Effect Analysis of Spreading Factor on Link Connection Probability in Finite CDMA-Based Ad Hoc Networks

In this paper, we investigate the relationship between link connection probability ( Ps) and spreading factor (SF) by analyzing the complementary cumulative distribution function (CCDF) of signal to interference ratio (SIR) for practical finite CDMA-based ad hoc networks. Modelling the nodes distribution with binomial point process (BPP), the network is provided as a bounded area with all nodes randomly deployed. Focused on a typical transmitter-receiver pair, we derive the expression of Ps, which is the CCDF of SIR experienced by the arbitrarily located receiver. Taking numerical and empirical analyses on the theoretical formula, we find that only within a certain range, increasing SF could result in an obvious improvement of Ps, while SF reaches some certain value, Ps will be stable. Besides, the efficiency of adjusting SF to increase Ps would be progressively weakened with the interferences number increasing. The CCDF obtained allows an precise estimation on average SIR. Meanwhile, it could be used to determine a critical SF to maintain a high link connection probability at the lowest cost of data rate.