Derivation of the Maximum Capacity Using the Jacobian Transformation Method for Systems Employing Adaptive Cooperation

The performance of cooperative transmission in wireless systems depends on the maximum signal quality from multiple transmission sources. The knowledge of the probabilistic distribution for the maximum statistics, therefore, plays an important role in determining the system performance. Obtaining the distribution in many cases relies on experimental results, especially when random variables of interest are mutually correlated. In this paper, we provide a derivation method for the maximum distribution using the Jacobian transformation rule, and investigate the performance of systems employing adaptive cooperation among remote antennas. A closed-form expression of the maximum achievable capacity is derived and verified by computer simulation.