Signal-to-noise Ratio Constraints Research Articles

Optimised radar waveform design based on the relative entropy constraint

A new strategy to optimise the waveform of multiple-input multiple-output (MIMO) radar under the relative entropy constraint and signal-to-noise ratio (SNR) constraint is presented. The Kullback–Leibler divergence (KLD) is exploited between the two probability density functions of binary hypothesis testing as the design metric. A particular analysis of detection performance is made here to illuminate the balance between the false alarm and missing alarm probabilities. The results of the simulation demonstrate that the waveform design process constrained by relative entropy outperforms the process employing an explicit SNR constraint when the SNR is relatively low (i.e., within the interval [−2 dB, 0.5 dB]). The enhanced performance is attributable to the capability of the proposed optimisation process to focus the energy of the transmission waveform onto components where the eigenvalues of the target signal are large and the eigenvalues of the noise are small.

Frequency Diverse Array Signal Optimization: From Non-Cognitive to Cognitive Radar

This paper addresses the problem of frequency diverse array (FDA) signal design for target localization in both non-cognitive and cognitive radars. For the non-cognitive case, the Cramr-Rao bound (CRB) for target localization in FDA radar is derived and optimized with respect to the transmit signal parameters. It is shown that FDA transmission introduces coupling between range and direction-of-arrival (DOA) estimation, and that the DOA estimation accuracy can be improved by increasing the signal bandwidth. Since the CRB ignores the threshold phenomenon, we propose to minimize it under a constraint which assures that the steered gain toward the target yields sufficiently large output signal-to-noise ratio (SNR). This method together with the FDA transmission properties establish the basis for developing the proposed cognitive FDA configuration, which is derived in the Bayesian approach. Based on the Bayesian CRB (BCRB) and the expected CRB (ECRB) for target localization, we propose a new criterion called the semi-ECRB (SECRB), and we prove that it is higher than the BCRB and lower than the ECRB. The SECRB is optimized with respect to the FDA signal parameters subject to mean SNR constraint. The target localization performances of the proposed methods in the non-cognitive and cognitive problems are analyzed via simulations and it is shown that they exhibit superior performance in terms of both threshold behavior and estimation accuracy, compared to other transmission methods.

Joint Radar-Communication Waveform Designs Using Signals From Multiplexed Users

Joint radar-communication designs are exploited in applications where radar and communications systems share the same frequency band or when both radar sensing and information communication functions are required in the same system. Finding a waveform that is suitable for both radar and communication is challenging due to the difference between radar and communication operations. In this paper, we propose a new method of designing dual-functional waveforms for both radar and communication using signals from multiplexed communications users. Specifically, signals from different communications users multiplexed in the time, code or frequency domains across different data bits are linearly combined to generate an overall radar waveform. Three typical radar waveforms are considered. The coefficients of the linear combination are optimized to minimize the mean squared error with or without a constraint on the signal-to-noise ratio (SNR) for the communications signals. Numerical results show that the optimization without SNR constraint can almost perfectly approximate the radar waveform in all the cases considered, giving good dual-functional waveforms for both radar and communication. Also, among different multiplexing techniques, time division multiple access is the best option to approximate the radar waveform, followed by code division multiple access and orthogonal frequency division multiple access.

Link Adaptation on an Underwater Communications Network Using Machine Learning Algorithms: Boosted Regression Tree Approach

