This dissertation, "Generalized Beamforming for Downlink of Multi-user MIMO Systems" by Zhengang, Pan, 潘振崗, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled "Generalized Beamforming for Downlink of Multi-user MIMO Systems" submitted by Pan Zhengang for the degree of Doctor of Philosophy at The University of Hong Kong in May 2004 Most research on multiple-input multiple-output (MIMO) systems has focused on single-user, point-to-point wireless communication systems. Although multi- user MIMO systems to support multiple users in the downlink is an important development, much still has to be done in this field. Existing techniques for multi- user MIMO systems fall into the class of generalized beamforming (GBF), which processes the antennas to form an abstract beam for performance enhancement given some channel information. In this thesis, several practical solutions are proposed with different performance and complexity tradeoffs, called the itera- tive nullspace-directed singular value decomposition (Iterative Nu-SVD), the it- erative pseudo-inverse with maximal-ratio-combining (Iterative Pinv-MRC), and QR triangularization with single-user sequential detection (QR-SD). Iterative Nu-SVD is based on the optimal solution for single-user MIMO trans- mission, but takes into account potential co-channel interferences. The iterative process adjusts the antenna weights from one user to another so that they fi- nally settle at a state where the users are invisible to each other and each user's performance is optimized. The derivation of necessary and sufficient conditions and complexity analysis for Iterative Nu-SVD reveal that it is more generally applicable than existing schemes, but at the cost of high computational complex- ity. Simulation results show that it is a flexible scheme that can easily trade off between users' performance and capacity by varying the number of spatially mul-tiplexing channels of the users. Moreover, the system performance is not sensitive to the spatial correlation among the antennas. Assuming single-stream communication for each user, the optimal problem of multi-user MIMO systems can be treated as two dependent optimal problems. One is the optimal transmission problem of multi-user multiple-input single- output systems. The other is the optimal receive combining problem with co- channel interferences. Iterative pseudo-inverse with minimum mean square error (Iterative Pinv-MMSE) method is proposed as a stepwise-optimal solution. Most importantly, under Zero-Forcing constraint, it is proved that a simple MRC re- ceiver can be used instead of an MMSE receiver. Simulation results demonstrate that the overall complexity of Iterative Pinv-MRC is much lower than that of the Iterative Nu-SVD, while achieving the same error probability performance. To further reduce complexity, the QR-SD method is proposed for the multi- stream scenario. This allows each user to be self-interfered with its own streams while keeping all the users orthogonal. A closed-form solution can then be found for the base station antenna weights. In order to minimize degradation in perfor- mance, triangularization of the signal streams for each user is proposed so that a simple decision feedback equalizer can be used to decode the signal streams with reasonable performance and complexity. Finally, the GBF schemes are combined with orthogonal frequency division multiplexing (OFDM) to support multiple users over frequency selective fading channels. This enables the actual performance of the proposed schemes to be evaluated in the presence