Short notes about "Multi-user Radio Communications Part 1

Short Notes about
“Multiuser Radio Communications”
Part One
Presented by:
Eng. Mohamed Mohy-El Din Shaheen
E-Mail; mohamedmohy24@gmail.com
Teaching Assistant, Dept. of Electrical
and Computer Engineering,
Higher Technological Institute,
Egypt

CONTENTS
8.1- Introduction.
8.2- Multiple-Access Techniques.
8.3- Satellite Communications.
8.4- Radio Link Analysis.
8.4.1- Free Space Propagation Model.
8.4.1.1- Directive Gain, Directivity , and Power Gain.
8.4.1.2- Effective Aperture.
8.4.1.3- Friis Free Space Equation.
8.4.2- Noise Figure.
8.4.2.1- Equivalent Noise Temperature.
8.4.2.2- Cascade Connection of Two Port Networks.

8.1- INTRODUCTION
 Multiuser Communication:
 Refers to the simultaneous use of communication channel
by a number of users.
 We discuss multiuser communication systems that,
 Rely on radio propagation for linking the receivers to the
transmitters.
 The first type of multiuser communications discussed in this
chapter is satellite communications.
 The discussion of satellite communications leads to the
analysis of radio propagation in free space.
 The other multiuser communication system studied in this
chapter offers mobility,
 Which permits a mobile unit to communicate with anyone,
anywhere in the world.

8.2- Multiple-Access
Technique

8.2- MULTIPLE ACCESS TECHNIQUE
 Multiple Access;
 Refers to the remote sharing of a communication channel
(satellite or radio channel) by users in highly dispersed
locations.
 Multiplexing;
 Refers to the sharing of a channel (such as telephone
channel) by users confined to a local site.
 We may identify four basic types of multiple access;
A. Frequency Division Multiple Access (FDMA).
B. Time Division Multiple Access (TDMA).
C. Code Division Multiple Access (CDMA).
D. Space Division Multiple Access (SDMA).

A. Frequency Division Multiple Access (FDMA).
Fig 8.1 Frequency Division Multiple
Access Idea [1].
 Disjoint sub-bands of
frequencies are allocated to
the different users on a
continuous time basis.
 In order to reduce
interference between users,
guard band are used to act
as buffer zones, as
illustrated in Fig 8.1

B. Time Division Multiple Access (TDMA).
 Each user is
allocated the full
spectral occupancy
of the channel, but
only for a short time
slot.
 Guard times are
inserted between
the assigned time
slots, as shown in
Fig 8.2.
 Guard times to
reduce interference
between users that
Fig 8.2 Time Division Multiple Access
Idea [1].

C. Code Division Multiple Access (CDMA).
 All users occupy the
same frequency, and
there are separated
from each by means of
a special code as
shown in Fig 8.3.
 Each user is assigned
a code, which is used
to transform user's
signal into spread-
spectrum-coded
version of the user's
data stream.
Fig 8.3 Code Division Multiple
Access [1].

D. Space Division Multiple Access (SDMA).
Fig 8.4 Space Division
Multiple Access [1].
 Multi-beam antennas are
used to separate radio
signals by,
 Pointing them along
different directions as
shown in Fig 8.4.
 Thus, different users are
enabled to access the
channel simultaneously,
 On the same frequency or
in the same time slot.

8.3- SATELLITE COMMUNICATIONS
 In a geostationary
satellite communication
system,
 A message signal is
transmitted from an
earth transmitting
station,
 Via an uplink to a
satellite, amplified in a
transponder on board
the satellite,
 And then retransmitting
from the satellite via a
downlink to an earth
receiving station as
shown in Fig 8.5.
Fig 8.5 Satellite Communications
System [2].

 The most popular frequency band for satellite
communications is 6 GHz for the uplink and 4 GHz for the
downlink.
 This frequency band offers the following advantages;
I. Relative inexpensive microwave equipment.
II. Low attenuation due to rainfall.
 The second generation communication satellites,
 That operate in the 14/12 GHz band.
 Eliminate radio interference in the 6/4 GHz band.
 Make it possible to build smaller and therefore less
expensive antennas.

 The block diagram of Fig 8.6 shows the basic components
of a transponder,
A. Band-pass Filter: to separate the received signal from
among the different radio channels.
B. Low-Noise Amplifier: is an electronic amplifier that
amplifies a very low-power signal [3].
C. Frequency Down Converter: to convert the received
radio frequency signal to the desired downlink frequency.
Fig 8.6 Block Diagram of

d. Travelling Wave Tube Amplifier: which provides high gain
over a wide band of frequencies.
 Speech signals sent by the satellite incur a transmission
delay of 270 [ms].
 Hence, for speech signals, any impedance mismatch at the
receiving end of a satellite,
 Results in an echo of the speaker’s voice.
 We may overcome this problem by using an echo canceller,
 Which is a device that subtracts an estimate of the echo
from the return path.

 In a satellite channel, non linearity of the transponder is,
 The primary cause of interference between users.
 To contain this problem,
 The travelling wave tube amplifier in the transponder is
operated below capacity.
 In a TDMA system, the users access the satellite
transponder once at a time,
 The satellite transponder is now able to operate close to the
full power efficiency,
 By permitting the travelling wave tube amplifier to run into
saturation.
 TDMA uses the transponder more efficiency than FDMA.

