C.3.4 Spatial correlation

38.1513GPPNRRelease 17TSUser Equipment (UE) Multiple Input Multiple Output (MIMO) Over-the-Air (OTA) performance requirements

This measurement checks whether the measured correlation curve follows the theoretical curve. For spatial correlation validation measurement, only Vertical validation measurement is required. Spatial correlation validation is only adopted for FR1 MIMO OTA.

The spatial correlation validation measurement setup is illustrated in Figure C.3.4-1. The network analyser transmits signals through the fading emulator and probes. The 16 probes radiate the signals within the anechoic chamber and a receiving test antenna is placed within the test zone. The test antenna is attached to a positioner that can move the antenna to pre-defined spatial locations on a fixed radius from the centre of the quiet zone. The received signal is measured with the network analyser.

The measurement and analysis procedure are as follows:

Set the target channel model to fading emulator.

1. For each position of the test antenna in the test zone, step & pause the emulator to different time instances. Measure the frequency responses for all stepped channel snapshots , where the interval between frequency and time samples is and , respectively. The number of channel snapshots and frequency samples should be sufficiently high so that the matrix can be estimated reliably.

2. Move the measurement antenna with a positioner to another location and repeat step 2 to record frequency responses of all stepped channel snapshots.

3. Repeat step 3 to record frequency responses at all spatial sample points.

4. Stack measured time and frequency samples to a vector and calculate correlation between the first spatial sample point (i.e. ) and other spatial points

5.

6. Take the theoretical reference spatial correlation of the corresponding spatial sample points. Plot both the measured and theoretical curves.

7. Calculate the weighted RMS correlation error between the measured and the reference.

Figure C.3.4-1: Configuration for spatial correlation validation

Beam-Specific Block Diagram

It is assumed that the beams are mapped to the inputs of the channel emulator as follows:

– Beam 1: Input 1 and Input 2

– Beam 2: Input 3 and Input 4 (CDL-C UMa only)

Figure C.3.4-2: Configuration for spatial correlation validation (CDL-C UMi)

Figure C.3.4-3: Configuration for spatial correlation validation (CDL-C UMa)

Time and frequency samples

The number of temporal snapshots N and frequency samples M is shown in Table C.3.4-1. The channel model specification is presented in Table C.3.4-2.

Table C.3.4-1: VNA settings for spatial correlation

Item	Unit	Value
Center frequency	MHz	Downlink centre frequency in Table C.3.1-1
Span	MHz	0 (Note 2)
RF output level	dBm	-15
Number of traces		1000
Distance between traces in channel model	Wavelength (Note 1)	> 2
Number of points		1 (or the smallest possible) (Note 2)
Averaging		1
NOTE1: Time in seconds = distance [] / MS speed [/s] MS speed [/s] = MS speed [m /s] / Speed of light [m/s] * Center frequency [Hz] NOTE 2: Span and number of points may be increased to estimate reliably

Table C.3.4-2: Channel model specification

Item	Unit	Value
Center frequency	MHz	Downlink centre frequency in Table C.3.1-1
Channel model samples	Wavelength	> 2000
Channel model		As specified in Annex C.1
Mobile speed	km/h	30

Spatial samples

The spatial samples for the correlation validation measurement are on the circumference of the quiet zone, as illustrated in Figure C.3.4-2. The test zone is a circle with 20 cm diameter in the horizontal plane. The reference point (denoted by a red marker) is in AoA 270°. The mean AoAs of the CDL-C UMi and CDL-C UMa models are slightly different, but the underlying geometry for the CDL model indicates that the mean AoA (or assumed LoS direction) of the model is 180°. The reference point orientation of the validation measurement is proposed to be with 90° offset to the channel model reference AoA to enable accurate sampling of the main lobe of the spatial correlation curve. The reference point orientation must be defined in the channel model coordinate system instead of the chamber/probe coordinate system to enable optimization of OTA model implementation to achieve better alignment with the cluster AoAs and probe directions. In order to have spatial samples that yield reasonable measurement times and adequately capture the main lobe of the correlation curve, a non-uniform sampling is used where the first quadrant i.e., 270°-180°, is sampled with dense sampling compared to the rest of the circle. The spacing of the spatial samples is summarized in Table C.3.4-1 for test frequencies less than 1800 MHz and equal to or greater than 1800 MHz.

Table C.3.4-1: Spacing of Spatial Samples

Test Frequencies [MHz]	First quadrant of test zone circumference (270o-180o)	Remaining quadrants
617, 722, 836.5 1575.42	/15	/4
1800, 2132.50, 2450, 3600, 4700	/10	/2

Figure C.3.4-2: Spatial sampling for spatial correlation validation measurement for test frequencies less than and equal to or greater than 1800 MHz: 617 MHz spatial sampling (left) and 4700 MHz spatial sampling (right).

Reference Spatial Correlation Curves

The spatial correlation validation reference curves are tabulated in Tables C.3.4-2 and C.3.4-3 for CDL-C UMi and CDL-C UMa, respectively, for a vertically polarized MPAC OTA setup with 16 uniformly spaced probes.

