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 is 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

Time and frequency samples

The number of temporal snapshots N and frequency samples M is TBD. They must be chosen to minimize the validation measurement time, but sufficiently high to keep an adequate correlation estimation accuracy. It is beneficial to choose the time sampling interval larger than the coherence time of the channel model. such that the recorded time samples represent independent fading occasions. The same principle applies also to frequency sampling interval and the channel coherence bandwidth.

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-A and CDL-C 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-A UMi and in Tables C.3.4-4 and C.3.4-5 for CDL-C UMa for a vertically polarized MPAC OTA setup with 16 uniformly spaced probes.

Table C.3.4-2: Spatial correlation reference curves for CDL-A UMi model for a vertically polarized MPAC OTA setup with 16 uniformly spaced probes at FR1 test frequencies below 1800 MHz

617 MHz

722 MHz

836.5 MHz

1575.42 MHz

Azimuth [o]

ref

Azimuth [o]

ref

Azimuth [o]

ref

Azimuth [o]

ref

270.0

1.000

270.0

1.000

270.0

1.000

270.0

1.000

251.4

0.999

254.1

0.999

256.3

0.999

262.7

0.999

232.9

0.997

238.3

0.997

242.6

0.996

255.5

0.996

214.3

0.992

222.4

0.993

228.9

0.993

248.2

0.992

195.8

0.981

206.6

0.984

215.2

0.987

240.9

0.987

110.40

0.809

190.7

0.969

201.6

0.975

233.7

0.982

40.80

0.823

120.52

0.778

187.9

0.955

226.4

0.977

331.21

0.96

61.05

0.731

128.66

0.751

219.1

0.971

 

 

1.57

0.88

77.33

0.645

211.9

0.962

 

 

302.09

0.99

25.99

0.762

204.6

0.949

 

 

 

 

334.66

0.928

197.3

0.929

 

 

 

 

283.32

0.998

190.0

0.903

 

 

 

 

 

 

182.8

0.868

 

 

 

 

 

 

152.74

0.620

 

 

 

 

 

 

125.48

0.363

 

 

 

 

 

 

98.23

0.299

 

 

 

 

 

 

70.97

0.364

 

 

 

 

 

 

43.71

0.460

 

 

 

 

 

 

16.45

0.58

 

 

 

 

 

 

349.20

0.71

 

 

 

 

 

 

321.94

0.86

 

 

 

 

 

 

294.68

0.97

Table C.3.4-3: Spatial correlation reference curves for CDL-A UMi model for a vertically polarized MPAC OTA setup with 16 uniformly spaced probes at FR1 test frequencies equal to or greater than 1800 MHz

1800 MHz

2132.5 MHz

2450 MHz

3600 MHz

4700 MHz

Azimuth [o]

ref

Azimuth [o]

ref

Azimuth [o]

ref

Azimuth [o]

ref

Azimuth [o]

ref

270.0

1.000

270.0

1.000

270.0

1.000

270.0

1.000

270.0

1.000

260.9

0.998

261.9

0.998

263.0

0.997

265.2

0.997

266.3

0.997

251.7

0.991

253.9

0.990

256.0

0.990

260.5

0.990

262.7

0.990

242.6

0.981

245.8

0.980

249.0

0.979

255.7

0.979

259.0

0.979

233.5

0.967

237.8

0.967

242.0

0.966

250.9

0.966

255.4

0.969

224.3

0.951

229.7

0.952

234.9

0.951

246.1

0.950

251.7

0.956

215.2

0.932

221.7

0.933

227.9

0.932

241.4

0.932

248.1

0.942

206.0

0.906

213.6

0.911

220.9

0.913

236.6

0.908

244.4

0.922

196.9

0.877

205.6

0.883

213.9

0.888

231.8

0.881

240.8

0.896

187.8

0.845

197.5

0.854

206.9

0.862

227.1

0.857

237.1

0.872

134.3

0.748

189.5

0.823

199.9

0.833

222.3

0.832

233.5

0.842

88.6

0.729

181.4

0.795

192.9

0.805

217.5

0.815

229.8

0.817

43.0

0.833

139.7

0.737

185.9

0.783

212.7

0.800

226.1

0.792

357.3

0.953

99.5

0.725

144.9

0.742

208.0

0.792

222.5

0.775

311.6

0.978

59.2

0.753

109.9

0.754

203.2

0.785

218.8

0.760

 

 

18.9

0.884

74.8

0.727

198.4

0.782

215.2

0.753

 

 

338.6

0.970

39.8

0.778

193.7

0.781

211.5

0.750

 

 

298.4

0.982

4.7

0.901

188.9

0.786

207.9

0.753

 

 

 

 

329.7

0.974

184.1

0.795

204.2

0.760

 

 

 

 

294.6

0.980

156.1

0.886

200.6

0.775

 

 

 

 

 

 

132.3

0.952

196.9

0.792

 

 

 

 

 

 

108.4

0.949

193.3

0.817

 

 

 

 

 

 

84.6

0.906

189.6

0.840

 

 

 

 

 

 

60.7

0.830

185.9

0.865

 

 

 

 

 

 

36.9

0.741

182.3

0.888

 

 

 

 

 

 

13.0

0.774

161.7

0.978

 

 

 

 

 

 

349.1

0.894

143.5

0.945

 

 

 

 

 

 

325.3

0.966

125.2

0.926

 

 

 

 

 

 

301.4

0.969

106.9

0.926

 

 

 

 

 

 

277.6

0.994

88.6

0.948

 

 

 

 

 

 

 

 

70.4

0.948

 

 

 

 

 

 

 

 

