Constant Modulus Shaped Beam Synthesis via Convex Relaxation

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Constant modulus shaped beam synthesis is widely employed in multiple-input-multiple-output (MIMO) radar systems and MIMO wireless communication systems to improve the effective power gain by using only phase adjustment. To achieve the maximum beam gain, we formulate a new optimization problem to maximize the main lobe gain and also properly suppress the sidelobes. However, this problem is NP-hard because of the constant modulus constraint. In order to efficiently solve this problem, we first relax the constant modulus constraint to a convex constraint, and then propose an alternating optimization algorithm to solve the relaxed problem. Interestingly, numerical results imply that the solutions of the relaxed optimization problem are (almost) constant modulus, and thus the convex relaxation is usually tight.Peer reviewe

Rakeness in the design of Analog-to-Information Conversion of Sparse and Localized Signals

Design of Random Modulation Pre-Integration systems based on the restricted-isometry property may be suboptimal when the energy of the signals to be acquired is not evenly distributed, i.e. when they are both sparse and localized. To counter this, we introduce an additional design criterion, that we call rakeness, accounting for the amount of energy that the measurements capture from the signal to be acquired. Hence, for localized signals a proper system tuning increases the rakeness as well as the average SNR of the samples used in its reconstruction. Yet, maximizing average SNR may go against the need of capturing all the components that are potentially non-zero in a sparse signal, i.e., against the restricted isometry requirement ensuring reconstructability. What we propose is to administer the trade-off between rakeness and restricted isometry in a statistical way by laying down an optimization problem. The solution of such an optimization problem is the statistic of the process generating the random waveforms onto which the signal is projected to obtain the measurements. The formal definition of such a problems is given as well as its solution for signals that are either localized in frequency or in more generic domain. Sample applications, to ECG signals and small images of printed letters and numbers, show that rakeness-based design leads to non-negligible improvements in both cases

Sequence Design via Semidefinite Programming Relaxation and Randomized Projection

Wideband is a booming technology in the field of wireless communications. The receivers in wideband communication systems are expected to cover a very wide spectrum and adaptively extract the parts of interest. The literature has focused on mixing the input spectrum to baseband using a pseudorandom sequence modulation and recovering the received signals from linearly independent measurements by parallel branches to mitigate the pressures from required extreme high sampling frequency. However, a pseudorandom sequence provides no rejection for the strong interferers received together with weak signals from distant sources. The interferers cause significant distortion due to the nonlinearity of the subsequent amplifier and mask the weak signals. In this dissertation, we optimize the modulation sequences with a specific spectrum shape to mitigate interferers while preserving messages; the sequences have binary entries to simplify hardware implementation. Though the resulting sequence design problems are NP-hard, we solve them approximately by semidefinite relaxation and randomized projection. First, we formulate the design algorithm for a single spectrally shaped binary sequence base on a randomized convex optimization method. We analyze the performance of the algorithm in obtaining binary sequences and show its advantages compared with method available in the literature. And, we show a comparison between the proposed sequence design method with the exhaustive approaches when feasible. Additionally, we propose several custom sequence scoring functions that allow for an improved selection of binary sequences for message preservation and interference rejection. Second, we propose an algorithm to design a multi-branch set of binary sequences one by one by introducing the constrains on the orthogonality between pairs of sequences. Numerical results show the proposed algorithm obtains sequences with a small search size compared with the exhaustive search. Finally, we extend the randomized method to multi-branch sequence design. In order to avoid the unstable performance and high complexity of designing multi-branch sequence iteratively, the whole branch sequences will be obtained directly via matrix randomized projection from the relaxed problems

A Machine Learning and Data-Driven Prediction and Inversion of Reservoir Brittleness from Geophysical Logs and Seismic Signals: A Case Study in Southwest Pennsylvania, Central Appalachian Basin

In unconventional reservoir sweet-spot identification, brittleness is an important parameter that is used as an easiness measure of production from low permeability reservoirs. In shaly reservoirs, production is realized from hydraulic fracturing, which depends on how brittle the rock is–as it opens natural fractures and also creates new fractures. A measure of brittleness, brittleness index, is obtained through elastic properties of the rock. In practice, problems arise using this method to predict brittleness because of the limited availability of elastic logs. To address this issue, machine learning techniques are adopted to predict brittleness at well locations from readily available geophysical logs and spatially using 3D seismic data. The geophysical logs available as input are gamma ray, neutron, sonic, photoelectric factor, and density logs while the seismic is a post-stack time migrated data of high quality. Support Vector Regression, Gradient Boosting, and Artificial Neural Network are used to predict the brittleness from the geophysical logs and Texture Model Regression to invert the brittleness from the seismic data. The Gradient Boosting outperformed the other algorithms in predicting brittleness. The result of this research further demonstrates the application of machine learning, and how these tools can be leveraged to create data-driven solutions to geophysical problems. Also, the seismic inversion of brittleness shows promising results that will be further investigated in the future

A review of differentiable digital signal processing for music and speech synthesis

The term “differentiable digital signal processing” describes a family of techniques in which loss function gradients are backpropagated through digital signal processors, facilitating their integration into neural networks. This article surveys the literature on differentiable audio signal processing, focusing on its use in music and speech synthesis. We catalogue applications to tasks including music performance rendering, sound matching, and voice transformation, discussing the motivations for and implications of the use of this methodology. This is accompanied by an overview of digital signal processing operations that have been implemented differentiably, which is further supported by a web book containing practical advice on differentiable synthesiser programming (https://intro2ddsp.github.io/). Finally, we highlight open challenges, including optimisation pathologies, robustness to real-world conditions, and design trade-offs, and discuss directions for future research