List of Tables
3.6 Feedback Mechanisms and Operation [10]
Again this section is mainly taken from [10].
3.6.1 Open-Loop Region
An OL region with max Mt MIMO streams is defined as a time-frequency resource using the max Mt MIMO streams pilot pattern and a given OL MIMO mode with Mt = max Mt
without rank adaptation. The OL region allows base stations to coordinate their OL MIMO transmissions, in order to offer a stable interference environment where the precoders and numbers of MIMO streams are not time-varying. The LRUs used for the OL region are indicated in the AAI SCD message. These LRUs shall be aligned across cells. Only a limited set of OL MIMO modes are allowed for transmission in the OL region, as specified in Fig. 3.8. All OL MIMO modes can also be used outside the OL region except for MIMO mode 5, as specified in Fig. 3.7. An OL region is associated with a specific set of parameters:
• type (number of MIMO streams max Mt, MIMO mode, MIMO feedback mode, type of permutation), and
• LRUs.
There are three types of OL regions, as specified in Fig. 3.9. Dynamic switching between MIMO modes 1 and 3 in downlink transmissions in OL region type 2 is allowed. The rank-2 precoders for transmission with MIMO mode 1 or 3 in OL region type 2 are the same on a given subband. All BSs that are coordinated over the same OL region should use the same number of MIMO streams, in order to guarantee low interference fluctuation and thus improve the CQI prediction at the AMS. All pilots are precoded by non-adaptive precoding with max Mt MIMO streams in the OL region. CQI measurements should be taken by the AMS on the precoded demodulation pilots rather than on the DL midamble. The max Mt precoded pilots streams shall be transmitted in all the LRUs in the OL region even if data are not being transmitted by the ABS on some or all of the LRUs.
v
Figure 3.9: Types of open-loop regions (from [10, Table 848]).
3.6.2 MIMO Feedback Mode Selection
An AMS may send an unsolicited event-driven report to indicate its preferred MIMO feed-back mode to the ABS. Event-driven reports for MIMO feedfeed-back mode selection may be sent on the P-FBCH during any allowed transmission interval for the allocated P-FBCH.
3.6.3 MIMO Feedback Modes
Each MIMO transmission mode can be supported by one or several MIMO feedback modes.
When allocating a feedback channel, the MIMO feedback mode shall be indicated to the AMS, and the AMS will feedback information accordingly. The description of MIMO feed-back modes and corresponding supported MIMO transmission modes is shown in Fig. 3.10.
Some detailed description of feedback and AMS processing are in the following subsections.
The feedback of the quantized wideband correlation matrix shall be requested by the ABS for operation with transformation codebook-based feedback mode using the Feedback Polling A-MAP IE. The ABS may request the feedback of the quantized wideband correlation matrix independently of the MIMO feedback mode requested in the Feedback Allocation A-MAP
IE. The quantized wideband correlation matrix may be used for wideband beamforming.
MIMO feedback mode 0 is used for the OL-SU SFBC and SM adaptation in diversity permutation. The AMS estimates the wideband CQI for both SFBC and SM, and reports the CQI and STC Rate. STC Rate 1 means SFBC with precoding and STC Rate 2 means rank-2 SM with precoding. MIMO feedback mode 0 may also be used for CQI feedback for sounding based beamforming. The AMS shall estimate the wideband CQI for SFBC mode (max Mt = 0b00), and report the CQI.
MIMO feedback mode 1 is used for the OL-SU CDR with STC rate 1/2 in diversity permutation. MIMO feedback mode 2 is used for the OL-SU SM in localized permutation for frequency selective scheduling. The STC Rate indicates the preferred number of MIMO streams for SM. The subband CQI shall correspond to the selected rank. MIMO feedback mode 3 is used for the CL-SU SM in localized permutation for frequency selective scheduling.
The STC Rate indicates the preferred number of MIMO streams for SM. The subband CQI shall correspond to the selected rank.
