|
Course: |
Wireless Networking (CS698T) |
|
Instructor: |
Dr. Bhaskaran Raman |
|
Lecture Number: |
06 |
|
Lecture Date: |
12th August 2005 |
|
Scribe: |
Mayank Mishra |
Contents : 1. Brief Overview of
Fourier Analysis
1.1 Fourier Series
1.2 Fourier Transform
2. Multiplexing
2.1 Space Division Multiplexing
2.2 Time Division Multiplexing
2.3 Frequency Division Multiplexing
2.4 Code Division Multiplexing
3. Modulation
3.1 Amplitude-shift Keying
3.2 Frequency-shift Keying
3.3 Phase-shift Keying
4.
Noise
1. Brief Overview of Fourier Analysis
1.1 Fourier Series:
A Fourier series is an expansion of
a periodic function 
in
terms of an infinite sum of sines and cosines (linear combination of complex
exponentials).
|
|
where
|
|
|
|
|
|
|
|
|
|
|
|
However it must be noted that this is valid only for periodic signals and none of the real life signals are periodic (since a periodic signal must have infinite time support i.e. the periodic definition must be valid for all times -∞<t<∞ )
1.2 Fourier Transform:
A large class of non periodic signals (including all signals with finite energy) can also be represented through a linear combination of complex exponentials. The difference is that whereas in case of periodic signals the complex exponentials building blocks were harmonically related, for non periodic signals they are infinitesimally close in frequency and hence the representation takes the form of an integral rather than a sum.
The motivation comes from formally considering Fourier series for functions of period 2T and letting T tend to infinity (an non periodic signal can be viewed as a periodic signal with infinite time period). The infinite spectrum of coefficients in the representations are called Fourier Transform, and the synthesis integral itself, which uses these coefficients to represent the signal, is called the Inverse Fourier Transform.
Thus Fourier Transform is a generalization of complex Fourier series that expresses a function in terms of frequency components.
Multiplexing is the process through which several information signals can be simultaneously transmitted over the same medium. Since there are several users who want to communicate with each other using the same medium, hence multiplexing is necessary for sharing the resources so as to communicate meaningfully.
There are four basic types of multiplexing:
2.1 Space Division Multiplexing
(SDM):
Here the users are communicating in groups that are separated in space hence any interference is avoided.
2.2 Time Division
Multiplexing (TDM):
Time division multiplexing allows multiple conversations to take place by the sharing of medium or channel in time. A channel is allocated the whole of the available bandwidth for a specific period of time. This means that each subscriber is allocated a time slot.
TDM is still used in satellite communication.
2.3 Frequency
Division Multiplexing (FDM):
FDM is a method in which each signal is allocated a frequency slot within the overall transmission bandwidth, In other words the total available frequency bandwidth on the transmission line is divided into frequency channels and each information signal occupies one of these channels The signal will have exclusive use of this frequency slot all the time
FDM is used in radio broadcasting.
2.4 Code Division
Multiplexing (CDM):
It’s a hybrid of TDM and FDM. During each successive time slot the frequency band allotted to the users are reordered. CDM leads to CDMA which is used for mobile communication today. GSM uses CDM and eight speech channels are put on each carrier(each frequency slot).
c
f
t
Modulation is the process
through which transmitter modifies the message signal into a form
Modulation is required because:
(i) The size of the antennae must be of the order of wavelength of signal. Hence, only high frequency signals can be practically transmitted.
(ii) Modulation makes FDM possible due to which several users can communicate simultaneously even if the original message signal is of same frequency.
(iii) Modulating the signal to high frequency brings ratio of highest frequency and lowest frequency present in the channel close to “1” and hence makes antennae design easier.
There are three basic kinds of modulation corresponding to the three parameters of the carrier that can be varied according to the message signal:
(i) Amplitude Modulation : amplitude of the carrier wave is varied according to the message signal.
(ii) Frequency Modulation : frequency of the carrier wave is varied according to the message signal.
(iii) Phase Modulation : phase of the carrier wave is varied according to the message signal.
Here we will deal only with the Digital Modulation. There are three major classes of digital modulation(keying) techniques used for transmission of digitally represented data:
3.1 Amplitude-shift
Keying(ASK) :
Digital data is represented by shift in the amplitude of the carrier wave to some predetermined levels. The simplest and most common form of ASK operates as a switch, using the presence of a carrier wave to indicate a binary one and its absence to indicate a binary zero.
Vd : digital signal to be transmitted
Vc : carrier wave
VASK : modulated signal.
3.2 Frequency-shift Keying(FSK) :
The modulating signal shifts the output frequency between predetermined values. Usually, the instantaneous frequency is shifted between two discrete values termed the mark frequency and the space frequency.
3.3 Phase-shift
Keying(PSK) :
The phase of the carrier signal is changed to predetermined values in accordance with the message signal. In Binary Phase-shift Keying(BPSK) there are two predetermined phases each of them representing different logic states. Thus BPSK can transmit only one bit sequence at a time. In Quadrature Phase-shift Keying(QPSK) there are four predetermined phases. Each one among a pair represents different logic states of same bit sequence while the two pairs themselves represent different bit sequence. Thus QPSK can transmit two bit sequence at a time.
802.11b specifies four different modulation schemes:
(i) : BPSK
(ii) : QPSK
(iii) : CCK(Complementary Code Keying)
(iv) : CCK2
Signal to Noise Ratio(SNR): signal-to-noise ratio is a measure of signal strength relative to background noise. The ratio is usually measured in decibels (dB)
The various causes for noise are thermal, impulse, crosstalk, intermodulation. The Thermal Noise is proportional to (k*T*B) where:
k=Boltzman constant
T=temperature
B=bandwidth
Therefore the bandwidth of the signal must be decreased in order to decrease noise. However that can not be done to any limit as reducing bandwidth reduces the speed at which data can be transferred.
Bit Error Rate(BER): BER is the percentage of bits that have errors relative to the total number of bits received in a transmission, usually expressed as ten to a negative power. Its inversely proportional to the SNR i.e. higher the SNR lower is the BER.
The figure shows different characteristics for different modulation schemes. As a maximum limit on BER is desirable a minimum limit on SNR has to be maintained.
The phenomenon refers to
Actually 802.11b uses frequency around 2.4 GHz for communication. The same frequency is also used by microwaves,cordless phones, etc which interfere with 802.11b communication. Now if the signal has a narrow bandwidth then it is more susceptible to catastrophic interference(if interference occurs in the bandwidth used by signal then most of the information will be lost). On the other hand if bandwidth is large then even if interference occurs, only a small part of information will be lost. Hence spread spectrum is used by 802.11b to avoid catastrophic interferences.
