0. Wireless Channel Model
Younglok Kim
WSoC Lab., Sogang University

1. Outline Introduction Wireless channel & model Jakes channel model
Shadow fading
Multipath fading
Doppler spectrum
Jakes channel model
Spacially correlated model (SCM)

2. Communication Channel
Means
Everything between the source and the sink of a signal
Includes
Physical medium between the transmitter and receiver
All of the equipment in the transmitter and receiver
Depends on the purpose of the simulation

3. Example for Discrete Channel Model of CDMA System

4. Physical Medium
Free space (idealization), atmosphere (wireless), wires, waveguide, optical fibers, coaxial cables, etc.
Require effective transfer function
Between receiver and transmitter
Depend on the carrier frequency, bandwidth and physical environment.
We will focus on
Wireless channel
Its discrete model

5. Characteristics of Wireless Channel
Shadow fading
Large scale fading
Cause attenuation
Multipath fading
Small scale fading
Cause fluctuation
Diffuse multipath channel
Discrete multipath channel

6. Signal Power Fluctuation

7. Shadow Fading Large-scale fading
Attenuation of the average signal power
Due to buildings, hills, etc
Described in the pathloss and statistical variations about the mean

8. Modeling of Shadow Fading
Rx signal power:

9. Passloss Model
Slope-intercept models
For the free space,

10. Hata Model for Pathloss Parameters

11. Passloss vs. Distance

12. Multipaths Due to Effect of Multipaths Atmospheric scattering (S)
Defflaction (D)
Reflections from buildings and other objects (R)
Effect of Multipaths
Dispersion of the signal
Time-variant behavior
Small scale fading

13. Multipath Environment

14. Frequency Selective & Non-Selective
Due to diffuse multipaths (unresolvable paths)
Fading depends on the operating frequency.
Frequency selective channel for the wideband signal.

15. Tapped Delay Line (TDL) Channel Model

16. Tapped Delay Line (TDL) Channel Model
Impulse response of channel

17. Channel Impulse Response Parameters
Number of taps, average powers, delays and Doppler spectrum are given by ITU
Indoor channel A & B
Outdoor to Indoor & Pedestrian channel A & B
Vehicular channel A & B
Rx signal magnitude is determined by the shadowing signal power.
The random weight has to be generated.

18. Indoor Office Test Parameters
Tap
Channel A
Channel B
Doppler
Rel. Delay (nsec)
Avg. Power (dB)
Rel. Delay (nsec)
Avg. Power (dB)
Spectrum 1
FLAT 2 50
-3.0
100
-3.6 3
110
-10.0
200
-7.2 4
170
-18.0
300
-10.8 5
290
-26.0
500 6
310
-32.0
700
-25.2

19. Outdoor to Indoor and Pedestrian Test Parameters
Tap
Channel A
Channel B
Doppler
Rel. Delay (nsec)
Avg. Power (dB)
Spectrum 1
CLASSIC 2
110
-9.7
200
-0.9 3
190
-19.2
800
-4.9 4
410
-22.8
1200
-8.0 5 -
2300
-7.8 6
3700
-23.9

20. Vehicular Test Parameters
Tap
Channel A
Channel B
Doppler
Rel. Delay (nsec)
Avg. Power (dB)
Spectrum 1
0.0
-2.5
CLASSIC 2
310
-1.0
300 3
710
-9.0
8900
-12.8 4
1090
-10.0
12900 5
1730
-15.0
17100
-25.2 6
2510
-20.0
20000
-16.0

21. Generation of Complex Tap Weight
How to generate random tap weight
that including following properties
Probability density function (PDF) of the amplitude
Rayleigh, Rician, etc.
Doppler effect
Correlated signal in time domain
Flat fading or Classic fading
Independent to each other

22. Distribution of Path Amplitude
Rayleigh distribution
For no line-of-sight (LOS) path
Amplitude of the complex Gaussian random number
Rician distribution
For LOS path

23. Doppler Effect Due to Rx or Tx movements
Due to the movements of reflected objects
Create time varying (time selective) channel

24. WSSUS Model
Wide sense stationary (WSS) uncorrelated scattering (US) mode
Create classical fading

25. Weight for WSSUS Model Classical power spectrum of WSSUS model
Tap weight that satisfies above

26. Classical Fading Power Spectrum

27. Flat Fading Flat Doppler spectrum for indoor channel
Tap weight that satisfies above

28. Flat Fading Power Spectrum

29. Jakes Channel Fading Model
Deterministic method to generate the correlated Rayleigh fading waveform including the Doppler effect.

