eme is often referred to as Per-Antenna Rate Control (PARC). The decoding complexity of the ML receiver can be reduced using a linear filter to separate the transmitted data streams, and then independently decode each stream. The ZF and MMSE linear detectors are examples of such receivers. The ZF matrix filter that separates the received signal into its component streams detector is given by: (10-39) where G ZF is an N X Nr matrix that inverts the channel matrix and H denotes the Moore-Penrose inverse of the channel matrix H. The output of the ZF receiver is obtained as follows: (10-40) Superscript(")Given a matrix A and vector b and equation Ax = b, we find the vector X that minimizes Ax - b|. Using the orthogonality principle, the error is taken perpendicular to the estimation vector such that (Ax-b) - = 0 which implies that AHAx = AHb(since x #)(), or X = (AHA)-1A One should note that Ax = A(AHA) AHb. The matrix A = (AHA)-1AH is defined as the Moore-Penrose inverse of the matrix A. If AH A is not invertible, the SVD algorithm is used to calculate the matrix pseudo-inverse. In that case, we may write A = VKUH and seek X such that |VKU bl is minimized. Using the orthogonality principle, we have or (assuming x#0) = 0 such that U- = 0, multiplying both sides by 2 yields U- = 0. The latter is true when 1butherefore CHAPTER 10 The IEEE 802. 16m Physical Layer (Part II) which shows that the ZF receiver decomposes the channel matrix into parallel scalar channels with additive spatially-colored noise. Each scalar channel is then decoded independently, irrespective of noise correlation across the processed streams. The ZF receiver transforms the joint decoding problem into single stream decoding problems, thereby significantly reducing receiver complexity. This complexity reduction is achieved at the expense of noise enhancement, which in general results in a significant performance degradation (compared to the ML decoder). The diversity order achieved by each of the individual data streams equals Nr - N + 1. Figure 10-