Table C.3.4-2: Spatial correlation reference curves for CDL-C UMi model for a vertically polarized MPAC OTA setup with 16 uniformly spaced probes at FR1 test frequencies

617 MHz		722 MHz		836.5 MHz		1575.42 MHz		1800 MHz
Azim []	|| beam 1	Azim []	|| beam 1	Azim []	|| beam 1	Azim []	|| beam 1	Azim []	|| beam 1
270.0	1.00	270.0	1.00	270.0	1.00	270.0	1.00	270.0	1.00
251.4	1.00	254.1	1.00	256.3	1.00	262.7	1.00	260.9	1.00
232.9	1.00	238.3	1.00	242.6	1.00	255.5	1.00	251.7	1.00
214.3	0.99	222.4	1.00	228.9	1.00	248.2	1.00	242.6	0.99
195.8	0.99	206.6	0.99	215.2	0.99	240.9	0.99	233.5	0.99
110.4	0.87	190.7	0.98	201.6	0.98	233.7	0.99	224.3	0.98
40.8	0.87	120.5	0.84	187.9	0.96	226.4	0.99	215.2	0.97
331.2	0.98	61.1	0.80	128.7	0.82	219.1	0.98	206.0	0.95
		1.6	0.91	77.3	0.73	211.9	0.97	196.9	0.92
		302.1	0.99	26.0	0.81	204.6	0.96	187.8	0.87
				334.7	0.95	197.3	0.94	134.3	0.39
				283.3	1.00	190.0	0.91	88.6	0.15
						182.8	0.87	43.0	0.24
						152.7	0.66	357.3	0.62
						125.5	0.44	311.6	0.94
						98.2	0.30
						71.0	0.28
						43.7	0.37
						16.5	0.54
						349.2	0.75
						321.9	0.91
						294.7	0.99
2132.5 MHz		2450 MHz		3600 MHz		4700 MHz
Azim []	|| beam 1	Azim []	|| beam 1	Azim []	|| beam 1	Azim []	|| beam 1
270.0	1.00	270.0	1.00	270.0	1.00	270.0	1.00
261.9	1.00	263.0	1.00	265.2	1.00	266.3	1.00
253.9	1.00	256.0	1.00	260.5	1.00	262.7	1.00
245.8	0.99	249.0	0.99	255.7	0.99	259.0	0.99
237.8	0.99	242.0	0.99	250.9	0.99	255.4	0.99
229.7	0.98	234.9	0.99	246.1	0.99	251.7	0.99
221.7	0.97	227.9	0.98	241.4	0.98	248.1	0.98
213.6	0.96	220.9	0.97	236.6	0.98	244.4	0.98
205.6	0.93	213.9	0.95	231.8	0.97	240.8	0.98
197.5	0.89	206.9	0.92	227.1	0.97	237.1	0.97
189.5	0.84	199.9	0.88	222.3	0.95	233.5	0.97
181.4	0.77	192.9	0.83	217.5	0.93	229.8	0.96
139.7	0.27	185.9	0.76	212.7	0.90	226.1	0.95
99.5	0.14	144.9	0.19	208.0	0.86	222.5	0.93
59.2	0.14	109.9	0.26	203.2	0.81	218.8	0.91
18.9	0.26	74.8	0.37	198.4	0.75	215.2	0.87
338.6	0.71	39.8	0.19	193.7	0.68	211.5	0.83
298.4	0.97	4.7	0.29	188.9	0.59	207.9	0.78
		329.7	0.74	184.1	0.49	204.2	0.72
		294.6	0.97	156.1	0.23	200.6	0.64
				132.3	0.62	196.9	0.56
				108.4	0.85	193.3	0.47
				84.6	0.93	189.6	0.37
				60.7	0.92	185.9	0.27
				36.9	0.79	182.3	0.18
				13.0	0.42	161.7	0.51
				349.1	0.15	143.5	0.83
				325.3	0.60	125.2	0.95
				301.4	0.90	106.9	0.89
				277.6	1.00	88.6	0.80
						70.4	0.78
						52.1	0.88
						33.8	0.98
						15.5	0.91
						357.3	0.53
						339.0	0.09
						320.7	0.50
						302.4	0.82
						284.2	0.97

Table C.3.4-3: Spatial correlation reference curves for CDL-C UMa model for a vertically polarized MPAC OTA setup with 16 uniformly spaced probes at FR1 test frequencies

