With the rise of cellular communications, the broadcast channel has gained prominence since it is an effective model of the cellular downlink channel. Multiple-input multiple-output (MIMO) communications has also gained in popularity due to its theoretically promised performance benefits over traditional single antenna systems. Combining these two theoretical objects yields the the MIMO, or vector, broadcast channel. To achieve the highest possible performance it is known that channel state information (CSI) from each user in the broadcast channel must be known at the transmitter. This requires each user to feed back this information, which is an unwanted overhead.;The first part of the dissertation discusses methods to reduce this feedback overhead by considering use of multiple receive antennas. Under the random beamforming transmit methodology, the feedback is reduced by considering only feeding back the largest SINR value observed at each user. Analysis of this reduced feedback scheme involves finding the distribution of the largest SINR over correlated random variables. Each user can also use the additional receive antennas to perform LMMSE reception. The distribution of the post-processed SINR is found and used to compute the system performance. Feedback can be reduced after LMMSE reception by feeding back only the largest post-processed SINR. Bounding techniques on the distribution function of the maximum post-processed SINR are used to evaluate the performance of this scheme. Fixed finite thresholds are shown to have no asymptotic effects on the system performance.;The second part of the thesis considers the design of thresholds as a function of the number of users to reduce feedback. The asymptotic properties of any successful threshold are derived, namely any threshold T (n) ∈ o(log n) asymptotically achieves the optimal sum-rate scaling rate while any threshold T(n) ∈ o(log n) loses all multi-user diversity. Under three proposed system performance metrics, the optimal threshold is obtained. These metrics are: constraining the average number of users providing feedback, constraining the probability that no user feeds back, and constraining the rate lost due to thresholding.;The final portion of the dissertation address the question of fairness in the random beamforming technique. To improve fairness the proportional fair sharing algorithm is proposed as a substitute for the greedy scheduling algorithm. Under the Rayleigh fading model, the asymptotic performance is found to be identical to the asymptotic performance of the greedy algorithm. The rate of convergence of the proportional fair sharing algorithm to the asymptotic performance limit is found. The distribution of the distance from the asymptotic limit is computed. Additional analysis is performed on the use of thresholds under proportional fair sharing.
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