## OFDM.. enabling New generation communication standards

The principles of orthogonal frequency division multiplexing (OFDM) modulation have been in

existence for several decades. However,its only recently that the techniques have moved out of

text books and researchers benches to modern communications systems. OFDM is conceptually

simple, but the devil is in the details! The implementation relies on very high speed digital signal processing and this has only in the last several years become available at a price that makes OFDM a competitive technology. The advantage of OFDM claims to have is its ability to cope with severe channel conditions. OFDM is sometimes called multi-carrier or discrete multi-tone modulation.

What is OFDM?

The Conventional single-carrier modulation system uses modulation of information onto one

single carrier, utilizing frequency, phase, or amplitude adjustments of carrier. Frequency

division multiplexing (FDM) extends this very concept by using multiple subcarriers within the same single channel. The total data is divided between the various subcarriers. FDM systems require a guardband between its subcarriers to prevent these frim interfering with each other. These guardbands effectively lower the system’s information rate. If the FDM systems use a set of subcarriers that were "orthogonal" to each other, a higher level of spectral efficiency can be achieved. The use of orthogonal subcarriers would allow the subcarriers’ spectra to overlap, thus increasing the spectral efficiency. As long as orthogonality is maintained,it is possible to recover the individual subcarriers’ signals eventhough the spectra are overlapped.

Orthogonality holds the Key...

The main concept of OFDM lies in the orthogonality of the carriers. To be orthogonal, the dot product of two signal must result in zero. It is common to use the following inner product for two functions f and g

The functions 1, sin(nx), cos(nx) : n = 1, 2, 3, ... are orthogonal with respect to Lebesgue measure on the interval from 0 to 2π. This fact is basic in the theory of Fourier series. The communication system can be viewed from a stochastic processes' perspective. If two random processes are uncorrelated, then they are orthogonal. This view of orthogonality gives a simpler understanding of the implications of orthogonality in OFDM. Relating it to the Fourier series, which is nothing but a representation of signals as a combination of mutually orthogonal signals,is really intutive. In fact,OFDM implementation is done using DFT techniques.

Imlpementation

The DFT and IDFT form a transform pair widely used to convert signals from time to frequency domain and back. carriers. For example, the IDFT is used to convert frequency-domain data to time-domain data. For this,the IDFT correlates its inputs with its orthogonal basis functions which are sinusoids at certain frequencies. This is equivalent to mapping the input data on to the sinusoidal basis functions. It is easier said than done! In practice, OFDM systems implement a combination of Fast Fourier Transform(FFT) and inverse Fast Fourier Transform(IFFT) blocks that are mathematically equivalent;but more efficient ways to implement DFT and IDFT.

Channel performance

For the purpose to eliminate the effect of ISI, the guard interval could consist of no signals at all. Guard interval (or cyclic extension) is used in OFDM systems to combat against multipath fading. In that case, however, the problem of intercarrier interference (ICI) would arise. The reason is that there is no integer number of cycles difference between subcarriers within the interval.To eliminate ICI, the OFDM symbol is cyclically extended in the guard interval. This ensures that delayed replicas of the OFDM symbol always have an integer number of cycles within the interval, as long as the delay is smaller than the guard interval.

OFDM Challenges

Experts agree that there are, practical difficulties to achieve real time synchronization for OFDM frames. The technique is extremely sensitive to the frequency offsets. Also, spectral nulls in the useful transmission band will conduce to severe performance degradation on the affected sub-carriers. OFDM symbols have a high peak-to-average power ratio (PAPR) that makes them unsuitable for RF amplifiers Finally, but not last, full capabilities of OFDM can be achieved only if the channel impulse response is known, assumption that is not always met; complex channel estimation techniques must be used in order to achieve this need. Present studies in OFDM range focus on these drawbacks and in the finding of the means to overcome them.

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