Chapter 2 statistical analysis of fading channels
This presentation is the property of its rightful owner.
Sponsored Links
1 / 28

Chapter 2: Statistical Analysis of Fading Channels PowerPoint PPT Presentation


  • 59 Views
  • Uploaded on
  • Presentation posted in: General

Chapter 2: Statistical Analysis of Fading Channels. Channel output viewed as a shot-noise process Point processes in general; distributions, moments Double-stochastic Poisson process with fixed realization of its rate Characteristic and moment generating functions Example of moments

Download Presentation

Chapter 2: Statistical Analysis of Fading Channels

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Chapter 2 statistical analysis of fading channels

Chapter 2: Statistical Analysis of Fading Channels

  • Channel output viewed as a shot-noise process

  • Point processes in general; distributions, moments

  • Double-stochastic Poisson process with fixed realization of its rate

    • Characteristic and moment generating functions

    • Example of moments

  • Central-limit theorem

  • Edgeworth series of received signal density

    • Details in presentation of friday the 13th

  • Channel autocorrelation functions and power spectra


Chapter 2 shot noise channel simulations

Chapter 2: Shot-Noise Channel Simulations

  • Channel Simulations Experimental Data (Pahlavan p. 52)


Chapter 2 shot noise channel model

Chapter 2: Shot-Noise Channel Model


Chapter 2 shot noise effect

Chapter 2: Shot-Noise Effect

ti

ti

  • Channel viewed as a shot-noise effect [Rice 1944]

Linear

system

Counting process

Response

Shot-Noise Process: Superposition of i.i.d. impulse responses occuring at times obeying a counting process, N(t).


Chapter 2 shot noise effect1

Chapter 2: Shot-Noise Effect

  • Measured power delay profile


Chapter 2 shot noise definition

Chapter 2: Shot-Noise Definition

  • Shot noise processess and Campbell’s theorem


Chapter 2 wireless fading channels as a shot noise

Chapter 2: Wireless Fading Channels as a Shot-Noise

  • Shot-Noise Representation of Wireless Fading Channel


Chapter 2 shot noise assumption

Chapter 2: Shot-Noise Assumption

  • Counting process N(t): Doubly-Stochastic Poisson Process with random rate


Chapter 2 joint characteristic function

Chapter 2: Joint Characteristic Function

  • Conditional Joint Characteristic Functional of y(t)


Chapter 2 joint moment generating function

Chapter 2: Joint Moment Generating Function

  • Conditional moment generating function of y(t)

  • Conditional mean and variance of y(t)


Chapter 2 joint characteristic function1

Chapter 2: Joint Characteristic Function

  • Conditional Joint Characteristic Functional of yl(t)


Chapter 2 joint moment generating function1

Chapter 2: Joint Moment Generating Function

  • Conditional moment generating function of yl(t)

  • Conditional mean and variance of yl(t)


Chapter 2 correlation and covariance

Chapter 2: Correlation and Covariance

  • Conditional correlation and covariance of yl(t)


Chapter 2 central limit theorem

Chapter 2: Central-Limit Theorem

  • Central Limit Theorem

  • yc(t)is a multi-dimensional zero-mean Gaussian process with covariance function identified


Chapter 2 edgeworth series expansion

Chapter 2: Edgeworth Series Expansion

  • Channel density through Edgeworth’s series expansion

  • First term: Multidimensional Gaussian

  • Remaining terms: deviation from Gaussian density


Chapter 2 edgeworth series simulation

Chapter 2: Edgeworth Series Simulation

  • Channel density through Edgeworth’s series expansion

  • Constant-rate, quasi-static channel, narrow-band transmitted signal


Chapter 2 edgeworth series vs gaussianity

Chapter 2: Edgeworth Series vs Gaussianity

  • Channel density through Edgeworth’s series expansion

  • Parameters influencing the density and variance of received signal depend on

  • Propagation environmentTransmitted signal

  • l(t) l(t) TsTs(signal. interv.)

