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A novel viewpoint based on the generalized approach to signal processing in the presence of noise and devoted to the collision
resolution problem is introduced in this paper for wireless slotted random access sensor networks. Signal separation principles borrowed from signal processing problems are used. The received collided packets are not discarded in this approach but are exploited to extract each individual sensor node packet information. In particular, if k sensor nodes collide in a given time slot, they repeat their transmission for a total of k times so that k copies of the collided packets are received. Then the receiver has to resolve a k x k source-mixing problem and separate each individual sensor node. The generalized receiver does not introduce throughput penalties since it requires only k slots to transmit k colliding packets. In
the course of analysis, we consider four channels models: ideal additive white Gaussian noise channel, in which the i-th sensor node’s gain is a deterministic but unknown constant; non-fading channel with power control but arbitrary phase, in which the amplitude of the i-th sensor node’s gain is constant (may be unknown), whereas the phase is random and uniformly distributed within the limits of the interval [0,2π]; Rayleigh fading channel, in which the phase is uniformly distributed within the limits of the interval [0,2π], whereas the amplitude is distributed with the parameter, σA and the amplitude and phase are independent; Rician fading channel, in which the phase is uniformly distributed within the limits of the interval [0,2π], whereas the amplitude is Rician distributed with the parameter A and σA and the amplitude and phase are independent. Performance issues that are related to the implementation of the collision detection algorithm based on the generalized approach to signal processing in the presence of noise demonstrate a great superiority in comparison with well-known methods. The protocol’s parameters are optimized to maximize the system throughput. Under the use of the generalized approach to signal processing in the presence of noise, the system throughput is higher in comparison with modern methods and algorithms.
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