#### Transcript 7-Channel Models

7. Channel Models Signal Losses due to three Effects: 2. Medium Scale Fading: due to shadowing and obstacles 1. Large Scale Fading: due to distance 3. Small Scale Fading: due to multipath 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. 10 log Prec 10 Ptransm log 10 distance 1.1. Large Scale Fading: Free Space Path Loss due to Free Space Propagation: For isotropic antennas: Transmit antenna 2 d Receive antenna Prec Ptransm 4 d wavelength c F Path Loss in dB: Ptransm L 10 log 10 20 log 10 ( F ( M H z )) 20 log 10 ( d ( km )) 32.45 Prec 2. Medium Scale Fading: Losses due to Buildings, Trees, Hills, Walls … The Power Loss in dB is random: L p E L p expected value random, zero mean approximately gaussian with 6 12 dB Average Loss Free space loss at reference distance d L0 E { L p } 10 log 10 d 0 dB Reference distance • indoor 1-10m Path loss exponent E L p L0 • outdoor 10-100m 10 20dB 10 2 10 1 10 0 10 log 10 ( d / d 0 ) Values for Exponent Free Space 2 Urban 2.7-3.5 Indoors (LOS) 1.6-1.8 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 t0 ) t0 y (t ) h k ( t t 0 k ) ... t0 time Example for 100m path difference we have a time delay 100 c 10 2 3 10 8 1 3 sec 1 2 3 Typical values channel time spread: x ( t ) ( t t0 ) channel t0 Indoor 10 50 n sec S uburbs 2 10 U rban 1 3 sec H illy 3-10 sec 1 2 sec t0 1 2 M AX b. Spreading in Frequency: motion causes frequency shift (Doppler) x (t ) X T e j 2 Fc t Receive Transmit y (t ) YR e j 2 Fc F t time v for each path Doppler Shift fc Fc F Frequency (Hz) time Put everything together Transmit x (t ) time v time Receive y (t ) channel x (t ) w (t ) y (t ) g T (t ) g R (t ) h (t ) Re{.} LPF LPF e j 2 FC t Each path has … e … attenuation… j 2 FC t …shift in time … j 2 ( Fc F y (t ) R e a (t ) x (t ) e paths )( t ) …shift in frequency … (this causes small scale time variations) 2.1 Statistical Models of Fading Channels Several Reflectors: x (t ) 1 t Transmit 2 v y (t ) t For each path with NO Line Of Sight (NOLOS): y (t ) average time delay v t v cos( ) • each time delay k • each doppler shift F FD t j 2 ( Fc F y (t ) R e a k e k )( t k ) x (t k ) Some mathematical manipulation … j 2 F t j 2 ( Fc F y (t ) R e a k e e k )( k ) j 2 Fc t x (t k ) e j 2 F t j 2 ( Fc F r (t ) a k e e k ) k x (t ) Assume: bandwidth of signal << 1 / k x (t ) x (t k ) … leading to this: y (t ) R e r (t ) e j 2 Fc t r (t ) c (t ) x (t ) with c (t ) k ak e j 2 F t e j 2 ( Fc F ) k random, time varying Statistical Model for the time varying coefficients M c (t ) a k e j 2 F t e j 2 ( Fc F ) k k 1 random By the CLT c ( t ) is gaussian, zero mean, with: E c ( t ) c ( t t ) P J 0 (2 F D t ) * with FD v c FC v the Doppler frequency shift. Each coefficient c ( t ) is complex, gaussian, WSS with autocorrelation E c ( t ) c ( t t ) P J 0 (2 F D t ) * and PSD 2 F S ( F ) F T J 0 (2 F D t ) D 0 with FD 1 1 ( F / FD ) 2 if | F | F D otherw ise maximum Doppler frequency. S (F ) This is called Jakes spectrum. FD F Bottom Line. This: x (t ) y (t ) time time v 1 N time … can be modeled as: 1 c1 ( t ) x (t ) y (t ) c (t ) time time N delays cN (t ) For each path c (t ) P c (t ) • time invariant • from power distribution • unit power • time varying (from autocorrelation) Parameters for a Multipath Channel (No Line of Sight): Power Attenuations: 1 P1 Doppler Shift: FD Time delays: 2 L sec P2 PL dB Summary of Channel Model: y (t ) c (t ) x (t ) c (t ) P c (t ) c (t ) WSS with Jakes PSD Hz Non Line of Sight (NOLOS) and Line of Sight (LOS) Fading Channels 1. Rayleigh (No Line of Sight). E {c ( t )} 0 Specified by: Time delays T [ 1 , 2 ,..., N ] Power distribution P [ P1 , P2 ,..., PN ] Maximum Doppler 2. Ricean (Line of Sight) FD E {c ( t )} 0 Same as Rayleigh, plus Ricean Factor K K Power through LOS PLOS Power through NOLOS PNOLOS 1 K PTotal 1 1 K PTotal Simulink Example M-QAM Modulation Bernoulli Binary Rectangular QAM Bernoulli Binary Generator Rectangular QAM Modulator Baseband Channel Transmitter Attenuation Gain Multipath Rayleigh Fading Channel -KB-FFT Spectrum Scope Bit Rate Rayleigh Fading Channel Parameters -K- Receiver Gain -K- Rayleigh Fading Set Numerical Values: velocity carrier freq. Recall the Doppler Frequency: Easy to show that: FD v c FD Hz FC 3 10 m / sec 8 v km / h FC GHz 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 Try a number of experiments transmitting a narrow pulse p (t ) at different random times x (t ) p (t t i ) We obtain a number of received pulses y i (t ) c (t ) p (t ti ) c 0 transmitted 1 c1 ( t i 1 ) 0 2 t t1 c 2 (ti 2 ) 1 (ti ) p (t ti ) c (ti ) 2 t ti 0 1 2 t tN Take the average received power at time t t i P1 P2 1 0 P E | c ( t ) | P 2 More realistically: Received Power 0 10 20 RM S M EAN time 2 This defines the Coherence Bandwidth. Take a complex exponential signal the channel is: y (t ) x (t ) with frequency F . The response of c (t ) e j 2 F ( t MEAN ) If | F | RMS 1 j 2 F ( t M EAN ) then y ( t ) c ( t ) e i.e. the attenuation is not frequency dependent Define the Frequency Coherence Bandwidth as Bc 1 5 RM S This means that the frequency response of the channel is “flat” within the coherence bandwidth: Channel “Flat” up to the Coherence Bandwidth Bc Coherence Bandwidth Flat Fading Signal Bandwidth < > 1 frequency 5 RM S Just attenuation, no distortion 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: 0 transmitted 1 c1 ( t i 1 ) 2 0 t t1 c 2 (ti 2 ) 1 c (ti ) 2 t ti 0 1 2 R2 ( t ) R (t ) R1 ( t ) t tN Where: R ( t ) E c ( t ) c ( t t ) * Take the FT of each one: S (F ) FD This shows how the multipath characteristics F c (t ) change with time. It defines the Time Coherence: TC 9 16 F D Within the Time Coherence the channel can be considered Time Invariant. Summary of Time/Frequency spread of the channel Frequency Spread Time Coherence TC 9 16 F D S (t , F ) F FD t mean RMS Frequency Coherence Bc 1 5 RM S Time Spread 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