B.2.3B MIMO Channel Correlation Matrices using two-dimension cross polarized antennas at eNB and cross polarized antennas at UE
36.1013GPPEvolved Universal Terrestrial Radio Access (E-UTRA)Release 18TSUser Equipment (UE) radio transmission and reception
The MIMO channel correlation matrices defined in B.2.3B apply for the antenna configuration using two-dimension (2D) cross polarized antennas at eNodeB and the antenna configuration using cross polarized antennas at UE. The cross-polarized antenna elements with +/-45 degrees polarization slant angles are deployed at eNB and cross-polarized antenna elements with +90/0 degrees polarization slant angles are deployed at UE.
For 2D cross-polarized antenna array at eNodeB, the N antennas are indexed by 
, and total number of antennas is 
, where
– 
is the number of antenna elements in first dimension (i.e. vertical direction) with same polarization,
– 
is the number of antenna elements in second dimension (i.e. horizontal direction) with same polarization, and
– 
is the number of polarization groups.
For the 2D cross-polarized antennas at eNB, the N antennas are labelled such that antennas shall be in increasing order of the second dimension firstly, then the first dimension, and finally the polarization group. For a specific antenna element at p-th polarization, n1-th row, and n2-th column within the 2D antenna array, the following index number is used for antenna labelling:
where N is the number of transmit antennas, p is the polarization group index, n1 is the row index, and n2 is the column index of the antenna element.
For the cross-polarized antennas at UE, the N antennas are labelled such that antennas for one polarization are listed from 1 to N/2 and antennas for the other polarization are listed from N/2+1 to N, where N is the number of receive antennas.
B.2.3B.1 Definition of MIMO Correlation Matrices using two-dimension cross polarized antennas at eNB and cross polarized antennas at UE
For the channel spatial correlation matrix, the following is used:
where
– 
is the spatial correlation matrix at the UE with same polarization,
– 
is the spatial correlation matrix at the eNB with same polarization,
– 
is a polarization correlation matrix, and
– 
denotes transpose.
The spatial correlation matrix at the eNB is further expressed as following:
where
– 
is the correlation matrix of antenna elements in first dimension with same polarization, and
– 
is the correlation matrix of antenna elements in second dimension with same polarization.
The matrix 
is defined as
A permutation matrix 
elements are defined as
.
where 
and 
is the number of transmitter and receiver respectively. This is used to map the spatial correlation coefficients in accordance with the antenna element labelling system described in B.2.3B.
B.2.3B.2 Spatial Correlation Matrices using two-dimension cross polarized antennas at eNB and cross polarized antennas at UE
B.2.3B.2.1 Spatial Correlation Matrices at eNB side
For one direction of the 2D antenna array at the eNB side, the followings are used to construct the spatial correlation matrix:
For 1 antenna element of the same polarization in one direction, 
.
For 2 antenna elements of the same polarization in one direction, 
.
For 3 antenna elements of the same polarization in one direction, 
.
For 4 antenna elements of the same polarization in one direction, 
.
where the index 
stands for first dimension and second dimension respectively.
B.2.3B.2.2 Spatial Correlation Matrices at UE side
For 2-antenna receiver using one pair of cross-polarized antenna elements, 
.
For 4-antenna receiver using two pairs of cross-polarized antenna elements, 
.
B.2.3B.3 MIMO Correlation Matrices using two-dimension cross polarized antennas at eNB and cross polarized antennas at UE
The values for parameters α1, α2, β and γ for high and medium spatial correlation are given in Table B.2.3B.3-1.
Table B.2.3B.3-1
|
Correlation type |
|
|
|
|
|
High |
0.9 |
0.9 |
0.9 |
0.3 |
|
Medium |
0.3 |
0.3 |
0.6 |
0.2 |
|
Note 1: Value of α1 applies when more than one pair of cross-polarized antenna elements in first dimension at eNB side. Note 2: Value of α2 applies when more than one pair of cross-polarized antenna elements in second dimension at eNB side. Note 3: Value of β applies when more than one pair of cross-polarized antenna elements at UE side. |
||||
The correlation matrices for high spatial correlation with12(2,3,2)x2 case and 16(2,4,2)x2 case are defined in Table B.2.3B.3-2 as below.
