Classical Additive White Gaussian Noise Research Articles

Covert Communication Gains From Adversary’s Uncertainty of Phase Angles

This work investigates the phase gain of intelligent reflecting surface (IRS) covert communication over complex-valued additive white Gaussian noise (AWGN) channels. The transmitter Alice intends to transmit covert messages to the legitimate receiver Bob via reflecting the broadcast signals from a radio frequency (RF) source, while rendering the adversary Willie’s detector arbitrarily close to ineffective. Our analyses show that, compared to the covert capacity for classical AWGN channels, we can achieve a covertness gain of value 2 by leveraging Willie’s uncertainty of phase angles. This covertness gain is achieved when the number of possible phase angle pairs <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> = 2. More interestingly, our results show that the covertness gain will not further increase with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> as long as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ≥ 2, even if it approaches infinity.

Blind Equalization and Channel Estimation in Coherent Optical Communications Using Variational Autoencoders

We investigate the potential of adaptive blind equalizers based on variational inference for carrier recovery in optical communications. These equalizers are based on a low-complexity approximation of maximum likelihood channel estimation. We generalize the concept of variational autoencoder (VAE) equalizers to higher order modulation formats encompassing probabilistic constellation shaping (PCS), ubiquitous in optical communications, oversampling at the receiver, and dual-polarization transmission. Besides black-box equalizers based on convolutional neural networks, we propose a model-based equalizer based on a linear butterfly filter and train the filter coefficients using the variational inference paradigm. As a byproduct, the VAE also provides a reliable channel estimation. We analyze the VAE in terms of performance and flexibility over a classical additive white Gaussian noise (AWGN) channel with inter-symbol interference (ISI) and over a dispersive linear optical dual-polarization channel. We show that it can extend the application range of blind adaptive equalizers by outperforming the state-of-the-art constant-modulus algorithm (CMA) for PCS for both fixed but also time-varying channels. The evaluation is accompanied with a hyperparameter analysis.

On Trading the Spreading Gain With the Coding Rate and Its Application to GNSS Data Component Design

The ubiquity of global navigation satellite system (GNSS)-based positioning and timing services is often frustrated by the necessity to operate in harsh environments, where the carrier-to-noise ratio is low, and hence, decoding of navigation data and even tracking of an acquired symbol are difficult. We consider the possibility of improving the decoding performance of the GNSS data component by trading the spreading gain against the coding rate. The rationale is that spreading codes can be seen as a form of repetition coding that can be (at least partially) replaced by more robust coding forms to improve robustness to (any form of) noise. This is true both for the classical additive white Gaussian noise channel case and for more realistic GNSS channel formats severely degraded by multiple access interference and near-far effects. By bringing results on finite-block-length channel capacity and coding rates from information/communication theory to the GNSS domain, we are able to establish and discuss the expected performance gap, as well as the limits of such tradeoff.

Probabilistic Shaping for the Optical Phase Conjugation Channel

Probabilistic constellation shaping is studied and developed for optical phase conjugation (OPC)-based nonlinearity compensation of Kerr nonlinearities in optical fiber links. The mid-link OPC scenario is considered for dispersion compensated systems. It is demonstrated in simulations and experimentally that transmission strategies optimal for classical additive white Gaussian noise (AWGN) channels can be sub-optimal for these systems without nonlinearity compensation. On the contrary, when nonlinearity compensation is applied with mid-link OPC, the channel noise is demonstrated to be Gaussian and AWGN-like transmission strategies thus remain effective. A channel-agnostic probability mass function (PMF) optimization algorithm is proposed for the input constellation in order to further improve the shaping gains in both scenarios. Operating arbitrary PMFs on arbitrary channels is enabled by a channel-agnostic digital signal processing (DSP) chain. After ≈2000 km of transmission, mid-link OPC is demonstrated to provide ≈1 dB of gain in effective SNR, which translates to ≈0.4 bits/QAM symbol of gain in achievable information rate. The gain is then increased by an extra 0.2 bits/QAM symbol by applying probabilistic shaping.

On the Capacity of a Class of Signal-Dependent Noise Channels

In some applications, the variance of additive measurement noise depends on the signal that we aim to measure. For instance, additive signal-dependent Gaussian noise (ASDGN) channel models are used in molecular and optical communication. Herein, we provide lower and upper bounds on the capacity of additive signal-dependent noise (ASDN) channels. The first lower bound is based on an extension of majorization inequalities, and the second lower bound utilizes the properties of the differential entropy. The lower bounds are valid for arbitrary ASDN channels. The upper bound is based on a previous idea of the authors (“symmetric relative entropy”) and is applied to the ASDGN channels. These bounds indicate that in the ASDN channels (unlike the classical additive white Gaussian noise channels), the capacity does not necessarily become larger by reducing the noise variance function. We also provide sufficient conditions under which the capacity becomes infinite. This is complemented by some conditions implying that the capacity is finite, and a unique capacity achieving measure exists (in the sense of the output measure).

