Wireless Channel Models and Fading Effects

7. Channel Models

Signal Losses due to three Effects: 2. Medium Scale Fading: due to shadowing and obstacles 3. Small Scale Fading: due to multipath 1. Large Scale Fading: due to distance

Wireless Channel Frequencies of Interest: in the UHF (.3GHz 3GHz) and SHF (3GHz 30 GHz) bands; Several Effects: Path Loss due to dissipation of energy: it depends on distance only Shadowing due to obstacles such as buildings, trees, walls. Is caused by absorption, reflection, scattering Self-Interference due to Multipath. P 10 log rec 10 transm P log10 distance

1.1. Large Scale Fading: Free Space Path Loss due to Free Space Propagation: For isotropic antennas: Transmit antenna 2 = P transm P Receive antenna rec 4 d d c F = wavelength Path Loss in dB: transm P P = = + + 10log 20log ( ( )) 20log ( ( )) 32.45 L F MHz d km 10 10 10 rec

2. Medium Scale Fading: Losses due to Buildings, Trees, Hills, Walls The Power Loss in dB is random: p L = + L E p expected value random, zero mean approximately gaussian with 6 12 dB

Average Loss Free space loss at reference distance d = + { } 10 log E L L dB 10 0 p d 0 Reference distance Path loss exponent indoor 1-10m outdoor 10-100m E L L 10 Values for Exponent : 0 p Free Space 2 20dB Urban 2.7-3.5 Indoors (LOS) 1.6-1.8 10 10 2 1 0 log ( / ) d d 10 10 10 0 Indoors(NLOS) 4-6

Empirical Models for Propagation Losses to Environment Okumura: urban macrocells 1-100km, frequencies 0.15-1.5GHz, BS antenna 30-100m high; Hata: similar to Okumura, but simplified COST 231: Hata model extended by European study to 2GHz

3. Small Scale Fading due to Multipath. a. Spreading in Time: different paths have different lengths; Receive Transmit = = + ) ... + ( ) x t ( ) t t ( ) y t ( h t t 0 k k 0 1 2 3 0t time 0t Example for 100m path difference we have a time delay 2 100 c 10 = = = sec 1 3 8 3 10

Typical values channel time spread: = ( ) x t ( ) t t 0 1 2 0t MAX 0t channel Indoor 10 50 sec Suburbs 2 10 Urban 1 3 Hilly 3-10 sec n 1 2 sec sec

b. Spreading in Frequency: motion causes frequency shift (Doppler) = 2 j F t ( ) x t X e c Receive Transmit T ( ) + 2 j F F t = ( ) y t Y e c R time v time for each path Doppler Shift + c F F cf Frequency (Hz)

Put everything together Transmit Receive (t ) (t ) x y time v rmc-002 time

(t ) w channel ( ) x t ( ) y t (t ) h (t ) (t ) gT gR Re{.} LPF LPF 2 2 j F t j F t e e C C shift in time Each path has attenuation 2 ( + = )( ) j F F t ( ) y t Re ( ) ( ) a t x t e c paths shift in frequency (this causes small scale time variations)

2.1 Statistical Models of Fading Channels Several Reflectors: ( ) x t ( ) y t t 1 Transmit 2 t v

For each path with NO Line Of Sight (NOLOS): ( ) y t average time delay t v cos( ) v + each time delay k F F each doppler shift D t 2 ( + = )( ) j F F t ( ) Re ( ) y t a e x t c k k k k

Some mathematical manipulation 2 ( + + = )( ) 2 2 j F F j F t j F t ( ) Re ( ) y t a e e x t e c k c k k k ( ) 2 ( + + ) j F F = 2 j F t ( ) ( ) r t a e e x t c k k k k / 1 Assume: bandwidth of signal << ( ) r t e x t ( ) x t ( ) k leading to this: = 2 j F t ( ) Re y t c = ( ) ( c t x t ( ) ) r t = ( ) 2 ( + + ) j F F 2 j F t ( ) c t a e e c k with random, time varying k k

Statistical Model for the time varying coefficients M = ( ) 2 ( + + ) j F F 2 j F t ( ) c t a e e c k k = 1 k random By the CLT is gaussian, zero mean, with: ( ) c t + = * ( ) ( ) (2 ) E c t c t t PJ F t 0 D v c v = = with the Doppler frequency shift. F F D C

Each coefficient is complex, gaussian, WSS with autocorrelation ( ) c t + = * ( ) ( ) (2 ) E c t c t t PJ F t 0 D and PSD 2 F 1 if | | F F D = = 1 ( 2 ( ) S F (2 ) FT J F t / ) F F D 0 D D 0 otherwise with maximum Doppler frequency. D F ( ) S F This is called Jakes spectrum. F F D

Bottom Line. This: (t ) (t ) x y time time v rmc-002 1 time N can be modeled as: 1 1( ) c t ( ) y t (t ) x ( ) c t time time N ( ) t N c delays

For each path = ( ) ( ) c t P c t unit power time invariant time varying (from autocorrelation) from power distribution