30. Power Profile of Jakes Model (30 km/h)
4 independent waveforms
No = 16
Tsample = 66.6 msec

31. Power Profile of Jakes Model (120 km/h)
4 independent waveforms
No = 16
Tsample = 66.6 msec

32. Power Profile of Flat Fading (30 km/h)
4 independent waveforms
No = 16
Tsample = 66.6 msec

33. References for Jakes Model and Modified Methods
[1] UMTS TR V3.2.0, Selection procedures for the choice of radio transmission technologies of the UMTS, April 1998.
[2] 3GPP TSG RAN WG4, Technical specification documents.
[3] W. C. Jakes (Editor), Microwave mobile communications, 1974, reprinted by IEEE Press.
[4] K. Pahlavan and A. H. Levesque, Wireless Information Networks, Wiley, 1995.
[5] P. Dent and T. Croft, “Jakes fading model revisited”, Electronics letters, Vol. 29, No. 13, June 1993.
[6] Y. Li and Y. L. Guan, “Modified Jakes’ model for simulating multiple uncorrelated fading waveforms”, 2000 IEEE 51th VTC, Tokyo, Japan, May 2000.

34. Typical Communication Modem

35. Rx Signal Model with TDL Channel
Frequency
error
Timing error
Sampled Rx signal
Channel delay
Tx symbol
oversampling
Tx amplitude
Phase error
Sampling period
Channel coefficient
Background
error

36. Spacially Correlated Model (SCM) for Multiple Antennas

37. Importance of Spatial Channel Models
The spatial properties of channels are extremely important in determining the performance of multiple antenna systems
Each diversity scheme has own channel model description
Need to consider
Time-varying angular spread
Angular distribution with plane wave assumptions
Adaptive array antenna geometries
Various estimations of spatial correlation based on various assumptions
Must verify models by field measurements
If we adopt more than two antenna elements for TxD scheme, SCM description is important to evaluate the performances of various different schemes.

38. Standard for Space Channel Model
Common & more reliable simulation spatial channel model is required
Need specific descriptions of more channel parameters, AOA, PAS, AS, etc
Spatial channel model by 3GPP-3GPP2
More spatial parameters for BS and UE
SCM Text V7.0, 8/2003
ftp://ftp.3gpp2.org/TSGC/Working/2003/3GPP_3GPP2_SCM_(Spatial_Modeling)/ConfCall /

39. Spatial Channel Models (SCM)
Develop and specify parameters and methods associated with
Link level spatial channel model
For calibration only
Reflect only one snapshot of the channel behavior
Do not account for system attributes such as scheduling and HARQ
Only for comparison of performance results from different implementation of a given algorithm
System level spatial channel model
Required for the final algorithm comparison
Define physical parameters and system evaluation methodology

40. Terminologies MS = UE = terminal = subscriber unit BS = Node-B = BTS
AS = angle spread = azimuth spread = PAS
Path = Ray
Path component = Sub-ray
PAS = power azimuth spectrum
DoT = direction of travel
AoA = angle of arrival
AoD = angle of departure
PDP = power delay profile

41. Spatial Correlated Channel Model
Assumptions
Long-term properties of the channel remain unchanged over time
Independence between different taps
Spatial covariance matrices are equal for each tap
Spatially correlated multiple channels can be generated by the linear transformation of the same number of uncorrelated channels

42. Block Diagram for SCM Generation

43. Time Invariant Eigenbeam Pattern (Macro)

44. Time Invariant Eigenbeam Pattern (Micro)

45. Assumptions of Link Level SCM
Spatial channel parameters per path
Each resolvable path is characterized by spatial channel parameters: AS, AoA, PAS
All paths are assumed independent
Array Topologies
Allow any type of antenna configuration, but must be shared to reproduce and verify the results
ULA with element spacing of 0.5, 4, 10 wavelengths

