While several recent matrix completion methods are developed to deal with non-uniform observation probabilities across matrix entries, very few allow the missingness to depend on the mostly unobserved matrix measurements, which is generally ill-posed. We aim to tackle a subclass of these ill-posed settings, characterized by a flexible separable observation probability assumption that can depend on the matrix measurements. We propose a regularized pairwise pseudo-likelihood approach for matrix completion and prove that the proposed estimator can asymptotically recover the low-rank parameter matrix up to an identifiable equivalence class of a constant shift and scaling, at a near-optimal asymptotic convergence rate of the standard well-posed (non-informative missing) setting, while effectively mitigating the impact of informative missingness. The efficacy of our method is validated via numerical experiments, positioning it as a robust tool for matrix completion to mitigate data bias.

Wind power forecasting has drawn increasing attention among researchers as the consumption of renewable energy grows. In this paper, we develop a deep learning approach based on encoder-decoder structure. Our model forecasts wind power generated by a wind turbine using its spatial location relative to other turbines and historical wind speed data. In this way, we effectively integrate spatial dependency and temporal trends to make turbine-specific predictions. The advantages of our method over existing work can be summarized as 1) it directly predicts wind power based on historical wind speed, without the need for prediction of wind speed first, and then using a transformation; 2) it can effectively capture long-term dependency 3) our model is more scalable and efficient compared with other deep learning based methods. We demonstrate the efficacy of our model on the benchmark real-world datasets.

In this paper, we study the implicit bias of gradient descent for sparse regression. We extend results on regression with quadratic parametrization, which amounts to depth-2 diagonal linear networks, to more general depth-$N$ networks, under more realistic settings of noise and correlated designs. We show that early stopping is crucial for gradient descent to converge to a sparse model, a phenomenon that we call \emph{implicit sparse regularization}. This result is in sharp contrast to known results for noiseless and uncorrelated-design cases. We characterize the impact of depth and early stopping and show that for a general depth parameter $N$, gradient descent with early stopping achieves minimax optimal sparse recovery with sufficiently small initialization $w_0$ and step size $\eta$. In particular, we show that increasing depth enlarges the scale of working initialization and the early-stopping window so that this implicit sparse regularization effect is more likely to take place.

We consider cooperative transmission in wireless relay networks, in which a source communicates with the destination with the help of a set of N cooperating amplify-and-forward relays. The relay weights are obtained to maximize the received signal-to-noise ratio at the destination, subject to individual power constraint. We consider two schemes that have appeared in the literature, i.e., (i) the optimal weight vector design method, which has been solved via second-order cone programming plus a bisection search, with complexity of O(N3.5), and (ii) the one-bit feedback phase control scheme, which has been formulated as a binary quadratic programming and has been solved for exact solution via exhaustive search. We propose algorithms for these two problems that have substantially reduced complexity, i.e., O(N log2N) or O(N) for the first problem, and polynomial time O(N log2N) for the second problem.

A wireless network with one source, one destination, one eavesdropper, and multiple decode-and-forward relays is considered. A two-slot cooperative relaying scheme is proposed that targets at maximizing the secrecy rate. In the first slot, the source transmits the information bearing signal, and at the same time, it cooperates with the destination in jamming the eavesdropper without creating interference at the relay. In the second slot, one optimally selected relay retransmits the decoded source signal, and at the same time, that particular relay cooperates with the source to jam the eavesdropper without creating interference at the destination. Optimal relay selection and also optimal power allocation among the first/second slot data signal and jamming noise are proposed. It is shown that the secrecy rate of the proposed scheme scales with the total system powerP0and the number of available relaysKaccording to 1/2log2(1 +P0/8logK) - 1.6 bits/channel use . Although the proposed power allocation and relay selection assume global CSI available, the performance under imperfect relay CSI is also investigated. Also, the performance under distributed relay selection with limited feedback is demonstrated.

