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

MC-CDMA 61Table 2-1 PAPR bounds of MC-CDMA uplinksignals; N c = LSpreading codeWalsh–HadamardPAPR≤ 2LGolay ≤ 4Zadoff–Chu 2(Gold ≤ 2 t(m)− 1 − t(m)+ 2 )LThe PAPR for different spreading codes can be upper-bounded for the uplink by [39]⎧⎨L−1∑⎫ 2⎬2maxc (k)⎩∣le j2πlt/T s∣ ⎭l=0PAPR ≤, (2.26)Lassuming that N c = L. Table 2-1 summarizes the PAPR bounds for MC-CDMA uplinksignals with different spreading codes.The PAPR bound for Golay codes and Zadoff–Chu codes is independent of the spreadingcode length. When N c is a multiple of L, the PAPR of the Walsh–Hadamard code isupper-bounded by 2N c .Downlink PAPRThe time samples of a downlink multi-carrier symbol assuming synchronous transmissionare given asK−1∑x v =k=0x (k)v . (2.27)The PAPR of an MC-CDMA downlink signal with K users and N c = L can be upperboundedby [39]⎧⎨K−1∑L−1∑⎫ 2⎬2maxc (k)⎩ ∣le j2πlt/T s∣ ⎭k=0 l=0PAPR ≤. (2.28)L2.1.4.3 One- and Two-Dimensional SpreadingSpreading in MC-CDMA systems can be carried out in the frequency direction, the timedirection or two-dimensional in the time and frequency direction. An MC-CDMA systemwith spreading only in the time direction is equal to an MC-DS-CDMA system. Spreadingin two dimensions exploits time and frequency diversity and is a flexible and powerfulalternative to the conventional approach with spreading in the frequency or time directiononly. A two-dimensional spreading code is a spreading code of length L where the chipsare distributed in the time and frequency directions. Two-dimensional spreading can be