On the Achievable Error Region of Physical Layer Authentication Techniques over Rayleigh Fading Channels
This work addresses security in wireless communication by improving authentication error bounds, but it is incremental as it focuses on refining existing theoretical models.
The paper tackles the problem of bounding the error region for physical layer authentication over Rayleigh fading channels, deriving the tightest bound on type I/II error probabilities by solving a constrained optimization problem for an attacker's strategy, with numerical results showing convergence of the proposed iterative algorithm.
For a physical layer message authentication procedure based on the comparison of channel estimates obtained from the received messages, we focus on an outer bound on the type I/II error probability region. Channel estimates are modelled as multivariate Gaussian vectors, and we assume that the attacker has only some side information on the channel estimate, which he does not know directly. We derive the attacking strategy that provides the tightest bound on the error region, given the statistics of the side information. This turns out to be a zero mean, circularly symmetric Gaussian density whose correlation matrices may be obtained by solving a constrained optimization problem. We propose an iterative algorithm for its solution: Starting from the closed form solution of a relaxed problem, we obtain, by projection, an initial feasible solution; then, by an iterative procedure, we look for the fixed point solution of the problem. Numerical results show that for cases of interest the iterative approach converges, and perturbation analysis shows that the found solution is a local minimum.