 Broadcasting satellites,
 Which are characterized by their high power transmission to
inexpensive receivers.
 This characteristic is exploited in the use of Direct Broadcast
Satellites (DBS),
 Designed for home reception of television services on a
wide scale.

8.4- RADIO LINK ANALYSIS
 An important issue in the design of satellite communication
system is that of,
 Link budget analysis.
 The link budget provides a detailed accounting of three
items:
1. Apportionment of the resources available to the transmitter
and the receiver.
2. Sources responsible for the loss of signal power.
3. Sources of noise.
 These three items used for evaluating the performance of a
radio link,
 Which could be the uplink or the downlink of a satellite
communication system.

 The first design task is to
specify two particular
values of 𝐸 𝑏 𝑁0 as
follows;
A. Required 𝑬 𝒃 𝑵 𝟎 ;
 Suppose the probability of
symbol error is 𝑃𝑒 = 10−3
.
 Using the waterfall curve
of Fig 8.7,
 The 𝐸 𝑏 𝑁0 required to
realize the 𝑃𝑒 = 10−3 is
determined.
 𝐸 𝑏 𝑁0 𝑟𝑒𝑞 and 𝑃𝑒 = 10−3
is designed as operating
point 1 on the curve of Fig
Fig 8.7 “Waterfall” Curve Relating
the Probability of Error to Eb/N0

B. Received 𝑬 𝒃 𝑵 𝟎 ;
 Let 𝐸 𝑏 𝑁0 𝑟𝑒𝑐 denote the actual or received 𝐸 𝑏 𝑁0 , which
defines a second point on the curve of Fig 8.7,
 Designated as operating point 2.
 The corresponding 𝑃𝑒 = 10−5 of operating point 2 is shown in
Fig 8.7.
 In any event we may write;
 Where;

𝐸 𝑏
𝑁0 𝑟𝑒𝑐
is the actual or received value of
𝐸 𝑏
𝑁0
.

𝐸 𝑏
𝑁0 𝑟𝑒𝑞
is the required value of
𝐸 𝑏
𝑁0
.
 𝑀 is the link margin.
(8.1)

 Link Margin 𝑴 :
 To assure reliable operation of the communication link,
 The link budget includes a safety measure called the Link Margin.
 The Link Margin provides protection against change.
 We may define the Link margin as;
 Where:
 𝑀 is the link margin.

𝐸 𝑏
𝑁0 𝑟𝑒𝑐
is the actual or received value of
𝐸 𝑏
𝑁0
.

𝐸 𝑏
𝑁0 𝑟𝑒𝑞
is the required value of
𝐸 𝑏
𝑁0
.
 The larger we make the Link Margin, the more reliable is the
communication link.
(8.2)

 The next step in formulating the
link budget is to calculate the
received signal power.
 In radio communication system,
 The propagation of the modulated
signal is accomplished by a
transmitting antenna as shown in
Fig 8.8.
 At the receiver, we have a
receiving antenna whose function
is the opposite of the transmitting
antenna.
 The receiver is located in the far-
field of the transmitting antenna,
in this case,
 We view the transmitting antenna
as a point source.
Fig 8.8 The transmitting and
Receiving Antenna [4].

 The poynting vector or power
density,
 Is the rate of energy flow per
unit area,
 It is measured in [watts/𝑚2].
 The treatment of transmitting
antenna as a point source,
 Means the radiated energy
streams from the source along
radial lines as shown in Fig
8.9.
Fig 8.9 The power density of a
Point source [5].

 Equation (8.3) states that,
 The power density varies
inversely as the square of the
distance from a point source as
shown in Fig 8.10.
(8.3)
 Where:
 𝜌 𝑑 is the power density at
any point on the sphere.
 𝑃𝑡 is the total power radiated
by an isotropic source
measured in [watts].
 4𝜋𝑑2 is the surface area of a
sphere through which the
radiated power is passed.
 𝑑 is the distance in [meter]
from the source.
Fig 8.10 The power density
through the Sphere [5].

 We may write,
(8.4)
 Where:
 (Φ) is the radiation intensity
measured in [watt/steradian].
 𝑑 is the distance at which the
radiation intensity is measured.
 𝜌 𝑑 is the power density at
any point on the sphere.
 In the case of a typical
transmitting or receiving radio
antenna,
 The radiation intensity is a
function of the spherical
coordinates 𝜃 and 𝜑
defined in Fig 8.11
Fig 8.11 The Spherical Coordinates
of a Point Source [6].

 Referring to Fig 8.11 and Fig 8.12,
 The infinitesimal solid angle,
 𝑑Ω =
𝑑𝐴
𝑟2 =
𝑟 𝑑𝜃 𝑟 𝑠𝑖𝑛𝜃 𝑑𝜙
𝑟2 = 𝑠𝑖𝑛𝜃 𝑑𝜃 𝑑𝜙
 Where;
 𝑑Ω is the infinitesimal solid angle through
which the power is radiated.
 The total power radiated is therefore;
 Where;
 𝑃 is the total power radiated in [watt]
 Φ 𝜃, 𝜙 is radiation intensity in
[watt/steradian].
 𝑑Ω is the infinitesimal solid angle in [steradian].
(8.5)
(8.6)
Fig 8.12 Solid Angle
[7].

