Wireless Communication Channels: Small-Scale Fading.

of 26 /26
Wireless Communication Channels: Small-Scale Fading

Embed Size (px)

Transcript of Wireless Communication Channels: Small-Scale Fading.

  • Slide 1
  • Wireless Communication Channels: Small-Scale Fading
  • Slide 2
  • Tallal Elshabrawy 2 Clarkes Model for Flat Fading Assumptions: Mobile traveling in x direction Vertically polarized wave Multiple waves in the x-y plane arrive at the mobile antenna at the same time Waves arrive at different angles in x-y plane z x y For N waves incident at the mobile antenna Each wave arriving at an angle n will experience a different Doppler shift f n E 0 amplitude of the local average E-field C n random variable representing the amplitude of individual waves f c carrier frequency n random phase shift due to distance traveled by the n th wave
  • Slide 3
  • Tallal Elshabrawy 3 Clarkes Model for Flat Fading Given that: n uniformly distributed over 2 N is sufficiently large (i.e., the central limit theorem is applicable) Therefore: Both T c (t) and T s (t) may be modeled as: Gaussian Random Processes
  • Slide 4
  • Tallal Elshabrawy 4 Clarkes Model for Flat Fading Power received at mobile antenna Rayleigh Distribution
  • Slide 5
  • Tallal Elshabrawy 5 Rayleigh Fading Distribution in x-y plane x y dd z Main Assumption: - No LOS - All waves at the mobile receiver experience approximately the same attenuation constant p(r) r 0.6065/ 2 : Time average received power : rms value of received voltage
  • Slide 6
  • Tallal Elshabrawy 6 Rayleigh Fading Statistics Probability the received signal does not exceed a value R Mean value of the Rayleigh distribution Variance of the Rayleigh distribution Median of the Rayleigh distribution
  • Slide 7
  • Tallal Elshabrawy 7 Ricean Fading Distribution in x-y plane x y dd z Main Assumption: - LOS - There is a dominant wave component at the mobile receiver in addition to experience multiple waves that experience approximately the same attenuation A : Peak amplitude of the dominant signal I(.): Modified Bessel function of the first kind and zero-order 2 : Time average received power of the non-dominant components
  • Slide 8
  • Tallal Elshabrawy 8 Riciean & Rayleigh Fading p(r) r Define K called the Ricean Factor: The ratio between the deterministic signal power and the power of the non-dominant waves K=6 dB K=- dB Rayleigh Distribution
  • Slide 9
  • Tallal Elshabrawy 9 Level Crossing Rate and Mean fade Duration for Rayleigh Fading Signals Level Crossing Rate Statistic: The expected rate at which Rayleigh fading envelope normalized to local rms level crosses a specified level in a positivegoing direction := R/R rms f m : Maximum Doppler shift Mean Fade Duration Statistic: The average period of time for which the received signal is below a specified level R Mean Fade duration is a very important statistic that helps define the time correlation behavior of BER performance at the receiver
  • Slide 10
  • Tallal Elshabrawy 10 Lognormal Shadowing Mobile Speed 3 Km/hr ARMA Correlated Shadow Model Distance Pathloss Mobile Speed 3 Km/hr PL=137.744+ 35.225log 10 (D KM ) Small-Scale Fading Mobile Speed 3 Km/hr Jakess Rayleigh Fading Model d d d How Wireless Channels Components Fit Together
  • Slide 11
  • Tallal Elshabrawy How Wireless Channels Components Fit Together 11 Wireless Channel PTGTPTGT GRGR P R =P T G T G R x Distance Pathloss x Shadowing Parameters x Small-Scale Fading Power
  • Slide 12
  • Tallal Elshabrawy System Modeling of Wireless Networks: Example 12
  • Slide 13
  • Diversity Techniques
  • Slide 14
  • Tallal Elshabrawy 14 What is Diversity? Diversity techniques offer two or more inputs at the receiver such that the fading phenomena among these inputs are uncorrelated If one radio path undergoes deep fade at a particular point in time, another independent (or at least highly uncorrelated) path may have a strong signal at that input By having more than one path to select from, both the instantaneous and average SNR at the receiver may be improved
  • Slide 15
  • Tallal Elshabrawy 15 TransmitterReceiver 0 1 2 M Diversity Techniques: Space Diversity Receiver Space Diversity M different antennas appropriately separated deployed at the receiver to combine uncorrelated fading signals
  • Slide 16
  • Tallal Elshabrawy 16 Receiver Transmitter 0 1 2 M Diversity Techniques: Space Diversity Transmitter Space Diversity M different antennas appropriately separated deployed at the transmitter to obtain uncorrelated fading signals at the receiver The total transmitted power is split among the antennas
  • Slide 17
  • Tallal Elshabrawy 17 t f f>B c Diversity Techniques: Frequency Diversity Modulate the signal through M different carriers The separation between the carriers should be at least the coherent bandwidth B c Different copies undergo independent fading Only one antenna is needed The total transmitted power is split among the carriers
  • Slide 18
  • Tallal Elshabrawy 18 f t t>T c Diversity Techniques: Time Diversity Transmit the desired signal in M different periods of time i.e., each symbol is transmitted M times The interval between transmission of same symbol should be at least the coherence time T c Different copies undergo independent fading
  • Slide 19
  • Diversity Combining Techniques
  • Slide 20
  • Tallal Elshabrawy 20 Select the strongest signal TransmitterReceiver Channel 1 Channel 2 Channel M SNR Monitor Select MAX SNR= max Selection Combining
  • Slide 21
  • Tallal Elshabrawy 21 Outage Probability of a Single Branch Selection Combining Consider M independent Rayleigh fading channels available at the receiver Average SNR at all Diversity Branches SNR = Instantaneous SNR at Diversity Branch i SNR = i Rayleigh Fading Voltage means Exponentially Distributed Power Outage Probability of of Selection Diversity Combining
  • Slide 22
  • Tallal Elshabrawy 22 TransmitterReceiver Channel 1 Channel 2 Channel M G1G1 G2G2 GMGM r1r1 r2r2 rMrM Maximal Ratio Combining Selection Combining does not benefit from power received across all diversity branches Maximal Ratio Combining conducts a weighted sum across all branches with the objective of maximizing SNR
  • Slide 23
  • Tallal Elshabrawy 23 Envelope applied to receiver detector Total Noise Power applied to detector SNR at the receiver detector Cauchys Inequality MRC is maximized when G i =r i (MRC requires channel measurements) Maximal Ratio Combining Consider M independent Rayleigh fading channels available at the receiver
  • Slide 24
  • Tallal Elshabrawy 24 MRC is maximized when G i =r i (MRC requires channel measurements) Rayleigh Fading Voltage means Exponentially Distributed Power SNR MRC is Gamma distributed (sum of M exponential random variables) Outage Probability of of Maximal Ratio Diversity Combining Maximal Ratio Combining
  • Slide 25
  • Tallal Elshabrawy 25 Maximal Ratio Combining requires estimation of the channel across all diversity branches Equal Gain Combining conducts a sum across all branches (i.e. G i =1 for all i) TransmitterReceiver Channel 1 Channel 2 Channel M r1r1 r2r2 rMrM Equal Ratio Combining
  • Slide 26
  • Tallal Elshabrawy 26 EGC is a special case of MRC with G i =1 SNR and outage probability performance in EGC is inferior to that of MRC Envelope applied to receiver detector Total Noise Power applied to detector SNR at the receiver detector Equal Gain Combining Consider M independent Rayleigh fading channels available at the receiver