Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

34 FundamentalsThe following matrix–vector notation is introduced to describe multi-carrier systemsconcisely. Vectors are represented by boldface small letters and matrices by boldfacecapital letters. The symbol (·) T denotes the transposition of a vector or a matrix. Thecomplex-valued source symbols S n , n = 0,...,N c − 1, transmitted in parallel in oneOFDM symbol, are represented by the vectors = (S 0 ,S 1 ,...,S Nc −1) T . (1.45)The N c × N c channel matrix⎛⎞H 0,0 0 ··· 00 H 1,1 0H = ⎜⎝.. ..⎟. ⎠0 0 ··· H Nc −1,N c −1(1.46)is of the diagonal type in the absence of ISI and ICI. The diagonal components of H arethe complex-valued flat fading coefficients assigned to the N c sub-channels. The vectorn = (N 0 ,N 1 ,...,N Nc −1) T (1.47)represents the additive noise. The received symbols obtained after inverse OFDM aregiven by the vectorr = (R 0 ,R 1 ,...,R Nc −1) T (1.48)and are obtained byr = Hs + n. (1.49)1.2.2 Advantages and Drawbacks of OFDMThis section summarizes the strengths and weaknesses of multi-carrier modulation basedon OFDM.Advantages:– High spectral efficiency due to nearly rectangular frequency spectrum for high numbersof sub-carriers.– Simple digital realization by using the FFT operation.– Low complex receivers due to the avoidance of ISI and ICI with a sufficiently longguard interval.– Flexible spectrum adaptation can be realized, e.g. notch filtering.– Different modulation schemes can be used on individual sub-carriers which areadapted to the transmission conditions on each sub-carrier, e.g. water filling.Disadvantages:– Multi-carrier signals with high peak-to-average power ratio (PAPR) require highlinear amplifiers. Otherwise, performance degradations occur and the out-of-bandpower will be enhanced.