, feedback overhead can be reduced if the correlation property can be efficiently exploited. Let's take time-domain correlation as an example to explain the differential feedback scheme. The operations at the MS and at the BS can be described as follows: Derivation of the differential codeword matrix at the MS, = = [V(t - 1), (() 2. Quantization of the differential codeword matrix at the MS,D=argmax||D"DillFwhere D"Dillpdenotes the chordal distance between the two codeword matrices D Di Therefore, the optimal codebook is selected based on the maximum between D and the codeword matrices contained in the codebook Q. 3. Beamforming matrix reconstruction at the BS, (t) = QV(1-1) = - 4. Beamforming at the BS, y = H (t) s+n "The asymptotic performance of a coding scheme is dominated by the shortest distance between any pair of codewords. The relevant distance measure between two codewords, X1 and X2, of an orthogonal code for a non-coherent MIMO system is the chordal distance d2(X1, X2) = M - 10.5 IEEE 802. 16m downlink MIMO schemes In the above equations, N t X NS matrices V(t) and (t) denote the ideal and quantized beamforming matrices at time instant t, respectively, the columns of v ( t - 1) have unit norm and are orthogonal to (t-1) where V can be calculated from (t-1) by a Householder transformation, vi Di is the codeword matrix of the differential codebook denoted by Q. The quantization criterion maximizes the received signal power. Other criteria such as channel capacity or mean squared error can also be used. If Ns = 1, V(t 1) would be a vector (with unit norm) and the rotation matrix is given by Qv(t-1) = 1 - 200H H 0 wherein = exp(-jo) V(t-1) E and A is the phase of the first entry of V(t-1) and [1,0,0,...,0]'. The advantage of the transformed codebook is demonstrated in the example given in Figure 10- 39, where a 2 x 1 non-complex channel is assumed. The ideal beamforming vector is uniformly distributed over a semicircle for uncorrelated channels. The uniform codeword distribution of the IEEE 802.16-2009 st