Achieving AWGN Capacity Under Stochastic Energy Harvesting

In energy harvesting communication systems, an exogenous recharge process supplies energy necessary for data transmission and the arriving energy can be buffered in a battery before consumption. We determine the information-theoretic capacity of the classical additive white Gaussian noise (AWGN) channel with an energy harvesting transmitter with an unlimited sized battery. As the energy arrives randomly and can be saved in the battery, codewords must obey cumulative stochastic energy constraints. We show that the capacity of the AWGN channel with such stochastic channel input constraints is equal to the capacity with an average power constraint equal to the average recharge rate. We provide two capacity achieving schemes: save-and-transmit and best-effort-transmit. In the save-and-transmit scheme, the transmitter collects energy in a saving phase of proper duration that guarantees that there will be no energy shortages during the transmission of code symbols. In the best-effort-transmit scheme, the transmission starts right away without an initial saving period, and the transmitter sends a code symbol if there is sufficient energy in the battery, and a zero symbol otherwise. Finally, we consider a system in which the average recharge rate is time varying in a larger time scale and derive the optimal offline power policy that maximizes the average throughput, by using majorization theory.

Convolutionally Coded Transmission over Markov-Gaussian Channels: Analysis and Decoding Metrics

It has been widely acknowledged that the aggregate interference at the receiver for various practical communication channels can often deviate markedly from the classical additive white Gaussian noise (AWGN) assumption due to various ambient phenomena. Moreover, the physical nature of the underlying interference generating process in such cases can lead to a bursty behaviour of the interfering signal, implying that it is highly likely that consecutive symbols are affected by similar noise levels. In this paper, we devise and analyze detection techniques, in conjunction with a convolution code, for such interference channels that possess non-negligible memory by considering optimum and sub-optimum decoding metrics. In particular the inherent memory in the noise process is modeled as a first-order Markov chain, whose state selects the variance of the instantaneous Gaussian noise, leading to a Markov-Gaussian channel model. Analytical expressions are obtained for the cut-off rate, which is an ensemble code parameter, and the bit error rate for a convolutionally coded system, that are subsequently employed for an extensive evaluation of the various metrics considered. Furthermore, the interleaving depth is considered as a design parameter and its effect on performance is analyzed over a range of noise scenarios.

Soft Decision LDPC Decoding Over Chi-Square Based Optical Channels

In this paper, we consider low density parity check (LDPC) codes as a solution to enhance the optical transmission performance. The decoding algorithm based on message passing algorithm uses the probability density function of the received signal. Its efficiency thus depends on the right evaluation of the signal distribution. We do not make here the classical additive white Gaussian noise (AWGN) assumption, but we investigate a chi-square based channel model which is more accurate for the description of optical impairments. As opposed to previous chi-square based models, no assumption on the signal power of 0 and 1 data is done. The calculation of the logarithmic likelihood ratio (LLR) needed to implement soft LDPC decoder is thus developed for a chi-square channel in a general manner. Computer simulations validate the efficiency of the soft decoder for this type of channel. The results also confirm that the adaptation of LDPC decoder to the specific chi-square channel statistic is necessary to obtain the optimal performance.

A modified design of trellis-coded MPSK for the fading channel

It is shown that the classical additive white Gaussian noise (AWGN) channel design can be retained for the fading channel with any degree of fading, if carried out with the appropriate signal set size M=M/sub min/. The size of the signal set M/sub min/ is shown to depend upon the number of parallel transitions between a given pair of states and the throughput rate. In the proposed multiple trellis-coded modulation (MTCM) scheme with a modified design (MTCM (MD)), the output bits from a rate m/m+1 trellis encoder are assigned multiple signals from an M/sub min/-PSK signal set. Compared to the MTCM with set partitioning proposed for the fading channel (SPF) design, the MTCM (MD) scheme provides the same signal diversity and the same or increased values of the branch distance product, and always leads to increased value of d/sup 2/(free). As a result, the performance is always improved on the Rician fading channel due to the increased d/sup 2/(free), and is improved on any fading channel when an increase in branch distance produce P takes place. When compared to the MTCM with the set partitioning optimum for the AWGN channel (SPA) design, the MTCM (MD) scheme, under certain conditions, provides the same value of d/sup 2/(free) as the MTCM (SPA) design, and is then asymptotically optimum for both the AWGN channel and the fading channels.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>