Interest in the study of next-generation underwater sensor networks for ocean investigations has increased owing to developing concerns over their utilization in areas such as oceanography, commercial operations in maritime areas, and military surveillance. Underwater acoustic communications (UAC) network channels are fast-varying (spatially and temporally) according to environmental conditions. It is tempting to use adaptive modulation and coding (AMC) for UAC networks to improve the system efficiency by matching transmission parameters to channel variations. This paper focuses on analyzing a measured sea trial dataset by using a rule-based strategy (i.e., three-dimensional analysis, modulation-wise analysis, and a fixed-SNR strategy) to find the suitable link adaptation procedure depending on the channel quality. Hence, we plot a scenario of the measured UAC network data rate vs. Signal to Noise Ratio (SNR) and/or Bit Error Rate (BER) to pick the best AMC combinations in the context of adaptivity to the channel. Due to non-reversibility limitation of rule-based strategy, the work further extends to use machine learning (ML) algorithms to classify the MCS levels by investigating the channel characteristics. Boosted regression tree, from among the four ML algorithms we adopted for the analysis, shows formidable accuracy of 99.97% in classifying MCS levels. This ensemble of trees learns from the uplink data of the buoy and the base station and relates the MCS levels to channel metrics and signal characteristics especially subject to SNR and BER constraints.

Secrecy-Oriented Transmitter Optimization for Visible Light Communication Systems

Securing visible light communication (VLC) systems with physical-layer technologies has drawn increasing attention. In this paper, we leverage both transmit beamforming and jamming techniques to enhance communication secrecy for a multiple-input single-output (MISO) VLC system with presence of multiple eavesdroppers. The transmit beamformer and jamming precoder are jointly optimized in the sense that the signal-to-noise ratio (SNR) of the legitimate user is maximized subject to maximum SNR constraints imposed on eavesdroppers, as well as light-emitting diode (LED) optical power constraints. Despite the fact that the corresponding optimization problem has a nonconvex fractional form, we are able to determine its locally optimal solution via Charnes–Cooper transformation and minorization-maximization algorithm. Furthermore, we study the extension to a more complicated scenario where perfect channel state information at the transmitter (CSIT) is not available. The superiority of the proposed algorithms is finally verified via simulations.

Robust fault detection for uncertain discrete-time systems subject to signal-to-noise ratio constrained channels

In this paper, the robust fault detection problem for uncertain discrete-time systems subject to signal-to-noise ratio (SNR) constrained communication channels is investigated. An optimal residual generation with no modeling errors is used as the reference residual model of robust fault detection filter design for the uncertain discrete-time systems with both modeling errors and SNR constraints; then, the robust fault detection filter design is formulated as an optimal H∞ filtering problem. In order to detect faults, a norm-based residual evaluation function is proposed, and an on-line dynamic threshold and its computing method are also given. Based on the notable Chebyshev׳s inequality, the false alarm rate is used to evaluate the performance of the designed threshold. The validity of the proposed method is illustrated by a numerical example.

Fat-Tree-Based Optical Interconnection Networks Under Crosstalk Noise Constraint

Optical networks-on-chip (ONoCs) have shown the potential to be substituted for electronic networks-on-chip (NoCs) to bring substantially higher bandwidth and more efficient power consumption in both on- and off-chip communication. However, basic optical devices, which are the key components in constructing ONoCs, experience inevitable crosstalk noise and power loss; the crosstalk noise from the basic devices accumulates in large-scale ONoCs and considerably hurts the signal-to-noise ratio (SNR) as well as restricts the network scalability. For the first time, this paper presents a formal system-level analytical approach to analyze the worst-case crosstalk noise and SNR in arbitrary fat-tree-based ONoCs. The analyses are performed hierarchically at the basic optical device level, then at the optical router level, and finally at the network level. A general 4 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\,\times\,$ </tex-math></inline-formula> 4 optical router model is considered to enable the proposed method to be adaptable to fat-tree-based ONoCs using an arbitrary 4 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\,\times\,$ </tex-math></inline-formula> 4 optical router. Utilizing the proposed general router model, the worst-case SNR link candidates in the network are determined. Moreover, we apply the proposed analyses to a case study of fat-tree-based ONoCs using an optical turnaround router (OTAR). Quantitative simulation results indicate low values of SNR and scalability constraints in large scale fat-tree-based ONoCs, which is due to the high power of crosstalk noise and power loss. For instance, in fat-tree-based ONoCs using the OTAR, when the injection laser power equals 0 dBm, the crosstalk noise power is higher than the signal power when the number of processor cores exceeds 128; when it is equal to 256, the signal power, crosstalk noise power, and SNR are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${-}{17.3}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${-}{11.9}$ </tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${-}{\rm 5.5}~{\rm dB}$ </tex-math></inline-formula> , respectively.

