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Register a new userSecure Massive IoT Using Hierarchical Fast Blind Deconvolution
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Added by
Benedikt Gro{\\ss}
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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The Internet of Things and specifically the Tactile Internet give rise to significant challenges for notions of security. In this work, we introduce a novel concept for secure massive access. The core of our approach is a fast and low-complexity blind deconvolution algorithm exploring a bi-linear and hierarchical compressed sensing framework. We show that blind deconvolution has two appealing features: 1) There is no need to coordinate the pilot signals, so even in the case of collisions in user activity, the information messages can be resolved. 2) Since all the individual channels are recovered in parallel, and by assumed channel reciprocity, the measured channel entropy serves as a common secret and is used as an encryption key for each user. We will outline the basic concepts underlying the approach and describe the blind deconvolution algorithm in detail. Eventually, simulations demonstrate the ability of the algorithm to recover both channel and message. They also exhibit the inherent trade-offs of the scheme between economical recovery and secret capacity.
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In the blind deconvolution problem, we observe the convolution of an unknown filter and unknown signal and attempt to reconstruct the filter and signal. The problem seems impossible in general, since there are seemingly many more unknowns than knowns . Nevertheless, this problem arises in many application fields; and empirically, some of these fields have had success using heuristic methods -- even economically very important ones, in wireless communications and oil exploration. Todays fashionable heuristic formulations pose non-convex optimization problems which are then attacked heuristically as well. The fact that blind deconvolution can be solved under some repeatable and naturally-occurring circumstances poses a theoretical puzzle. To bridge the gulf between reported successes and theorys limited understanding, we exhibit a convex optimization problem that -- assuming signal sparsity -- can convert a crude approximation to the true filter into a high-accuracy recovery of the true filter. Our proposed formulation is based on L1 minimization of inverse filter outputs. We give sharp guarantees on performance of the minimizer assuming sparsity of signal, showing that our proposal precisely recovers the true inverse filter, up to shift and rescaling. There is a sparsity/initial accuracy tradeoff: the less accurate the initial approximation, the greater we rely on sparsity to enable exact recovery. To our knowledge this is the first reported tradeoff of this kind. We consider it surprising that this tradeoff is independent of dimension. We also develop finite-$N$ guarantees, for highly accurate reconstruction under $Ngeq O(k log(k) )$ with high probability. We further show stable approximation when the true inverse filter is infinitely long and extend our guarantees to the case where the observations are contaminated by stochastic or adversarial noise.
Sparse blind deconvolution is the problem of estimating the blur kernel and sparse excitation, both of which are unknown. Considering a linear convolution model, as opposed to the standard circular convolution model, we derive a sufficient condition for stable deconvolution. The columns of the linear convolution matrix form a Riesz basis with the tightness of the Riesz bounds determined by the autocorrelation of the blur kernel. Employing a Bayesian framework results in a non-convex, non-smooth cost function consisting of an $ell_2$ data-fidelity term and a sparsity promoting $ell_p$-norm ($0 le p le 1$) regularizer. Since the $ell_p$-norm is not differentiable at the origin, we employ an $epsilon$-regularized $ell_p$-norm as a surrogate. The data term is also non-convex in both the blur kernel and excitation. An iterative scheme termed alternating minimization (Alt. Min.) $ell_p-ell_2$ projections algorithm (ALPA) is developed for optimization of the $epsilon$-regularized cost function. Further, we demonstrate that, in every iteration, the $epsilon$-regularized cost function is non-increasing and more importantly, bounds the original $ell_p$-norm-based cost. Due to non-convexity of the cost, the accuracy of estimation is largely influenced by the initialization. Considering regularized least-squares estimate as the initialization, we analyze how the initialization errors are concentrated, first in Gaussian noise, and then in bounded noise, the latter case resulting in tighter bounds. Comparisons with state-of-the-art blind deconvolution algorithms show that the deconvolution accuracy is higher in case of ALPA. In the context of natural speech signals, ALPA results in accurate deconvolution of a voiced speech segment into a sparse excitation and smooth vocal tract response.
We investigate the optimality and power allocation algorithm of beam domain transmission for single-cell massive multiple-input multiple-output (MIMO) systems with a multi-antenna passive eavesdropper. Focusing on the secure massive MIMO downlink transmission with only statistical channel state information of legitimate users and the eavesdropper at base station, we introduce a lower bound on the achievable ergodic secrecy sum-rate, from which we derive the condition for eigenvectors of the optimal input covariance matrices. The result shows that beam domain transmission can achieve optimal performance in terms of secrecy sum-rate lower bound maximization. For the case of single-antenna legitimate users, we prove that it is optimal to allocate no power to the beams where the beam gains of the eavesdropper are stronger than those of legitimate users in order to maximize the secrecy sum-rate lower bound. Then, motivated by the concave-convex procedure and the large dimension random matrix theory, we develop an efficient iterative and convergent algorithm to optimize power allocation in the beam domain. Numerical simulations demonstrate the tightness of the secrecy sum-rate lower bound and the near-optimal performance of the proposed iterative algorithm.
Multichannel blind deconvolution is the problem of recovering an unknown signal $f$ and multiple unknown channels $x_i$ from their circular convolution $y_i=x_i circledast f$ ($i=1,2,dots,N$). We consider the case where the $x_i$s are sparse, and convolution with $f$ is invertible. Our nonconvex optimization formulation solves for a filter $h$ on the unit sphere that produces sparse output $y_icircledast h$. Under some technical assumptions, we show that all local minima of the objective function correspond to the inverse filter of $f$ up to an inherent sign and shift ambiguity, and all saddle points have strictly negative curvatures. This geometric structure allows successful recovery of $f$ and $x_i$ using a simple manifold gradient descent (MGD) algorithm. Our theoretical findings are complemented by numerical experiments, which demonstrate superior performance of the proposed approach over the previous methods.
This paper presents a novel framework for traffic prediction of IoT devices activated by binary Markovian events. First, we consider a massive set of IoT devices whose activation events are modeled by an On-Off Markov process with known transition probabilities. Next, we exploit the temporal correlation of the traffic events and apply the forward algorithm in the context of hidden Markov models (HMM) in order to predict the activation likelihood of each IoT device. Finally, we apply the fast uplink grant scheme in order to allocate resources to the IoT devices that have the maximal likelihood for transmission. In order to evaluate the performance of the proposed scheme, we define the regret metric as the number of missed resource allocation opportunities. The proposed fast uplink scheme based on traffic prediction outperforms both conventional random access and time division duplex in terms of regret and efficiency of system usage, while it maintains its superiority over random access in terms of average age of information for massive deployments.
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