B.2.3.1 MIMO Correlation Matrices using Uniform Linear Array (ULA)
38.521-43GPPNRPart 4: PerformanceRadio transmission and receptionRelease 17TSUser Equipment (UE) conformance specification
The MIMO channel correlation matrices defined in B.2.3.1 apply for the antenna configuration using uniform linear array (ULA) at both gNB and UE.
B.2.3.1.1 Definition of MIMO Correlation Matrices
Table B.2.3.1.1-1 defines the correlation matrix for the gNB.
Table B.2.3.1.1-1: gNB correlation matrix
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One antenna |
Two antennas |
Four antennas |
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gNB Correlation |
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Table B.2.3.1.1-2 defines the correlation matrix for the UE:
Table B.2.3.1.1-2 UE correlation matrix
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One antenna |
Two antennas |
Four antennas |
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UE Correlation |
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Table B.2.3.1.1-3 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 gNB and UE.
Table B.2.3.1.1-3: 
correlation matrices
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1×2 case |
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1×4 case |
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2×1 case |
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2×2 case |
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2×4 case |
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4×1 case |
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4×2 case |
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4×4 case |
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For cases with more antennas at either gNB or UE or both, the channel spatial correlation matrix can still be expressed as the Kronecker product of 
and 
according to 
.
B.2.3.1.2 MIMO Correlation Matrices at High, Medium and Low Level
The α and β for different correlation types are given in Table B.2.3.1.2-1.
Table B.2.3.1.2-1: The α and β parameters for ULA MIMO correlation matrices
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Correlation Model |
α |
β |
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Low correlation |
0 |
0 |
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Medium Correlation |
0.3 |
0.9 |
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Medium Correlation A |
0.3 |
0.3874 |
|
High Correlation |
0.9 |
0.9 |
The correlation matrices for high, medium, medium A and low correlation are defined in Tables B.2.3.1.2-2, B.2.3.1.2-3, B.2.3.1.2-4 and B.2.3.1.2-5 as below.
The values in Table B.2.3.1.2-2 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.2.3.1.2-3 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.2.3.1.2-2: MIMO correlation matrices for high correlation
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1×2 case |
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2×1 case |
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2×2 case |
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4×2 case |
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4×4 case |
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Table B.2.3.1.2-3: MIMO correlation matrices for medium correlation
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1×2 case |
N/A |
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2×1 case |
N/A |
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2×2 case |
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2×4 case |
 |
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4×2 case |
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4×4 case |
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Table B.2.3.1.2-4: MIMO correlation matrices for medium correlation A
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2×4 case |
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4×4 case |
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Table B.2.3.1.2-5: MIMO correlation matrices for low correlation
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1×2 case |
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1×4 case |
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2×1 case |
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2×2 case |
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2×4 case |
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4×1 case |
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4×2 case |
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4×4 case |
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In Table B.2.3.1.2-5, Id is the d×d identity matrix.