Unit I Introduction of Wireless Channel

1.  A two-ray model, which consists of two overlapping waves at the receiver, one direct path and
one reflected wave from the ground so it is called as Two ray model.
 As Free space model is inaccurate when
used alone
GROUND-REFLECTION (TWO RAY) MODEL
 The total received E-field is the result of the direct line of sight component ELOS and the ground
reflected component Eg.
The free space propagating E-field for d>d0 is given by
 where E0 is the transmitted signal amplitude at a reference distance d0, and d is the propagation
distance for the LOS component
Certain Assumptions
1. ht & hr >> λ
2. ht & hr << d
3. Earth may be assumed to be flat
 Two ray model considers both the direct
path and a ground reflected propagated
path between transmitter and receiver.

2.  According to the law of reflection in a dielectric,
GROUND-REFLECTION (TWO RAY) MODEL
and
 The E-field due to the LOS component at the receiver
can be expressed as
 The E-fleld for the ground reflected wave, which has
a propagation distance of d", can be expressed as
 We know from the laws of reflection in dielectric,
the value of reflection coefficient Г is (-1)
 Total resultant E-field given by
where Γ is the reflection coefficient for ground.
 The electric field received by receiver
is can be expressed as
 Two propagating waves arrive at the receiver, one LOS wave which travels a distance of d’ and another
ground reflected wave, that travels d”.
By law of reflection in dielectric , = -1

3. Ground-Reflection (Two ray) model
Fig shows the method of images is used to find the path difference LOS & the ground reflected paths.
 Both rays travelled from different paths & have different distances so it is must to find path
difference

4. Ground-Reflection (Two ray) model
Using the method of images,
 we find the path difference between LOS & the
ground reflected path dg which is denoted as Δ
 Assuming now that ht, hr << d, the expression
for Δd can be approximated as
and
 Put the value of dLOS & dg in above equation we
get
 So, the Path differencd Δ is

5. Ground-Reflection (Two ray) model
2. Phase difference between two E -Field
components denoted as
3. Time delay between the arrival of the two
components easily find using following
relations denoted as
 Using Path difference Δ we can find out the value of Phase difference & Time delay
1. Path Difference Δ

6. Ground-Reflection (Two ray) model
By referring phasor diagram the total E field
received by receiver can be expressed as
Fig. shows Phasor diagram of electrical field
components of Line of sight, ground reflected
& total E field received
By using trigonometric identities
By increasing distance d the E tot(d) decays an oscillatory fashion

7. Ground-Reflection (Two ray) model
sin When
= .
=
> ≈
=
=
 We can represent the power in terms of E Field as
Power = (
 Received power is given by
= (
=
=
 As total power radiated is =
=
=
Total received Power
is given by

8. Ground-Reflection (Two ray) model
1. The received power falls off at a rate of 40dB/decade
2.The received power & path loss becomes independent of frequency
 The path loss for Two Ray model is expressed as
= 40logd – (10log )
=
Point be noted
1. At small T-R separation distances,
total E-Field is calculated using
equation
2. Where the ground appears in the first
Fresnel zone between Tx & Rx
for = π
d=