B.2.3 MIMO Channel Correlation Matrices

36.1013GPPEvolved Universal Terrestrial Radio Access (E-UTRA)Release 18TSUser Equipment (UE) radio transmission and reception

The MIMO channel correlation matrices defined in B.2.3 apply for the antenna configuration using uniform linear arrays at both eNodeB and UE.

B.2.3.1 Definition of MIMO Correlation Matrices

Table B.2.3.1-1 defines the correlation matrix for the eNodeB

Table B.2.3.1-1 eNodeB correlation matrix

	One antenna	Two antennas	Four antennas	Eight antennas
eNode B Correlation

Table B.2.3.1-2 defines the correlation matrix for the UE:

Table B.2.3.1-2 UE correlation matrix

	One antenna	Two antennas	Four antennas	Eight antennas
UE Correlation

Table B.2.3.1-3 defines the channel spatial correlation matrix . The parameters, α and β in Table B.2.3.1-3 defines the spatial correlation between the antennas at the eNodeB and UE.

Table B.2.3.1-3: correlation matrices

1×2 case
1×4 case
2×1 case
2×2 case
2×4 case
4×1 case
4×2 case
4×4 case
2×8 case
4×8 case
8×8 case

For cases with more antennas at either eNodeB or UE or both, the channel spatial correlation matrix can still be expressed as the Kronecker product of and according to.

B.2.3.2 MIMO Correlation Matrices at High, Medium and Low Level

The and for different correlation types are given in Table B.2.3.2-1.

Table B.2.3.2-1: The  and  parameters for ULA MIMO correlation matrices

Correlation Model	α	β
Low correlation	0	0
Medium Correlation	0.3	0.9
Medium Correlation A	0.3	0.3874
Medium Correlation B	0.3	0.005154
High Correlation	0.9	0.9

The correlation matrices for high, medium, low and medium A correlation are defined in Table B.2.3.1-2, B.2.3.2-3, B.2.3.2-4 and B.2.3.2-5 as below.

The values in Table B.2.3.2-2 have been adjusted for the 4×2 and 4×4 high correlation cases 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 4×2 high correlation case, a=0.00010. For the 4×4 high correlation case, a=0.00012.

The same method is used to adjust the 2×4 and 4×4 medium correlation matrix in Table B.2.3.2-3 to insure the correlation matrix is positive semi-definite after round-off to 4 digit precision with a = 0.00010 and a = 0.00012.

Table B.2.3.2-2: MIMO correlation matrices for high correlation

1×2 case
2×1 case
2×2 case
4×2 case
4×4 case

Table B.2.3.2-3: MIMO correlation matrices for medium correlation

1×2 case	N/A
2×1 case	N/A
2×2 case
2×4 case
4×2 case
4×4 case

Table B.2.3.2-4: MIMO correlation matrices for low correlation

1×2 case
1×4 case
2×1 case
2×2 case
2×4 case
4×1 case
4×2 case
4×4 case

In Table B.2.3.2-4, is the identity matrix.

Table B.2.3.2-5: MIMO correlation matrices for medium correlation A

2×4 case
4×4 case