Eigenvalue statistics for Collision Multiplicity estimation

In the context of wireless networks, a new technique is proposed for the estimation of the Collision Multiplicity (CM), i.e., the number of packets involved in a collision. The collision signals are observed and a sample covariance matrix of the observations is computed first. Then, an eigenvalue decomposition of this matrix is performed and the eigenvalues are sorted in descending order. Our approach is based on two properties: (i) signal eigenvalues are much larger than noise eigenvalues, (ii) noise eigenvalues are distributed according to a Tracy-Widom (TW) distribution whereas signal eigenvalues are Gaussian distributed. So each eigenvalue is tested until a TW distributed eigenvalue has been detected. When the detection occurs at step i, the CM estimates is set to i-1. Simulations results show that this approach outperforms typical approaches based on the Minimum Description Length (MDL) criterion.