On the Capacity of the Wiener Phase-Noise Channel: Bounds and Capacity Achieving Distributions

In this paper, the capacity of the additive white Gaussian noise (AWGN) channel, affected by time-varying Wiener phase noise is investigated. Tight upper and lower bounds on the capacity of this channel are developed. The upper bound is obtained by using the duality approach, and considering a specific distribution over the output of the channel. In order to lower-bound the capacity, first a family of capacity-achieving input distributions is found by solving a functional optimization of the channel mutual information. Then, lower bounds on the capacity are obtained by drawing samples from the proposed distributions through Monte-Carlo simulations. The proposed capacity-achieving input distributions are circularly symmetric, non-Gaussian, and the input amplitudes are correlated over time. The evaluated capacity bounds are tight for a wide range of signal-to-noise-ratio (SNR) values, and thus they can be used to quantify the capacity. Specifically, the bounds follow the well-known AWGN capacity curve at low SNR, while at high SNR, they coincide with the high-SNR capacity result available in the literature for the phase-noise channel.Comment: IEEE Transactions on Communications, 201

Optimization of capacity in non-Gaussian noise models with and without fading channels for sustainable communication systems

The highest rate at which information may be reliably sent via a communication link is known as its capacity. In the case of non-Gaussian noise, the capacity of the channel depends on the specific characteristics of the noise, which can cause severe errors and reduce the reliability of communication systems over a fading channel. The Gaussian mixture impulsive noise model (GMINM), which is a more general and flexible non-Gaussian model for impulsive noise, has been compared in this paper with the Middleton Class-A impulsive noise model (MCAINM) in terms of derived channel capacity normalized by channel bandwidth (C/BW) with and without Rayleigh fading (Rf) channels. It also investigated the trade-off between complexity and accuracy in modeling the impulsive noise using two simplified Middleton Class-A impulsive noise models based on derived C/BW. The derived C/BW of these models under various conditions, such as different signal-to-noise ratios and impulsive noise parameters and models, have been performed and evaluated using two different scenarios: the exact method and the semi-analytical method. When the impulsive noise parameters  and A are both near 0 in GMINM and MCAINM, respectively, the capacity of the impulsive noise channel is found to be equivalent to that of the Gaussian channel sustainable, as shown by the findings based on Monte-Carlo simulations. We have shown that when the impulsive noise decreases, the capacity increases in all models; however, the capacity of Gaussian noise is higher than the capacity of non-Gaussian noise, which in turn is higher than the capacity of non-Gaussian noise over the Rf channel overall values of SNR in dB. Moreover, multi-channel configuration introduces spatial diversity and multiplexing gains that have been proposed to sustainably optimize the ergodic capacity for the challenge case when the channel state information (CSI) is unknown at the transmitter in non-Gaussian noise over Rf channel. In today's rapidly evolving world, sustainable communication systems play a crucial role in ensuring efficient and responsible utilization of resources. As the demand for wireless communication continues to rise, it becomes imperative to optimize the capacity of communication channels, especially in scenarios involving non-Gaussian noise models and fading channels.

