Memoryless Additive White Gaussian Noise Research Articles

On Capacity-Achieving Distributions for Complex AWGN Channels Under Nonlinear Power Constraints and Their Applications to SWIPT

The capacity of a complex and discrete-time memoryless additive white Gaussian noise (AWGN) channel under three constraints, namely, input average power, input amplitude and output delivered power is studied. The output delivered power constraint is modelled as the average of linear combination of even moments of the channel input being larger than a threshold. It is shown that the capacity of an AWGN channel under transmit average power and receiver delivered power constraints is the same as the capacity of an AWGN channel under an average power constraint. However, depending on the two constraints, the capacity can be either achieved by a Gaussian distribution or arbitrarily approached by using time-sharing between a Gaussian distribution and On-Off Keying. As an application, a simultaneous wireless information and power transfer (SWIPT) problem is studied, where an experimentally-validated nonlinear model of the harvester is used. It is shown that the delivered power depends on higher order moments of the channel input. Two inner bounds, one based on complex Gaussian inputs and the other based on further restricting the delivered power are obtained for the Rate-Power (RP) region. For Gaussian inputs, the optimal inputs are zero mean and a tradeoff between transmitted information and delivered power is recognized by considering asymmetric power allocations between inphase and quadrature subchannels. Through numerical algorithms, it is observed that input distributions (obtained by restricting the delivered power) attain larger RP region compared to Gaussian input counterparts. The benefits of the newly developed and optimized input distributions are also confirmed and validated through realistic circuit simulations. The results reveal the crucial role played by the energy harvester (EH) nonlinearity on SWIPT and provide new engineering guidelines on how to exploit this nonlinearity in the design of SWIPT modulation, signal and architecture.

Signal-to-noise ratio constrained feedback control: Robust stability analysis

The explicit consideration of a communication channel model in a feedback control loop is known to be constrained by a fundamental limitation for stabilizability on the channel signal-to-noise ratio (SNR) when the linear time invariant (LTI) plant model is unstable. The LTI modelling approach for real, usually nonlinear, processes compromises accuracy versus complexity of the resulting model. This in turn introduces a gap between the proposed model and the real process, which is known as the model uncertainty. In this paper we then study SNR limitations by considering the continuous-time scenario and the case of an additive coloured Gaussian noise (ACGN) channel with bandwidth limitation, for which we then quantify the infimal SNR subject to the simultaneous presence of plant, channel and noise model uncertainties. We observe, for the special case of memoryless additive white Gaussian noise (AWGN) channels, that the obtained SNR limitation subject to plant model uncertainty can be redefined as a channel capacity limitation for stabilization.

Useful Mathematical Tools for Capacity Approaching Codes Design

Focus of this letter is the oldest class of codes that can approach the Shannon limit quite closely, i.e., low-density parity-check (LDPC) codes, and two mathematical tools that can make their design an easier job under appropriate assumptions. In particular, we present a simple algorithmic method to estimate the threshold for regular and irregular LDPC codes on memoryless binary-input continuous-output additive white Gaussian noise (AWGN) channels with sum-product decoding, and, to determine how close are the obtained thresholds to the theoretical maximum, i.e., to the Shannon limit, we give a simple and invertible expression of the AWGN channel capacity in the binary input-soft output case. For these codes, the thresholds are defined as the maximum noise level, such that an arbitrarily small bit-error probability can be achieved as the block length tends to infinity. We assume a Gaussian approximation for message densities under density evolution, a widely used simplification of the decoding algorithm.

Signal-to-Noise Ratio Requirements for Discrete-time PID Controllers

In networked control a channel model is explicitly considered in discrete-time within the classic feedback loop scheme. It is well known by now that the channel model signal-to-noise ratio (SNR) happens to be an important parameter related to the overall stabilisability of the output feedback loop. In this paper we offer the rules for the design of discrete-time proportional-integral-derivative (PID) controllers for given closed loop bandwidth that quantifies the SNR requirement for the memoryless additive white Gaussian noise (AWGN) channel over the feedback path, which is a common used communication channel model. The design is centered on a PID controller structure due to its wide use in the industry. Since we focus on a PID controller structure, we then reduce the analysis to plant models of first and second order which are the structures more compatible with the PID controller design.

Step reference tracking in signal-to-noise ratio constrained feedback control

In this paper we address the problem of step reference tracking in the context of signal-to-noise ratio (SNR) constrained feedback control. We study the presence of a channel model in the feedback loop either over the measurement path, between the plant and the controller, or the control path, between the controller and the plant. We start the analysis by considering the memoryless additive white Gaussian noise (AWGN) channel model, and follow-up with the additive coloured Gaussian noise (ACGN) channel with memory model. We observe that the standard SNR constrained feedback loop configuration, when tracking step references, will result in an infinite channel SNR. We show that this situation can be ameliorated by extending the feedback loop configuration with an encoder and decoder. The proposed configurations result in a finite SNR that converges back to the infimal SNR for regulation when the amplitude of the reference signal tends to zero.

