This work was supported by the National Basic Research Program of China (“973” Program) under Grant No. 2007CB307101 and No. 2007CB307106.
In the evolution of Long Term Evolution (LTE) standards, Coordinated Multi-Point (CoMP) transmission is an important technology. The core idea of the technology is to construct a Virtual Multiple-Input Multiple-Output (VMIMO) architecture featuring in multi-point coordination, thus enhancing the cell-edge performance. Coordination in CoMP occurs in several forms, including coordination between Remote Radio Units (RRUs) within an eNodeB, coordination between an eNodeB and its relays, and coordination between eNodeBs. The implementation of all coordination modes of CoMP is based on the following two conditions:
(1) Information Sharing Among Cooperative Points
Such information includes part or entire Channel State Information (CSI) that is directed to User Equipment (UE) and data information that has to be shared with UE in some coordination modes.
(2) Joint Resource Allocation/Scheduling
In the 3rd Generation Partnership Project (3GPP) RAN1-57 meeting, all manufacturers agreed that the following three feedback mechanisms be adopted in CoMP[1]:
- Explicit channel state/statistical information feedback
- Implicit channel state/statistical information feedback, e.g. Channel Quality Indicator (CQI), Precoding Matrix Indicator (PMI) and Rank Indication (RI)
- UE transmission of Sounding Reference Signal (SRS) used for downlink CSI estimation at RRU exploiting channel reciprocity in Time Division Duplex (TDD) mode Each feedback mechanism has its own precoding methods.
By information sharing, CoMP can be classified into two categories: Joint Processing (JP) and Coordinated Beamforming (CBF). In CBF, only UE’s CSI is required to be shared among all cooperative points, while in JP, both CSI and data information of UE are required to be shared.
As JP-based CoMP-Multi-User (CoMP-MU) can achieve greater performance enhancement than other transmission schemes, this paper will mainly discuss JP-based CoMP-MU precoding methods in the scenario containing one Base Band Unit (BBU) and several RRUs.
1 System Model
In the CoMP system, joint precoding can be performed in a centralized manner within several RRUs under the same BBU. These cooperative RRUs are called CoMP-RRUs, serving a UE group that uses the same frequency at the same time. They adopt joint signal precoding to reduce the inter-cell interference and improve the system’s spectrum efficiency, especially the cell-edge user throughput.
Here we suppose there are nt transmit antennas at each RRU, and nr receive antennas at each UE. One CoMP-RRU group is composed of M cooperative RRUs, which serve M UEs that use the same frequency at the same time. In the downlink, the M cooperative RRUs and M UEs can form a (Mn r )×(Mn t ) VMIMO system, as shown in Figure 1.
The channel matrix from the CoMP RRU to the u th user on the n th subcarrier is denoted by Hu [n ]=Gu[n ]Fu[n ], where Gu[n ] is a n t×(Mn r ) dimension matrix representing the normalized complex channel gain, and Fu[n ] is a (Mnt ×Mn t ) diagonal matrix expressed as:
where is the average received signal power at the u th UE from the i th transmit antenna.
Hence, the composite channel matrix of the cooperative virtual MIMO system on the n th subcarrier is given by:
The data vector intended for the u th UE on the nth subcarrier is:
where l is the number of layers for the u th UE.
The joint precoding matrix for the u th UE’s data vector is denoted as
Bu[n ]∈(Mn t×l ), and the transmit vector of the CoMP-RRU is given by:
where
The receive vector at the u th UE is expressed as:
where N [n ] is a nr ×1 dimension noise and interference vector.
The algorithms used to obtain joint precoding matrix Bu[n ]∈(Mn t×l ) for each UE will be discussed in this paper.
2 CoMP-JP Precoding
2.1 Channel Matrix-Based Precoding
The direct precoding method is implemented when the transmitter can get channel matrix H [n ]. In TDD mode, we can exploit the channel reciprocity and use SRS of uplink channels to estimate downlink H [n ]. In Frequency Division Duplex (FDD) mode, H [n ] has to be obtained from UE’s feedback.
The following are several H [n ]-based precoding methods[2].
(1) Zero-Forcing (ZF) Beamforming Algorithm
ZF beamforming algorithm makes a complete diagonalization of H [n ] by means of pseudo-inverse of H [n ] . The beamforming matrix B [n ] can be obtained from the following formula:
B [n ] is the pseudo-inverse matrix of H [n ]. F [n ] is used to ensure normalization of transmit power, which is expressed as:
where f k [n ](1≤k≤Mn r ) is given by:
H[n ]B[n ] is a diagonal matrix, which means all interference within
multi-antenna users is eliminated. However, a user with multiple receiving antennas can process the signals received from its own antennas. This makes ZF beamforming algorithm not an ideal approach. Hence, Block Diagonalization (BD) algorithm is proposed.
