ordal distance, SO does the proposed rank-three codebook. Near-optimum performance for ranks two and four. The proposed construc- tion achieves high throughput for ranks two and four. Nested structure. Clearly, the rank-one codebook just consists of the first columns of the matrices in the rank-four codebook. Further, by construc- tion, codebooks of ranks two and three are also submatrices of the rank-four codebook. Efficient computation. The householder structure greatly simplifies signal-to- interference-plus-noise ratio (SINR) computation for rank-two and rank- three precoding matrices. Link-level simulation results comparing the proposed codebook to other code- book structures are shown in the following subsections. 5.2.3.5.1 Four Node-B, Two UE Antennas, TU6 Channel Model Figure 5.2 plots the percentage throughput gains versus geometry when each code- book is compared to an antenna selection codebook. Gains are shown for antenna correlations of 0.1 and 0.5, respectively. As seen from the figure, Precoding provides significant gains over antenna selection even at high geome- tries. In particular, impressive gains are obtained at high antenna correlations. The proposed householder-based codebook constructions consistently out- perform discrete Fourier transform (DFT)-based codebook constructions. Even when the DFT-based codebooks are optimized, they suffer a 3-5% loss when compared to the proposed constructions at low geometry. At higher geometries, the performance of all codebooks is comparable. © 2009 by Taylor & Francis Group, LLC Long Term Evolution: 3GPP LTE Radio and Cellular Technology TU6 4 x 2 Corr = (0.10,0.10) Householder codebook based on Grassmanian Constant-modulus Householder codebook Optimized DFT codebook Unoptimized DFT codebook Antenna selection Geometry (dB) TU6 4 X 2 Corr = (0.50, 0.50) Householder codebook based on Grassmanian Constant-modulus Householder codebook Optimized DFT codebook Unoptimized DFT codebook Antenna selection Geometry (dB) Figure 5.2 Throughput gains over antenna selec