J.2 Multi-path fading propagation conditions

38.176-23GPPIntegrated Access and Backhaul (IAB) conformance testingNRPart 2: radiated conformance testingRelease 17TS

Tools: ARFCN - Frequency Conversion for 5G NR/LTE/UMTS/GSM

The multipath propagation conditions consist of several parts:

– A delay profile in the form of a "tapped delay-line", 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.

– Different models are used for FR1 (410 MHz – 7.125GHz) and FR2 (24.25 GHz – 52.6 GHz).

J.2.1 Delay profiles

The delay profiles are simplified from the TR 38.901 [26] TDL models. The simplification steps are shown below for information. These steps are only used when new delay profiles are created. Otherwise, the delay profiles specified in annex J.2.1.1 and J.2.1.2 can be used as such.

Step 1: Use the original TDL model from TR 38.901 [26].

Step 2: Re-order the taps in ascending delays.

Step 3: Perform delay scaling according to the procedure described in clause 7.7.3 in TR 38.901 [26].

Step 4: Apply the quantization to the delay resolution 5 ns. This is done simply by rounding the tap delays to the nearest multiple of the delay resolution.

Step 5: If multiple taps are rounded to the same delay bin, merge them by calculating their linear power sum.

Step 6: If there are more than 12 taps in the quantized model, merge the taps as follows:

– Find the weakest tap from all taps (both merged and unmerged taps are considered)

– If there are two or more taps having the same value and are the weakest, select the tap with the smallest delay as the weakest tap.

– When the weakest tap is the first delay tap, merge taps as follows:

– Update the power of the first delay tap as the linear power sum of the weakest tap and the second delay tap.

– Remove the second delay tap.

– When the weakest tap is the last delay tap, merge taps as follows:

– Update the power of the last delay tap as the linear power sum of the second-to-last tap and the last tap.

– Remove the second-to-last tap.

– Otherwise:

– For each side of the weakest tap, identify the neighbour tap that has the smaller delay difference to the weakest tap.

– When the delay difference between the weakest tap and the identified neighbour tap on one side equals the delay difference between the weakest tap and the identified neighbour tap on the other side.

– Select the neighbour tap that is weaker in power for merging.

– Otherwise, select the neighbour tap that has smaller delay difference for merging.

– To merge, the power of the merged tap is the linear sum of the power of the weakest tap and the selected tap.

– When the selected tap is the first tap, the location of the merged tap is the location of the first tap. The weakest tap is removed.

– When the selected tap is the last tap, the location of the merged tap is the location of the last tap. The weakest tap is removed.

– Otherwise, the location of the merged tap is based on the average delay of the weakest tap and selected tap. If the average delay is on the sampling grid, the location of the merged tap is the average delay. Otherwise, the location of the merged tap is rounded towards the direction of the selected tap (e.g. 10 ns & 20 ns 🡪 15 ns, 10 ns & 25 ns 🡪 20 ns, if 25 ns had higher or equal power; 15 ns, if 10 ns had higher power). The weakest tap and the selected tap are removed.

– Repeat step 6 until the final number of taps is 12.

Step 7: Round the amplitudes of taps to one decimal (e.g. -8.78 dB 🡪 -8.8 dB)

Step 8: If the delay spread has slightly changed due to the tap merge, adjust the final delay spread by increasing or decreasing the power of the last tap so that the delay spread is corrected.

Step 9: Re-normalize the highest tap to 0 dB.

NOTE 1: Some values of the delay profile created by the simplification steps may differ from the values in tables J.2.1.1-2, J.2.1.1-3, J.2.1.1-4, and J.2.1.2-2 for the corresponding model.

NOTE 2: For Step 5 and Step 6, the power values are expressed in the linear domain using 6 digits of precision. The operations are in the linear domain.

J.2.1.1 Delay profiles for FR1

The delay profiles for FR1 are selected to be representative of low, medium and high delay spread environment. The resulting model parameters are specified in Table J.2.1.1-1 and the tapped delay line models are specified in tables J.2.1.1-2 to J.2.1.1-4.