 Equation (8.6) states that,
 If the radiation intensity pattern Φ 𝜃, 𝜑 ,
 Is known for all values of angle pair 𝜃, 𝜑 ,
 Then the total power radiated is given by,
 The integral of Φ 𝜃, 𝜑 over a solid angle of 4𝜋 steradians.
 The radiation intensity that is,
 Produced by an isotropic source radiating,
 The total power 𝑃 is given by;
 Where:
 𝑃𝑎𝑣 is the average power radiated per unit solid angle.
 Φ 𝜃, 𝜑 is the radiation intensity.
 𝑑Ω is the infinitesimal solid angle.
 𝑃 is the total power radiated by an isotropic source.
(8.7)

 Directive Gain of an Antenna is defined as,
 The ratio of the radiation intensity specified by the
angle pair 𝜃, 𝜑 ,
 To the average radiated power, as shown by;
 Where:
 g 𝜃, 𝜙 is the Directive Gain of an Antenna.
 Φ 𝜃, 𝜙 is the radiation intensity specified by the
angle pair 𝜃, 𝜙 .
 𝑃𝑎𝑣 is the average power radiated per unit solid
angle.
 𝑃 is the total power radiated by an isotropic
source.
(8.8)
Fig 8.13 Directive
Gain of an Antenna
[8].

 Directivity is defined as,
 The maximum value of Directive
gain g 𝜃, 𝜙 .
 Directivity is denoted by 𝐷 .
 Directive gain is a function of angle pair
𝜃, 𝜙 ,
 Where as the Directivity is a constant.
 The power gain of a transmitting
antenna is defined as,
 The power transmitted per unit solid
angle in direction 𝜃, 𝜙 ,
 Divided by the power transmitted per
unit solid angle from an isotropic
antenna,
 Driven by a transmitter supplying the
same total power.
 Power Gain is denoted by 𝐺 .
 Power Gain is shown in Fig 8.14.
Fig 8.14 Power Gain of a
Transmitting Antenna [9].

 We may relate the Power Gain to the Directivity as follows,
 Where;
 𝐺 is the Power Gain.
 𝜂 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛 is the Radiation Efficiency Factor of the Antenna.
 𝐷 is the Directive gain.
 If any losses is present in the Antenna,
 It means 𝜂 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛 < 1 so,
 The Power Gain is less than the Directivity.
 If the Antenna is efficient,
 It means 𝜂 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛 = 1 so,
 The Power Gain is equal to the Directivity.
(8.9)

 The power Gain of an Antenna
is the result of,
 Concentrating the power
density in,
 A restricted region < 4𝜋 as
shown in Fig 8.15.
 We may introduce (EIRP);
 Where;
 𝐸𝐼𝑅𝑃 is the Effective
Radiated Power.
 𝑃𝑡 is the Transmitted Power.
 𝐺𝑡 is the Power Gain of a
Transmitting Antenna.
Fig 8.15 The Concentration of Power
Density of a Transmitting Antenna
inside a Region smaller than 𝟒𝝅
(8.10)

 Antenna Beamwidth is defined as,
 The angle that subtends the two points,
 On the mainlobe of the field power pattern,
 At which the peak field power is,
 Reduced by 3 dB.
 The higher the power Gain of the Antenna,
 The narrower is the Antenna Beamwidth.
 Every physical antenna has Sidelobes,
 Which are responsible for absorbing,
 Unwanted interfering radiations.

8.4.1.2- Effective Aperture
 The effective aperture of an
antenna is;
 The area presented to the
radiated or received signal, as
shown in Fig 8.16.
 We may write;
 Where;
 𝐴 is the Effective Aperture of
An Antenna.
 𝜆 is the wavelength of the
carrier.
 𝐺 is the Power Gain of An
Antenna.
Fig 8.16 Effective Aperture of An
Antenna [10].
(8.11)

8.4.1.2- Effective Aperture.
 The wavelength and frequency are related as;
 Where;
 𝜆 is the wavelength of the carrier.
 𝑓 is the frequency of the carrier.
 𝑐 is the speed of light equals 3 × 108 𝑚/𝑠𝑒𝑐 .
(8.12)
 An Antenna's Aperture Efficiency 𝜂 𝑎𝑝𝑒𝑟𝑡𝑢𝑟𝑒 :
 Measures how close the antenna comes to
using all the radio power entering its physical
aperture.
 Nominal values for Aperture Efficiency ;
 Lie in the range of 45 to 75 percent.

 We may write;
 Where;
 𝑃𝑟 is the Power absorbed by the receiving
Antenna as shown in Fig 8.17.
 𝑃𝑡 is the Power of the transmitted signal.
 𝐸𝐼𝑅𝑃 is the Effective Radiated Power.
 𝐺𝑡 is the Power Gain of a Transmitting
Antenna.
 𝐺𝑟 is the Power Gain of a Receiving
Antenna.
 𝐴 𝑟 is the Effective Area of the Receiving
Antenna.
(8.13)
Fig 8.17 Friis Transmission
Parameters [11].