(2) BD Algorithm
BD algorithm is another suboptimal solution when each receiver is equipped with multiple antennas. It can eliminate all inter-user interference within the user group.
BD algorithm adopts the precoding matrix that satisfies . This means all inter-user interference will be eliminated. is the channel matrix for users except the user i .
The Singular Value Decomposition (SVD) of Hi [n ] is given by:
In Formula (10), the superscript H indicates the Hermitian transpose, is a diagonal matrix whose diagonal elements are with singular values of and whose dimension is equal to the rank of Hi [n ], Vi (1)[n ] consists of the singular vectors corresponding to non-zero singular values, and Vi (0)[n ] consists of the singular vectors corresponding to zero singular values. Thus, Vi (0)[n ] is an orthogonal basis for the null space of
Hi[n ].
The number of independent data streams for user i (denoted as li ) should be no more than the column number of Vi (0)[n ], so we choose li columns from the right of Vi (0)[n ], represented by Vi (0)[n ], as the BD precoding matrix for the user i .
With the precoding matrix B[n ], the effective channel matrix H[n ]B[n ] is block diagonal, which means all inter-user interference is eliminated but intra-user interference still exists.
(3) BD and SVD algorithm
After is obtained, =0(foruser i≠j ) is fulfilled. In this case, the capacity can be improved by means of MIMO eigen beamforming. The SVD of the effective channel matrix is denoted as:
where Vi (1)[n ] is made up of the singular vectors corresponding to
non-zero singular values and can be used to maximize the received Signal to Interference plus Noise Ratio (SINR) for user i :
The precoding matrix on the nth subcarrier then can be defined as:
Direct H[n ] feedback[3] has several variants; for example, feedback on subcarriers at certain interval only or feed back H[n ] along with some additional time-zone information.
Upon precoding, the transmitter can learn the equivalent channel, thus obtaining the capacity of UE. As a result, users can be paired based on the principle of capacity maximization.
Direct channel matrix feedback can provide rich channel information, but in FDD mode, it is impossible to have a perfect knowledge of the channel matrix. The channel correlation in the time or frequency domain has to be used to compress the feedback and suitable quantization technology has to be adopted.
Either averaging or quantizing H in the time or frequency domain may lead to serious distortion. Reference [4] analyzes the impact of averaging and quantization on the performance in various scenarios.
On the other hand, in TDD mode, SRS design in Rel.8 may pose problems such as insufficient SRS power of cooperative cell[5] and poor cross-correlation between SRS sequences of different cells[6]. To support CoMP-JP, enhancing existing SRSs is required.
2.2 Spatial Correlation Matrix-Based Precoding
In some cases, averaging or compression of channel matrix in the time or frequency domain greatly decreases the effectiveness of the matrix, so compression of feedback of the channel matrix becomes quite difficult. In contrast, averaging the spatial correlation matrix of a channel in the time or frequency domain will not result in serious distortion. Therefore, another efficient precoding method is precoding based on the channel covariance
matrix[7], which is defined as:
where Ri can be obtained by selecting the set S and averaging it on different subcarrier groups. In this way, the feedback can be more flexibly adjusted or compressed.
Suppose there are two users, UEi and UEj , that use the same frequency to conduct downlink transmission at the same time. In R-based precoding, the precoding matrixes of the two users are:
where Noi the sum of interference received by UEi (excluding interference from UEj ) and noise power; α is the adjustment factor, Ri and Rj are spatial correlative matrixes of UEi and UEj respectively; eig (M ) is the eigen vector of matrix M corresponding to the top L eigen values and L is the number of data streams to UE. Consequently, the capacity calculated with the following formula can be used as the basis for user pairing.
The spatial correlation matrix is a compound symmetrical matrix of nt ×nt , so feedback can be compressed accordingly. For instance, if nt =4, we can just feed back only 16 real numbers.
Compared with feedback in Rel.8, the feedback overhead with spatial correlation matrix is still very large. Moreover, as some manufacturers have inherent interests in codebook-based feedback, all parties are far from agreeing on the adoption of this precoding approach.
2.3 Codebook-Based Precoding
The principle of codebook-based precoding is to store a codebook (i.e. the set of precoding matrixes) at both the transmitter and the receiver in advance. The receiver then follows certain rules to select the optimal precoding matrix according to the current channel state and returns the PMI of the selected matrix to the transmitter. As this method involves limited feedback and has good compatibility with Rel.8, it is widely recognized by many manufacturers in the process of standardization. Mainly designed for Single-User (SU)-MIMO, Rel.8 codebook does not perform very well for MU-MIMO or CoMP-MU.
