channel model, which has slightly higher correlation. As seen from the figure, The proposed constant-modulus codebook still outperforms DFT-based precoders at all geometries for both channel models. This holds even when the DFT-based codebook is optimized and ordered for maximum sum throughput. Using a householder codebook based on Grassmanian rank-one vectors fur- ther increases the throughput gains by 2-4%. It should be noted that the two householder-based codebooks outper- form each other under different channel conditions. However, with proper choice of the base rank-one codebook, the householder structure itself appears to achieve good performance when compared to DFT-like codebooks. With the SCME channel model, ordering seems to provide significant gain for DFT-based codebooks. However, it should be noted that ordering adds five additional bits on top of the 4-b precoding indicator. However, this 9-b composite DFT-based codebook still performs worse compared to the two 4-b householder-based designs. 5.2.3.6 Precoding for Transmit Diversity The precoding operation for transmit diversity is defined for two and four antenna ports. For transmission on two antenna ports, pe {0,1}, the outputy(i) = © 2009 by Taylor & Francis Group, LLC MIMO OFDM Schemes for 3GPP LTE 4 X 4, SCM-C channel model Householder codebook based on Grassmanian Constant-modulus Householder codebook Optimized DFT codebook + ordering Optimized DFT codebook + no ordering Unoptimized DFT codebook + no ordering Geometry (dB) 4 X 4, SCM-D Householder codebook based on Grassmanian Constant-modulus Householder codebook Optimized DFT codebook + ordering Optimized DFT codebook + no ordering Unoptimized DFT codebook + no ordering Geometry (dB) Figure 5.4 Throughput gains over unoptimized, unordered DFT codebook for various size-16 codebooks, with four UE antennas and SCM channel models. C 2009 by Taylor & Francis Group, LLC Long Term Evolution: 3GPP LTE Radio and Cellular Technology of the precoding operation is defined by Im(x()(i)) Im(x(1)(i)) for i