 The Friis Free Space Equation can be expressed as follows;
 Where;
 𝑃𝑟 is the Power absorbed by the receiving Antenna.
 𝑃𝑡 is the Power of the transmitted signal.
 𝐺𝑡 is the Power Gain of a Transmitting Antenna.
 𝐺𝑟 is the Power Gain of a Receiving Antenna.
 𝜆 is the wavelength of the carrier signal.
 𝑑 is the Distance between Transmitting and Receiving Antennas.
(8.14)

 The “Path Loss” representing “Signal
Attenuation” as shown in Fig 8.18,
 Across the entire communication link can
be expressed as follows;
 Where;
 𝐏𝐋 is the “Path Loss” across the entire
communication link .
 𝑃𝑡 is the Power of the transmitted
signal.
 𝑃𝑟 is the Power absorbed by the
receiving Antenna.
Antenna.
(8.15)
 𝑑 is the Distance between
Transmitting and Receiving
Antennas.
 𝜆 is the wavelength of the carrier
signal.
 𝐿 𝑓𝑟𝑒𝑒 𝑠𝑝𝑎𝑐𝑒 =
4𝜋𝑑
𝜆
2
is the free
space loss.
Fig 8.18 The Path Loss [12].

 Consider a linear two port device as
shown in Fig 8.19,
 Connected to a signal source,
 Of internal impedance,
 𝑍 𝑓 = 𝑅 𝑓 + 𝑗𝑋 𝑓 ,
 As in Fig 8.19.
 𝑣 𝑡 is the Noise Voltage,
 Represents the Thermal Noise,
 Associated with the Internal
Resistance of the source 𝑅 𝑓 .
 The output noise of the device due to;
1) The source and,
2) The Device itself.
 The Noise Figure of Two Port Device
is;

𝑇ℎ𝑒 𝑇𝑜𝑡𝑎𝑙 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑂𝑢𝑡𝑝𝑢𝑡 𝑁𝑜𝑖𝑠𝑒 𝑃𝑜𝑤𝑒𝑟 𝑑𝑢𝑒 𝑡𝑜 𝐷𝑒𝑣𝑖𝑐𝑒 𝑎𝑛𝑑 𝑆𝑜𝑢𝑟𝑐𝑒 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑏𝑎𝑛𝑑𝑤𝑖𝑑𝑡ℎ
𝑇ℎ𝑒 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑂𝑢𝑡𝑝𝑢𝑡 𝑁𝑜𝑖𝑠𝑒 𝑃𝑜𝑤𝑒𝑟 𝑑𝑢𝑒 𝑡𝑜 𝑆𝑜𝑢𝑟𝑐𝑒 𝑜𝑛𝑙𝑦
Fig 8.19 Linear Two Port
Device.

 We may express the Noise Figure of the device as follows;
 Where;
 𝐹 is the Noise Figure of the Device.
 𝑆 𝑁𝑂 𝑓 is the Spectral Density of the Noise Power of the Device
Output.
 𝑆 𝑁𝑆 𝑓 is the Spectral Density of the Noise Power of the Device
Input due to the Source.
 𝐺 𝑓 is the Power Gain of Two Port Device.
 In a physical device,
 𝑆 𝑁𝑂 𝑓 > 𝐺 𝑓 𝑆 𝑁𝑆 𝑓 ,
 So that 𝐹 > 1 always.
 𝐺 𝑓 =
𝑆𝑖𝑔𝑛𝑎𝑙 𝑃𝑜𝑤𝑒𝑟 𝑎𝑡 𝑡ℎ𝑒 𝑂𝑢𝑡𝑝𝑢𝑡 𝑜𝑓 𝑡ℎ𝑒 𝐷𝑒𝑣𝑖𝑐𝑒
𝑆𝑖𝑔𝑛𝑎𝑙 𝑃𝑜𝑤𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑆𝑜𝑢𝑟𝑐𝑒
,
(8.16)

 Under the condition that;
 The Load connected to the source
equals:
 𝑍∗
𝑓 = 𝑅 𝑓 − 𝑗𝑋 𝑓 ,
 Where the asterisk denotes complex
conjugation,
 We find that;
 Where;
 𝑃𝑠 𝑓 is the signal power from the
source.
 𝑉𝑜 is the open circuit voltage.
 𝑅 𝑓 is the Real component of the
(8.17)
 We may write;
 Where;
 𝑃𝑂 𝑓 is the signal power
at the output of the device.
 𝐺 𝑓 is the Power Gain of
Two Port Device.
 𝑃𝑠 𝑓 is the signal power
from the source.
(8.18)

 Then, multiplying both the
numerator and denominator of
Equation (8.16) by 𝑃𝑠 𝑓 ∆ 𝑓
we obtain;
 Where;
 𝐹 is the Noise Figure of the
Device.
 𝑃𝑠 𝑓 is the signal power from
the source.
(8.19)
 𝑆 𝑁𝑂 𝑓 is the Spectral Density of
the Noise Power of the Device
Output.
 ∆ 𝑓 is Narrow bandwidth
centered at 𝑓 .
 𝐺 𝑓 is the Power Gain of Two
Port Device.
 𝑆 𝑁𝑆 𝑓 is the Spectral Density of
 𝑃𝑂 𝑓 is the signal power at the
output of the device
 𝜌𝑠 𝑓 is the signal to noise ratio
of the source.
 𝜌 𝑂 𝑓 is the signal to noise ratio
at the device output.