From the perspective of CoMP, the codebook should support 8 antennas. Compared with 4-bit 4 Tx codebook, the performance enhancement of 4-bit 8 Tx codebook is limited[8]. Therefore, more bits are required to support CoMP-MU.
One solution is fixed codebook design, where the increased bits are used to support a large-size codebook. This solution is simple to implement and has small feedback overload. But the codebook cannot be flexibly adapted to diversified scenarios and can only enhance limited system performance. Studies show that as the codebook size increases, the performance enhancement will eventually come to an end. Different codebooks (e.g. Discrete Fourier Transform (DFT)-based codebook, Householder reflection-based codebook) perform almost the same once their bounds are reached.
Another solution is adaptive codebook design, where the long feedback interval of channel correlationmatrix is used to adjust the codebook[9-11]. As in slow fading channel, the channel correlation matrix R changes slowly, the feedback interval of R (i.e. the adaptive interval of the codebook) can be set to be a long period. In this way, there is only a small increase in feedback compared with fixed codebook design. Besides, in some cases, uplink SRSs can be used to estimate R.
In adaptive codebook design, a baseline codebook has to be determined first. Let’s take for example a 8×16 Complex Hadamard Transformation (CHT)-based codebook[8]. In the absence of spatial channel correlation matrix R, the codebook is WDS; while when R is employed, the codebook is:
where the function normalize ( ) normalizes each column to be of norm 1. In addition, R can be replaced with , which is made up of the k leading eigenvectors. That is,
Adaptive codebook design can achieve greater performance enhancement than fixed codebook design, but compared with channel matrix-/spatial correlation matrix-base precoding, this enhancement is quite small. Moreover, in codebook-based precoding, user pairing is a tough problem, which restricts this precoding method’s capability of enhancing system performance. In case of fixed codebook-based precoding, users can only be paired on the principle of Minimum Beam Distance (MBD) of precoding matrixes selected by all users; while in adaptive codebook-based precoding, one solution is to pair users based on R, but as the R is fed back at a long interval, the effectiveness of the solution is to be verified.
3 Conclusions
To sum up, in LTE-A, CoMP-JP precoding methods vary in terms of complexity, signaling and resource requirements as well as performance enhancement. Currently, research focuses on feedback compression and codebook design optimization. As manufacturers have not come to an agreement regarding the approach to CoMP precoding implementation, which needs further study, the standardization process of CoMP moves slowly.
References
[1] 3GPP TR 36.814. Further Advancements for E-UTRA Physical Layer Aspects [S]. 2009.
[2] 3GPP R1-090922. Downlink CoMP-MU-MIMO Transmission Schemes [S]. 2009.
[3] 3GPP R1-092024.CSI Feedback [S]. 2009.
[4] 3GPP R1-092475.Investigation on Explicit Channel Matrix Feedback in CoMP [S]. 2009.
[5] 3GPP R1-092776.Analysis of SRS Scheme for CoMP [S]. 2009.
[6] 3GPP R1-093039.Interference Analysis on SRS for CoMP [S]. 2009.
[7] 3GPP R1-091936. Spatial Correlation Feedback to Support LTE-A MU-MIMO and CoMP: System Operation and Performance Results [S]. 2009.
[8] 3GPP R1-090618. Codebook Design for 8 Tx Transmission in LTE-A [S]. 2009.
[9] XIA Pengfei, GIANNAKIS G B. Design and analysis of transmit- beamforming based on limited-rate feedback [C]//Proceedings of the 60th Vehicular Technology Conference (VTC-Fall’04): Vol 3, Sep 26-29, 2004, Los Angeles, CA, USA. Piscataway, NJ, USA: IEEE, 2004: 1653-1657.
[10] LOVE D J, HEATH R W. Limited feedback diversity techniques for correlated channels [J]. IEEE Transactions on Vehicular Technology, 2006, 55(2): 718-722.
[11] 3GPP R1-091820. Adaptive codebook designs for DL MIMO [S]. 2009.
[Abstract]
Coordinated Multi-Point (CoMP) transmission is a technology targeted for Long Term Evolution Advanced (LTE-A). It is designed to reduce cell-edge interference, improve cell-edge spectrum efficiency and enlarge effective cell-edge coverage by means of multi-point coordination including coordination between Remote Radio Units (RRUs) within an eNodeB, coordination between an eNodeB and its relays, and coordination between eNodeBs. The Joint Processing (JP) technique for CoMP can maximize system performance, which is achieved mainly with channel information-based precoding algorithms. Precoding methods perform differently in various CoMP scenarios. Currently, research focuses on compressing the feedback and optimizing codebook design in order to optimize precoding algorithms.