On power minimisation and SNR maximisation of distributed beamforming in cooperative communication systems

A comparison of relay power minimisation subject to received signal-to-noise ratio (SNR) at the receiver and SNR maximisation subject to the total transmitted power of relays for a typical wireless network with distributed beamforming is presented. It is desirable to maximise receiver quality-of-service (QoS) and also to minimise the cost of transmission in terms of power. Hence, these two optimisation problems are very common and have been addressed separately in the literature. It is shown that SNR maximisation subject to power constraint and power minimisation subject to SNR constraint yield the same results for a typical wireless network. It proves that either one of the optimisation approaches is sufficient.

Cognitive Beamforming for Multiple Secondary Data Streams With Individual SNR Constraints

In this paper, we consider cognitive beamforming for multiple secondary data streams subject to individual signal-to-noise ratio (SNR) requirements for each secondary data stream. In such a cognitive radio system, the secondary user is permitted to use the spectrum allocated to the primary user as long as the caused interference at the primary receiver is tolerable. With both secondary SNR constraint and primary interference power constraint, we aim to minimize the secondary transmit power consumption. By exploiting the individual SNR requirements, we formulate this cognitive beamforming problem as an optimization problem on the Stiefel manifold. Both zero forcing beamforming (ZFB) and nonzero forcing beamforming (NFB) are considered. For the ZFB case, we derive a closed-form beamforming solution. For the NFB case, we prove that the strong duality holds for the nonconvex primal problem and thus the optimal solution can be easily obtained by solving the dual problem. Finally, numerical results are presented to illustrate the performance of the proposed cognitive beamforming solutions.

Distributed power allocation algorithm in wireless networks under SNR constraints

In this work, the distributed power allocation problem in wireless networks is studied under signal-to-noise ratio (SNR) constraints. The sources of uncertainty are assumed to come from the quantization process and measurement noise in the feedback system. The power allocation is formulated as a reference tracking problem of a pre-defined signal to noise-interference ratio. First, the synthesis problem with SNR constraints is studied as a 2-norm minimization process, which is equivalent to a linear-quadratic-regulator (LQR) problem. The solution of the associated Riccati equation in the LQR formulation is completely characterized, resulting in a feedback law with a recurrent structure. This control law is re-written in a transfer function format, where a simple control strategy is obtained which is dependant on the round-trip delay in the feedback system. In addition, the corresponding 2-norm closed-loop performance is also studied. Thus, the selection of the weight in the LQR problem establishes a compromise between robustness to quantization errors and measurement noise, and tracking performance. A comprehensive simulation evaluation validates the analytical derivations described in the paper.

Energy efficient opportunistic cooperative transmission with different ratio combinings: from a new perspective

In cooperative communication, different ratio combining approaches can be utilized at the receiver based on the channel state information (CSI) available to the destination. In this paper, we focus on optimal energy allocation under amplify-and-forward (AF) cooperative communications when various ratio combining methods are utilized. More specifically, we consider a suite of important and fundamental problems, including signal-to-noise ratio (SNR) maximization under a weighted total energy constraint, weighted total energy minimization under an SNR constraint, weighted total energy minimization under an outage probability constraint and outage probability minimization under instantaneous weighted total energy constraint, and analyze the relationship among these problems. We first consider maximal ratio combining (MRC) and derive exact analytical solutions. To reveal the key factors in the resource allocation problem, we further transform the exact results with multiple parameters into more intuitive results with only two quantities. The resulting solutions provide a new perspective to understand optimal energy-efficient opportunistic cooperative transmissions. We then consider fixed ratio combining (FRC) and show that an explicit analytical solution does not exist to the original problem. To this end, based on the convexity proofs for the objective functions, we utilize numerical convex optimizations to obtain the unique solution. Both numerical and simulation studies are conducted to validate our theoretical analysis.

