Joint Design and Separation Principle for Opportunistic Spectrum Access in the Presence of Sensing Errors

We address the design of opportunistic spectrum access (OSA) strategies that allow secondary users to independently search for and exploit instantaneous spectrum availability. Integrated in the joint design are three basic components: a spectrum sensor that identifies spectrum opportunities, a sensing strategy that determines which channels in the spectrum to sense, and an access strategy that decides whether to access based on imperfect sensing outcomes. We formulate the joint PHY-MAC design of OSA as a constrained partially observable Markov decision process (POMDP). Constrained POMDPs generally require randomized policies to achieve optimality, which are often intractable. By exploiting the rich structure of the underlying problem, we establish a separation principle for the joint design of OSA. This separation principle reveals the optimality of myopic policies for the design of the spectrum sensor and the access strategy, leading to closed-form optimal solutions. Furthermore, decoupling the design of the sensing strategy from that of the spectrum sensor and the access strategy, the separation principle reduces the constrained POMDP to an unconstrained one, which admits deterministic optimal policies. Numerical examples are provided to study the design tradeoffs, the interaction between the spectrum sensor and the sensing and access strategies, and the robustness of the ensuing design to model mismatch.Comment: 43 pages, 10 figures, submitted to IEEE Transactions on Information Theory in Feb. 200

Convex Subspace Clustering by Adaptive Block Diagonal Representation

Subspace clustering is a class of extensively studied clustering methods and the spectral-type approaches are its important subclass whose key first step is to learn a coefficient matrix with block diagonal structure. To realize this step, sparse subspace clustering (SSC), low rank representation (LRR) and block diagonal representation (BDR) were successively proposed and have become the state-of-the-arts (SOTAs). Among them, the former two minimize their convex objectives by imposing sparsity and low rankness on the coefficient matrix respectively, but so-desired block diagonality cannot neccesarily be guaranteed practically while the latter designs a block diagonal matrix induced regularizer but sacrifices convexity. For solving this dilemma, inspired by Convex Biclustering, in this paper, we propose a simple yet efficient spectral-type subspace clustering method named Adaptive Block Diagonal Representation (ABDR) which strives to pursue so-desired block diagonality as BDR by coercively fusing the columns/rows of the coefficient matrix via a specially designed convex regularizer, consequently, ABDR naturally enjoys their merits and can adaptively form more desired block diagonality than the SOTAs without needing to prefix the number of blocks as done in BDR. Finally, experimental results on synthetic and real benchmarks demonstrate the superiority of ABDR.Comment: 13 pages, 11 figures, 8 table

ADE Bundles over Surfaces

This is a review paper about ADE bundles over surfaces. Based on the deep connections between the geometry of surfaces and ADE Lie theory, we construct the corresponding ADE bundles over surfaces and study some related problems

Coupling behavior between adhesive and abrasive wear mechanism of aero-hydraulic spool valves

AbstractLeakage due to wear is one of the main failure modes of aero-hydraulic spool valves. This paper established a practical coupling wear model for aero-hydraulic spool valves based on dynamic system modelling theory. Firstly, the experiment for wear mechanism verification proved that adhesive wear and abrasive wear did coexist during the working process of spool valves. Secondly coupling behavior of each wear mechanism was characterized by analyzing actual time-variation of model parameters during wear evolution process. Meanwhile, Archard model and three-body abrasive wear model were utilized for adhesive wear and abrasive wear, respectively. Furthermore, their coupling wear model was established by calculating the actual wear volume. Finally, from the result of formal test, all the required parameters for our model were obtained. The relative error between model prediction and data of pre-test was also presented to verify the accuracy of model, which demonstrated that our model was useful for providing accurate prediction of spool valve’s wear life