Wireless Channel Model Younglok Kim WSoC Lab., Sogang University ylkim@sogang.ac.kr 02-705-8911

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

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

Example for Discrete Channel Model of CDMA System

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

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

Signal Power Fluctuation

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

Modeling of Shadow Fading Rx signal power:

Passloss Model Slope-intercept models For the free space,

Hata Model for Pathloss Parameters

Passloss vs. Distance

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

Multipath Environment

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

Tapped Delay Line (TDL) Channel Model

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

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.

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

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

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

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

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

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

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

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

Classical Fading Power Spectrum

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

Flat Fading Power Spectrum

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

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

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

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

References for Jakes Model and Modified Methods [1] UMTS TR 101 112 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.

Typical Communication Modem

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

Spacially Correlated Model (SCM) for Multiple Antennas

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.

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-16-20030417/

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

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

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

Block Diagram for SCM Generation

Time Invariant Eigenbeam Pattern (Macro)

Time Invariant Eigenbeam Pattern (Micro)

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

Time Varying Correlation Model Discrete uniform distribution model

Steering Vector of ULA Phase Difference between two adjacent antenna

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 %

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

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

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

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) 4 + 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

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)

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

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

Sector Antenna Patterns at BS…

Sector Antenna Patterns at BS…

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

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

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

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

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