We consider a Gaussian wiretap channel model with a single-antenna source, destination and eavesdropper. The communication is assisted by multiple multiantenna helpers that transmit noise to confound the eavesdropper. First, we consider a nulling scheme, in which each helper independently transmits noise, designed to maximize the system secrecy rate while creating no interference to the destination. In this scheme, each helper requires only local relay-destination channel state information (CSI). When global CSI is available at the relays, the nulling scheme is not optimal. The optimal jamming noise structure is also provided under global CSI. Interestingly, it is shown both analytically and via simulations that, despite its reduced CSI requirements, the nulling scheme may have secrecy rate performance that is very close to the optimal one. The probability of outage of the nulling scheme is provided in closed form based on the statistics of the eavesdropper CSI.

A wireless relay channel is considered, consisting of a multi-antenna source, a single-antenna destination, a single-antenna eavesdropper and a set of multi-antenna relays (helpers) that act as jammers to the eavesdropper. Each helper knows only its own link to the receiver and independently transmits jamming noise, lying in the null space of its own link to the destination, thus causes no interference to the destination. The source, knowing the main channel explicitly and having statistical information on the eavesdropper channel, designs the input covariance matrix so that the secrecy rate is maximized subject to an outage probability constraint and a sum power constraint. We show that the optimal input covariance matrix has rank one. Assuming that the eavesdropper channels follow a zero-mean Gaussian distribution with known covariance, the outage probability and outage secrecy rate are derived in closed form. Simulation results in support of the analysis are provided.

This paper presents a single loop 3rdorder 5-bit audio ΣΔ modulator with feed forward path. Feed forward technology relaxes the amplifier design requirement by reducing output swing of the integrators. Chopper stabilization technology is employed to mitigate the flicker noise introduced by 1stintegrator. A kind of asynchronous successive approximation (SAR) quantizer without extra fast clock replaces the traditional flash quantizer. Two voltage reference buffers are integrated on this chip as the input stages of Vrefpand VCMOto simplify off-chip circuits. Simulation results show that the modulator achieves 120dB SNDR under 5 kHz input signal within 20Hz~24kHz bandwidth. The modulator alone consumes only 20mW and the overall power consumption is less than 60mW from 3.3V supply. The active core area is 2.3×1 mm2fabricated in 0.18μm standard CMOS.

The paper considers transmit beamforming for physical-layer multicasting in a wireless system consisting of a single transmitter with multiple antennas and multiple single antenna users. The beamforming weights are obtained so that the transmitted power is minimized subject to meeting the minimum signal-to-noise (SNR) requirements of each user. As in previous works, semidefinite programming (SDP) relaxation is considered. The contribution of this paper lies in that it provides effective and convergent algorithms to obtain the solution for the cases in which SDP yields a solution with rank greater than one. Two methods are proposed, namely, the coordinate descent method, which is applicable for the case of at least as many transmit antennas as users, and the p-norm approximation, which is is applicable for general case. Numerical results are presented to illustrate the performance of the proposed algorithms.

A Gaussian multiple-antenna wiretap channel model is considered, where there exists a transmitter equipped with multiple antennas, a legitimate receiver equipped with a single antenna, and an eavesdropper equipped with multiple antennas. We study the problem of finding the optimal input covariance that maximizes the ergodic secrecy rate subject to a power constraint, assuming that full information on the legitimate channel is available to the transmitter, but only statistical information on the eavesdropper channel is known. More specifically, we investigate the case of MIMO Rician fading for the eavesdropper channel. We show that the optimal input covariance has rank one, which allows us to reduce the original optimization problem to a smooth one variable optimization problem. We propose a Newton-type method for a local maximizer, and Piyavskii's algorithm for the global maximizer. Numerical results are presented to illustrate the proposed algorithms.

