Prior performance analyses of diversity receptions over arbitrarily correlated Nakagami-  $m$   fading channels use power correlation matrix to define correlation among branches. However, the power correlation matrix cannot uniquely determine the joint probability density function of the branch amplitudes as well as the system performance. In this paper, we derive asymptotically tight and closed-form upper and lower bounds for the error rates and the outage probabilities of maximum-ratio combining, equal-gain combining, and selection combining over arbitrarily correlated Nakagami-  $m$   fading channels. The correlation between the Nakagami-  $m$   random variables is defined through the correlation matrix of the accompanying Gaussian random variables, which can uniquely determine the joint probability density function of the Nakagami-  $m$   variables. Using the analytical results and Monte Carlo simulation, we show that the performance of diversity reception systems over Nakagami-  $m$   fading channels cannot be uniquely determined by the power correlation matrix of the branches. Furthermore, we also study the factors that determine the asymptotic performance of the diversity receptions.
['Bingcheng Zhu', 'Fan Yang', 'Julian Cheng', 'Lenan Wu']
Performance Bounds for Diversity Receptions Over Arbitrarily Correlated Nakagami- $m$ Fading Channels