Sensitivity of Quadratic Gaussian Matching to Interference

It is well known that uncoded transmission of a memoryless Gaussian source over a memoryless additive white Gaussian noise channel results in optimal performance theoretically attainable. When there is additional interference in the channel, uncoded transmission is robust. It achieves the same sensitivity performance as optimal performance, measured using sensitivity results of Pinsker, Prelov, and Verdu.

Signal-to-Noise Ratio Limitations in Feedback Control

The present article is focused in the area of control over networks. The main difference with classic control is that we deal with an explicit communication channel model in the feedback control structure. The channel model is modeled as to have limited bandwidth and additive colored Gaussian noise. This allows us to study the interaction between the control and communication goals. We first briefly revisit the assumption behind the present work and formally define the problem at hand. We then review its solution in the form of the Signal-to-Noise Ratio (SNR) fundamental limitation for stabilizability result. We extend the stabilizability result to include the following performance scenarios: closed-loop arbitrary pole assignment, robustness, set point tracking and the effect of channel input quantization. We finally conclude the present paper by studying the capacity resulting from these performance limitations for the case of a memoryless additive white Gaussian noise (AWGN) channel.

Infimal SNR for Output Disturbance Rejection

AbstractIn the present paper we address the problem of plant output disturbance rejection in the context of feedback control over a signal-to-noise ratio (SNR) constrained communication channel. We study separately the case of the communication channel when located between the controller and the plant (control path) and when located between the plant and the controller (measurement path). We also study separately the case of a memoryless additive white Gaussian noise channel model and the case of an additive colored Gaussian noise channel with memory. When possible we express the resulting infimal SNR for performance in closed-form, whilst where not possible we use a numerical approach such as linear quadratic Gaussian (LQG) optimization with loop transfer recovery (LTR).

List Decoding Techniques for Intersymbol Interference Channels Using Ordered Statistics

In this paper, we present a generalization of the ordered statistics decoding (OSD) techniques for the class of intersymbol interference (ISI) channels, and show decoding results for the extended Bose-Chaudhuri-Hocquenghem (eBCH) [128, 64, 22] code and the [255, 239, 17] Reed-Solomon (RS) binary image, over the PR2 partial response channel. Using the generalized OSD technique, we go on to generalize the Box-and- Match Algorithm (BMA) to the class of ISI channels. The BMA is an enhancement of OSD, and prior work has shown it to provide significant performance gain over OSD for memoryless additive white Gaussian noise (AWGN) channels. We present decoding results of the BMA for ISI channels, for the same eBCH and RS (binary image) codes, and PR2 channel. Our results show that the BMA (generalized for ISI channels) is superior to the OSD in terms of its performance/complexity trade-off. More specifically, the BMA may be tuned such that both algorithms have similar complexity, whereby the BMA still outperforms the OSD by a significant margin.

Pattern-Flipping Chase-Type Decoders with Error Pattern Extracting Viterbi Algorithm over Partial Response Channels

Towards the goal of achieving better error correction performance in data storage systems, iterative soft decoding of low density parity check (LDPC) codes and soft-decision decoding of Reed-Solomon (RS) codes have started receiving increasing research attention. However, even with increased computing power, complexities of soft-decision decoding algorithms are still too high for real products which require high throughput and small hardware area. Another problem is that the performance gains of those approaches are smaller for magnetic recording channels than they are for memoryless additive white Gaussian noise (AWGN) channels. We propose a new soft-decision decoding algorithm (based on the Chase algorithm), which takes advantage of pattern reliability instead of symbol reliability or bit reliability. We also present a modified Viterbi algorithm that provides probable error patterns with corresponding reliabilities. Simulation results of the proposed algorithms over the partial response (PR) channel show attractive performance gains. The proposed algorithm dramatically reduces the number of iterations compared to the conventional Chase2 algorithm over the PR channel.

Signal-to-noise ratio performance limitations for input disturbance rejection in output feedback control

Communication channels impose a number of obstacles to feedback control. One recent line of research considers the problem of feedback stabilization subject to a constraint on the channel signal-to-noise ratio (SNR). We use the spectral factorization induced by the optimal solution and quantify in closed-form the infimal SNR required for both stabilization and input disturbance rejection for a minimum phase plant with relative degree one and memoryless additive white Gaussian noise (AWGN) channel. Finally we conclude by presenting a closed-form expression of the difference between the infimal AWGN channel capacity for input disturbance rejection and the infimal AWGN channel capacity required only for stabilizability.

Extrinsic information in iterative decoding: a unified view

We address the use of the extrinsic information generated by each component decoder in an iterative decoding process. The BJCR algorithm proposed by Bahl et al. (1974) and the soft-output Viterbi algorithm (SOVA) are considered as component decoders. In both cases, we consider, in a unified view, various feedback schemes which use the extrinsic information in different fashions. Numerical results for a classical rate-1/2 turbo code and a serially concatenated code transmitted over a memoryless additive white Gaussian noise (AWGN) channel are provided. The performance of the considered schemes leads to interesting remarks about the nature of the extrinsic information.