3.3 Coded Orthogonal Frequency Division Multiplexing (COFDM)
An essential technique of HDTV is the COFDM (Coded Orthogonal Frequency Division Multiplexing), which is the most advanced and vivid modulation technique in the world. In this term, Coded(C) stands for the essential forward error-correction coding, referring to the channel coding employs the convolutional coding method known as variable bit rate coding to adapt different protection specifications for different data. Orthogonal Frequency Division Modulation (OFDM) denotes Multi-carrier Modulation Method, using a quantity of subcarriers. The subcarriers are spaced by a fixed frequency interval, which is n times of the base oscillation frequency.
Like CDMA (Code Division Multiple Access), COFDM was first developed for military use. It was proposed by ETSI(European Telecommunication Standards Institute) for the purpose of security of military radio transmission, then applied in civic technology field. With more applications in the public field, COFDM is adopted in the HDTV popularization. Because it is best-suited to the needs of the terrestrial broadcasting channel, and COFDM can cope with high levels of multipath propagation, with a wide spread of delays between the received signals, it is the best choice for HDTV broadcasting.
3.3.1 Advantages of Multiple Carriers
In COFDM system, we can see it adopts a multipath system which uses multiple carriers using FDM technique. From the following analysis we can find the advantages of using multiple carriers in COFDM. In the digital modulation, suppose each symbol is transmitted with a particular phase and amplitude which are chosen from the constellation. Now imagine that the signal is received via two channels, with a relative delay between each one.
When a symbol n is transmitted, the receiver will demodulate the data by examining all the received information relating to symbol n, never mind whether it is a directly-received or a delayed one. From the figure, in the long delay(the delay is more than one symbol period), the signal received via the second path is always acting as interference. Such ISI implies that only very small levels of the delayed signal are acceptable. As in the short delay (the delay is less than one symbol period), part of the signal received via the second path acts as interference, because it only carries information belonging to a previous symbol. That is to say, if we cope with appreciable level of delayed signals, the symbol rate have to be reduced sufficiently so that the total delay spread is reduced enough to a fraction of the symbol period. Since a single carrier can certainly not satisfy the required information rate, we have to divide the high-rate data into many low-rate parallel ones to achieve the specification. This is the basic principle of FDM, which leads to the more advanced technique we are discussing now – COFDM. Now we can see the advantage of multiple carriers that the more carriers in use, with an appreciable symbol rate, the higher main stream symbol rate will achieve.
3.3.2 Advantages of Orthogonality
However, the application of multiple-carriers leads to new problems that multipath requires much larger bandwidth. This problem could fortunately be dispelled if we specify that the carriers are spaced by precisely fu=1/Tu, where Tu is the period over the receiver integrates the demodulated signal. And this is how orthogonality of COFDM realized.
The orthogonality condition should satisfy that
And the kth carrier can be written
When demodulation, multiply it by a carrier of the same frequency and integrate it to the result, all of the other carriers will be integrated to zero since they are the unwanted signals. From this aspect, we can see that it is convenient and effective to realize the multipath via the advantages of orthogonality.
A key advantage of OFDM is that it can be generated by using FFT (Fast Fourier Transformation) techniques. As an example, if we suppress the frequency offset (N-1)/2T of equation , where  and substitute this into the orthogonal expression , where t=kT/N, then the elements of IFFT vector are obtained. As a result, the OFDM signal may be generated by using the IFFT algorithm. In this example, the complex envelope,g(t), is indicated by the In-phase and Quadrature components, as described by g(t)=x(t)+jy(t).
3.3.3 Advantages of Error Correction Coding
In COFDM, a forward error correction coding is employed for an acceptable BER and a reasonably low SNR. A high SNR would not be necessary when the channel is relatively flat. Since the Uncoded OFDM is not satisfactory for use in the extremely selective channels, forward error correction (FEC) coding techniques, are used in systems where a reverse channel is not available for requesting retransmission, the delay with retransmission would be excessive, the expected number of errors would require a large number of retransmissions, or retransmission would be awkward to implement.
3.3.4 Conclusion
From all above, we can see the chief advantages of COFDM scheme in the multipath transmission, and how COFDM is satisfactory for use in the extremely selective channels, which are adopted in the HDTV broadcasting system.
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