Performance limitations for single-input LTI plants controlled over SNR constrained channels with feedback

This paper studies control problems for discrete-time single-input linear time-invariant plants when controlled over a signal-to-noise ratio (SNR) constrained channel. Our focus is on the performance limitations in an architecture that uses channel feedback. We explicitly characterize the interplay between stabilization, optimal performance, and SNR constraints, highlighting the way in which plant dynamical features affect the best achievable performance. We also apply our results to the study of networked control systems where communication takes place over a power constrained erasure channel. In that scenario, we first show that stabilization problems, and problems involving stationary second-order moments, can be dealt with by focusing on a related SNR constrained networked situation. This observation allows one to obtain results valid in the alternative scenario as corollaries of the results obtained when a single SNR constraint is present.

A Real-Time and Offline Quality Control Methodology for SeaSonde High-Frequency Radar Currents

Abstract A near-real-time and offline quality control methodology for SeaSonde systems is proposed. It is applied on radial current maps and is based on the determination of the signal-to-noise ratio (SNR) values of the Doppler lines that contribute to the hourly radial current at each range-bearing (R, θ) pair, under the assumption that SNR is a proxy for radar data quality. The retrieval of the sequence of Doppler lines is performed through a minimization procedure that takes advantage of the statistical descriptors output in the short-term radial maps. The separation of the contributing Doppler velocities into valid observations and anomalous velocities is based on their spectral quality factor and on a range-dependent noise threshold derived from statistics (average and standard deviation) of the signal amplitudes in the tails of the Doppler spectra. The final product of the quality control procedure is a radial current map, in which Doppler velocities are weighted by their SNR values and their spectral quality factors, and averaged to produce an output that is fully compatible with the proprietary software. This procedure is fast, despite the fact that a large number of combinations might be required during the retrieval of the Doppler lines, and effective, because it removes both evident spikes as well as Doppler velocities that are not clearly identified as anomalous velocities. In principle, this approach can be used to fill gaps in the radar coverage without the need for interpolation in time or space, proved that the Doppler velocities satisfy predetermined SNR constraints.

SNR-aware and power-efficient multicast cooperative routing algorithm in wireless networks

Power-efficient multicast routing is an active research field in wireless networks because most network nodes are powered by battery. However, this kind of multicast routing only considers the transmission radius coverage without addressing whether the signal quality is able to meet bandwidth requirement of the users. In this article, by leveraging on the Maximum Ratio Combining signal processing technique, a novel cooperative multicast routing scheme that meets the Signal-to-Noise Ratio (SNR) requirements of the traffic demands in power efficient way is developed. This problem is formulated as an optimization problem where the objective is to minimize the total transmission power subject to the SNR constraint. This is a challenging cross-layer design problem to simultaneously consider the cooperative routing in the network layer and the SNR-aware power control in the physical layer. A heuristic algorithm called bandwidth-aware cooperative radius adjustment (BACRA) is proposed to tackle this problem. The basic idea of BACRA is to select the node with the maximum ratio of contributed SNR to the power (denoted as SNR/P) to expand its power one at a time until the SNR requirements are all satisfied. The BACRA is proved to be optimal in terms of the SNR/P performance ratio. Numerical results demonstrate that the BACRA outperforms the other heuristics under all tested cases, especially in stringent SNR requirements and sparse network.

