Convergence results on broadband wireless communication systems and their implications

With the goal of making the best possible use of wireless communication system resources, such as power, bandwith, and allowable implementation complexity, many techniques have been proposed in the physical layer to combat the inherent impairments introduced by wireless channels: multipath fading, time delay spread and co-channel interference. This dissertation considers three promising schemes, link layer adaptation, orthogonal frequency division multiplexing (OFDM) and multiple-element antenna arrays (MEA), through which to meet the increasing demand for high performance in the current and future broadband wireless systems.; To implement adaptive transmission, channel state information (CSI) is required to adjust the transmission parameters, such as the coded modulation scheme, and/or the transmission power. One important piece of CSI is the average received signal-to-noise ratio (SNR), which is obtained by taking power measurements. This dissertation provides an accurate description of the power measurement error in the form of the probability distribution of the value of the average received power at the time of interest conditioned on an outdated measurement. This dissertation then provides a novel approach to power control under measurement uncertainty, which includes the derivation of a number of novel power control algorithms.; One of the key challenges in implementing an OFDM system is the large peak-to-mean-envelope-power-ratio (PMEPR), which brings disadvantages such as an increased complexity of the A/D and D/A converters, and a reduced efficiency of the radio frequency (RF) power amplifier. To calculate the probability distribution function (PDF) of the PMEPR, it has been widely assumed that the complex baseband bandlimited OFDM signal converges to a complex Gaussian random process as the number of subcarriers is large. This dissertation provides the first rigorous proof of this weak convergence. In addition, the analysis of the PDF of the PMEPR is advanced by employing extreme value theory, which results in a novel and simple accurate approximation of the PDF of the PMEPR for both uncoded and coded OFDM systems.; Multiple antenna technologies enable high capacities suited for wireless Internet and multimedia services, and also dramatically increase system range and reliability. For a MEA system with the restriction that the elements of the array must occupy a fixed length at either the mobile unit or at both sides, this dissertation concludes with the convergence analysis of the instantaneous mutual information I_N,N of such a MEA system under various assumptions.