An Analytical Model of Packet Collisions in IEEE 802.15.4 Wireless Networks

Numerous studies have shown that concurrent transmissions can help to boost wireless networkperformance despite the possibility of packet collisions. However, while these works provide empiricalevidence that concurrent transmissions may be received reliably, existing signal capture models onlypartially explain the root causes of this phenomenon. We present a comprehensive mathematicalmodel for MSK-modulated signals that makes the reasons explicit and thus provides fundamentalinsights on the key parameters governing the successful reception of colliding transmissions. A majorcontribution is the closed-form derivation of the receiver bit decision variable for an arbitrary numberof colliding signals and constellations of power ratios, time offsets, and carrier phase offsets. Wesystematically explore the factors for successful packet delivery under concurrent transmissions acrossthe whole parameter space of the model. We confirm the capture threshold behavior observed inprevious studies but also reveal new insights relevant to the design of optimal protocols: We identifycapture zones depending not only on the signal power ratio but also on time and phase offsets.