Table J.2.1.1-1: Delay profiles for NR channel models

Model	Number of channel taps	Delay spread (r.m.s.)	Maximum excess tap delay (span)	Delay resolution
TDLA30	12	30 ns	290 ns	5 ns
TDLB100	12	100 ns	480 ns	5 ns
TDLC300	12	300 ns	2595 ns	5 ns

Table J.2.1.1-2: TDLA30 (DS = 30 ns)

Tap #	Delay (ns]	Power (dB)	Fading distribution
1	0	-15.5	Rayleigh
2	10	0
3	15	-5.1
4	20	-5.1
5	25	-9.6
6	50	-8.2
7	65	-13.1
8	75	-11.5
9	105	-11.0
10	135	-16.2
11	150	-16.6
12	290	-26.2

Table J.2.1.1-3: TDLB100 (DS = 100ns)

Tap #	Delay (ns]	Power (dB)	Fading distribution
1	0	0	Rayleigh
2	10	-2.2
3	20	-0.6
4	30	-0.6
5	35	-0.3
6	45	-1.2
7	55	-5.9
8	120	-2.2
9	170	-0.8
10	245	-6.3
11	330	-7.5
12	480	-7.1

Table J.2.1.1-4: TDLC300 (DS = 300 ns)

Tap #	Delay (ns]	Power (dB)	Fading distribution
1	0	-6.9	Rayleigh
2	65	0
3	70	-7.7
4	190	-2.5
5	195	-2.4
6	200	-9.9
7	240	-8.0
8	325	-6.6
9	520	-7.1
10	1045	-13.0
11	1510	-14.2
12	2595	-16.0

J.2.1.2 Delay profiles for FR2

The delay profiles for FR2 are specified in J.2.1.2-1 and the tapped delay line models are specified in table J.2.1.2-2.

Table J.2.1.2-1: Delay profiles for NR channel models

Model

Number of
channel taps

Delay spread

(r.m.s.)

Maximum excess tap delay (span)

Delay resolution

TDLA30

30 ns

290 ns

5 ns

Table J.2.1.2-2: TDLA30 (DS = 30 ns)

Tap #	Delay (ns]	Power (dB)	Fading distribution
1	0	-15.5	Rayleigh
2	10	0
3	15	-5.1
4	20	-5.1
5	25	-9.6
6	50	-8.2
7	65	-13.1
8	75	-11.5
9	105	-11.0
10	135	-16.2
11	150	-16.6
12	290	-26.2

J.2.2 Combinations of channel model parameters

The propagation conditions used for the performance measurements in multi-path fading environment are indicated as a combination of a channel model name and a maximum Doppler frequency, i.e., TDLA<DS>-<Doppler>, TDLB<DS>-<Doppler> or TDLC<DS>-<Doppler> where ‘<DS>’ indicates the desired delay spread and ‘<Doppler>’ indicates the maximum Doppler frequency (Hz).

Table J.2.2-1 and J.2.2-2 show the propagation conditions that are used for the performance measurements in multi-path fading environment for low, medium and high Doppler frequencies for FR1 and FR2, respectively.

Table J.2.2-1: Channel model parameters for FR1

Combination name	Model	Maximum Doppler frequency
TDLA30-5	TDLA30	5 Hz
TDLA30-10	TDLA30	10 Hz
TDLB100-400	TDLB100	400 Hz
TDLC300-100	TDLC300	100 Hz

Table J.2.2-2: Channel model parameters for FR2

Combination name	Model	Maximum Doppler frequency
TDLA30-75	TDLA30	75 Hz
TDLA30-300	TDLA30	300 Hz

J.2.3 MIMO channel correlation matrices

The MIMO channel correlation matrices defined in J.2.3 apply for the antenna configuration using uniform linear arrays at both IAB-DU and IAB-MT and for the antenna configuration using cross polarized antennas.

J.2.3.1 MIMO correlation matrices using Uniform Linear Array (ULA)

The MIMO channel correlation matrices defined in J.2.3.1 apply for the antenna configuration using uniform linear array (ULA) at both IAB-DU and IAB-MT.

J.2.3.1.1 Definition of MIMO correlation matrices

Table J.2.3.1.1-1 defines the correlation matrix for the IAB-DU.

