Orthogonal Frequency Division Multiplexing is a process for the transmission of data using quite a large quantity of modulated sub-carriers, and this data is sent in the parallel form. The offered bandwidth is divided by the sub-carriers and they have a separation among them to avoid interference i.e. they are orthogonal to each other. The carrier orthogonality is defined over a symbol period; each carrier has an integer number of cycles over that periodwhich will be explained later. No interference is achieved because each carrier's spectrum contains a null at the center frequencies of all other carriers of the system and it is due to orthogonality.This increases the spectral efficiency in OFDM. Spectral Efficiency is a measure of how efficiently the bandwidth is being utilized.
The conventional technique of frequency was Frequency Division Multiplexing (FDM). An example of FDM is frequency modulated radio stations. These radio stations use different carrier frequency for transmission and reception. Furthermore there are sufficiently spaced far apart in frequency domain so that there spectra do not overlap during transmission. At receiver each signal is received individually by using band pass filters. The filtered signal is then demodulated to recover the original signal.
There is a significant difference between OFDM and FDM. The radio stations use different frequencies for transmission in conventional broadcasting and separation between the stations is maintained by the effective use of FDM but no synchronization is carried out among these stations.The signals of various stations are merged to form a single multiplexed stream of data in OFDM transmission, for example. An OFDM ensemble is used for the transmission of this data.A compact placement of many sub-carriers makes up an OFDM ensemble.
The interference among the sub-carriers in OFDM is controlled by the maintenance of time and frequency synchronization of the sub-carriers with each other. The spectra of these sub-carriers overlap, but do not cause Inter-Carrier Interference (ICI) due to the orthogonal nature of the modulation.
A pulse in time domain corresponds to sinc in the frequency domain. As the sinc is of infinite length there is interference among them in the frequency domain. As these carriers are orthogonal in nature this implies that the interference does not affect the message signal.
Figure 2.1 Sub-carriers (Time Domain) 
Figure 2.2 Sub-carriers (Frequency Domain) 
Typically with FDM the transmission signals need to have a large frequency guard-band between channels to prevent interference. This lowers the overall spectral efficiency. In OFDM the guard band is provided by orthogonal packing of the sub-carriers, which improves the spectral efficiency.
The communication system needs modulation to effectively transmit the signal on the channel.
The carriers in FDM transmission can use an analogue or digital modulation scheme. In a single OFDM transmission all the sub-carriers are synchronized to each other, restricting the transmission to digital modulation schemes. As in a single OFDM transmission all the sub-carriers are synchronized to each other, so the transmission can only be done using digital modulation techniques. Common modulation schemes for digital communications include Amplitude Shift Keying (ASK), Frequency Shift Keying (FSK), Phase Shift Keying (PSK) and Quadrature Amplitude Modulation (QAM).
All the carriers in OFDM transmit in unison using synchronized time and frequency, forming a single block of spectrum. This is to ensure that the orthogonal nature of the structure is maintained. Since these multiple carriers form a single OFDM transmission, they are commonly referred to as 'sub-carriers', with the term of 'carrier' reserved for describing the RF carrier mixing the signal from base band. There are several ways of looking at what make the sub-carriers in an OFDM signal orthogonal and why this prevents interference between them.
2.1 Principles of OFDM
'The main features of a practical OFDM system are as follows:
Some processing is done on the source data, such as coding for correcting errors, interleaving and mapping of bits onto symbols. An example of mapping used is QAM.
The symbols are modulated onto orthogonal sub-carriers. This is done by usingInverse Fast Fourier Transform (IFFT).
Orthogonality is maintained during channel transmission. This is achieved byadding a cyclic prefix to the OFDM frame to be sent. The cyclic prefix consists ofthe L last samples of the frame, which are copied and placed in the beginning ofthe frame. It must be longer than the channel impulse response.
Synchronization: the introduced cyclic prefix can be used to detect the start ofeach frame. This is done by using the fact that the L first and last samples are the same and therefore correlated. This works under the assumption that one OFDMframe can be considered to be stationary.
Demodulation of the received signal by using FFT
Channel equalization: the channel can be estimated either by using a trainingsequence or sending known so-called pilot symbols at predefined sub-carriers.
Decoding and de-interleaving'
A block diagram showing a simplified configuration for an OFDM transmitter andreceiver is shown below:
Figure 2.3OFDM Transmitter 
Figure 2.4 OFDMReceiver 
Orthogonality is defined for both real and complex valued functions. The functions Ï•m(t) and Ï•n(t) are said to be orthogonal with respect to each other over the interval a < t < b if they satisfy the condition:
The available bandwidth is split into numerous narrowband channels (usually 100-8000) and each has its own sub-carrier. The orthogonality of these sub-carriers is achieved by integer number of cycles over a symbol period. Figure 2.6 shows that each sub-carrier's spectrum has a null at the centre frequencies of all sub-carriers. This helps in no interference among the sub-carriers so they can be placed very close to each other, as theoretically possible.This eliminates the need of time multiplexing of the users and also switching among the users can be done with no overhead. This overcomes the problem of overhead carrier spacing required in FDMA.
