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Parametric frugal sensing of power spectra for moving average models
 IEEE Trans. Signal Process
, 2015
"... Abstract—Wideband spectrum sensing is a fundamental component of cognitive radio and other applications. A novel frugal sensing schemewas recently proposed as ameans of crowdsourcing the task of spectrum sensing. Using a network of scattered lowend sensors transmitting randomly filtered power meas ..."
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Abstract—Wideband spectrum sensing is a fundamental component of cognitive radio and other applications. A novel frugal sensing schemewas recently proposed as ameans of crowdsourcing the task of spectrum sensing. Using a network of scattered lowend sensors transmitting randomly filtered power measurement bits to a fusion center, a nonparametric approach to spectral estimation was adopted to estimate the ambient power spectrum. Here, a parametric spectral estimation approach is considered within the context of frugal sensing. Assuming a MovingAverage (MA) representation for the signal of interest, the problem of estimating admissible MA parameters, and thus the MA power spectrum, from single bit quantized data is formulated. This turns out being a nonconvex quadratically constrained quadratic program (QCQP), which is NP–Hard in general. Approximate solutions can be obtained via semidefinite relaxation (SDR) followed by randomization; but this rarely produces a feasible solution for this particular kind of QCQP. A new Sequential Parametric Convex Approximation (SPCA) method is proposed for this purpose, which can be initialized from an infeasible starting point, and yet still produce a feasible point for the QCQP, when one exists, with high probability. Simulations not only reveal the superior performance of the parametric techniques over the globally optimum solutions obtained from the nonparametric formulation, but also the better performance of the SPCA algorithm over the SDR technique. Index Terms—Cognitive radio, distributed spectrum sensing, parametric spectral analysis, movingaverage processes, quantization, quadratically constrained quadratic programming (QCQP), semidefinite programming (SDP) relaxation. I.
An Iterative Approach to Nonconvex QCQP with Applications in Signal Processing
"... AbstractThis paper introduces a new iterative approach to solve or to approximate the solutions of the nonconvex quadratically constrained quadratic programs (QCQP). First, this constrained problem is transformed to an unconstrained problem using a specialized penaltybased method. A tight upperbo ..."
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AbstractThis paper introduces a new iterative approach to solve or to approximate the solutions of the nonconvex quadratically constrained quadratic programs (QCQP). First, this constrained problem is transformed to an unconstrained problem using a specialized penaltybased method. A tight upperbound for the alternative unconstrained objective is introduced. Then an efficient minimization approach to the alternative unconstrained objective is proposed and further studied. The proposed approach involves power iterations and minimization of a convex scalar function in each iteration, which are computationally fast. The important design problem of multigroup multicast beamforming is formulated as a nonconvex QCQP and solved using the proposed method.