A Gaussian multiple-input single-output (MISO) wiretap channel model is considered, where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper, each equipped with a single antenna. We study the problem of finding the optimal input covariance that maximizes the ergodic secrecy rate subject to a power constraint, where only statistical information about the eavesdropper channel is available at the transmitter. This is a non-convex optimization problem that is in general difficult to solve. Existing results address the case in which the eavesdropper or/and legitimate channels have independent and identically distributed Gaussian entries with zero mean and unit variance, i.e., the channels have trivial covariances. This paper addresses the general case in which the eavesdropper and legitimate channels have nontrivial covariances. A set of equations describing the optimal input covariance matrix are proposed along with an algorithm to obtain the solution. Based on this framework, it is shown that when full information on the legitimate channel is available to the transmitter, the optimal input covariance has always rank one. It is also shown that when only statistical information on the legitimate channel is available to the transmitter, the legitimate channel has some general non-trivial covariance and the eavesdropper channel has trivial covariance, the optimal input covariance has the same eigenvectors as the legitimate channel covariance.

A Gaussian multiple-input single-output (MISO) wiretap channel model is considered, where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper each equipped with a single antenna. We study the problem of finding the optimal input covariance that achieves ergodic secrecy rate subject to a power constraint where the full information on the legitimate channel is known to the transmitter, but only statistical information on the eavesdropper channel is available at the transmitter. Existing results address the case in which the eavesdropper channel has independent and identically distributed Gaussian entries with zero-mean, i.e., the channel has trivial covariance. This paper addresses the general case where eavesdropper channel has nontrivial covariance. A set of equations describing the optimal input covariance matrix are proposed. Based on this framework, we show that the optimal input covariance has always rank one. Numerical results are presented to illustrate the algorithm.

We consider a multiple-input multiple-output (MIMO) Gaussian wiretap channel model, where there exists a transmitter, a legitimate receiver and an eavesdropper, each node equipped with multiple antennas. We study the problem of finding the optimal input covariance that achieves secrecy capacity subject to a power constraint, which in general leads to a difficult non-convex optimization problem. For the Gaussian multiple-input single-output (MISO) wiretap channel where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper each equipped with one antenna, the optimal input covariance is obtained in closed form. For the general case, we derive the necessary conditions for the optimal input covariance in the form of a set of equations. We show that for MISO case, the derived conditions guarantee the optimal input covariance. Numerical results are presented to illustrate the proposed theoretical findings.

The optimal transmit-beam number and power allocation over generic correlated multiple-input multiple-output (MIMO) Rayleigh fading channels are investigated. By fully exploiting the algebraic structures and properties of the optimization problem, we obtain a procedure for determining the thresholds of optimal beam number and derive a set of elementary equations for optimal power allocation, which can be efficiently solved by using a Broyden-like method. A closed-form criterion for the optimality of beamforming is also proposed. Numerical results are presented for illustration.

Although optimal transmit directions over generic correlated multiple-input multiple-output (MIMO) Rayleigh fading channels are well known to be the eigen beams defined by the transmit covariance matrix, general techniques for determining optimal transmit-beam number and power allocation remain unavailable. In this paper, by formulating the problem in the framework of Lagrange multipliers and by fully exploiting the algebraic structures and properties of the optimization problem at hand, we obtain a simple criterion for optimal beam number determination and a set of elementary equations for optimal power allocation, which can be efficiently solved by using the recursive algorithm derived in this paper. Numerical results are presented for the illustration of the theory.

Transmitter optimization for correlated multiple input single-output (MISO) channels with average channel information feedback is of theoretical and practical importance. It was tackled in the past by mainly focusing on cases with either mean or covariance feedback alone. The difficulty with generic MISO optimization arises from the fact that the treatment of optimal beam directions and power allocation are no longer separable, thereby making the problem nearly impossible to be tackled on the basis of its current formulation. We therefore take a different philosophy by representing the derivative of the ergodic capacity as a single integral and linking it to the channel characteristic function. This new formulation allows us to obtain the sufficient and necessary conditions, simply in the form of two vector equations which can be efficiently solved by a Newton-Raphson type algorithm developed in this paper. Numerical results are presented for illustration.