52.1

0.896

 

 

 

 

 

 

 

 

33.8

0.747

 

 

 

 

 

 

 

 

15.5

0.682

 

 

 

 

 

 

 

 

357.3

0.799

 

 

 

 

 

 

 

 

339.0

0.912

 

 

 

 

 

 

 

 

320.7

0.956

 

 

 

 

 

 

 

 

302.4

0.968

 

 

 

 

 

 

 

 

284.2

0.973

Table C.3.4-4: 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 below 1800 MHz

617 MHz

722 MHz

836.5 MHz

1575.42 MHz

Azimuth [o]

ref

Azimuth [o]

ref

Azimuth [o]

ref

Azimuth [o]

ref

270.0

1.000

270.0

1.000

270.0

1.000

270.0

1.000

251.4

0.999

254.1

0.999

256.3

0.999

262.7

0.999

232.9

0.997

238.3

0.997

242.6

0.996

255.5

0.996

214.3

0.992

222.4

0.993

228.9

0.993

248.2

0.992

195.8

0.981

206.6

0.984

215.2

0.987

240.9

0.987

110.40

0.809

190.7

0.969

201.6

0.975

233.7

0.982

40.80

0.823

120.52

0.778

187.9

0.955

226.4

0.977

331.21

0.96

61.05

0.731

128.66

0.751

219.1

0.971

 

 

1.57

0.88

77.33

0.645

211.9

0.962

 

 

302.09

0.99

25.99

0.762

204.6

0.949

 

 

 

 

334.66

0.928

197.3

0.929

 

 

 

 

283.32

0.998

190.0

0.903

 

 

 

 

 

 

182.8

0.868

 

 

 

 

 

 

152.74

0.620

 

 

 

 

 

 

125.48

0.363

 

 

 

 

 

 

98.23

0.299

 

 

 

 

 

 

70.97

0.364

 

 

 

 

 

 

43.71

0.460

 

 

 

 

 

 

16.45

0.58

 

 

 

 

 

 

349.20

0.71

 

 

 

 

 

 

321.94

0.86

 

 

 

 

 

 

294.68

0.97

Table C.3.4-5: 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 equal to or greater than 1800 MHz

1800 MHz

2132.5 MHz

2450 MHz

3600 MHz

4700 MHz

Azimuth [o]

ref

Azimuth [o]

ref

Azimuth [o]

ref

Azimuth [o]

ref

Azimuth [o]

ref

270.0

1.000

270.0

1.000

270.0

1.000

270.0

1.000

270.0

1.000

260.9

0.998

261.9

0.998

263.0

0.997

265.2

0.997

266.3

0.996

251.7

0.991

253.9

0.991

256.0

0.992

260.5

0.989

262.7

0.988

242.6

0.984

245.8

0.984

249.0

0.983

255.7

0.979

259.0

0.976

233.5

0.976

237.8

0.975

242.0

0.975

250.9

0.969

255.4

0.966

224.3

0.967

229.7

0.966

234.9

0.965

246.1

0.960

251.7

0.957

215.2

0.955

221.7

0.955

227.9

0.953

241.4

0.954

248.1

0.951

206.0

0.936

213.6

0.940

220.9

0.939

236.6

0.947

244.4

0.945

196.9

0.908

205.6

0.918

213.9

0.921

231.8

0.937

240.8

0.940

187.8

0.863

197.5

0.888

206.9

0.898

227.1

0.925

237.1

0.935

134.3

0.309

189.5

0.846

199.9

0.867

222.3

0.903

233.5

0.928

88.6

0.269

181.4

0.793

192.9

0.829

217.5

0.876

229.8

0.918

43.0

0.396

139.7

0.280

185.9

0.786

212.7

0.837

226.1

0.902

357.3

0.619

99.5

0.252

144.9

0.245

208.0

0.798

222.5

0.882

311.6

0.879

59.2

0.257

109.9

0.299

203.2

0.753

218.8

0.851

 

 

18.9

0.471

74.8

0.215

198.4

0.708

215.2

0.816

 

 

338.6

0.661

39.8

0.251

193.7

0.669

211.5

0.767

 

 

298.4

0.937

4.7

0.489

188.9

0.624

207.9

0.708

 

 

 

 

329.7

0.652

184.1

0.580

204.2

0.651

 

 

 

 

294.6

0.946

156.1

0.175

200.6

0.580

 

 

 

 

 

 

132.3

0.565

196.9

0.516

 

 

 

 

 

 

108.4

0.745

193.3

0.444

 

 

 

 

 

 

84.6

0.820

189.6

0.383

 

 

 

 

 

 

60.7

0.750

185.9

0.310

 

 

 

 

 

 

36.9

0.493

182.3

0.229

 

 

 

 

 

 

13.0

0.120

161.7

0.445

 

 

 

 

 

 

349.1

0.272

143.5

0.750

 

 

 

 

 

 

325.3

0.498

125.2

0.879

 

 

 

 

 

 

301.4

0.843

106.9

0.813

 

 

 

 

 

 

277.6

0.991

88.6

0.733

 

 

 

 

 

 

 

 

70.4

0.740

 

 

 

 

 

 

 

 

52.1

0.873

 

 

 

 

 

 

 

 

33.8

0.944

 

 

 

 

 

 

 

 

15.5

0.643

 

 

 

 

 

 

 

 

357.3

0.250

 

 

 

 

 

 

 

 

339.0

0.178

 

 

 

 

 

 

 

 

320.7

0.375

 

 

 

 

 

 

 

 

302.4

0.726

 

 

 

 

 

 

 

 

284.2

0.929

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.