Parameters for a Multipath Channel (No Line of Sight): P P Time delays: Power Attenuations: sec 1 2 L L P dB 1 2 F Hz Doppler Shift: D Summary of Channel Model: = = ( ) ( ) ( ) y t c t x t ( ) ( ) c t P c t (t ) c WSS with Jakes PSD

Non Line of Sight (NOLOS) and Line of Sight (LOS) Fading Channels { E = ( )} 0 c t 1. Rayleigh (No Line of Sight). Specified by: = [ , ,..., ] T Time delays 1 2 N P = [ , ,..., ] P P P Power distribution 1 2 N F Maximum Doppler D { ( )} 0 E c t 2. Ricean (Line of Sight) K Same as Rayleigh, plus Ricean Factor K + =1 LOS P Total P Power through LOS K 1 =1 NOLOS P Total P Power through NOLOS + K

Simulink Example M-QAM Modulation Rayleigh Fading Channel Parameters Bernoulli Binary Rectangular QAM -K- Channel Attenuation Transmitter Gain -K- Bernoulli Binary Generator Rectangular QAM Modulator Baseband Multipath Rayleigh Fading Channel Rayleigh Fading -K- B-FFT Receiver Gain Spectrum Scope Bit Rate

Set Numerical Values: velocity carrier freq. v F = F Recall the Doppler Frequency: D C c 8m 3 10 / sec ( ) ( ) v ( )GHz F F Easy to show that: / D C km h Hz modulation power channel

Channel Parameterization 1. Time Spread and Frequency Coherence Bandwidth 2. Flat Fading vs Frequency Selective Fading 3. Doppler Frequency Spread and Time Coherence 4. Slow Fading vs Fast Fading

1. Time Spread and Frequency Coherence Bandwidth (t ) p Try a number ofexperiments transmitting a narrow pulse at different random times ) ( t x = ( ) p t it We obtain a number of received pulses = + ( ) ( ) ( c t p t ) ( ) ( p t ) y t t c t t i i i i t 1t 2 ( i c t 1 0 + ) transmitted 2 2 + ( ) c it 1 1 + ( ) c t i t t 2 1 i 0 t t 2 1 N 0

= t t Take the average received power at time i 1P 2P = P 2| ) t | ( P E c 2 1 0 More realistically: Received Power 0 10 20 time RMS MEAN

This defines the Coherence Bandwidth. (t ) x F Take a complex exponential signal with frequency . The response of the channel is: = 2 ( ) je F t ( ) ( ) y t c t MEAN MEAN = 2 ( ) j F t ( ) y t ( ) c t e | | 1 F If then RMS i.e. the attenuation is not frequency dependent Define the Frequency Coherence Bandwidth as 1 = B c 5 RMS

This means that the frequency response of the channel is flat within the coherence bandwidth: Channel Flat up to the Coherence Bandwidth frequency 1 = B Coherence Bandwidth c 5 RMS Flat Fading Just attenuation, no distortion < > Signal Bandwidth Frequency Coherence Frequency Selective Fading Distortion!!!

Example: Flat Fading Channel : Delays T=[0 10e-6 15e-6] sec Power P=[0, -3, -8] dB Symbol Rate Fs=10kHz Doppler Fd=0.1Hz Modulation QPSK Very low Inter Symbol Interference (ISI) Spectrum: fairly uniform

Example: Frequency Selective Fading Channel : Delays T=[0 10e-6 15e-6] sec Power P=[0, -3, -8] dB Symbol Rate Fs=1MHz Doppler Fd=0.1Hz Modulation QPSK Very high ISI Spectrum with deep variations

3. Doppler Frequency Spread and Time Coherence Back to the experiment of sending pulses. Take autocorrelations: t 1t 2 ( i c t 1 0 + transmitted ) 2 2 + ( ) c it 1 1 + ( ) c t i t t 2 1 i 0 t t 2 1 N 0 t 2( ) R Where: ) t ( t ) R t 1( ) R = + * ( ) ( ) ( R t E c t c t

Take the FT of each one: ( ) S F F F D (t ) c This shows how the multipath characteristics change with time. It defines the Time Coherence: 9 T C 16 F D Within the Time Coherence the channel can be considered Time Invariant.

Summary of Time/Frequency spread of the channel Frequency Spread ( F t , ) S Time F Coherence F 9 D T t Time Spread mean C 16 F D RMS Frequency Coherence 1 = B c 5 RMS

Stanford University Interim (SUI) Channel Models Extension of Work done at AT&T Wireless and Erceg etal. Three terrain types: Category A: Hilly/Moderate to Heavy Tree density; Category B: Hilly/ Light Tree density or Flat/Moderate to Heavy Tree density Category C: Flat/Light Tree density Six different Scenarios (SUI-1 SUI-6). Found in IEEE 802.16.3c-01/29r4, Channel Models for Wireless Applications, http://wirelessman.org/tg3/contrib/802163c-01_29r4.pdf V. Erceg etal, An Empirical Based Path Loss Model for Wireless Channels in Suburban Environments, IEEE Selected Areas in Communications, Vol 17, no 7, July 1999