Information-theoretic analysis of a family of additive energy channels

This dissertation studies a new family of channel models for non-coherent com- munications, the additive energy channels. By construction, the additive en- ergy channels occupy an intermediate region between two widely used channel models: the discrete-time Gaussian channel, used to represent coherent com- munication systems operating at radio and microwave frequencies, and the discrete-time Poisson channel, which often appears in the analysis of intensity- modulated systems working at optical frequencies. The additive energy chan- nels share with the Gaussian channel the additivity between a useful signal and a noise component. However, the signal and noise components are not complex- valued quadrature amplitudes but, as in the Poisson channel, non-negative real numbers, the energy or squared modulus of the complex amplitude. The additive energy channels come in two variants, depending on whether the channel output is discrete or continuous. In the former case, the energy is a multiple of a fundamental unit, the quantum of energy, whereas in the second the value of the energy can take on any non-negative real number. For con- tinuous output the additive noise has an exponential density, as for the energy of a sample of complex Gaussian noise. For discrete, or quantized, energy the signal component is randomly distributed according to a Poisson distribution whose mean is the signal energy of the corresponding Gaussian channel; part of the total noise at the channel output is thus a signal-dependent, Poisson noise component. Moreover, the additive noise has a geometric distribution, the discrete counterpart of the exponential density. Contrary to the common engineering wisdom that not using the quadrature amplitude incurs in a signi¯cant performance penalty, it is shown in this dis- sertation that the capacity of the additive energy channels essentially coincides with that of a coherent Gaussian model under a broad set of circumstances. Moreover, common modulation and coding techniques for the Gaussian chan- nel often admit a natural extension to the additive energy channels, and their performance frequently parallels those of the Gaussian channel methods. Four information-theoretic quantities, covering both theoretical and practi- cal aspects of the reliable transmission of information, are studied: the channel capacity, the minimum energy per bit, the constrained capacity when a given digital modulation format is used, and the pairwise error probability. Of these quantities, the channel capacity sets a fundamental limit on the transmission capabilities of the channel but is sometimes di±cult to determine. The min- imum energy per bit (or its inverse, the capacity per unit cost), on the other hand, turns out to be easier to determine, and may be used to analyze the performance of systems operating at low levels of signal energy. Closer to a practical ¯gure of merit is the constrained capacity, which estimates the largest amount of information which can be transmitted by using a speci¯c digital modulation format. Its study is complemented by the computation of the pairwise error probability, an e®ective tool to estimate the performance of practical coded communication systems. Regarding the channel capacity, the capacity of the continuous additive energy channel is found to coincide with that of a Gaussian channel with iden- tical signal-to-noise ratio. Also, an upper bound |the tightest known| to the capacity of the discrete-time Poisson channel is derived. The capacity of the quantized additive energy channel is shown to have two distinct functional forms: if additive noise is dominant, the capacity is close to that of the continu- ous channel with the same energy and noise levels; when Poisson noise prevails, the capacity is similar to that of a discrete-time Poisson channel, with no ad- ditive noise. An analogy with radiation channels of an arbitrary frequency, for which the quanta of energy are photons, is presented. Additive noise is found to be dominant when frequency is low and, simultaneously, the signal-to-noise ratio lies below a threshold; the value of this threshold is well approximated by the expected number of quanta of additive noise. As for the minimum energy per nat (1 nat is log2 e bits, or about 1.4427 bits), it equals the average energy of the additive noise component for all the stud- ied channel models. A similar result was previously known to hold for two particular cases, namely the discrete-time Gaussian and Poisson channels. An extension of digital modulation methods from the Gaussian channels to the additive energy channel is presented, and their constrained capacity determined. Special attention is paid to their asymptotic form of the capacity at low and high levels of signal energy. In contrast to the behaviour in the vi Gaussian channel, arbitrary modulation formats do not achieve the minimum energy per bit at low signal energy. Analytic expressions for the constrained capacity at low signal energy levels are provided. In the high-energy limit simple pulse-energy modulations, which achieve a larger constrained capacity than their counterparts for the Gaussian channel, are presented. As a ¯nal element, the error probability of binary channel codes in the ad- ditive energy channels is studied by analyzing the pairwise error probability, the probability of wrong decision between two alternative binary codewords. Saddlepoint approximations to the pairwise error probability are given, both for binary modulation and for bit-interleaved coded modulation, a simple and e±cient method to use binary codes with non-binary modulations. The meth- ods yield new simple approximations to the error probability in the fading Gaussian channel. The error rates in the continuous additive energy channel are close to those of coherent transmission at identical signal-to-noise ratio. Constellations minimizing the pairwise error probability in the additive energy channels are presented, and their form compared to that of the constellations which maximize the constrained capacity at high signal energy levels

Frequency Domain Independent Component Analysis Applied To Wireless Communications Over Frequency-selective Channels

In wireless communications, frequency-selective fading is a major source of impairment for wireless communications. In this research, a novel Frequency-Domain Independent Component Analysis (ICA-F) approach is proposed to blindly separate and deconvolve signals traveling through frequency-selective, slow fading channels. Compared with existing time-domain approaches, the ICA-F is computationally efficient and possesses fast convergence properties. Simulation results confirm the effectiveness of the proposed ICA-F. Orthogonal Frequency Division Multiplexing (OFDM) systems are widely used in wireless communications nowadays. However, OFDM systems are very sensitive to Carrier Frequency Offset (CFO). Thus, an accurate CFO compensation technique is required in order to achieve acceptable performance. In this dissertation, two novel blind approaches are proposed to estimate and compensate for CFO within the range of half subcarrier spacing: a Maximum Likelihood CFO Correction approach (ML-CFOC), and a high-performance, low-computation Blind CFO Estimator (BCFOE). The Bit Error Rate (BER) improvement of the ML-CFOC is achieved at the expense of a modest increase in the computational requirements without sacrificing the system bandwidth or increasing the hardware complexity. The BCFOE outperforms the existing blind CFO estimator [25, 128], referred to as the YG-CFO estimator, in terms of BER and Mean Square Error (MSE), without increasing the computational complexity, sacrificing the system bandwidth, or increasing the hardware complexity. While both proposed techniques outperform the YG-CFO estimator, the BCFOE is better than the ML-CFOC technique. Extensive simulation results illustrate the performance of the ML-CFOC and BCFOE approaches