MIMO feedback mode 4 is used for the CL SU MIMO using wideband beamforming with rank 1. In this mode, AMS shall feedback the wideband CQI. The wideband CQI shall be estimated at the AMS assuming short-term or long-term precoding at the ABS, according to the feedback period. The channel state information may be obtained at the ABS via the feedback of the correlation matrix, or via the feedback of the wideband PMI.
MIMO feedback mode 5 is used for OL MU MIMO in localized permutation with fre-quency selective scheduling. In the mode, AMS shall feedback the subband selection, MIMO stream indicator and the corresponding CQI.
MIMO feedback mode 6 is used for CL MU MIMO in localized permutation with fre-quency selective scheduling. In this mode, AMS shall feedback the subband selection, cor-responding CQI and subband PMI. The subband CQI refers to the CQI of the best PMI
in the subband. Rank-1 base codebook (or its subset) is used to estimate the PMI in one subband.
MIMO feedback mode 7 is used for CL MU MIMO in diversity permutation using wide-band beamforming MU MIMO. In this mode, AMS shall feedback the widewide-band CQI. The wideband CQI shall be estimated at the AMS assuming short-term or long-term precoding at the ABS, according to the feedback period. The channel state information may be obtained at the ABS via the feedback of the correlation matrix. or via the feedback of the wideband PMI.
3.6.4 Downlink Signaling Support of DL-MIMO Modes
The BS shall send some parameters necessary for DL MIMO operation in a broadcast mes-sage. The broadcast information is carried in the S-SFH SP3 IE or in the additional broadcast information such as AAI SCD or AAI DL IM messages. The BS shall send some param-eters necessary for DL MIMO operation in a unicast message. The unicast information is carried in the DL Basic Assignment A-MAP IE, DL Subband Assignment A-MAP IE, DL Persistent A-MAP IE, Feedback Polling A-MAP IE, and Feedback Allocation A-MAP IE.
Figure 3.12 specifies the DL control parameters required for MIMO operation. When CS indication indicates the use of a codebook subset and MFM indicates a CL SU MIMO mode (MFM = 3 and 4), the MS shall use the SU base codebook subset of Fig. 3.13 when Nt = 4.
When CS indication indicates the use of a codebook subset and MFM indicates a CL MU MIMO mode (MFM = 6 and 7), the MS shall use the MU base codebook subset of Fig. 3.13 when Nt= 4.
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Figure 3.11: DL MIMO control parameters (from [10, Table 850]).
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Figure 3.13: Subset selection of the base codebok for four transmit antennas (from [10, Table 866]).
3.6.5 Quantized MIMO Feedback for Closed-loop Transmit Pre-coding
An AMS feedbacks a Preferred Matrix Index (PMI) to support DL precoding. There are three types of codebook feedback modes as follows.
• The base mode: the PMI feedback from a AMS shall represent an entry of the base codebook. It shall be sufficient for the ABS to determine a new precoder.
• The transformation mode: the PMI feedback from a AMS shall represent an entry of the transformed base codebook according to long term channel information.
• The differential mode: the PMI feedback from a AMS shall represent an entry of the differential codebook or an entry of the base codebook at PMI reset times. The feedback from a AMS provides a differential knowledge of the short-term channel infor-mation. This feedback represents information that is used along with other feedback information known at the ABS for determining a new precoder.
An AMS shall support the base and transformation modes and may support the differential mode. The transformation and differential feedback modes are applied to the base codebook or to a subset of the base codebook.
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Figure 3.14: Base codebook c(2,1,3) (from [10, Table 851]).
The base codebook is a unitary codebook. That is each of its matrices consists of columns of a unitary matrix. The AMS selects its preferred matrix from the base codebook based on channel measurements. The AMS sends back the index of the preferred codeword, and the ABS determines the precoder W according to the index. Both ABS and AMS use the same codebook for correct operation. The base codebooks are defined below for two, four, and eight transmit antennas at the ABS, where the notation C(Nt, Mt, NB) denote the codebook, which consists of 2NB complex, matrices of dimension Nt by Mt, and Mt denotes the number of MIMO streams. The notation C(Nt, Mt, NB, i) denotes the i-th codebook entry of C(Nt, Mt, NB).
