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This paper studies spatial capacity in a stochastic wireless ad hoc network. We propose a novel signal-to-interference-ratio (SIR) threshold based scheduling scheme with multi-stage probing and data transmission, where each transmitter iteratively decides to further probe or stay idle, depending on whether the estimated SIR in the proceeding probing is no smaller than a predefined threshold. Though the locations of the initial transmitters can be modeled as a homogeneous Poisson Point Process (PPP), the SIR based scheduling makes the PPP model no longer applicable in the subsequent probing and data transmission phases. We first focus on single-stage probing and find that when the SIR threshold is set sufficiently small to assure an acceptable network interference level, the proposed scheme can greatly outperform the reference scheme without any transmission scheduling in terms of spatial capacity. We clearly characterize the spatial capacity with exact/approximate closed-form expressions, by proposing a new approximate approach to deal with the correlated SIR distributions over non-PPPs. Then, we successfully extend to multi-stage probing, by properly designing the multiple SIR thresholds to assure gradual improvement of the spatial capacity. Furthermore, we analyze the impact of multi-stage probing overhead and present a probing-capacity tradeoff in scheduling design. Finally, extensive numerical results are presented to demonstrate the scheduling performance.

On Spatial Capacity of Wireless Ad Hoc Networks with Threshold Based Scheduling