ABSTRACT This paper proposes a model for three-dimensional (3-D) wireless ad hoc networks with randomly distributed nodes and unknown node locations. In this model, the nodes are assumed to be randomly distributed in a cubic torus. The distances between neighbouring nodes (hop lengths) and the distance between thesource and destination nodes (route length) are assumed to be random. In the first part of this paper, exact analytical expressions are derived for the cumulative distribution function (CDF) and the probability density function (PDF) of the hop and route lengths.Then, these distributions are used to find the average hop length,route length and number of hops analytically and numerically. The performance of the system is studied in terms of the average route bit error rate (BER) and the optimal transmit power needed to achieve a given threshold BER to maintain network connectivity. Moreover, the performance of decode-and-forward (DF) relaying scheme over Rayleigh fading channels in the presence of cochannelinterference (CCI) is studied. It is assumed that CCI is modelled as the sum of independent-not-identically distributed Rayleigh variates.