  • s (var. I(t),Q(t)) K

  • rs


Chapter 2 channel autocorrelation functions

Chapter 2: Channel Autocorrelation Functions

Fc(t )

Power Delay

Profile

|Fc(Df)|

t

Tm

Ft

Bc

Df

Dt=0

Power Delay

Spectrum

Fc( Dt;t )

Ft

FDt

|Fc(Dt;Df)|

Dt=0

Scattering

Function

Df

WSSUS Channel

Sc( l;t )

Dt

Sc(l; Df)

Ft

FDt

Df=0

Df=0

Sc(l;t)

|Fc(Dt)|

Sc( l )

t

Doppler Power

Spectrum

Tc

Dt

FDt

l

Bd

l


Chapter 2 channel autocorrelations and power spectra

Chapter 2: Channel Autocorrelations and Power-Spectra

  • Consider a Wide-Sense Stationary Uncorrelated Scattering (WSSUS) channel with moving scatters

  • Non-Homogeneous Poisson rate: l(t)

  • ri(t,t) = ri(t): quasi-static channel

  • pf(f)=1/2p , pq(q)=1/2p


Chapter 2 channel autocorrelations and power spectra1

Chapter 2: Channel Autocorrelations and Power-Spectra

  • Time-spreading: Multipath characteristics of channel


Chapter 2 channel autocorrelations power spectra

Chapter 2: Channel Autocorrelations Power-Spectra

  • Time-spreading: Multipath characteristics of channel


Chapter 2 channel autocorrelations and power spectra2

Chapter 2: Channel Autocorrelations and Power-Spectra

  • Time-spreading: Multipath characteristics of channel

  • Autocorrelation in Frequency Domain, (space-frequency, space-time)


Chapter 2 channel autocorrelations and power spectra3

Chapter 2: Channel Autocorrelations and Power-Spectra

Double Fourrier transform

  • Time variations of channel: Frequency-spreading:


Chapter 2 channel autocorrelations and power spectra4

Chapter 2: Channel Autocorrelations and Power-Spectra

  • Time variations of channel: Frequency-spreading


Chapter 2 channel autocorrelations and power spectra5

Chapter 2: Channel Autocorrelations and Power-Spectra

  • Time variations of channel: Frequency-spreading


Chapter 2 shot noise simulations

Chapter 2: Shot-Noise Simulations

  • Temporal simulations of received signal


Chapter 2 references

Chapter 2: References

  • K.S. Miller. Multidimentional Gaussian Distributions. John Wiley&Sons, 1964.

  • S. Karlin. A first course in Stochastic Processes. Academic Press, New York 1969.

  • A. Papoulis. Probability, Random Variables and Stochastic Processes. McGraw Hill, 1984.

  • D.L. Snyder, M.I. Miller. Random Point Processes in Time and Space. Springer Verlag, 1991.

  • E. Parzen. Stochastic Processes. SIAM, Classics in Applied Mathematics, 1999.

  • P.L. Rice. Mathematical Analysis of random noise. Bell Systems Technical Journal, 24:46-156, 1944.

  • W.F. McGee. Complex Gaussian noise moments. IEEE Transactions on Information Theory, 17:151-157, 1971.


Chapter 2 references1

Chapter 2: References

  • R. Ganesh, K. Pahlavan. On arrival of paths in fading multipath indoor radio channels. Electronics Letters, 25(12):763-765, 1989.

  • C.D. Charalambous, N. Menemenlis, O.H. Karbanov, D. Makrakis. Statistical analysis of multipath fading channels using shot-noise analysis: An introduction. ICC-2001 International Conference on Communications, 7:2246-2250, June 2001.

  • C.D. Charalambous, N. Menemenlis. Statistical analysis of the received signal over fading channels via generalization of shot-noise. ICC-2001 International Conference on Communications, 4:1101-1015, June 2001.

  • N. Menemenlis, C.D. Charalambous. An Edgeworth series expansion for multipath fading channel densities. Proceedings of 41stIEEE Conference on Decision and Control, to appear, Las Vegas, NV, December 2002.


  • Login