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

Spatial Pre-Coding for Multi-Carrier Transmission 3276.4.5.1 Lower BoundsFor the performance analysis of different pre-coding schemes three different propagationscenarios are considered. The first environment corresponds to environment A, whereH n (1) and H n(2) have constant amplitude but random independent phase to each other.It is important to note that the superimposed channel H n at the receive antenna resultsin a fading channel due to constructive and destructive superposition of H n (1) and H n (2) .The second is environment B, where |H n (1) | and |H n(2) | are each Rice distributed with aRice factor of 10; i.e. there is a LOS component and multi-path propagation. The thirdis environment C, where |H n (1) | and |H n(2) | are each Rayleigh distributed, i.e. no LOScomponent. Each symbol s n is faded with an independent fading coefficient, assumingperfect interleaving. The symbol mapping is QPSK. Results are presented for an uncodedtransmission as well as with rate 1/2 coded transmission using convolutional codes withmemory 6. Perfect channel estimation is assumed. As reference the performance of anOFDM system with one transmit antenna (1Tx) is included in the results.Figure 6-29 presents the BER versus the SNR for different spatial pre-coding schemesin environment A. This enables the array gain to be analyzed since the diversity gain isomitted. The system is uncoded. Since the individual channels have constant amplitude theperformance of SD is identical to the performance of the 1Tx scheme. The lower bound isgiven by EGT and MRT, which perform identically in environment A. The performance of10.11Tx = SDSPCMRT = EGTBER0.010.0010.0001−2 0 2 4 6 8 10SNR in dBFigure 6-29 Achievable array gain by showing the BER versus SNR for environment A withoutchannel coding