 Where;
 𝜌𝑠 𝑓 is the signal to noise ratio
of the source.
 𝑃𝑠 𝑓 is the signal power from
the source.
 𝑆 𝑁𝑆 𝑓 is the Spectral Density of
 ∆𝑓 is Narrow bandwidth
centered at 𝑓 .
(8.20)
 Where;
 𝜌 𝑂 𝑓 is the signal to noise
ratio at the device output.
 𝑃𝑂 𝑓 is the signal power at
the output of the device.
 𝑆 𝑁𝑂 𝑓 is the Spectral Density
of the Noise Power of the Device
Output.
 ∆ 𝑓 is Narrow bandwidth
centered at 𝑓 .
(8.21)

 We may write the following equation;
 Where;
 𝐹𝑂 is the Average Noise Figure of a Two
Port Device.
 (𝑆 𝑁𝑂 𝑓 ) is the Spectral Density of the
Noise Power of the Device Output.
 −∞
∞
𝑆 𝑁𝑂 𝑓 𝑑𝑓 is The Total Noise Power
at The Device Output.
 𝐺 𝑓 is the Power Gain of Two Port
Device.
 𝑆 𝑁𝑆 𝑓 is the Spectral Density of the
Noise Power of the Device Input due to
the Source.
 −∞
∞
𝐺 𝑓 𝑆 𝑁𝑆 𝑓 𝑑𝑓 is the
Output Noise Power due solely
to the Source.
 Spot Noise Figure;
 Is the Noise Figure 𝐹 as a
function of Frequency.
(8.22)

Fig 8.20 Linear Two Port Device
Matched to the Internal
Resistance of a Source
 When Noise Figure 𝑭 is used
to,
 Compare low noise devices,
 All the values obtained are close
to unity,
 So, it is preferable to use the
“Equivalent Noise Temperature”.
 Consider a Linear Two Port
Device as shown at Fig 8.20,
 Where:
 𝑹 𝒔 is the Internal Resistance of
the Source.
 𝑹𝒊𝒏 is the input Resistance of
the linear Two Port Device.
 𝟒𝑲𝑻𝑹 𝒔∆𝒇 is the Mean Square
Value of this Noise Voltage
Generator.
 𝑲 is Boltzmann’s Constant.
 𝑻 is Temperature of Noise

 We may write;
 Where;
 𝑵 𝟏 is The Available Noise
Power at Device Input.
 𝑲 is Boltzmann’s
Constant.
 𝑻 is Temperature of Noise
Source.
 ∆𝒇 is Narrow bandwidth
centered at (𝑓).
𝑵 𝟏 = 𝑲 𝑻 ∆𝒇 (8.23)
 We define 𝑁 𝑑 as follows;
 Where;
 𝑵 𝒅 is The Noise Power
Contributed by the Two Port
Device.
 𝑮 is the Power Gain of Two Port
Device.
 𝑻 𝒆 is Equivalent Noise
Temperature of the Device.
centered at (𝑓).
𝑵 𝒅 = 𝑮 𝑲 𝑻 𝒆 ∆𝒇 (8.24)

 Then it follows the following
equation;
 Where;
 𝑵 𝟐 is Total Output Noise Power.
 𝑮 is the Power Gain of Two Port
Device.
 𝑵 𝟏 is The Available Noise Power
at Device Input.
 𝑵 𝒅 is The Noise Power
Contributed by the Two Port Device.
𝑵 𝟐 = 𝑮𝑵 𝟏+𝑵 𝒅
= 𝑮𝑲( 𝑻 (8.25)
 𝑻 𝒆 is Equivalent Noise
Temperature of the Device.
centered at (𝑓).
 So we can write;
 Where;
 𝑭 is the Noise Figure of the
Device.
𝑭 =
𝑵 𝟐
𝑵 𝟐 − 𝑵 𝒅
=
𝑻 + 𝑻 𝒆
𝑻
(8.26)

 Then we may write;
 Where;
 𝑻 𝒆 is Equivalent Noise Temperature of
the Device.
 𝑻 is Temperature of Noise Source.
 𝑭 is the Noise Figure of the Device.
 Note;
 𝑻 is taken as room temperature namely
290 [Kelvin].
 𝑭 is measured under matched input
conditions.
𝑻 𝒆 = 𝑻 𝑭 − 𝟏 (8.27)

 Consider a pair of Two Port
Networks as shown in Fig
8.21.
 Where;
 𝑭 𝟏 is Noise Figure of the
1st Network.
 𝑭 𝟐 is Noise Figure of the
2nd Network.
 𝑮 𝟏 is Power Gain of the
1st Network.
 𝑮 𝟐 is Power Gain of the
2nd Network.
 𝑵 𝟏 is Noise Power
Contributed by the Source.
 𝑭 𝟏 − 𝟏 𝑵 𝟏 is Noise
Power Contributed by the
1st Network.
Fig 8.21 A Cascade of Two Noisy Two Port
Networks.
 𝑭 𝟏 𝑮 𝟏 𝑵 𝟏 is Output Noise Power from the 1st
Network.
 𝑭 𝟐 − 𝟏 𝑵 𝟏 is Noise Power Contributed by
the 2nd Network.
 𝑭 𝟏 𝑮 𝟏 𝑵 𝟏 𝑮 𝟐 + 𝑭 𝟐 − 𝟏 𝑵 𝟏 𝑮 𝟐 is Output Noise
from the 2nd Network.

