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The authors employ a statistical method to characterise the wireless ad hoc network capacity problem. The channel parameters such as path loss and fading are considered in the analysis. Moreover, a simulation method based on the probability density function of signal-to-interference-plus-noise power-ratio is introduced. In both analysis and simulation, two receiving methods, matched filter (MF) and minimum-mean-square-error (MMSE) detector, are considered. After establishing the accuracy of the analytic approximation and comparing its results with simulation results, the scalability of a random network is studied. Moreover, the outage and ergodic capacities are determined for various network and channel parameters. It is shown that when MMSE detector is used in the network, the capacity is higher than when MF is used. When number of the nodes increases the total ergodic capacity raises, but per node capacity reduces when using both MF and MMSE detectors. It is shown that the total outage capacity reaches a maximum. This leads to the conclusion that an optimum value for the number of nodes in the network exists, which maximises the outage capacity.