Distribution of the Largest or the Smallest Characteristic Root Under Null Hypothesis Concerning Complex Multivariate Normal Populations

Tightness of Jensen’s Bounds and Applications to MIMO Communications

“…These results have been effectively applied to analyze the performance of SU-MIMO systems in different particular cases. More specifically, the joint probability density function (pdf) of ordered eigenvalues [9,10] was used to evaluate the information theoretical limits of SU-MIMO systems, while the pdfs of the smallest eigenvalue [11] and largest eigenvalue [12,13] have been utilized for designing antenna selection and multichannel beamforming schemes.…”

Exact and Asymptotic Analysis of Largest Eigenvalue Based Spectrum Sensing

“…When σ 2 cn = 1, the above result reduces to the result in (Khatri, 1964). By elementary manipulations, F c x |σ 2 cn can be simplified to …”

“…For the signal model in the last section, computable closed-form expressions for the largest eigenvalue distributions of central and non-central (non-central matrix M b e i n gr a n ko n e ) Wishart matrices can be derived from the results in (Kang & Alouini, 2003;Khatri, 1964). Specifically, assuming independent and identically distributed (i.i.d) entries in the received data matrices Y for both hypotheses, the matrix variate distribution of Y under H 0 is…”

“…Then the joint eigenvalue distribution of the covariance matrix R is derived by using the result in (James, 1964). Finally, following steps in (Khatri, 1964) the cumulative distribution function (CDF) of the largest eigenvalue of the covariance matrix R, denoted by F c (x |σ 2 cn ), is derived as…”

“…Firstly we derive the exact largest eigenvalue distributions for central and non-central Wishart matrices. We modify the results on the largest eigenvalue distributions from (Dighe et al, 2003;Kang & Alouini, 2003;Khatri, 1964) in order to derive distribution functions suitable for performance analysis. As a result we obtain exact characterizations for both the false alarm probability and the probability of missed detection.…”