it antennas is assumed to be 4 a (wavelength) and 0.5 a for low and high correlation cases, respectively. One spatial stream is transmitted. The information is coded with R = 0.5 and modulated with 16 QAM. Three types of codebooks are compared in the figures; i.e. the conventional IEEE 802.16-2009 standard base codebook, the DFT codebook, and the transformed codebook. It is observed that under the above assumptions, the transformed codebook has better performance relative vi In linear algebra, Householder transformation is defined as a linear transformation that describes a reflection about a plane or hyper-plane containing the origin. Householder transformations are widely used in linear algebra to perform QR decompositions. This is a linear transformation given by the Householder matrix Q = I - 2uuH where I denotes the identity matrix and u is given as a column unit vector. The Householder matrix has the following properties: it is hermitian, i.e., Q = QH; and it is unitary, i.e., Q- 1 = QH CHAPTER 10 The IEEE 802. 16m Physical Layer (Part II) 4-bit DFT Codebook 6-bit Legacy Base Codebook 6.5-bit Transformed Codebook 3.5-bit Transformed Codebook SNR (dB) FIGURE 10-41 A comparison of the performance of closed-loop SU-MIMO rate-1 codebooks in highly-correlated channels (0.5) and angle spread 3°) to the legacy base codebook and the DFT codebook (see Figure 10-43 for a comparison of the performance of transformed, DFT, and legacy base codebooks). The user only knows the instantly average sub-band interference power for CQI calculation, and an identity matrix for the interference cell is used for average power calculation. After scheduling of all cells, the real interference precoding is used for detection because wrap-around simulation is used. All of these three cases are considered to have a CQI feedback delay of 5 ms. To assist in the calculation of the precoding matrix for SU-MIMO or MU-MIMO, the BS may request the MS to transmit a sounding signal in a UL sounding channel. The BS may map the measured UL channel