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Fundamental Limits of Communication Channels under Non-Gaussian Interference

Le, Anh Duc
http://rave.ohiolink.edu/etdc/view?acc_num=akron1469011496

Abstract Details

2016, Doctor of Philosophy, University of Akron, Electrical Engineering.
Recent years have witnessed an exponential growth in data traffic over both wired and wireless links. This unabated growth in demand for data and dense network deployments mixed with limited spectral resources indicates that co-channel interference will be the main performance-limiting factor in next-generation communication systems. In many cases, the traditional approach of treating co-channel interference plus noise as Gaussian no longer holds. In particular, non-Gaussian interference caused by undesirable signals in the form of random bursts severely affects the throughput and reliability of many modern communication systems, including power line communications, digital subscriber lines, urban and indoor wireless communications, heterogeneous wireless networks, cognitive radio, and underwater acoustic communications. However, despite its ubiquity and importance, communication under non-Gaussian interference is still not fully understood, especially from an information-theoretic perspective. For instance, the optimal signaling scheme and the maximum transmission rate referred to as the Shannon capacity of a static link under Bernoulli-Gaussian (BG) noise that is widely used to model the impulsive behavior in communication systems are not known. The overall scientific goal of this dissertation is therefore to provide an in-depth investigation of channels with non-Gaussian interference from an information-theoretic perspective. The main focus is on the additive BG impulsive noise channel and the general class of Gaussian mixture (GM) noise channel, which has been considered as one of the most general models to represent non-Gaussian interference. The first part of this dissertation is concerned with the fundamental limits of additive BG noise channels. By first considering such channels in the form of a CR link under imperfect spectrum sensing, we propose simple yet accurate methods to evaluate the achievable rates and the outage probabilities when a Gaussian and finite-alphabet inputs are used. Both static and wireless fading environments where channel state information (CSI) is known perfectly at the receiver but not the transmitter are considered. Specifically, using novel piece-wise linear curve fitting (PWLCF)-based methods, we demonstrate that the achievable rates in static channels, the ergodic achievable rates in fast fading, and the outage probabilities in slow fading can be calculated effectively to achieve any given accuracy level. In this part of the dissertation, the investigation on the fundamental limits of BG interference channel is also extended to the case of Rayleigh fading channels where CSI is known at both the transmitter and receiver. In particular, the channel capacity is investigated via tight lower and upper bounds. At first, the upper bound on the channel capacity is derived in closed-form under the assumption of a Gaussian-distributed output. By using a Gaussian input, we then establish a lower bound on channel capacity and provide a simple approximation of the lower bound with a predetermined error level. Both analytical and numerical results show the bounds can be used effectively to estimate the channel capacity. In the second part of the dissertation, attention is paid to the fundamental limits of a general class of GM noise channels. At first, our focus is on the detailed characterization of the capacity-achieving input signals for a non-coherent Rayleigh fading channel where neither the transmitter nor the receiver has CSI knowledge. By first establishing an integrable upper bound on the absolute function of the integrand in the output entropy equation, it is demonstrated that there exists a unique input distribution that achieves the channel capacity. By formulating the Kuhn-Tucker condition (KTC) and establishing a diverging lower bound on this KTC, we show that the capacity-achieving input distribution is discrete having a finite number of mass points. Finally, novel methods are proposed to estimate the achievable rates and capacity of channels to achieve any desired level of accuracy. To this end, a simple technique is proposed to calculate the GM noise entropy without the need of numerical integrals or simulations. Then this result is extended to calculate the output entropy and the achievable rate when the input is Gaussian distributed, which is shown to be asymptotically optimal. Simple PWLCF-based methods are proposed to estimate the output entropy for a real GM channel when the input is discrete, and for a complex GM channel when the input is discrete in amplitude with independent uniform phase. It is demonstrated that the output entropy, and consequently, the achievable rates, can be computed to achieve any pre-determined accuracy level.
Nghi Tran (Advisor)
Arjuna Madanayake (Committee Member)
Kye-Shin Lee (Committee Member)
Lan Zhang (Committee Member)
Truyen Nguyen (Committee Member)
163 p.
Communication; Electrical Engineering; Engineering
non-Gaussian channels; Gaussian mixture; Rayleigh fading; achievable rates; capacity; Gaussian input; discrete inputs; optimal input; piecewise linear approximation

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Citations

  • Le, A. D. (2016). Fundamental Limits of Communication Channels under Non-Gaussian Interference [Doctoral dissertation, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1469011496

    APA Style (7th edition)

  • Le, Anh. Fundamental Limits of Communication Channels under Non-Gaussian Interference. 2016. University of Akron, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1469011496.

    MLA Style (8th edition)

  • Le, Anh. "Fundamental Limits of Communication Channels under Non-Gaussian Interference." Doctoral dissertation, University of Akron, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=akron1469011496

    Chicago Manual of Style (17th edition)

akron1469011496
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This open access ETD is published by University of Akron and OhioLINK.