Artin Conjecture for p-adic Galois Representations of Function Fields

For a global function field K of positive characteristic p, we show that Artin conjecture for L-functions of geometric p-adic Galois representations of K is true in a non-trivial p-adic disk but is false in the full p-adic plane. In particular, we prove the non-rationality of the geometric unit root L-functions.Comment: Remove the condition 6|k in Lemma 3.8; final versio

Sidelobe Suppression for Capon Beamforming with Mainlobe to Sidelobe Power Ratio Maximization

High sidelobe level is a major disadvantage of the Capon beamforming. To suppress the sidelobe, this paper introduces a mainlobe to sidelobe power ratio constraint to the Capon beamforming. it minimizes the sidelobe power while keeping the mainlobe power constant. Simulations show that the obtained beamformer outperforms the Capon beamformer.Comment: 8 pages, 2 figure

Enhanced Compressive Wideband Frequency Spectrum Sensing for Dynamic Spectrum Access

Wideband spectrum sensing detects the unused spectrum holes for dynamic spectrum access (DSA). Too high sampling rate is the main problem. Compressive sensing (CS) can reconstruct sparse signal with much fewer randomized samples than Nyquist sampling with high probability. Since survey shows that the monitored signal is sparse in frequency domain, CS can deal with the sampling burden. Random samples can be obtained by the analog-to-information converter. Signal recovery can be formulated as an L0 norm minimization and a linear measurement fitting constraint. In DSA, the static spectrum allocation of primary radios means the bounds between different types of primary radios are known in advance. To incorporate this a priori information, we divide the whole spectrum into subsections according to the spectrum allocation policy. In the new optimization model, the minimization of the L2 norm of each subsection is used to encourage the cluster distribution locally, while the L0 norm of the L2 norms is minimized to give sparse distribution globally. Because the L0/L2 optimization is not convex, an iteratively re-weighted L1/L2 optimization is proposed to approximate it. Simulations demonstrate the proposed method outperforms others in accuracy, denoising ability, etc.Comment: 23 pages, 6 figures, 4 table. arXiv admin note: substantial text overlap with arXiv:1005.180

Sidelobe Suppression for Robust Beamformer via The Mixed Norm Constraint

Applying a sparse constraint on the beam pattern has been suggested to suppress the sidelobe of the minimum variance distortionless response (MVDR) beamformer recently. To further improve the performance, we add a mixed norm constraint on the beam pattern. It matches the beam pattern better and encourages dense distribution in mainlobe and sparse distribution in sidelobe. The obtained beamformer has a lower sidelobe level and deeper nulls for interference avoidance than the standard sparse constraint based beamformer. Simulation demonstrates that the SINR gain is considerable for its lower sidelobe level and deeper nulling for interference, while the robustness against the mismatch between the steering angle and the direction of arrival (DOA) of the desired signal, caused by imperfect estimation of DOA, is maintained too.Comment: 10 pages, 3 figures; accepted by Wireless Personal Communication

A Robust Beamformer Based on Weighted Sparse Constraint

Applying a sparse constraint on the beam pattern has been suggested to suppress the sidelobe level of a minimum variance distortionless response (MVDR) beamformer. In this letter, we introduce a weighted sparse constraint in the beamformer design to provide a lower sidelobe level and deeper nulls for interference avoidance, as compared with a conventional MVDR beamformer. The proposed beamformer also shows improved robustness against the mismatch between the steering angle and the direction of arrival (DOA) of the desired signal, caused by imperfect estimation of DOA.Comment: 4 pages, 2 figure

Geodesic-Einstein metrics and nonlinear stabilities

In this paper, we introduce notions of nonlinear stabilities for a relative ample line bundle over a holomorphic fibration and define the notion of a geodesic-Einstein metric on this line bundle, which generalize the classical stabilities and Hermitian-Einstein metrics of holomorphic vector bundles. We introduce a Donaldson type functional and show that this functional attains its absolute minimum at geodesic-Einstein metrics, and we also discuss the relations between the existence of geodesic-Einstein metrics and the nonlinear stabilities of the line bundle. As an application, we will prove that a holomorphic vector bundle admits a Finsler-Einstein metric if and only if it admits a Hermitian-Einstein metric, which answers a problem posed by S. Kobayashi.Comment: 21 pages, the final version, to appear in Transactions of the American Mathematical Societ