B.2.3A MIMO Channel Correlation Matrices using cross polarized antennas

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

The MIMO channel correlation matrices defined in B.2.3A apply for the antenna configuration using cross polarized (XP/X-pol) antennas at both eNodeB and 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 the cross-polarized antennas, 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 transmit or receive antennas.

B.2.3A.1 Definition of MIMO Correlation Matrices using cross polarized antennas

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 matrix is defined as

A permutation matrixelements 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.2.3A.

B.2.3A.2 Spatial Correlation Matrices using cross polarized antennas at eNB and UE sides

B.2.3A.2.1 Spatial Correlation Matrices at eNB side

For 2-antenna transmitter using one pair of cross-polarized antenna elements, .

For 4-antenna transmitter using two pairs of cross-polarized antenna elements, .

For 8-antenna transmitter using four pairs of cross-polarized antenna elements, .

B.2.3A.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.2.3A.3 MIMO Correlation Matrices using cross polarized antennas

The values for parameters α, β and γ for the cross polarized antenna models are given in Table B.2.3A.3-1.

Table B.2.3A.3-1: : The  and  parameters for cross-polarized MIMO correlation matrices

Correlation Model	α	β	
Medium Correlation A	0.3	0.6	0.2
High Correlation	0.9	0.9	0.3
Note 1: Value of α applies when more than one pair of cross-polarized antenna elements at eNB side. Note 2: Value of β applies when more than one pair of cross-polarized antenna elements at UE side.

The correlation matrices for high spatial correlation and medium correlation A are defined in Table B.2.3A.3-2 and Table B.2.3A.3-3 as below.

The values in Table B.2.3A.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 8×2 high spatial correlation case, a=0.00010.

Table B.2.3A.3-2: MIMO correlation matrices for high spatial correlation

4×2 case
8×2 case

Table B.2.3A.3-3: MIMO correlation matrices for medium correlation A

4×4

B.2.3A.4 Beam steering approach

Given the channel spatial correlation matrix in B.2.3A.1, the corresponding random channel matrix H can be calculated. The signal model for the k-th subframe is denoted as

Where

– H is the N­r xNt channel matrix per subcarrier.

– is the steering matrix,

For 8 transmission antennas, ;

For 4 transmission antennas, .

– controls the phase variation, 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.2.3A.4-1, and k is the linear increment of 1 for every subframe throughout the simulation,

– is the precoding matrix for Nt transmission antennas,

– is the received signal, is the transmitted signal, and is AWGN.

Table B.2.3A.4-1: The step of phase variation

Variation Step	Value (rad/subframe)
	1.2566×10-3