In 1895, Jagadish Chandra Bose gave a new dimension to wireless communication by transmitting the three-dot Morse code for the letter 'S' over a distance of three kilometres using electromagnetic waves. Today, wireless communication has developed in to an integral part of the modern society specially the long range communications such as satellite communication, radio and television broadcasting to the expansive mobile communication industry . Two aspects that make wireless communication challenging and interesting are signal fading and interference. First in the phenomenon of fading the strength of the signal gets affected due to multipath fading as well as larger scale effects such as path of the signal being lost due to distance attenuation and obstacles. Secondly unlike wired connections where transmission-receiver pair is connected via wires, wireless users have to communicate over the air and there is bound to have interference between them .
1.1 ELEMENTS OF COMMUNICATION SYSTEMS
The three essential parts which plays an important role in signal transmission in any communication system are transmitter, transmission channel and the receiver. The transmitter generates an input signal according to the characteristics of the transmission channel which also involves modulation for its signal processing and may also include coding . The transmission channel is a medium through which information signals are sent from one or several senders (source) to one or several receivers (destination). It can be a pair of wires or a coaxial cable . Signals transmitted through the channels are subjected to loss and attenuation resulting in decrease of the signal power progressively with increasing distance. The receiver processes the output signal coming from the channel preparing for delivering it to the transducer at the destination. Operations involved at the receiver stage include amplification to make the signal stronger, and demodulation and decoding to reverse the signal processing performed at the transmitter. Another important function is filtering .
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Figure-1 Elements of communication system 
During the course of filtering various unwanted effects like distortion, interference and noise crop up in the course of signal transmission and alters the shape of the signal. Attenuation is unwanted since it reduces signal strength at the receiver. Although such errors can happen anywhere during the transmission but it is the channel which is to be blamed, treating the transmitter and receiver as being ideal .
Distortion is a waveform disturbance caused by the imperfect response of the input signal from the system. When compared to noise and interference, distortion disappears when the signal is turned off. Distortion is unwanted and many methods have been implemented to reduce it. If the channel has continuous but less distorting response, then this distortion can be reduced or corrected with the help of special filters called equalizers .
Interference is anything caused by additional signals from human sources like power lines, other transmitters, switching circuits and machinery etc. It usually occurs in radio systems whose receiving antenna catches several signals at the same time . Radio- frequency interference (RFI) or electromagnetic interference (EMI) also appears to be found in cable systems due to the electromagnetic induction or electromagnetic radiation radiated from nearby sources. The source may be an object, artificial or natural that carries rapidly changing currents in the cables. Interference can be removed to an extent by appropriate filtering but then the interfering signals occupy different frequency bands than the desired signal .
Noise refers to unwanted perturbation, random and random electrical signals caused by natural processes both internal and external too the system. When such random variations are imposed on the signal carrying information, the message receiving at the receiver may be partially corrupted or totally eliminated. Filters can be used to reduce noise but there always be some amount of noise which cannot be removed .
/ * Figure 1 represents a simplex transmission (SX). For a two way communication we of course require a transmitter and receiver at each end. A full-duplex system (FDX) has a channel which allows communication at the same time in both directions. Land line telephone networks are full-duplex, since it allows both the callers to speak and to listen at the same time. A half-duplex system (HDX) allows communication in either direction, but only one direction at a time. Walkie- talkies are half-duplex since one user talk can transmit at a time as both the users are transmitting on the same frequency . */
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"Digital transmission of information has sufficiently overwhelming advantage that is increasingly dominates communication systems" . Today in computer to computer communication the information to be transmitted is truly digital and there is note alternative for that. But digital communication is a small part of today's communication in which it is being used. A much larger fraction has been devoted to transmit analog signals like speech, video, images etc. But information in continuous time and continuous amplitude can also be represented digitally by converting them to digital. The advantages of converting from analog to digital are 1.The encoding of analog signals in digital form has benefited from compression of algorithms, which reduces the bit rate slowly while maintaining high accuracy. 2. Coding techniques and signal processing has increased the bit rate dramatically with the help of physical channels like optical fibres or radio wave. 3. Complex circuits make coding functions and signal processing cost effective. 4. The cost of transmitting high bit rates over long distances have been reduced with optical fibres been introduced. The applications of Digital communications are Continuous Time signals and Data .