 We may write the following Equation;
 Where;
 𝑭 is the overall Noise Figure of the
Cascade Connection of Fig 8.21.
 𝑭 𝟏 𝑮 𝟏 𝑵 𝟏 𝑮 𝟐 + 𝑭 𝟐 − 𝟏 𝑵 𝟏 𝑮 𝟐 is the
Actual Output Noise Power of the
Cascade Connection of Fig 8.21.
𝑭 =
𝑭 𝟏 𝑮 𝟏 𝑵 𝟏 𝑮 𝟐 + 𝑭 𝟐 − 𝟏 𝑵 𝟏 𝑮 𝟐
𝑵 𝟏 𝑮 𝟏 𝑮 𝟐
= 𝑭 𝟏 +
𝑭 𝟐 − 𝟏
𝑮 𝟏
(8.28)
 𝑵 𝟏 𝑮 𝟏 𝑮 𝟐 is the Output Noise
Power of the Cascade
Connection of Fig 8.21,
assuming the Networks to be
Noiseless.

 Equation (8.28) may extends to
the cascade connection of;
 Any number of two port networks
as follows ;
 Where;
 𝑭 is the overall Noise Figure of
Any number of cascade
connection two port networks.
 𝑭 𝟏, 𝑭 𝟐, 𝑭 𝟑 is the Individual Noise
Figures.
 𝑮 𝟏, 𝑮 𝟐, 𝑮 𝟑 is the Individual
Power Gains.
𝑭 = 𝑭 𝟏 +
𝑭 𝟐 − 𝟏
𝑮 𝟏
+
𝑭 𝟑 − 𝟏
𝑮 𝟏 𝑮 𝟐
+
𝑭 𝟒 − 𝟏
𝑮 𝟏 𝑮 𝟐 𝑮 𝟑
+ ⋯ (8.29)

 Correspondingly, we may write the
following equation;
 Where;
 𝑻 𝒆 is the overall Equivalent Noise
Temperature of Any number of
cascade connection Noisy two port
networks.
 𝑻 𝟏, 𝑻 𝟐, 𝑻 𝟑 are the Equivalent Noise
Temperatures of the Individual
Networks.
 𝑮 𝟏, 𝑮 𝟐, 𝑮 𝟑 are the Power Gains of
the Individual Networks.
𝑻 𝒆 = 𝑻 𝟏 +
𝑻 𝟐
𝑮 𝟏
+
𝑻 𝟑
𝑮 𝟏 𝑮 𝟐
+
𝑻 𝟒
𝑮 𝟏 𝑮 𝟐 𝑮 𝟑
+ ⋯ (8.30)

Example 8.1
Fig 8.22 Block Diagram of
Earth Terminal Receiver
 Fig 8.22 has the
following components;
A. Receiving Antenna;
 Which has;
 𝑇𝑎𝑛𝑡𝑒𝑛𝑛𝑎 = 50 (𝐾)
B. Low Noise Radio
Frequency Amplifier
(LNA);
 Which has;
 𝑇𝑅𝐹 = 50 (𝐾)
 𝐺 𝑅𝐹 = 200 = 23 𝑑𝐵
C. Frequency Down
Converter (Mixer);
 Which has;
 𝑇 𝑚𝑖𝑥𝑒𝑟 = 500 𝐾
D. Intermediate Frequency Amplifier;
 Which has;
 𝑇𝐼𝐹 = 1000 (𝐾)
 𝐺𝐼𝐹 = 1000 = 30 𝑑𝐵
 Note;
 𝑇 is Equivalent Noise Temperature.
 𝐺 is Power Gains.

 To calculate the Equivalent Noise Temperature 𝑇𝑒 ,
 From Equation (8.30)
 𝑇𝑒 = 𝑇1 +
𝑇2
𝐺1
+
𝑇3
𝐺1 𝐺2
+
𝑇4
𝐺1 𝐺2 𝐺3
 𝑇𝑒 = 𝑇𝑎𝑛𝑡𝑒𝑛𝑛𝑎 +
𝑇 𝑅𝐹
𝐺 𝑎𝑛𝑡𝑒𝑛𝑛𝑎
+
𝑇 𝑚𝑖𝑥𝑒𝑟
𝐺 𝑎𝑛𝑡𝑒𝑛𝑛𝑎 𝐺 𝑅𝐹
+
𝑇 𝐼𝐹
𝐺 𝑎𝑛𝑡𝑒𝑛𝑛𝑎 𝐺 𝑅𝐹 𝐺 𝑚𝑖𝑥𝑒𝑟
 𝑇𝑒 = 50 +
50
1
+
500
(1)(200)
+
1000
(1)(200)(1)
 𝑇𝑒 = 107.5 (𝐾)

Example 8.2.
 This example presents a sample down
link budget analysis of a digital satellite
communication system as shown in Fig
8.23.
 From equation (8.14);
 𝑷 𝒓 = 𝑷 𝒕 𝑮 𝒕 𝑮 𝒓
𝝀
𝟒𝝅𝒅
𝟐
 Where;
 𝑃𝑟 is the Power absorbed by the
receiving earth terminal Antenna.
signal of satellite Antenna.
satellite Antenna.
earth terminal Antenna.
 𝜆 is the wavelength of the carrier
Antennas.
Fig 8.23 Satellite
Communication [13].

