 transmitter, ZF-precoding requires increased feedback to achieve the full multiplexing gain. Hence, inaccurate channel state information at the transmitter may result in significant loss of performance due to residual interference among transmit streams. Dirty paper coding is a coding technique that cancels known interference without power penalty, provided that the transmitter has perfect knowledge of the interfering signals regardless of whether the receiver has knowledge of channel state information. This category includes Costa precoding [71], Tomlinson-Harashima precoding [15,31], and the vector perturbation technique [73]. Vector pertur- bation uses modulo operation at the transmitter to perturb the transmitted signal vector to avoid the transmit power enhancement incurred by zero-forcing methods. The optimal perturbation method is found by solving a minimum distance problem and thus can be implemented using sphere encoding or full search-based algorithms [57]. In the downlink direction of a precoded MU-MIMO system (alternatively known as broadcast channel in the literature) with N transmitter antennas at the BS and one receive antenna for the kth CHAPTER 10 The IEEE 802. 16m Physical Layer (Part II) user, the input-output relationship can be written as yk = htxx-nk,k = ,2, Nu, where X = is the N X 1 vector of weighted transmitted symbols Si, yk and Nk are the received signal and noise, respectively, hk is the kth N X 1 channel vector, where matrix H = [h1,h2, is the X N complex-valued downlink channel matrix and Wk is the kth N X 1 normalized linear precoding vector. The mathematical relationship for the input and output of a precoded MU-MIMO system in the uplink (alternatively known as multiple access channel in the literature) with N1 receive antennas at BS and one transmit antenna for each user can be written as y = + n where SkVk is the weighted complex-valued modulated symbol from user k, y = [y1,y2,...,ynr]" and n = are the Nr X 1 vectors of received signal and noise, respectively, hk is the kth Nr 