in the BS are rowwise indexed; the channel matrix from user

When the antenna elements in the BS are columnwise indexed, the channel matrix between user

The user

For MU-MIMO, assume that the set of the scheduled users is

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 LTE-Advanced for horizontal domain. Based on the ZoD distribution in 3D-UMa and 3D-UMi scenarios, we focus on the codebook design for the vertical dimension to balance the feedback overhead and the system performance.

Figure

The definition of ZoD.

The CDF of users’ ZoD in the cellular network under 3D-UMa scenario and 3D-UMi scenario.

We can see that the distribution range of ZoD mainly concentrates on

For small ZSD in the vertical domain, increasing the codebook size

Considering the feedback overhead and system performance, we assign

The uniform quantization can be calculated as

Also we can select the angles nonuniformly based on the CDF of the users’ ZoD. Codebooks 1-3-b, 1-2, 1-1-a, 1-1-b, and 1-1-c select the angles which account for a large percentage of the ZoD distribution under 3D-UMa scenario in Figure

The uniform quantization of

Also, in codebooks 2-3-b, 2-2-a, 2-2-b, 2-1-a, 2-1-b, and 2-1-c, the angle set is made up of the angles which account for a large percentage of the ZoD distribution under 3D-UMi scenario in Figure

Discrete Fourier Transform- (DFT-) based codebook is favored by LTE for its simplicity. And in [

The code word

To select 8 code words from

Here we just cope with the condition in which

Here we utilize the construction of codebook 1-3-c as an example to show how to select code word elements from

The elements in

The elements in

Via the same method, we can construct the codebook

Because the range of ZoD under 3D-UMa scenario is small, the 3-bit DFT codebook 1-3-c corresponding to codebook 1-3-a and codebook 1-3-d corresponding to codebook 1-3-b are the same.

Here we will adopt the same method above to design the 3-bit 32-DFT codebook for 3D-UMi scenario.

The angle set of codebook 2-3-a is

To evaluate the proposed scheme and codebook design, the system-level simulation is performed. In the simulation, the cellular network layout adopts wrap-round technique. As depicted in Figure

Simulation parameters configuration.

Parameters | Settings |
---|---|

Bandwidth | 10 MHz |

Antenna element interval | 0.5 |

Carrier frequency | 2 GHz |

The number of users per cell | 10 |

User distribution | Refer to [ |

User speed | 3 km/h |

Traffic model | Full buffer |

Schedule | Proportional fair |

Channel estimation | Ideal |

Receiver | MMSE |

HARQ | The maximal number of retransmissions is 4 |

Wrapping method | Geographical distance based |

To make a comparison with the proposed scheme, we introduce the method in [

Figure

The system-level simulation results of the proposed feedback scheme.

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 cross-polarized antenna array is adopted. The antenna array configuration is (10, 4, 2); namely,

Simulation results of the codebooks for the vertical domain under 3D-UMa scenario.

Simulation results of the codebooks for the vertical domain under 3D-UMi scenario.

For 3D-UMa scenario, relative to the performance of the 5-bit 32-DFT codebook in vertical domain, the performances of codebooks 1-4, 1-3-a, 1-3-b, 1-3-c, and 1-3-d decline slightly as shown in Figure

For 3D-UMi scenario, Figure

The 4-bit codebooks, such as codebooks 1-4 and 2-4, behave well for 3D-UMa and 3D-UMi scenarios. To reduce the feedback overhead, the 3-bit codebook is viable and worth recommending for 3D-UMi scenario while for 3D-UMa scenario 2-bit codebook tends to be attractive. The reason is that the distribution range of ZoD in 3D-UMi scenario is larger than that in 3D-UMa 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 3-bit DFT-based codebooks achieve a slight improvement in performance. In general, the performances of the 3-bit DFT-based codebook and the corresponding angle quantization codebook are also close because of the small ZoD distribution range.

In the simulations above, the feedback periods for the horizontal and vertical domains are both 5 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 5 ms and let the feedback period for vertical domain vary from 5 ms to 20 ms, 100 ms, and 200 ms. In the simulation, codebook 1-3-a is used for 3D-UMa scenario and codebook 2-3-a is used for 3D-UMi scenario for the vertical domain. The antenna array configuration is the same to the configuration in Section

From Figures

Feedback period for vertical domain with different values in 3D-UMa scenario.

Feedback period for vertical domain with different values in 3D-UMi scenario.

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 3D-UMa scenario and 3D-UMi scenario, the angle quantization codebooks for vertical domain are proposed. Also the 3-bit DFT-based codebook selected from 32-DFT 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.

In [

The channel model with

For simplicity, here we just analyse the uniform quantization angle codebook. The

Because formula (

Define

This means that we can increase the codebook size

This means that increasing the codebook size cannot improve the sum rate in this situation.

The authors declare that there is no conflict of interests regarding the publication of this paper.

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).