 From equation (1.94) we have;
 𝑵 𝟎 = 𝑲𝑻 𝒆
 Where;
 𝑁𝑜 is Noise Spectral Density.
 𝐾 is Boltzmann’s Constant.
 𝑇𝑒 is Equivalent Noise
Temperature.
 From equation (8.10) we have;
 𝑬𝑰𝑹𝑷 = 𝑷 𝒕 𝑮 𝒕
 Where;
 (𝐸𝐼𝑅𝑃) is the Effective Radiated
Power.
signal of satellite Antenna.
 𝐺𝑡 is the Power Gain of a
Transmitting satellite Antenna.
 Hence, Dividing equation (8.14) by
equation (1.94) as follows;

𝑷 𝒓
𝑵 𝒐
=
𝑷 𝒕 𝑮 𝒕 𝑮 𝒓
𝝀
𝟒𝝅𝒅
𝟐
𝑲𝑻 𝒆
 Using equation (8.10);

𝑷 𝒓
𝑵 𝟎
= 𝑬𝑰𝑹𝑷 𝒔𝒂𝒕𝒆𝒍𝒍𝒊𝒕𝒆
𝑮 𝒓
𝑻 𝒆 𝒆𝒂𝒓𝒕𝒉
𝝀
𝟒𝝅𝒅
𝟐 𝟏
𝑲
 We express
𝑃𝑟
𝑁 𝑜
as
𝐶
𝑁 𝑜
.
 Where;
 𝐶 is Received Carrier Power.
Example 8.2.

 Then we get;
 Where;
 𝐸𝐼𝑅𝑃 𝑠𝑎𝑡𝑒𝑙𝑙𝑖𝑡𝑒 is the Effective
Radiated Power of Transmitting
satellite Antenna.
 𝐺𝑟 is the Power Gain of a
Receiving earth terminal
Antenna.
 𝑇𝑒 is Equivalent Noise
Temperature of a Receiving
𝑪
𝑵 𝒐 𝒅𝒐𝒘𝒏𝒍𝒊𝒏𝒌
= 𝑬𝑰𝑹𝑷 𝒔𝒂𝒕𝒆𝒍𝒍𝒊𝒕𝒆
𝑮 𝒓
𝑻 𝒆 𝒆𝒂𝒓𝒕𝒉 𝒕𝒆𝒓𝒎𝒊𝒏𝒂𝒍
𝝀
𝟒𝝅𝒅
𝟐
𝟏
𝑲 (8.31)
 𝜆 is the wavelength of the
carrier downlink signal.
Antennas.
 𝐾 is Boltzmann’s Constant.
Example 8.2.

Example 8.2.
 Given the following data;
 𝐸𝐼𝑅𝑃 = 46.5 [𝑑𝐵𝑊] means (dB) referenced to 1 (W).
 Receiving Earth Dish Antenna = 2 [m].
 The Power Gain of a Receiving earth terminal Antenna = 45 [dB].
 Equivalent Noise Temperature of a Receiving earth terminal Antenna = 107.5 [K].
 Hence;

𝐺 𝑟
𝑇𝑒 𝑒𝑎𝑟𝑡ℎ 𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑙
is usually shortened to;

𝐺
𝑇 𝑒𝑎𝑟𝑡ℎ 𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑙
= 𝐺 𝑑𝐵 − 𝑇 𝑑𝐵

𝐺
𝑇 𝑒𝑎𝑟𝑡ℎ 𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑙
= 45 − 10 𝑙𝑜𝑔10107.5 = 24.7
𝑑𝐵
𝐾
.

Example 8.2.
𝑳 𝒇𝒓𝒆𝒆−𝒔𝒑𝒂𝒄𝒆 = 𝟗𝟐. 𝟒 + 𝟐𝟎 𝒍𝒐𝒈 𝟏𝟎 𝒇 + 𝟐𝟎 𝒍𝒐𝒈 𝟏𝟎 𝒅 [𝒅𝑩] (8.32)
 Where;
 𝐿 𝑓𝑟𝑒𝑒−𝑠𝑝𝑎𝑐𝑒 is the Free Space
Loss equals(10 𝑙𝑜𝑔10
4𝜋𝑑
𝜆
2
) in
(dB).
 𝑓 is Downlink Carrier Frequency
in (GHz).
 𝑑 is Distance between Satellite
and Earth Terminal in (Km).
 𝑑 = 40000 𝐾𝑚 .
 𝑓 = 12 𝐺𝐻𝑧 .
 Use of Equation (8.32) then:
 𝐿 𝑓𝑟𝑒𝑒−𝑠𝑝𝑎𝑐𝑒 = 92.4 + 20𝑙𝑜𝑔10 12
+ 20𝑙𝑜𝑔10 40000 = 206 (𝑑𝐵).
 At equation (8.31) we have;

1
𝐾
since,
 𝐾 𝑖𝑠 𝐵𝑜𝑙𝑡𝑧𝑚𝑎𝑛𝑛′ 𝑠 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 .
 𝐾 = 1.38 × 10−23 𝑗𝑜𝑢𝑙𝑒
𝐾𝑒𝑙𝑣𝑖𝑛
.

