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This paper considers the cooperation between a cognitive system and a primary system where multiple cognitive base stations (CBSs) relay the primary user's (PU) signals in exchange for more opportunity to transmit their own signals. The CBSs use amplify-and-forward (AF) relaying and coordinated beamforming to relay the primary signals and transmit their own signals. The objective is to minimize the overall transmit power of the CBSs given the rate requirements of the PU and the cognitive users (CUs). We show that the relaying matrices have unity rank and perform two functions: Matched filter receive beamforming and transmit beamforming. We then develop two efficient algorithms to find the optimal solution. The first one has a linear convergence rate and is suitable for distributed implementation, while the second one enjoys superlinear convergence but requires centralized processing. Further, we derive the beamforming vectors for the linear conventional zero-forcing (CZF) and prior zero-forcing (PZF) schemes, which provide much simpler solutions. Simulation results demonstrate the improvement in terms of outage performance due to the cooperation between the primary and cognitive systems. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of designing the projection matrix \Phi for a compressive sensing (CS) system in which the dictionary \Psi is assumed to be given. The optimal projection matrix design is formulated in terms of finding those \Phi such that the Frobenius norm of the difference between the Gram matrix of the equivalent dictionary \Phi \Psi and the identity matrix is minimized. A class of the solutions is derived in a closed-form, which is a generalization of the existing results. More interestingly, it is revealed that this solution set is characterized by an arbitrary orthonormal matrix. This freedom is then used to further enhance the performance of the CS system by minimizing the coherence between the atoms of the equivalent dictionary. An alternating minimization-based algorithm is proposed for solving the corresponding minimization problem. Experiments are carried out and simulations show that the projection matrix obtained by the proposed approach significantly improves the signal recovery accuracy of the CS system and outperforms those by existing algorithms. [ABSTRACT FROM PUBLISHER]

The aim of this paper is to develop efficient online adaptive algorithms for the generalized eigen-decomposition problem which arises in a variety of modern signal processing applications. First, we reinterpret the generalized eigen-decomposition problem as an unconstrained minimization problem by constructing a novel cost function. Second, by applying projection approximation method and recursive least-square (RLS) technique to the cost function, a parallel adaptive algorithm for a basis for the r-dimensional (r > 0) dominant generalized. eigen-subspace and a sequential algorithm based on deflation technique for the first v-dominant generalized eigenvectors are derived. These algorithms can be viewed as counterparts of the extended projection approximation subspace tracking (PAST) and PASTd algorithms, respectively. Furthermore, we modify the parallel algorithm to explicitly estimate the first v-generalized eigenvectors in parallel, not the generalized eigen-subspace. More important, the modified parallel algorithm can be used to extract multiple generalized eigenvectors of two nonstationary sequences, while the proposed sequential algorithm lacks this ability because of slow convergence of minor generalized eigenvectors due to error propagation of the deflation technique. Third, following convergence analysis methods for PAST and PASTd, we prove the asymptotic convergence properties of the proposed algorithms. Finally, computer simulations are performed to investigate the accuracy and the speed advantages of the proposed algorithms. [ABSTRACT FROM AUTHOR]