Random Matrix Theory And Performance Analysis Of Multiple-Input Multiple-Output Communication Systems

During the past decade, multiple-input multiple-output (MIMO) has become a very hot research topic due to it great potential in high spec-tral efficiency and link robustness. In analyzing the performance of MIMO systems, a powerful mathematical tool, random matrix theory, has attract-ed considerable attention. In this thesis, we apply random matrix theory to analyze the performance of different MIMO techniques under various fading conditions. To be specific, our work covers four main aspects, as detailed below.1. We investigate the exact error rate performance of the MIMO multi-channel bcamforming (MIMO MB) under the double-scattering chan-nel. A general framework for deriving the marginal distribution of each ordered cigenvalue is developed, under which we present an ex-act expression for the marginal cigenvalue distribution of the double-scattering channel matrix. Based on the marginal eigenvalue distri-bution, we get an exact expression on the symbol error rate (SER) of the MIMO MB.2. We investigate the asymptotic error rate performance of the MIMO MB under the double-scattering channel. In order to get the asymp-totic expansion on the marginal eigenvalue distribution, which is es sential to the asymptotic analysis, we propose a "layer-by-layer" op-eration procedure that turns out to be very effective in solving the non-differentiable dilemma. Based on the asymptotic expansion, we present exact expressions on the diversity gain and array gain of the MIMO MB. Analysis on these exact expressions offers important in-sights into the double-scattering aspects of the fading channel.3. We investigate the connections between two spatial diversity tech-niques, orthogonal space-time codes (OSTBC) and MIMO single-channel bcamforming (MIMO BF), under the assumption of general fading condition. The two techniques were studied in the literature extensively and independently. However, we formally prove that they arc indeed closely related to each other:under general fading condi-tion, the diversity gain of OSTBC is always equal to that of MIMO BF; although MIMO BF attains a higher array gain over OSTBC, the difference in this gain is dominated by the number of the transmit an-tennas. Using these connections, we can solve many open problems in the area of asymptotic analysis.4. We investigate the marginal distribution of the smallest eigenvalue of Wishart matrix. By using a new deriving method, we present an exact expression for the marginal eigenvalue distribution, which ap-plies for arbitrary parameters and is friendly to both integration and differentiation. The new result makes it possible to analyze the false alarm probability of the eigenvalue-based spectrum sensing algorithm in a closed form manner.