Huseyin A. Inan

Online power control for the energy harvesting multiple access channel

We consider online power control for a K-user energy harvesting multiple-access channel (MAC). We show that a simple online power control policy that requires each user to know only the mean of its own energy harvesting process and does not require any information regarding the energy harvesting processes of the other users is near optimal for any joint distribution of the energy harvesting processes and for arbitrary battery sizes at the K users. In particular, for any parameter values this strategy achieves a throughput region which is within a constant gap to the capacity region of the classical additive white Gaussian noise (AWGN) MAC. When the number of users in the MAC becomes large, the gap becomes negligible. Therefore, an interesting consequence of our result is that in the limit when the number of users becomes large, the sum throughput of the online energy harvesting MAC approaches the sum capacity of the classical AWGN MAC. While it has been known that the online throughput of an energy harvesting system can approach the AWGN capacity in the limit when the battery size goes to infinity, it is interesting that the AWGN capacity can be also approached in limit of large number of users.

Convolutive Bounded Component Analysis Algorithms for Independent and Dependent Source Separation

Bounded component analysis (BCA) is a framework that can be considered as a more general framework than independent component analysis (ICA) under the boundedness constraint on sources. Using this framework, it is possible to separate dependent as well as independent components from their mixtures. In this paper, as an extension of a recently introduced instantaneous BCA approach, we introduce a family of convolutive BCA criteria and corresponding algorithms. We prove that the global optima of the proposed criteria, under generic BCA assumptions, are equivalent to a set of perfect separators. The algorithms introduced in this paper are capable of separating not only the independent sources but also the sources that are dependent/correlated in both component (space) and sample (time) dimensions. Therefore, under the condition that the sources are bounded, they can be considered as extended convolutive ICA algorithms with additional dependent/correlated source separation capability. Furthermore, they have potential to provide improvement in separation performance, especially for short data records. This paper offers examples to illustrate the space-time correlated source separation capability through a copula distribution-based example. In addition, a frequency-selective Multiple Input Multiple Output equalization example demonstrates the clear performance advantage of the proposed BCA approach over the state-of-the-art ICA-based approaches in setups involving convolutive mixtures of digital communication sources.

A Convolutive Bounded Component Analysis Framework for Potentially Nonstationary Independent and/or Dependent Sources

Bounded Component Analysis (BCA) is a recent framework which enables development of methods for the separation of dependent as well as independent sources from their mixtures. This paper extends a recent geometric BCA approach introduced for the instantaneous mixing problem to the convolutive mixing problem. The paper proposes novel deterministic convolutive BCA frameworks for the blind source extraction and blind source separation of convolutive mixtures of sources which allows the sources to be potentially nonstationary. The global maximizers of the proposed deterministic BCA optimization settings are proved to be perfect separators. The paper also illustrates that the iterative algorithms corresponding to these frameworks are capable of extracting/separating convolutive mixtures of not only independent sources but also dependent (even correlated) sources in both component (space) and sample (time) dimensions through simulations based on a Copula distributed source system. In addition, even when the sources are independent, it is shown that the proposed BCA approach have the potential to provide improvement in separation performance especially for short data records based on the setups involving convolutive mixtures of digital communication sources.

Adaptive mixture methods based on Bregman divergences

We investigate adaptive mixture methods that linearly combine outputs of m constituent filters running in parallel to model a desired signal. We use Bregman divergences and obtain certain multiplicative updates to train the linear combination weights under an affine constraint or without any constraints. We use unnormalized relative entropy and relative entropy to define two different Bregman divergences that produce an unnormalized exponentiated gradient update and a normalized exponentiated gradient update on the mixture weights, respectively. We then carry out the mean and the mean-square transient analysis of these adaptive algorithms when they are used to combine outputs of m constituent filters. We illustrate the accuracy of our results and demonstrate the effectiveness of these updates for sparse mixture systems.

A Bounded Component Analysis approach for the separation of convolutive mixtures of dependent and independent sources

Bounded Component Analysis is a new framework for Blind Source Separation problem. It allows separation of both dependent and independent sources under the assumption about the magnitude boundedness of sources. This article proposes a novel Bounded Component Analysis optimization setting for the separation of the convolutive mixtures of sources as an extension of a recent geometric framework introduced for the instantaneous mixing problem. It is shown that the global maximizers of this setting are perfect separators. The article also provides the iterative algorithm corresponding to this setting and the numerical examples to illustrate its performance especially for separating convolutive mixtures of sources that are correlated in both space and time dimensions.

Capacity of the energy harvesting Gaussian MAC

We consider an energy harvesting multiple access channel where the transmitters are powered by an exogenous stochastic energy harvesting process and equipped with finite batteries. We characterize the capacity region of this channel as n-letter mutual information rate and develop inner and outer bounds that differ by a constant gap. An interesting conclusion that emerges from our results is that in a symmetric system, where transmitters are statistically equivalent to each other, the largest achievable common rate point approaches that of a standard AWGN MAC with an average power constraint, as the number of users in the MAC becomes large.

Robust estimation in flat fading channels under bounded channel uncertainties

We investigate channel equalization problem for time-varying flat fading channels under bounded channel uncertainties. We analyze three robust methods to estimate an unknown signal transmitted through a time-varying flat fading channel. These methods are based on minimizing certain mean-square error criteria that incorporate the channel uncertainties into their problem formulations instead of directly using the inaccurate channel information that is available. We present closed-form solutions to the channel equalization problems for each method and for both zero mean and nonzero mean signals. We illustrate the performances of the equalization methods through simulations.

Adaptive mixture methods using Bregman divergences

We investigate affinely constrained mixture methods adaptively combining outputs of m constituent filters running in parallel to model a desired signal. We use Bregman divergences and obtain multiplicative updates to train these linear combination weights under the affine constraints. We use the unnormalized relative entropy and the relative entropy that produce the exponentiated gradient update with unnormalized weights (EGU) and the exponentiated gradient update with positive and negative weights (EG), respectively. We carry out the mean and the mean-square transient analysis of the affinely constrained mixtures of m filters using the EGU or EG algorithms. We compare performances of different algorithms through our simulations and illustrate the accuracy of our results.

Stationary Point Characterization for a Class of BCA Algorithms

Bounded component analysis (BCA) is a recently introduced approach including independent component analysis as a special case under the assumption of source boundedness. In this paper, we provide a stationary point analysis for the recently proposed instantaneous BCA algorithms that are capable of separating dependent, even correlated as well as independent sources from their mixtures. The stationary points are identified and characterized as either perfect separators, which are the global maxima of the proposed optimization scheme or saddle points. The important result emerging from the analysis is that there are no local optima that can prevent the proposed BCA algorithms from converging to perfect separators.

An extended family of bounded component analysis algorithms

Bounded Component Analysis (BCA) is a recent concept proposed as an alternative method for Blind Source Separation problem. BCA enables the separation of dependent as well as independent sources from their mixtures under the practical assumption on source boundedness. This article extends the optimization setting of a recent BCA approach which can be used to produce a variety of BCA algorithms. The article also provides examples of objective functions and the corresponding iterative algorithms. The numerical examples illustrate the advantages of proposed BCA examples regarding the correlated source separation capability over the state of the art ICA based approaches.