Statistical multipath channel models Hassan fayed DR.ENG MOHAB MANGOUD

introduction The wireless radio channel poses a severe challenge as a medium for reliable high-speed communication It is not only susceptible to noise, interference, and other channel impediments, but these impediments change over time in unpredictable ways due to user movement

we will characterize in brief the variation in received signal power over distance due to path loss and shadowing. the variation in received signal power over distance due to path loss and shadowing.. Path loss is caused by dissipation of the power radiated by the transmitter as well as effects of the propagation channel

Types of path loss models free space path loss ray tracing

two ray

ten ray

Types of Statistical multipath models Time-Varying Channel Impulse Response

show the single reflector& reflector cluser

Then the received signal can be rewritten as

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

where the last equality follows from the sifting property of delta functions α ( זּ - αn(t))u(t - זּ )d זּ = α (t - αn(t)).u(t) = u(t-αn(t)). Some channel models assume a continuum of multipath delays, in which case the sum in (6) becomes an integral which simplifies to a time- varying complex amplitude associated with each multipath delay זּ :

The time-varying impulse response corresponding to t1 equals

The time-varying impulse response at t2 equals

For stationary channels the response to an impulse at time t1 is just a shifted version of its response to an impulse at time t2, t1 _= t2. For stationary channels the response to an impulse at time t1 is just a shifted version of its response to an impulse at time t2, t1 _= t2. multipath component corresponds to a single reflector. At time t1&t2

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

Narrowband Fading Models

s(t) to be an un modulated carrier with random phase offset Φ0: s(t) to be an un modulated carrier with random phase offset Φ0:

Autocorrelation, Cross Correlation, and Power Spectral Density Autocorrelation, Cross Correlation, and Power Spectral Density

In this model we will focus on the uniform scattering environment 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 Models Multipath Resolution.

deterministic scattering function

Power Delay Profile

Coherence Bandwidth

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

Discrete-Time Model Point Scatterer Channel Model

Discrete Time Approximation

Space-Time Channel Models