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

62 MC-CDMA and MC-DS-CDMA1D spreading2D spreadinginterleaved2nd direction1st directionFigure 2-3One- and two-dimensional spreading schemesperformed by a two-dimensional spreading code or by two cascaded one-dimensionalspreading codes. An efficient realization of two-dimensional spreading is to use a onedimensionalspreading code followed by a two-dimensional interleaver, as illustrated inFigure 2-3 [26]. With two cascaded one-dimensional spreading codes, spreading is firstcarried out in one dimension with the first spreading code of length L 1 . In the next step,the data-modulated chips of the first spreading code are again spread with the secondspreading code in the second dimension. The length of the second spreading code is L 2 .The total spreading length with two cascaded one-dimensional spreading codes results inL = L 1 L 2 . (2.29)If the two cascaded one-dimensional spreading codes are Walsh–Hadamard codes, theresulting two-dimensional code is again a Walsh–Hadamard code with total length L.For large L, two-dimensional spreading can outperform one-dimensional spreading in anuncoded MC-CDMA system [16, 46].Two-dimensional spreading for maximum diversity gain is efficiently realized by usinga sufficiently long spreading code with L ≥ D O ,whereD O is the maximum achievabletwo-dimensional diversity (see Section 1.1.7). The spread sequence of length L has to beappropriately interleaved in time and frequency, such that all chips of this sequence arefaded independently as far as possible.Another approach with two-dimensional spreading is to locate the chips of the twodimensionalspreading code as close together as possible in order to get all chips similarlyfaded and, thus, preserve orthogonality of the spreading codes at the receiver as far aspossible [3, 42]. Due to reduced multiple access interference, low complex receivers canbe applied. However, the diversity gain due to spreading is reduced such that powerfulchannel coding is required. If the fading over all chips of a spreading code is flat, theperformance of conventional OFDM without spreading is the lower bound for this spreadingapproach; i.e. the BER performance of an MC-CDMA system with two-dimensionalspreading and Rayleigh fading which is flat over the whole spreading sequence results inthe performance of OFDM with L = 1, shown in Figure 1-3. One- or two-dimensionalspreading concepts with interleaving of the chips in time and/or frequency are lowerboundedby the diversity performance curves in Figure 1-3, which correspond to thechosen spreading code length L.