The values in Table B.2.3B.3-2 have been adjusted to insure the correlation matrix is positive semi-definite after round-off to 4 digit precision. This is done using the equation:
where the value “a” is a scaling factor such that the smallest value is used to obtain a positive semi-definite result. For the 16(2,4,2)x2 high spatial correlation case, a=0.00012.
The same method is used to adjust the the 24(3,4,2)x2 and 32(4,4,2)x2 high correlation matrix to insure the correlation matrix is positive semi-definite after round-off to 4 digit precision with a =0.00012 and a=0.00022.
Table B.2.3B.3-2: MIMO correlation matrices for high spatial correlation
|
12(2,3,2)x2 case |
|
|
16(2,4,2)x2 case |
|
, where
, where
B.2.3B.4 Beam steering approach
Given the channel spatial correlation matrix in B.2.3B.1, the corresponding random channel matrix H can be calculated. The signal model for the k-th subframe is denoted as
And the steering matrix is further expressed as following:
where
– H is the Nr xNt channel matrix per subcarrier.
– 
is the steering matrix,
– 
is the steering matrix in first dimension with same polarization,
– 
is the steering matrix in second dimension with same polarization,
– 
is the number of antenna elements infirst dimension with same polarization,
– 
is the number of antenna elements in second dimension with same polarization,
For 1 antenna element of the same polarization in one direction, 
.
For 2 antenna elements of the same polarization in one direction, 
.
For 3 antenna elements of the same polarization in one direction,
.
For 4 antenna elements of the same polarization in one direction, 
.
where the index 
stands for first dimension and second dimension respectively.
– 
controls the phase variation in first dimension and second dimension respectively, and the phase for k-th subframe is denoted by
, where 
is the random start value with the uniform distribution, i.e., 
, 
is the step of phase variation, which is defined in Table B.2.3B.4-1, and k is the linear increment of 1 for every subframe throughout the simulation, the index 
stands for first dimension and second dimension respectively.
– 
is the precoding matrix for Nt transmission antennas,
– 
is the received signal, 
is the transmitted signal, and 
is AWGN.
Table B.2.3B.4-1: The step of phase variation
|
Variation Step |
Value (rad/subframe) |
|
|
1.2566×10-3 |
B.2.3B.4A Beam steering approach with dual cluster beams
Given the channel spatial correlation matrix in B.2.3B.1, the corresponding random channel matrix H can be calculated. The signal model for the k-th subframe is denoted as
And the steering matrix is further expressed as following:
where
– 
,
are independent channels for the first beam and second beam with the Nr xNt channel matrix per subcarrier.
– 
, 
are the steering matrix for first beam and second beam
– 
is the steering matrix in first dimension with same polarization,
– 
is the steering matrix in second dimension with same polarization,
– 
is the number of antenna elements infirst dimension with same polarization,
– 
is the number of antenna elements in second dimension with same polarization,
– 
is the relative power ratio of the second beam to the first beam, the value of 
is specific to a test case,
For 1 antenna element of the same polarization in one direction, 
.
For 2 antenna elements of the same polarization in one direction, 
.
For 3 antenna elements of the same polarization in one direction,
.
For 4 antenna elements of the same polarization in one direction, 
.
where the index 
stands for first dimension and second dimension respectively.
– 
controls the phase variation in first dimension and second dimension respectively, and the phase for k-th subframe is denoted by
, where 
is the random start value with the uniform distribution, i.e., 
, 
is the step of phase variation, which is defined in Table B.2.3B.4-1, and k is the linear increment of 1 for every subframe throughout the simulation, the index 
stands for first dimension and second dimension respectively.
– 
is the precoding matrix for Nt transmission antennas,
– 
is the received signal, 
is the transmitted signal, and 
is AWGN.
Table B.2.3B.4A-1: The step of phase variation
|
Variation Step |
Value (rad/subframe) |
|
|
1.2566×10-3 |
|
|
2.5132×10-3 |
