Statistical Statistical multipath multipath channel channel modelsmodels

Hassan fayedHassan fayed

DR .ENG DR .ENG MOHAB MANGOUDMOHAB MANGOUD

introductionintroduction

TheThe wireless radio channel poses a wireless radio channel poses a severe challenge as a medium for severe challenge as a medium for reliable high-speed communicationreliable high-speed communication

It is not only susceptible to noise, It is not only susceptible to noise, interference, and other channel interference, and other channel impediments, but these impediments, but these impediments change over time in impediments change over time in unpredictable ways due to user unpredictable ways due to user movementmovement

we will characterize in briefwe will characterize in brief the variation in received signal the variation in received signal

power over distance due to path power over distance due to path loss and shadowingloss and shadowing..

. .Path loss is caused by dissipation Path loss is caused by dissipation of the power radiated by the of the power radiated by the

transmitter as well as effects of transmitter as well as effects of the propagation channelthe propagation channel

Types of path Types of path loss modelsloss models

free space path lossfree space path loss

ray tracingray tracing

two raytwo ray

ten rayten ray

Types ofTypes of Statistical Statistical multipathmultipath modelsmodels

TimeTime--Varying Channel Impulse Varying Channel Impulse ResponseResponse

show the single show the single reflector& reflector reflector& reflector

clusercluser

Then the received signal can be rewritten as

We see from the last two equationsC(T,t) must be given by

where the last equality follows from the sifting where the last equality follows from the sifting property of delta functionsproperty of delta functions

αα( ( - ּז - ּזααnn((tt))))uu((tt - - ּז ּז))dd ּז ּז = =αα ( (tt - - ααnn((tt))))..uu((tt) = ) = uu((tt--ααnn((tt))))..

Some channel models assume a continuum of Some channel models assume a continuum of multipath delays, in which case the sum in multipath delays, in which case the sum in

((66) ) becomes an integral which simplifies to a becomes an integral which simplifies to a timetime--varying complex amplitude associated varying complex amplitude associated

with each multipath delaywith each multipath delay ּז ּז::

The timeThe time--varying impulse varying impulse response corresponding toresponse corresponding to

tt1 equals1 equals

The timeThe time--varying impulse varying impulse response atresponse at tt2 equals2 equals

For stationary channels the For stationary channels the response to an impulse at response to an impulse at

timetime tt1 is just a shifted 1 is just a shifted version of its response to an version of its response to an impulse at timeimpulse at time tt22, t, t11 __= = tt22..

multipath component corresponds to a single reflector. At time t1&t2

The time-varying impulse response corresponding to t1&t2 equals

Narrowband Fading Narrowband Fading ModelsModels

s(s(tt) ) to be an un modulated to be an un modulated carrier with random phase carrier with random phase

offsetoffset ΦΦ00::

Autocorrelation, Cross Autocorrelation, Cross Correlation, and PowerCorrelation, and Power

Spectral DensitySpectral Density

In this model we will focus on In this model we will focus on the uniform scattering the uniform scattering

environmentenvironment

Dense Scattering Environment

In-Phase and Quadrature PSD

:S r I (f) = S r Q(f)

Combined Path Loss, Shadowing, and Narrowband Fading.

Narrowband Fading.

Wideband Fading Wideband Fading ModelsModels

Multipath Resolution.

deterministic scattering deterministic scattering

functionfunction

Power Delay ProfilePower Delay Profile

Coherence Coherence BandwidthBandwidth

Power Delay Profile, RMS Delay Power Delay Profile, RMS Delay Spread, and Coherence Spread, and Coherence

BandwidthBandwidth..

Discrete-Time ModelDiscrete-Time Model

Point Scatterer Channel Model

Discrete Time Discrete Time ApproximationApproximation

Space-Time Channel Space-Time Channel ModelsModels