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

58 MC-CDMA and MC-DS-CDMA2.1.4 Spreading TechniquesThe spreading techniques in MC-CDMA schemes differ in the selection of the spreadingcode and the type of spreading. Different strategies exist to map the spreading codes intime and frequency directions with MC-CDMA. Moreover, the constellation points ofthe transmitted signal can be improved by modifying the phase of the symbols to bedistinguished by the spreading codes.2.1.4.1 Spreading CodesVarious spreading codes exist which can be distinguished with respect to orthogonality,correlation properties, implementation complexity, and peak-to-average power ratio(PAPR). The selection of the spreading code depends on the given scenario. In thesynchronous downlink, orthogonal spreading codes are of advantage, since they reducethe multiple access interference compared to nonorthogonal sequences. However, in theuplink, the orthogonality between the spreading codes gets lost due to different distortionsof the individual codes. Thus, simple PN sequences can be chosen for spreading inthe uplink. If the transmission is asynchronous, Gold codes have good cross-correlationproperties. In cases where pre-equalization is applied in the uplink, orthogonality can beachieved at the receiver antenna, such that in the uplink orthogonal spreading codes canalso be of advantage.Moreover, the selection of the spreading code has influence on the PAPR of the transmittedsignal (see Chapter 4). Especially in the uplink, the PAPR can be reduced byselecting, for example, Golay or Zadoff–Chu codes [8, 39, 40, 43, 56]. Spreading codesapplicable in MC-CDMA systems are summarized in the following.Walsh–Hadamard CodesOrthogonal Walsh–Hadamard codes are simple to generate recursively by using the followingHadamard matrix generation,[ ]CL/2 CC L =L/2, ∀L = 2C L/2 −C m , m ≥ 1, C 1 = 1. (2.15)L/2The maximum number of available orthogonal spreading codes is L, which determinesthe maximum number of active users K.The Hadamard matrix generation described in Equation (2.15) can also be used toperform an L-ary Walsh–Hadamard modulation, which in combination with PN spreadingcan be applied in the uplink of an MC-CDMA system [14, 15].Fourier CodesThe columns of an FFT matrix can also be considered as spreading codes, which areorthogonal to each other. The chips are defined asc (k)l= e −j2πlk/L . (2.16)Thus, if Fourier spreading is applied in MC-CDMA systems, the FFT for spreading andthe IFFT for the OFDM operation cancels out if the FFT and IFFT have the same size;