617 MHz		722 MHz		836.5 MHz		1575.42 MHz		1800 MHz
Azim []	|| comb	Azim []	|| comb	Azim []	|| comb	Azim []	|| comb	Azim []	|| comb
270.0	1.00	270.0	1.00	270.0	1.00	270.0	1.00	270.0	1.00
251.4	0.99	254.1	0.99	256.3	0.99	262.7	0.99	260.9	0.99
232.9	0.99	238.3	0.98	242.6	0.98	255.5	0.98	251.7	0.96
214.3	0.98	222.4	0.97	228.9	0.97	248.2	0.96	242.6	0.93
195.8	0.96	206.6	0.96	215.2	0.96	240.9	0.94	233.5	0.90
110.4	0.61	190.7	0.94	201.6	0.95	233.7	0.92	224.3	0.89
40.8	0.47	120.5	0.58	187.9	0.92	226.4	0.91	215.2	0.88
331.2	0.85	61.1	0.30	128.7	0.56	219.1	0.90	206.0	0.87
		1.6	0.56	77.3	0.19	211.9	0.89	196.9	0.84
		302.1	0.95	26.0	0.27	204.6	0.88	187.8	0.79
				334.7	0.70	197.3	0.87	134.3	0.16
				283.3	0.99	190.0	0.84	88.6	0.30
						182.8	0.79	43.0	0.22
						152.7	0.42	357.3	0.36
						125.5	0.13	311.6	0.57
						98.2	0.30
						71.0	0.31
						43.7	0.29
						16.5	0.33
						349.2	0.29
						321.9	0.48
						294.7	0.88

2132.5 MHz		2450 MHz		3600 MHz		4700 MHz
Azim []	|| comb	Azim []	|| comb	Azim []	|| comb	Azim []	|| comb
270.0	1.00	270.0	1.00	270.0	1.00	270.0	1.00
261.9	0.99	263.0	0.99	265.2	0.98	266.3	0.98
253.9	0.95	256.0	0.95	260.5	0.95	262.7	0.94
245.8	0.92	249.0	0.91	255.7	0.90	259.0	0.89
237.8	0.89	242.0	0.87	250.9	0.84	255.4	0.83
229.7	0.86	234.9	0.85	246.1	0.80	251.7	0.78
221.7	0.85	227.9	0.83	241.4	0.77	248.1	0.73
213.6	0.85	220.9	0.82	236.6	0.75	244.4	0.70
205.6	0.83	213.9	0.82	231.8	0.73	240.8	0.68
197.5	0.80	206.9	0.80	227.1	0.72	237.1	0.66
189.5	0.75	199.9	0.77	222.3	0.71	233.5	0.65
181.4	0.67	192.9	0.73	217.5	0.70	229.8	0.64
139.7	0.22	185.9	0.66	212.7	0.69	226.1	0.63
99.5	0.24	144.9	0.26	208.0	0.67	222.5	0.62
59.2	0.03	109.9	0.23	203.2	0.64	218.8	0.61
18.9	0.16	74.8	0.19	198.4	0.61	215.2	0.60
338.6	0.37	39.8	0.13	193.7	0.56	211.5	0.59
298.4	0.73	4.7	0.15	188.9	0.49	207.9	0.57
		329.7	0.38	184.1	0.41	204.2	0.55
		294.6	0.74	156.1	0.42	200.6	0.52
				132.3	0.19	196.9	0.48
				108.4	0.64	193.3	0.42
				84.6	0.47	189.6	0.35
				60.7	0.44	185.9	0.26
				36.9	0.28	182.3	0.18
				13.0	0.16	161.7	0.59
				349.1	0.16	143.5	0.26
				325.3	0.41	125.2	0.79
				301.4	0.40	106.9	0.43
				277.6	0.95	88.6	0.68
						70.4	0.63
						52.1	0.75
						33.8	0.87
						15.5	0.67
						357.3	0.09
						339.0	0.25
						320.7	0.32
						302.4	0.42
						284.2	0.73

Time Domain Alternative Method:

Time domain techniques can also be used to validate the spatial correlation. The spatial correlation validation measurement setup is illustrated in Figure C.3.4-3. In this case a Signal generator transmits a CW signal through the MIMO test system. The signal is received by a test antenna within the test area. Finally, the signal is collected by a signal analyser and the measured signal is stored for postprocessing.

Figure C.3.4-3: Configuration for spatial correlation validation based on time domain techniques

For each spatial point, the channel emulator should issue a trigger signal each time fading is started. For each point collect a time domain trace with the signal analyser, when done, stop fading. Data recording is synchronized with the channel emulator trigger.

Follow the same procedure to postprocess the data and calcalate the spatial correlation by setting m to 1. The settings for the Signal Generator and Signal Analyser are in Table C.3.4-6 and C.3.4-7 respectively.

Table C.3.4-6: Signal Generator Settings

Item	Unit	Value
Centre frequency	MHz	Downlink centre frequency in Table C.3.1-1
Output power	dBm	Function of the CE. Sufficiently above Noise Floor

Table C.3.4-7: Signal Analyser Settings

Item	Unit	Value
Centre frequency	MHz	Downlink centre frequency in Table C.3.1-1
Sampling	Hz	At least 15 times bigger than the max Doppler spread (fd=v/λ)
Observation time	s	At least 16s. Channel Model length should be the same or greater than the observation time.

Beam-Simultaneous Block Diagram

It is assumed that the beams are mapped to the inputs of the channel emulator as follows:

– Beam 1: Input 1 and Input 2

– Beam 2: Input 3 and Input 4 (CDL-C UMa only)

Figure C.3.4-4: Configuration for spatial correlation validation based on time domain techniques (CDL-C UMi)

Figure C.3.4-5: Configuration for spatial correlation validation based on time domain techniques (CDL-C UMa)