The base codebook of SU-MIMO with two transmit antennas consist of rank-1 codebook C(2,1,3) and rank-2 codebook C(2,2,3), as illustrated in Figs. 3.14 and 3.15, respectively.
The base codebook for MU-MIMO is the same as the rank 1 base codebook for SU-MIMO.
The base codebooks of SU-MIMO with four transmit antennas consist of rank-1 codebook C(4,1,6), rank-2 codebook C(4,2,6), rank-3 codebook C(4,3,6) and rank-4 codebook C(4,4,6).
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Figure 3.15: Base codebook c(2,2,3) (from [10, Table 852]).
Transformation Codebook Based Feedback Mode
The base codebooks and their subsets of rank 1 for SU and MU MIMO can be transformed as a function of the ABS transmit correlation matrix. A quantized representation of the ABS transmit correlation matrix shall be fed back by the AMS as instructed by the ABS.
Both ABS and AMS transform the rank 1 base codebook to a rank 1 transformed codebook using the correlation matrix. The transformation for codewords of rank 1 is of the form
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where vi is the ith codeword of the base codebook, ˜vt is the ith codeword of the transformed codebook, and R is the Nt×Nttransmit correlation matrix. After obtaining the transformed codebook, both AMS and ABS shall use the transformed codebook for the feedback and precoding process of rank 1.
The codebooks of rank > 1 shall be used without transformation when the AMS is operating with the transformation codebook-based feedback mode.
Figure 3.16: Quantization parameters for diagonal entries of R (from [10, Table 867]).
The correlation matrix R shall be fed back to support the transformation mode of codebook-based precoding. It is fed back periodically and one correlation matrix is valid for whole band. During some time period and in the whole band, the correlation matrix is measured as
R = E[HHijHij] (3.16)
where Hij is the correlated channel matrix in the ith OFDM symbol period and jth subcar-riers. Because of the symmetry of the correlation matrix, only the upper triangular elements shall be fed back after quantization.
The R matrix is normalized by the maximum element amplitude, and then quantized to reduce the feedback overhead. The equation of normalization is
R =˜ R
max(|rij|) i, j = 1, ..., Nt, (3.17) where ri,j denotes the ijth elemnet of R. The normalized diagonal elements are quantized by 1 bit, and the normalized complex elements are quantized by 4 bits. The equation for quantization is
q = a · e(j·b·2π) (3.18)
where either a = [0.6 0.9] and b = 0 or a = [0.1 0.5] and b = [0 1/8 1/4 3/8 1/2 5/8 3/4 7/8]
for diagonal entries. The total number of bits of feedback is 6 for 2 transmit antennas, 28for 4 transmit antennas, and 120 for 8 transmit antennas. The AMS and ABS shall use the same transformation based on the correlation matrix fed back by the AMS.
Figure 3.17: Quantization parameters for non-diagonal entries of R (from [10, Table 868]).
Differential Codebook-Based Feedback Mode
The differential feedbacks exploit the correlation between precoding matrices adjacent in time or frequency. The feedback shall start initially and restart periodically by sending a one-shot feedback that fully depicts the precoder by itself. At least one differential feedback shall follow the start and restart feedback. The start and restart feedback employs the codebook defined for the base mode and is sent through long term report defined in Feedback Allocation A-MAP IE for MFM 3 and 6. The differential feedback is sent through short term report defined in Feedback Allocation A-MAP IE for MFM 3 and 6.
Denote the feedback index, the corresponding feedback matrix, and the corresponding
precoder by t, D(t), and V(t), respectively. The sequential index is reset to 0 at Tmax+ 1.
