B.2 Multipath fading Propagation Conditions
36.52113GPPEvolved Universal Terrestrial Radio Access (EUTRA)Part 1: Conformance testingRadio transmission and receptionRelease 17TSUser Equipment (UE) conformance specification
The multipath propagation conditions consist of several parts:
– A delay profile in the form of a "tapped delayline", characterized by a number of taps at fixed positions on a sampling grid. The profile can be further characterized by the r.m.s. delay spread and the maximum delay spanned by the taps.
– A combination of channel model parameters that include the Delay profile and the Doppler spectrum that is characterized by a classical spectrum shape and a maximum Doppler frequency
– A set of correlation matrices defining the correlation between the UE and eNodeB antennas in case of multiantenna systems.
B.2.1 Delay profiles
The delay profiles are selected to be representative of low, medium and high delay spread environments. The resulting model parameters are defined in Table B.2.11 and the tapped delay line models are defined in Tables B.2.12, B.2.13 and B.2.14.
Table B.2.11: Delay profiles for EUTRA channel models
Model 
Number of 
Delay spread (r.m.s.) 
Maximum excess tap delay (span) 
Extended Pedestrian A (EPA) 
7 
45 ns 
410 ns 
Extended Vehicular A model (EVA) 
9 
357 ns 
2510 ns 
Extended Typical Urban model (ETU) 
9 
991 ns 
5000 ns 
Table B.2.12: Extended Pedestrian A model (EPA)
Excess tap delay [ns] 
Relative power [dB] 
0 
0.0 
30 
1.0 
70 
2.0 
90 
3.0 
110 
8.0 
190 
17.2 
410 
20.8 
Table B.2.13: Extended Vehicular A model (EVA)
Excess tap delay [ns] 
Relative power [dB] 
0 
0.0 
30 
1.5 
150 
1.4 
310 
3.6 
370 
0.6 
710 
9.1 
1090 
7.0 
1730 
12.0 
2510 
16.9 
Table B.2.14: Extended Typical Urban model (ETU)
Excess tap delay [ns] 
Relative power [dB] 
0 
1.0 
50 
1.0 
120 
1.0 
200 
0.0 
230 
0.0 
500 
0.0 
1600 
3.0 
2300 
5.0 
5000 
7.0 
B.2.2 Combinations of channel model parameters
The propagation conditions used for the performance measurements in multipath fading environment are indicated as EVA[number], EPA[number] or ETU[number] where ‘number’ indicates the maximum Doppler frequency (Hz).
Table B.2.21: Void
B.2.3 MIMO Channel Correlation Matrices
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.2.3.11 defines the correlation matrix for the eNodeB
Table B.2.3.11: eNodeB correlation matrix
One antenna 
Two antennas 
Four antennas 

eNode B Correlation 
Table B.2.3.12 defines the correlation matrix for the UE:
Table B.2.3.12: UE correlation matrix
One antenna 
Two antennas 
Four antennas 

UE Correlation 
Table B.2.3.13 defines the channel spatial correlation matrix . The parameters, α and β in Table B.2.3.13 defines the spatial correlation between the antennas at the eNodeB and UE.
Table B.2.3.13: correlation matrices
1×2 case 

2×1 case 

2×2 case 

4×2 case 

4×4 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.2.3.21.
Table B.2.3.21
Low correlation 
Medium Correlation 
High Correlation 

α 
β 
α 
β 
α 
β 
0 
0 
0.3 
0.9 
0.9 
0.9 
The correlation matrices for high, medium and low correlation are defined in Table B.2.3.22, B.2.3.23 and B.2.3.24,as below.
The values in the Table B.2.3.22 table have been adjusted for the 4×2 and 4×4 high correlation cases to insure the correlation matrix is positive semidefinite after roundoff 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 semidefinite 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 4×4 medium correlation matrix in Table B.2.3.23 to insure the correlation matrix is positive semidefinite after roundoff to 4 digit precision with a = 0.00012.
Table B.2.3.22: MIMO correlation matrices for high correlation
1×2 case 

2×1 case 

2×2 case 

4×2 case 

4×4 case 
Table B.2.3.23: MIMO correlation matrices for medium correlation
1×2 case 
N/A 
2×1 case 
N/A 
2×2 case 

4×2 case 

4×4 case 
Table B.2.3.24: MIMO correlation matrices for low correlation
1×2 case 

2×1 case 

2×2 case 

4×2 case 

4×4 case 
In Table B.2.3.24, is the identity matrix.
B.2.3A MIMO Channel Correlation Matrices using cross polarized antennas
The MIMO channel correlation matrices defined in B.2.3A apply for the antenna configuration using cross polarized (XP/Xpol) antennas at both eNodeB and UE. The crosspolarized antenna elements with +/45 degrees polarization slant angles are deployed at eNB and crosspolarized antenna elements with +90/0 degrees polarization slant angles are deployed at UE.
For the crosspolarized 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 matrix element is defined as:
Where N_{t} and N_{r} 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 2antenna transmitter using one pair of crosspolarized antenna elements, .
For 4antenna transmitter using two pairs of crosspolarized antenna elements, .
For 8antenna transmitter using four pairs of crosspolarized antenna elements, .
B.2.3A.2.2 Spatial Correlation Matrices at UE side
For 2antenna transmitter using one pair of crosspolarized antenna elements, .
For 4antenna transmitter using two pairs of crosspolarized antenna elements, .
B.2.3A.3 MIMO Correlation Matrices using cross polarized antennas
The values for parameters α, β and γ for low correlation and high spatial correlation are given in Table B.2.3A.31.
Table B.2.3A.31: The and parameters for crosspolarized 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 crosspolarized antenna elements at eNB side. Note 2: Value of β applies when more than one pair of crosspolarized antenna elements at UE side. 
The correlation matrices for high spatial and low correlation are defined in Table B.2.3A.32 and Table B.2.3A.33 as below.
The values in Table B.2.3A.32 have been adjusted to insure the correlation matrix is positive semidefinite after roundoff 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 semidefinite result. For the 8×2 high spatial correlation case, a=0.00010.
Table B.2.3A.32: MIMO correlation matrices for high spatial correlation
4×2 case 
8×2 case 
Table B.2.3A.33: 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 kth subframe is denoted as:
Where
– H is the N¬r 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 kth 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.41, 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.41: The step of phase variation
Variation Step 
Value (rad/subframe) 
1.2566×10^{3} 
B.2.4 Propagation conditions for CQI tests
[For Channel Quality Indication (CQI) tests, the following additional multipath profile is used:
in continuous time representation, with the delay, a a constant andthe Doppler frequency.]
B.2.5 FFS
B.2.6 MBSFN Propagation Channel Profile
Table B.2.61 shows propagation conditions that are used for the MBSFN performance requirements in multipath fading environment in an extended delay spread environment.
Table B.2.61: Propagation Conditions for MultiPath Fading Environments for MBSFN Performance Requirements in an extended delay spread environment
Extended Delay Spread 

Maximum Doppler frequency [5Hz] 

Relative Delay [ns] 
Relative Mean Power [dB] 
0 
0 
30 
1.5 
150 
1.4 
310 
3.6 
370 
0.6 
1090 
7.0 
12490 
10 
12520 
11.5 
12640 
11.4 
12800 
13.6 
12860 
10.6 
13580 
17.0 
27490 
20 
27520 
21.5 
27640 
21.4 
27800 
23.6 
27860 
20.6 
28580 
27.0 