46. Time Varying Correlation Model
Discrete uniform distribution model

47. Steering Vector of ULA Phase Difference between two adjacent antenna

48. Time Varying Model Parameters
Propagation Environment
Macro Cell
Micro Cell
Distance from BS to UE
2000 m
500 m
Angular spread
10 °
45 °
Channel models
&
UE velocities (km/h)
1-path Rayleigth: 3,10,40,120
Vehicular A: 10,40,120
Pedestrian A: 3, 10, 40
Number of sub-paths (Q) 10
100
Closed loop feedback error rate
4 %

49. Time Varying Correlation Model…
Angle of sub-paths:
Angle of center:
Steering vector of ULA:

50. Time Varying Coeffs (Macro Cell)
Power of dominant eigenvector is about 99.9%

51. Time Varying Coeffs (Micro Cell)
Power of dominant eigenvector ranges from 75.4 to 99.7%

52. Parameters of Link Level SCM
Multipath fading propagation conditions
Model
Case I
Case II
Case III
Case IV
3GPP
Case B
Case C
Case D
Case A
3GPP2
Model A, D, E
Model C
Model B
Model F
PDP
Mod. Pedestrian A
Vehicular A
Pedestrian B
Single path
Speed (Km/h)
1) 3
2) 30, 120
3, 30, 120 3
# of paths
1) (LOS on, K=6 dB)
2) 4 (LOS off) 6 1
Relative path power (dB)
& Delay (ns)
LOS on
0.0
-6.51
-16.21
-25.71
-29.31
LOS off
–Inf
-9.7
-19.2
-22.8
110
190
410
-1.0
-9.0
-10.0
-15.0
-20.0
310
710
1090
1730
2510
-0.9
-4.9
-8.0
-7.8
-23.9
200
800
1200
2300
3700

53. Parameters of Link Level SCM…
Spatial parameters for NodeB
Model
Case I
Case II
Case III
Case IV
Topology
Reference: ULA with 0.5, 4, 10 spacing
N/A
PAS
Laplacian distribution with
RMS angle spread of 2 or 5 degrees per path
depending on AoA/AoD
AoD/AoA
(degrees)
50 for 2 RMS AS per path
20 for 5 RMS AS per path
Antenna gain pattern
3 or 6 sector antenna pattern
(For diversity oriented applications rather than beamforming applications)

54. Parameters of Link Level SCM…
Spatial parameters for UE
Model
Case I
Case II
Case III
Case IV
Topology
Reference 0.5
N/A
PAS
1) LOS on: Fixed AoA for LOS component, remaining power has 360 degree uniform PAS. ( RMS angle spread of 104 degrees)
2) LOS off: Laplacian distribution with RMS angle spread of 35 degrees per path
Laplacian distribution with RMS angle spread of 35 degrees per path OR
360 degree uniform PAS ( RMS angle spread of 104 degrees)
DoT
(degrees)
22.5
-22.5
AoA
22.5 (LOS component)
67.5 (all other paths)
67.5 (all paths)
22.5 (odd paths)
-67.5 (even paths)
Antenna gain pattern
Omni directional with -1 dBi gain

55. Antenna Gain Patterns UE: -1 dBi gain omni-direction
Node B uplink/downlink
Only for diversity oriented implementations (large spacing)
Need different antenna patterns for beamforming applications
3 sector cell
Bandwidth 70°, Maximum attenuation 20 dB, 14 dBi gain
6 sector cell
Bandwidth 35°, Maximum attenuation 23 dB, 17 dBi gain
Sector antenna formula in dB scale

56. Sector Antenna Patterns at BS…

57. Sector Antenna Patterns at BS…

58. Average Received Power
Laplacian distributed PAS
Angle of Arrival
RMS angle spread
Normalization factor
Antenna gain in linear scale

59. Average Received Power at BS
3 sectored antenna with AoA = 20 and RMS AS = 5

60. Average Received Power at MS
Laplacian distributed PAS with omni-directional gain

61. Average Received Power at MS…
22.5 AoA & 35 RMS AS

62. Average Received Power at MS…
22.5 AoA & 104 RMS AS (uniform over 360 degree PAS)