Magnetic resonance imaging of triangular fibrocartilage

Due to their small size and complex structure, diagnosing injury of the proximal wrist ligamentous structures can be challenging. The triangular fibrocartilage complex (TFCC) is an example of one such structure, for which lesions may be missed unless high-resolution magnetic resonance imaging (MRI) obtained via a standard matrix with a small field of view or high-resolution imaging matrix (small spatial scale matrix elements/large matrix size) is utilized. While there have been recent advances in increasing MRI spatial resolution, attempts at improved visualization by isolated increase in the spatial resolution will be ineffective if the signal-to-noise ratio (SNR) of the images obtained is low. Additionally, high contrast resolution is important to facilitate a more precise visualization of these structures and their pathology. Thus, a balance of the three important imaging factor qualifications of high spatial resolution, high SNR, and high contrast resolution must be struck for optimized TFCC and wrist imaging. The goal of this article, then, is to elucidate the theory and techniques of effective high-resolution imaging of the proximal ligamentous structures of the wrist, balancing SNR and high contrast resolution constraints, and focusing on imaging of the TFCC as a prototypical example.

Control of LTI systems over digital erasure channels

AbstractThis paper studies networked control systems closed over digital erasure channels, when a class of source coding schemes is employed. Building upon recent results, we show that it is possible to convert analysis and design problems involving digital erasure channels into problems involving two signal-to-noise ratio (SNR) constrained channels in series, one subject to an equality SNR constraint, and the second one subject to an inequality SNR constraint. This insight is then used to establish a sufficient condition on the channel average data-rate and dropout probability that allow one to achieve mean square stability. We also provide performance guarantees and a numerical example to illustrate our results.

Signal Estimation over Channels with SNR Constraints and Feedback

AbstractWe consider the problem of designing optimal linear encoders and decoders for estimation and transmission of a signal over an analog communication channel with additive noise and a signal-to-noise ratio (SNR) constraint. The objective is to minimize the variance of the estimation error at the receiving end, subject to a real-time constraint. It has been previously shown that, for channels without feedback, a solution can be obtained by solving a mixed norm minimization problem and performing a spectral factorization, see Johannesson et al. (2010b). In this paper, these results are extended to the case when the encoder has access to feedback from the channel output. This results in improved performance, which is demonstrated by a numerical example.

On the Power of MIMO Broadcast Systems Under SNR Constraints With Limited Feedback

The power problem of joint zero-forcing beamforming and scheduling is addressed in a multiple-input-multiple-output (MIMO) broadcast channel under individual signal-to-noise ratio (SNR) constraints. Perfect channel knowledge is assumed to be available for each single antenna user, whereas the base station (BS) with multiple antennas is provided with partial channel-state information through limited-rate feedback channels. Each user can feed back its quantized channel direction information and needed power information. Only the user with the minimum power is selected to communicate with the BS. Expressions for the average minimum power used to transmit are derived, and tradeoffs between the number of feedback bits, the number of users, and the number of transmit antennas are observed.

Optimal State-Feedback Design for MIMO systems subject to multiple SNR constraints

AbstractThis paper studies optimal control problems associated to networked systems. In particular, we focus on a case where a multiple-input multiple-output (MIMO) plant is controlled over a channel subject to multiple signal-to-noise ratio (SNR) constraints. For this setup, we establish necessary and sufficient conditions for the existence of static state-feedback controllers that stabilize the plant in a mean square sense. Such conditions are given in terms of a convex optimization problem involving linear matrix inequalities (LMIs). An optimal design procedure is also presented. As an application of our results, we study a class of networked systems closed over erasure channels.

Control system design subject to SNR constraints

This paper deals with networked control systems comprising LTI plants controlled over scalar additive noise channels subject to signal-to-noise ratio (SNR) constraints. We present a general framework, based upon convex optimization concepts, that can accommodate several situations of interest. Our results make explicit the fact that exploiting feedback around the channel plays a key role in reducing the minimal SNR that is compatible with stability. The results also provide a characterization of the best achievable performance subject to an SNR constraint. We apply the results to specific networked control architectures, and provide a numerical example.