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Nt1310 Unit 10 Research Paper

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2.2.1 Orthogonal Frequency-Division Multiplexing
Conventionally, the multi-carrier transmitter consists of a set of modulators, each with different carrier frequencies. The transmitter then combines the modulator outputs and generates the transmitted signal. Suppose that the N data to be transmitted are Xk, k ¼ 0; 1; . . . ; N  1, where Xk is a complex number in a given constellation, such as
QPSK or QAM. Also suppose that the kth carrier frequency for Xk is fk. Then, the complex-valued multi-carrier transmitter output is given by xðtÞ ¼
XN1
k¼0
Xkej2pfk t:
Modern communication systems often implement their transmitters and receivers digitally whenever they can. A digital transmitter will generate its output in a sampled-data fashion. By letting t ¼ nTs, where Ts is the sample interval, the digitalmulti-carrier transmitter output is now xðnTsÞ ¼
XN1
k¼0
Xkej2pfknTs :
Furthermore, if the carrier frequencies are uniformly spaced in the frequency domain by a …show more content…

fk ¼ kfS; k ¼ 0; 1; . . . ; N  1, then xðnTsÞ ¼
XN1
k¼0
Xkej2pkfSnTs :
Let fS ¼ 1=ðNTsÞ–the minimum separation to keep orthogonality among signals on different modulators–then the OFDM signal is given by xn ¼ xðnTsÞ ¼
XN1
k¼0
Xkej2pnk=N:
These carriers are called subcarriers and usually there is one more modulation to translate all these subcarriers to a higher frequency band. Except for a multiplying constant (1=N), the above formula is the equation of an N-point inverse discrete Fourier transform (IDFT). If N is a power of two, then there exist many fast and efficient algorithms and architectures for implementing such an IDFT operation. It is such efficient digital realization of the OFDM transmitter that makes the OFDMtechnology a feasible solution to advanced communication systems.Without specific time-domain windowing on the OFDMsymbol (xn) to shape its waveform, the OFDM subcarriers have sinc-shaped spectra, as shown in Figure

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