Figure 2.5Orthogonality of sub-carriers
The signals in black, green and red are not mixed because they are orthogonal to each other.
The orthogonality in sub-carriers of OFDM can be proved by multiplying the waveforms of two sub-carriers and integrate over the symbol period. The result comes out to be zero. The orthogonal signals do not interfere, and they can be separated at the receiver by correlation techniques.
2.3 Concept ofOrthogonality Frequency Domain
The orthogonality property can more easily be understood in the frequency domain. As discussed earlier a pulse or rectangle in time domain corresponds to a sinc in the frequency domain. The sinc is given by sin(x)/x. The OFDM symbol is transmitted for a fixed time Tfft. This symbol time is the sub-carrier spacing given by 1/Tfft Hz.
A narrow main lobe makes the shape of a sinc and it hasnumerous side-lobes those follow aslow decaying trendwith the magnitude of the frequency difference away from the centre. The peak of each carrier is at the centre frequency andthe nulls areuniformly spaced with a frequency seperationequivalent to the carrier spacing. The relevance of each sub-carrier to the nulls of all sub-carriers results in the orthogonality of the transmission.
The spectrum remains no longer continous if discrete fourier transform (DFT) is applied on the signal, as demonstrated in figure 2.6.Discrete samples of the spectrum are created. Figure 2.7 shows the sampled spectrum.Only the peaks of sub-carriers are associated with the time synchronized frequency samples of the DFT, therefore the receiver is not affectedby the sub-carriers' overlapping frequency region. The measured peaks correspond to the nulls for all other sub-carriers, resulting in orthogonality between the sub-carriers.
Figures 2-6 &2.7 Frequency response of the sub-carriers in a 5 tone OFDM signal.
2.6shows the spectrum of each carrier, and the discrete frequency samples seen by an OFDM receiver. Note, each carrier is sinc, sin(x)/x, in shape.
2.7shows the overall combined response of the 5 sub-carriers (thick black line).
2.4 Basic OFDM Transceiver/OFDM Generation and Reception
As the generation of analog signals at a particular frequency involves some difficulty due to all the phase lock loop oscillators and Frequency Synthesizer involved .Therefore OFDM signals are generated digitally. The basic block diagram of an OFDM transceiver is shown in Figure 2.8.
Figure 2.8Basic OFDM Transceiver
The main blocks of the transmitter section are as shown in figure 2.4. The serial digital pulses are converted to parallel data. This digital data is modulated by some phase and amplitude mapping technique. The net result would have a phase and an amplitude specification. The resulting signal is obtained in the frequency domain. For conversion to time domain, we apply it to an IFFT block and a time domain signal is obtained. The modulating frequency is then boosted to a higher RF range by using an RF oscillator.
The generated data is in serial format. An OFDM symbol usually transmits 40 to 4000 bits. So there is need of a serial to parallel converter. Suppose an OFDM symbol has 50 frequencies, and if modulation of each carrier is done using 16 QAM i.e.4 bits data is supported by each carrier, then the number of bits per symbol is 200 (50x4). Therefore high data rate can be achieved. The change of modulation scheme can help to control the data rate like 2,4,8,16,32 QAM and in result Signal to Noise Ratio (SNR) is also contained.
The data sub-carriers are set to an amplitude and phase after the sub-carrier modulation stage and it is done by the use of the data being sent and the modulation scheme; the amplitude of all the unused sub-carriers isfixed to zero. The OFDM signal in the frequency domain is obtained as a result. The time domain signal is transmitted therefore IFFT is utilized for the conversion of this signal to the time domain. All the discrete samples are linked to individual sub-carriers in the frequency domain before taking the IFFT.The data is modulated with majority of the sub-carriers. The outer sub-carriers remain un-modulated and their amplitude is made zero. The frequency guard band is provided by these zero sub-carriers.It serves as an interpolation of the signal and helps in recovering original data using analog anti-aliasing reconstruction filter.
Figure 2.9 OFDM Generation, IFFT Stage
The modulated carrier produces a base band signal of a lower frequency and it has to be frequency boosted to a higher transmissible level. This is done by the RF section of the transmitter.
The high multi-path effects tolerance and the ability of transmission with a higher spectral efficiency are the main advantages of OFDM. The little symbol rate and the effective use of guard band provides high toleranceto multi-path propagation effects.The OFDM symbol is extended by the guard band but it is useful to eliminate Inter-Symbol Interference (ISI). A small fraction of the symbol time is enough for the guard band and it helpsto adjust the delay spread tolerance by the useof a large number of narrow bandwidth carriers. The delay spread is adjusted in accordance with the radio conditions.In addition to protecting the OFDM from the ISI the guard period also provides protection against time offset errors in the receiver.
