A Secure Transmission Scheme Based on Artificial Fading for Wireless CrowdSensing Networks

For secure transmission of low cost single antenna communication nodes in wireless crowdsensing networks under static channel, a physical layer communication scheme is proposed, where each digital modulated symbol is encrypted by a random key at the transmitter and decrypted with the same key at the receiver. The legal users exploit the synchronized chaotic sequence and the two-stage block interleaver to generate a complex random variable (random key), whereby its envelope obeys the Rayleigh distribution and its phase obeys the uniformly distribution. The modulated symbol is multiplied by the complex random variable (encryption) to imitate the Rayleigh fading of the channel at the transmitting end. The received symbol is divided by the identical complex random variable (decryption) to recover the transmitted message before the digital demodulation at the receiving end. Simulation results show that the bit error ratio (BER) performance of the legitimate users is consistent with the theoretical value of the Rayleigh fading channel, while the corresponding BER of the eavesdropper is too high (about 0.5) to intercept any information.

RANDOM MATRICES: THE CIRCULAR LAW

Let x be a complex random variable with mean zero and bounded variance σ2. Let Nn be a random matrix of order n with entries being i.i.d. copies of x. Let λ1, …, λn be the eigenvalues of [Formula: see text]. Define the empirical spectral distributionμn of Nn by the formula [Formula: see text] The following well-known conjecture has been open since the 1950's: Circular Law Conjecture: μn converges to the uniform distribution μ∞ over the unit disk as n tends to infinity. We prove this conjecture, with strong convergence, under the slightly stronger assumption that the (2 + η)th-moment of x is bounded, for any η > 0. Our method builds and improves upon earlier work of Girko, Bai, Götze–Tikhomirov, and Pan–Zhou, and also applies for sparse random matrices. The new key ingredient in the paper is a general result about the least singular value of random matrices, which was obtained using tools and ideas from additive combinatorics.