**3. Linear precoding for MU-MIMO system**

Keeping in mind the computational complexity of the nonlinear DPC precoding methods, the research community, as we mentioned before, gives more preference to the investigations of computationally simple linear precoding techniques. Many design metrics and conditions are

used to develop these linear precoding methods that are hard to deeply survey in one chapter. Generally, one can divide the MU-MIMO linear precoding methods in the literature into two categories - methods that formulate the design objective function for both the precoder and decoder independently such as the methods in [30, 46, 47] and methods that jointly design both the precoding and decoding matrices at the transmitter site (also called iterative method), such as the work in [20, 47-52]. In spite of the good performance joint precoding design obtains relative to the independent formulation methods, the downlink channel overload and complexity are the main drawbacks of this kind of design. One more possible classification is to distinguish between formulations that lead to a closed-form solution expressions such as the works in [53-55] versus those that lead to iterative solutions such as the works in [47, 50, 56, 57]. For comparison, formulations leading to iterative solutions tends to have higher computational complexity than closed form solution methods that are linear. Among the stateof-the-art methods in recent research works, the precoding method originally proposed by Mirette M. Sadek in [34] and based on Per-User Signal to Leakage plus Noise Ratio- General‐ ized Eigenvalue Decomposition (SLNR-GEVD) and its computationally stable extended version that appeared in [58] which is based on Per-User Signal to Leakage plus Noise Ratio-Generalized Singular Value Decomposition (SLNR-GSVD) are the best in performance. In the next section, we will review these state-of-the-art linear precoding method that seek to maximize Per-user Signal to Leakage plus Noise Ratio (SLNR), which will then be followed by a detailed derivation of our proposed precoding method which is based on maximizing Per-Antenna Signal to Leakage plus Noise Ratio (PA-SLNR) followed by simulation results under WiMAX Physical layer assuming the TDD mode of operation.