2.4.2 Guard Period
There are many useful signals either from multi-path echoes or from other Single Frequency Networks. Typically the signals arrive at the receiver at different intervals of time which cause the synchronization of the receiver to the desired frequency impossible. Take two consecutive symbols n and (n-1) .Suppose there is some delay in the arrival of the symbol n-1 by a small timeinterval, without a guard band, the information will fall in the FFT window of the symbol n and cause interference. This type of interference is called ISI or the inter symbol interference. ISI can be overcome by copying a part of the beginning of the symbol is copied to the end to increase the symbol time by a quantity called as the guard band time. The insertion of a guard band reduces the data capacity significantly as the entire transmission time is not useful time.
The robustness to multi-path effects is the most important property of OFDM. This is important as the sub-carriers have to preservethe orthogonality in the process of transmission. The robustness to multi-path propagation effects can be achieved by the insertion guard period between the symbols to be transmitted. The multi-path signals of the previous symbol are provided with the time by the guard period, to be decoded before reception of multi-path signals of the current symbol.
The cyclic prefix is considered to be the most effective guard period and it isinserted in the beginning of each OFDMsymbol. The cyclic prefix is usually thereplica of the last part of the OFDM symbol, and its length is adjusted according to the maximum delay spread of the channel, as depicted in figure 2.6.The bandwidth efficiency is reduced by the introduction of the cyclic prefix but a compromise between performance and efficiency has to be made to overcome ISI and the cyclic prefix is thought to be the best compromise.
Figure 2.10 Implementation of Cyclic Prefix
The main block diagram of a receiver is as shown in the figure 2.8. We now observe the main blocks and analyze the receiver functioning. While transmitting the OFDM signal the basic modulated signal has a raised frequency level to match the transmission frequency requirements. In the initial RF demodulation stage the frequency of the signal is reduced to the original modulated frequency.
2.4.4 FFT Window Synchronization
Synchronization in an OFDM receiver has to be done in two stages.
Initial synchronization in time is usually done by taking samples Ts apart in time.The receiver can detect the start of a new symbol when a waveform repeats. The repetition of a waveform causes the correlator output to exceed a threshold value.
In a real time environment a number of echoes are encountered by the receiver which complicates the task of secondary synchronization, i.e. finding the best position for the FFT window. Thus various strategies can be employed to optimize receiver performance. In a multi frequency network, the receiver receives one direct signal and different echoes. The direct signal need not be the strongest signal nor is there a direct signal at all as in the case of mobile communications. There may be only the direct signal also in many cases.
Most coverage prediction methods use two dimensional prediction models, taking into account only the direct path. Thus the positioning of the FFT window in this case is simple and unique as there is only one direct path present. In some three dimensional prediction models a multi-path propagation environment for each transmitter is considered. Hence windowing is more complex.
2.4.5 Timing Synchronization
'Since it is unknown to the receiver at what time instant the symbol was transmitted and how long the dispersion of the channel is, it is essential to find the beginning of the OFDM signal. Thus the time scales of the receiver and transmitter have to be synchronized and the removal of guard band can be done with the desired accuracy.' 
2.4.6 Frequency Synchronization
The signal is generally frequency shifted to a higher transmitting frequency before transmissionand this frequency is known to the receiver. A frequency deviation may result as the RF components usually havelarge. This frequency deviation may be too large and distort the transmission for many of the cases.Therefore some measures have to be taken to estimate and compensate it at the receiver.
2.4.7 Sampling Clock Synchronization
An analog RF signal is generated from the output. The down converted RF signal is sampled to get a discrete time signal at the receiver for the purpose of further processing. The degradation of the performance should be avoided by making sure that all the sampling times are equivalent at the receiver.Some measure must be taken to evaluate and compensate any possible variation between transmitter and receiver.
In the remainder of the chapter basic concepts related to OFDM technology will be discussed in detail.
2.5 Serial to Parallel Conversion
As discussed earlier data generated is typically in the form of a serial data stream.
In OFDM, each symbol transmits 40 - 4k bits, so a serial to parallel convertor is needed to convert the input serial bit stream to the data to be transmitted in each OFDM symbol. The data assigned to each symbol depends on the modulation used and number of sub carriers. For example, for a sub-carrier modulation of 16-QAM each carrier carries 4 bits of data, and so for a transmission using 100 sub-carriers the number of bits/symbol would be 400. In adaptive modulation schemes, the modulation scheme used on each sub-carrier can vary and so the number of bits per sub carrier also varies.
Therefore, the serial to parallel convertor fills the data payload for each sub carrier. At the receiver the parallel data is converted to serial, with the data from the sub carriers being converted back to the original serial data stream.