1
𝐾 𝑑𝐵
= −10𝑙𝑜𝑔10 𝐾
 = −10 𝑙𝑜𝑔10 1.38 × 10−23
 = 228.6 (
𝑑𝐵𝑊
𝐾 𝐻𝑧
)

Example 8.2.
 Table 8.1 summarizes the four
terms for the Downlink Power
Budget for Digital Satellite
Communication System.
 Using these results at equation
(8.31) then;

𝐶
𝑁 𝑜 𝑑𝑜𝑤𝑛𝑙𝑖𝑛𝑘
= 46.5 + 24.7
− 206 + 228.6 = 93.8(𝑑𝐵 − 𝐻𝑧)
Variable Value
EIRP 46.5 (dBW)
G/T Ratio 24.7 (dB/K)
Free-Space Loss -206 (dB)
Boltzmann Constant 228.6 (dBW/K-Hz)
Table 8.1 Downlink Power Budget for
Example 8.2

Example 8.2.
 We may write the following
equation;
𝑪
𝑵 𝒐 𝒅𝒐𝒘𝒏𝒍𝒊𝒏𝒌
=
𝑬 𝒃
𝑵 𝒐 𝒓𝒆𝒒
+ 𝟏𝟎𝒍𝒐𝒈 𝟏𝟎 𝑴 + 𝟏𝟎𝒍𝒐𝒈 𝟏𝟎 𝑹 (𝒅𝑩) (8.33)
 Where;

𝐸 𝑏
𝑁 𝑜 𝑟𝑒𝑞
is the Required value
of Bit Energy to Noise Spectral
Density Ratio.
 𝑀 is Link Margin in (dB).
 𝑅 is Data Rate in Bit/Sec.

Example 8.2.

𝐶
𝑁 𝑜 𝑑𝑜𝑤𝑛𝑙𝑖𝑛𝑘
= 93.8 (dB-Hz).
 10 𝑙𝑜𝑔10 𝑀 = 6 (dB).

𝐸 𝑏
𝑁 𝑜 𝑟𝑒𝑞
= 12.5 (dB).
 The use of equation (8.33) yields;
 10 𝑙𝑜𝑔10 𝑅 = 93.8 − 12.5 − 6 = 75.3.
 𝑅 = 33.9 ( 𝑀𝑏 𝑠).
 Then we can say that;
 Data transmission on the downlink at a rate 𝑅 = 33.9 𝑀𝑏 𝑠 .

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cq_LXAhWKKewKHQ0rCGE4yAEQMwgPKA0wDQ..i&w=300&h=369&bih=602&biw=1242&q=solid%20angle%20image&ved=
0ahUKEwi-24-cq_LXAhWKKewKHQ0rCGE4yAEQMwgPKA0wDQ&iact=mrc&uact=8
[8]
https://www.google.com.eg/imgres?imgurl=https%3A%2F%2Fm.eet.com%2Fmedia%2F1072203%2FRFID_p5_325.gif&imgref
url=https%3A%2F%2Fwww.eetimes.com%2Fdocument.asp%3Fdoc_id%3D1276310&docid=7Lg753jLj5whCM&tbnid=jQzpS0r
mbiVBhM%3A&vet=10ahUKEwiByO2XvfLXAhUE_qQKHTNaDyUQMwhbKBUwFQ..i&w=448&h=229&bih=602&biw=1242&q=
Directive%20Gain%20of%20an%20Antenna%20image&ved=0ahUKEwiByO2XvfLXAhUE_qQKHTNaDyUQMwhbKBUwFQ&ia
ct=mrc&uact=8

REFERENCES
[9]
https://www.google.com.eg/imgres?imgurl=https%3A%2F%2Fportalvhdshs6615cqnmf91.blob.core.windows.net%2Fslides%2
F634710788635811878.jpg&imgrefurl=https%3A%2F%2Fwww.exploregate.com%2Fvideo.aspx%3Fvideo_id%3D47&docid=-
gjqDm7RKQZW0M&tbnid=yIxmYDGAbSLzTM%3A&vet=10ahUKEwjJ87Pi4fLXAhXE6xQKHSO9B5M4ZBAzCDgoNjA2..i&w=
960&h=720&bih=602&biw=1242&q=power%20gain%20antenna%20image&ved=0ahUKEwjJ87Pi4fLXAhXE6xQKHSO9B5M4
ZBAzCDgoNjA2&iact=mrc&uact=8
[10]
http://www.radartutorial.eu/06.antennas/Antenna%20Characteristics.en.html
[11]
https://www.everythingrf.com/rf-calculators/friis-transmission-calculator
[12]
https://www.google.com.eg/imgres?imgurl=https%3A%2F%2Fcdn2.hubspot.net%2Fhub%2F213677%2Ffile-246417777-
jpg%2Fimages%2Fantenna_gain-resized-
600.jpg&imgrefurl=https%3A%2F%2Fwww.avalan.com%2Fblog%2Fbid%2F324806%2Findoor-wireless-path-loss-four-factors-that-must-
be-considered-for-transmission-range&docid=NcQ79DJerPWRmM&tbnid=VjmT1GKL7qNIxM%3A&vet=10ahUKEwiWxv39xvfXAhUS-
qQKHYesDTcQMwhtKCYwJg..i&w=600&h=172&bih=602&biw=1242&q=path%20loss%20image&ved=0ahUKEwiWxv39xvfXAhUS-
qQKHYesDTcQMwhtKCYwJg&iact=mrc&uact=8

REFERENCES
[13]
https://www.harris.com/solution/geostationary-operational-environmental-satellites-r-series-ground-segment-and-antenna

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