1.2 MODULATION SCHEMES
Phase-shift keying (PSK) is a digital modulation technique that conveys data by modulating the phase of the carrier signal. To represent digital data PSK uses a finite number of phases, each phase being assigned to a unique pattern of binary digits while other digital modulation schemes use a finite number of distinct signals. In PSK each phase ciphers equal number of bits resulting in the formation of a symbol to represent the particular phase. The demodulator designed for the symbol is used by the modulator to determine the phase of the received signal and maps it back to the symbol and thus recovering the original data .
Figure -2 Modulation Schemes 
Amplitude-shift keying (ASK) is a modulation technique that represents data by varying the amplitude of the carrier wave. Keeping the frequency and phase constant the amplitude of the signal varies according to the modulating signal. The range of values at amplitude is used to represent binary logic 0's and 1's. This binary logic numbers represent ON and OFF switch in a carrier signal. For example logic 0 refers to OFF and logic 1 refers to ON. ASK is linear and sensitive to noise, distortions. The ASK technique is commonly used over optical fibres to transmit digital data. For LED transmitters, binary 0 refers to absence of light and binary 1 by a short pulse of light .
Frequency-shift keying (FSK) is a frequency modulation technique that transmits digital data through discrete frequency changes of a carrier wave. The simplest FSK is binary FSK which uses a pair of discrete frequencies to transmit binary (0's and 1's) data. '1' refers to mark the frequency and '2' refers to the space frequency .
Quadrature amplitude modulation (QAM) is both an analog and a digital modulation scheme. It transmits two analog or two digital signals by modulating the amplitude of their respective carrier waves using amplitude phase shift keying (ASK) or amplitude modulation (AM). The resulting wave forms in QAM which are usually sinusoids are out of phase with each other by 90 degrees and are thus called quadrature signals. The resulting modulated waves are summed up from both analog and digital QAM. In the digital QAM a finite number of at least two phases and two amplitudes are used .
1.3 ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING (OFDM)
Orthogonal frequency-division multiplexing (OFDM) is a multi carrier modulation i.e. there is a certain bandwidth which is used for communication. We don't want to take a single carrier and modulate the carrier in some way and transmit it . The purpose is to take multi carriers and divide the bandwidth into many small bands and to assign each carrier in each band thus dividing the data stream into many parallel data streams of lower rate. We then modulate the individual carriers by individual lower rate data streams and then sum up all the signals to transmit it together, so that we will be using the complete bandwidth. But we will be modulating the individual subcarriers by lower rate data streams and add all those signals to transmit it .
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/* The Problems with the single carrier communication are 1. The channel may not have flat response in the frequency domain as a result they will be intersymbol interference at the receiver. 2. Doing equalization at the receiver doesn't solve the problem because by equalization we may actually make the channel flat. But then the noise in the bands will also be amplified to a higher extent and that will cause in overall amplification of the noise . */ CAN BE USED SOME WHERE
If low symbol rate modulation schemes suffer from inter symbol interference caused by multipath propagation then it is necessary to transmit a number of low-rate streams in parallel instead of a single high-rate stream. Since, each symbol is very long it is feasible to insert a guard interval between the OFDM symbols resulting in the elimination of inter symbol interference.
Figure-3 Multipath Channels 
The cyclic prefix acts as a buffer accumulator where it stores the delayed information from the previous symbols . The receiver has to remove unwanted samples from the cyclic prefix from the previous symbol which has been corrupted when choosing the samples for an OFDM symbol. For demodulating the received symbol, the receiver can choose 3.1 micro seconds samples from a region as shown in the figure above. The samples can be chosen from the two regions above.
If there are such a channels (shown in the figure) and have high selective frequency then the channel curving on the left hand side is very good and on the other hand the channel curving to the right hand side is bad. This is because of high attenuation .