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

310 Additional Techniques for Capacity and Flexibility EnhancementtransmitterOFDM0receivere jΦ 1, nn = 0...N c − 1OFDM1IOFDMe jΦ M − 1, nn = 0...N c − 1OFDMM − 1Figure 6-9Phase diversityIn order to achieve frequency-selective fading within the transmission bandwidth of theN c sub-channels, the phase m,n has to fulfill the condition m, n ≥ 2πf nB≥ 2πnN c, (6.10)where f n = n/T s is the nth sub-carrier frequency, T s is the OFDM symbol durationwithout a guard interval, and B = N c /T s . To increase the frequency diversity by multipletransmit antennas, the phase offset of the nth sub-carrier at the mth antenna should bechosen as m, n = 2πkmnN c, k ≥ 1, (6.11)where k is a constant factor introduced for the system design that has to be chosen largeenough (k ≥ 1) to guarantee a diversity gain. The constant k corresponds to k introducedin Section 6.3.1.1. Since no delay of the signals at the transmit antennas occurs with phasediversity, no extension of the guard interval is necessary compared to delay diversity.In Figure 6-10, the SNR gain to reach a BER of 3 × 10 −4 with two transmit antennasapplying delay diversity and phase diversity compared to a one transmit antenna schemeover the parameter k introduced in Equations (6.9) and (6.11) is shown for OFDM andOFDM-CDM. The results are presented for an indoor and outdoor scenario. The performanceof delay diversity and phase diversity is the same for the chosen system parameters,since the guard interval duration exceeds the maximum delay of the channel and the additionaldelay due to delay diversity. The curves show that gains of more than 5 dB in theindoor scenario and of about 2 dB in the outdoor scenario can be achieved for k ≥ 2and justify the selection of k = 2 as a reasonable value. It is interesting to observe thateven in an outdoor environment, which already has frequency-selective fading, significantperformance improvements can be achieved.