Table J.2.3.1.1-1: IAB-DU correlation matrix

	IAB-DU correlation
One antenna
Two antennas
Four antennas
Eight antennas

Table J.2.3.1.1-2 defines the correlation matrix for the IAB-MT:

Table J.2.3.1.1-2: IAB-MT correlation matrix

	One antenna	Two antennas	Four antennas
IAB-MT correlation

Table J.2.3.1.1-3 defines the channel spatial correlation matrix. The parameters, α and β in table J.2.3.1.1-3 defines the spatial correlation between the antennas at the IAB-DU and IAB-MT respectively.

Table J.2.3.1.1-3: correlation matrices

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

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

J.2.3.1.2 MIMO correlation matrices at high, medium and low level

The and for different correlation types are given in table J.2.3.1.2-1.

Table J.2.3.1.2-1: Correlation for high, medium and low level

Low correlation		Medium correlation		High correlation
α	β	α	β	α	β
0	0	0.9	0.3	0.9	0.9

The correlation matrices for high, medium and low correlation are defined in tables J.2.3.1.2-2, J.2.3.1.2-3 and J.2.3.1.2-4 as below.

The values in table J.2.3.1.2-2 have been adjusted for the 2×4 and 4×4 high correlation cases to ensure 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 2×4 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 J.2.3.1.2-3 to ensure the correlation matrix is positive semi-definite after round-off to 4 digit precision with a =0.00012.

Table J.2.3.1.2-2: MIMO correlation matrices for high correlation

1×2 case
2×2 case
2×4 case
4×4 case

Table J.2.3.1.2-3: MIMO correlation matrices for medium correlation

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

Table J.2.3.1.2-4: MIMO correlation matrices for low correlation

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

In table J.2.3.1.2-4, is a identity matrix.

NOTE: For completeness, the correlation matrices were defined for high, medium and low correlation but performance requirements exist only for low correlation.

J.2.3.2 Multi-antenna channel models using cross polarized antennas

The MIMO channel correlation matrices defined in J.2.3.2 apply to two cases as presented below:

– One TX antenna and multiple RX antennas case, with cross polarized antennas used at gNB

– Multiple TX antennas and multiple RX antennas case, with cross polarized antennas used at both UE and gNB

The cross-polarized antenna elements with +/-45 degrees polarization slant angles are deployed at gNB. For one TX antenna case, antenna element with +90 degree polarization slant angle is deployed at UE. For multiple TX antennas case, 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 TX or RX antennas.

J.2.3.2.1 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 gNB with same polarization,

– is a polarization correlation matrix,

– is a permutation matrix, and

– denotes transpose.

Table J.2.3.2.1-1 defines the polarization correlation matrix.

Table J.2.3.2.1-1 : Polarization correlation matrix

	One TX antenna	Multiple TX antennas
Polarization correlation matrix

The matrixis defined as

where and is the number of TX and RX antennas respectively, and is the ceiling operator.

The matrix is used to map the spatial correlation coefficients in accordance with the antenna element labelling system described in J.2.3.2.

J.2.3.2.2 Spatial correlation matrices at IAB-MT and IAB-DU sides

J.2.3.2.2.1 Spatial correlation matrices at IAB-MT side

For 1-antenna transmitter, .

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

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

J.2.3.2.2.2 Spatial correlation matrices at IAB-DU 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,.

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

J.2.3.2.3 MIMO correlation matrices using cross polarized antennas

The values for parameters α, β and γ for low spatial correlation are given in table J.2.3.2.3-1.

Table J.2.3.2.3-1: Values for parameters α,  and γ

Low spatial correlation
α		γ
0	0	0
Note 1: Value of α applies when more than one pair of cross-polarized antenna elements at gNB side. Note 2: Value of β applies when more than one pair of cross-polarized antenna elements at UE side.

The correlation matrices for low spatial correlation are defined in table J.2.3.2.3-2 as below.

Table J.2.3.2.3-2: MIMO correlation matrices for low spatial correlation

1×8 case
2×8 case

In table J.2.3.2.3-2, is a identity matrix.