The index for the start and restart feedbacks are 0. Let A be a vector or a matrix and QA
be the rotation matrix determined by A. The precoder corresponding to each index is given by
V(t) = QV(t−1)D(t), t = 0, 1, 2, ..., Tmax, (3.19) where the rotation matrix QV(t−1) is a unitary matrix Nt× Nt computed from the previous precoder V(t − 1) with Nt is the number of transmit antennas. The dimension of the feedback matrix D(t) is , where Mt is the number of spatial streams. QV(t−1) has the form QV(t−1) = [V(t − 1) V⊥(t − 1)], where V⊥(t − 1) consists of columns each of which has a unit norm and is orthogonal to the other columns of QV(t−1).For Mt= 1, where V(t − 1) is a vector,
Qv(t−1) =
I − 2
kωk2ωωH, for kωk > 0,
I, otherwise,
(3.20)
where kV(t − 1)k = 1 and ω = e−jθV(t − 1) − e1; θ is the phase of the first entry of V(t−1), and e1 = [1 0 . . . 0]T. For Mt > 1, let L = Nt− Mt for computing QV(t−1). L columns are appended to V(t − 1) forming a square matrix M = [V(t − 1)E] and the appended columns are
E = [eτ1. . . eτL] (3.21)
where eτj is the Nt× 1 vector whose τjth entry is one and whose other entries are zeros.
QV(t−1) is computed by orthogonalizing and normaling the columns of M. The indexes τj for j = 1, ..., L are selected for the numerical stability of the orthogonalization and normalization process. Let
g = (| ℜ(V(t − 1)) | + | ℑ(V(t − 1)) |)a (3.22) where a is the 1 × Mt vector with all entries equal to one; ℜ() and ℑ() take the real and imaginary parts of the inputs, respectively; | | takes the absolute values of the input matrix
entry by entry. The ith element of the vector g is the sum of the absolute values of all the real and imaginary parts of V(t − 1) on the same row. The entries of g are stored in an increasing numerical order. If gi = gj and i < j, then gi < gj is used in the order list. The order list is
gk1 < ... < gkNt (3.23) where ki for i = 1, ..., Ntare row indexes of g. The first L indexes in the list are assigned to the indexes τj in E as
τj = kj, for j = 1, ..., L. (3.24)
The Gram-Schmidt orthogonalization and a normalization process are applied to the last L columns of M column by column and result in QV(t−1) as
For j = 1 : L
For k = 1 : j + Mt− 1 mj+Mt = mj+Mt − m∗τj,kmk
End
mj+Mt = mj+Mt
k mj+Mt k End
QV(t−1) = M
(3.25)
where mk is the kth column of M and mi,j is the ijth element of M.
The feedback matrix D(t) is selected from a differential codebook. Denote the code-book by D(Nt, Mt, Nw), where Nw is the number of codewords in the codebook. The codebooks D(2, 1, 4)and D(2, 2, 4) are listed in Figs. 3.18 and 3.19, respectively. Denote Di(Nt, Mt, Nw) the ith codeword of D(Nt, Mt, Nw). The rotation matrices QDi(Nt,Mt,Nw)s of the D(Nt, Mt, Nw)s comprise a set of Nt by Nt matrices that is denoted by QD(Nt,Mt,Nw).
The differential codebook D(4, 3, Nw) is computed from QD(4,1,Nw). The ith codeword of
D(4, 3, Nw), denoted by Di(4, 3, Nw), respectively, are given by
Di(8, 5, Nw) =
H
Figure 3.18: D(2,1,4) codebook (from [10, Table 869]).
g
Figure 3.19: D(2,2,4) codebook (from [10, Table 870]).
where ˜Qi(8, k, Nw) consists of the last 8 columns of the ith matrix in ˜QD(8,k,Nw). The differ-ential codebook D(8, 8, Nw) is computed from D(8, 4, Nw). The ith codeword of D(8, 8, Nw) is the ith matrix in ˜QD(8,k,Nw).