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The outage probability of maximal-ratio combining (MRC) for a multiple-inputmultiple-output (MIMO) wireless communications system under Rician fading isgiven by the cumulative distribution function (CDF) for the largest eigenvalueof a complex noncentral Wishart matrix. This CDF has previously been expressedas a determinant whose elements are integrals of a confluent hypergeometricfunction. For the determinant elements, conventional evaluation approaches,e.g., truncation of infinite series ensuing from the hypergeometric function ornumerical integration, can be unreliable and slow even for moderate antennanumbers and Rician $ K $-factor values. Therefore, herein, we derive by handand by computer algebra also differential equations that are then solved frominitial conditions computed by conventional approaches. This is the holonomicgradient method (HGM). Previous HGM-based evaluations of MIMO relied ondifferential equations that were not theoretically guaranteed to converge, and,thus, yielded reliable results only for few antennas or moderate $ K $. Herein,we reveal that gauge transformations can yield differential equations that are{\emph{stabile}}, i.e., guarantee HGM convergence. The ensuing HGM-based CDFevaluation is demonstrated reliable, accurate, and expeditious in computing theMRC outage probability even for very large antenna numbers and values of $ K $.

Holonomic Gradient Method-Based CDF Evaluation for the Largest Eigenvalue of a Complex Noncentral Wishart Matrix