Matrix Differential Calculus with Applications in Statistics and Econometrics

We study a certain random groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.

Shape Fluctuations and Random Matrices

In this chapter we deal with the following nonlinear fractional programming problem: 

$$P:\mathop{{\max }}\limits_{{x \in s}} q(x) = (f(x) + \alpha )/((x) + \beta )$$

where f, g: R n → R, α, β ∈ R, S ⊆ R n . To simplify things, and without restricting the generality of the problem, it is usually assumed that, g(x) + β + 0 for all x ∈ S,S is non-empty and that the objective function has a finite optimal value.

Nonlinear Fractional Programming

Radio waves carry both energy and information simultaneously. Nevertheless, radio-frequency (RF) transmissions of these quantities have traditionally been treated separately. Currently, the community is experiencing a paradigm shift in wireless network design, namely, unifying wireless transmission of information and power so as to make the best use of the RF spectrum and radiation as well as the network infrastructure for the dual purpose of communicating and energizing. In this paper, we review and discuss recent progress in laying the foundations of the envisioned dual purpose networks by establishing a signal theory and design for wireless information and power transmission (WIPT) and identifying the fundamental tradeoff between conveying information and power wirelessly. We start with an overview of WIPT challenges and technologies, namely, simultaneous WIPT (SWIPT), wirelessly powered communication networks (WPCNs), and wirelessly powered backscatter communication (WPBC). We then characterize energy harvesters and show how WIPT signal and system designs crucially revolve around the underlying energy harvester model. To that end, we highlight three different energy harvester models, namely, one linear model and two nonlinear models, and show how WIPT designs differ for each of them in single-user and multi-user deployments. Topics discussed include rate-energy region characterization, transmitter and receiver architectures, waveform design, modulation, beamforming and input distribution optimizations, resource allocation, and RF spectrum use. We discuss and check the validity of the different energy harvester models and the resulting signal theory and design based on circuit simulations, prototyping, and experimentation. We also point out numerous directions that are promising for future research.

Fundamentals of Wireless Information and Power Transfer: From RF Energy Harvester Models to Signal and System Designs

Radiative wireless power transfer (WPT) is a promising technology to provide cost-effective and real-time power supplies to wireless devices. Although radiative WPT shares many similar characteristics with the extensively studied wireless information transfer or communication, they also differ significantly in terms of design objectives, transmitter/receiver architectures and hardware constraints, and so on. In this paper, we first give an overview on the various WPT technologies, the historical development of the radiative WPT technology and the main challenges in designing contemporary radiative WPT systems. Then, we focus on the state-of-the-art communication and signal processing techniques that can be applied to tackle these challenges. Topics discussed include energy harvester modeling, energy beamforming for WPT, channel acquisition, power region characterization in multi-user WPT, waveform design with linear and non-linear energy receiver model, safety and health issues of WPT, massive multiple-input multiple-output and millimeter wave enabled WPT, wireless charging control, and wireless power and communication systems co-design. We also point out directions that are promising for future research.

Communications and Signals Design for Wireless Power Transmission

This paper studies linear precoding and decoding schemes for K-user interference channel systems. It was shown by Cadambe and Jafar that the interference alignment (IA) algorithm achieves a theoretical bound on degrees of freedom (DOF) for interference channel systems. Based on this, we first introduce a non-iterative solution for the precoding and decoding scheme. To this end, we determine the orthonormal basis vectors of each user's precoding matrix to achieve the maximum DOF, then we optimize precoding matrices in the IA method according to two different decoding schemes with respect to individual rate. Second, an iterative processing algorithm is proposed which maximizes the weighted sum rate. Deriving the gradient of the weighted sum rate and applying the gradient descent method, the proposed scheme identifies a local-optimal solution iteratively. Simulation results show that the proposed iterative algorithm outperforms other existing methods in terms of sum rate. Also, we exhibit that the proposed non-iterative method approaches a local optimal solution at high signal-to-noise ratio with reduced complexity.

Linear precoder designs for K-user interference channels

This paper considers both one-way and two-way relaying systems with multiple relays between two terminal nodes where all nodes have multiple-input multiple-output (MIMO) antennas. We propose a unified algorithm which computes the optimal linear transceivers jointly at the source node and the relay nodes for amplify-and-forward (AF) protocols. First, optimization designs based on the sum-rate and the mean-square error (MSE) criteria are formulated for the two-way AF relaying channel. Due to non-convexity of the given problems, the proposed schemes iteratively identify local-optimal source and relay filters by deriving the gradients of the cost functions for a gradient descent algorithm. Then, the proposed algorithm can optimize a one-way multiple relay system as a special case of the two-way channel. Finally, we prove the global optimality of the maximum sum-rate scheme under an asymptotically large antenna assumption. From simulation results, it is confirmed that the proposed methods yield the near optimum result for the MIMO multiple relay channel even with a moderate number of antennas. Consequently, we show that the proposed algorithm outperforms conventional schemes in terms of the sum-rate and the error performance for both one-way and two-way protocols.

Joint Optimization for One and Two-Way MIMO AF Multiple-Relay Systems

This paper studies multiuser wireless powered communication networks, where energy constrained users charge their energy storages by scavenging energy of the radio frequency signals radiated from a hybrid access point (H-AP). The energy is then utilized for the users’ uplink information transmission to the H-AP in time division multiple access mode. In this system, we aim to maximize the uplink sum rate performance by jointly optimizing energy and time resource allocation for multiple users in both infinite capacity and finite capacity energy storage cases. First, when the users are equipped with the infinite capacity energy storages, we derive the optimal downlink energy transmission policy at the H-AP. Based on this result, analytical resource allocation solutions are obtained. Next, we propose the optimal energy and time allocation algorithm for the case where each user has finite capacity energy storage. Simulation results confirm that the proposed algorithms offer about 30% average sum rate performance gain over conventional schemes.

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Resource Allocation Techniques for Wireless Powered Communication Networks With Energy Storage Constraint

In this paper, we propose a new design strategy based on the minimum mean-squared error (MMSE) in closed-loop non-regenerative multiple-input multiple-output relaying systems. Instead of conventional singular value decomposition based methods, we address the problem for joint MMSE design in a different approach using the Wiener filter solution which leads to simple derivations of the optimal MMSE designs. First, allowing the channel state information (CSI) at the source, we provide a new closed form solution for a source-relay-destination joint MMSE design by extending existing relay-destination joint MMSE designs. Second, for the limited feedback scenario, we address a codebook design criteria for the multiple streams preceding design with respect to the MMSE criterion. From our design strategy, we observe that compared to conventional non-regenerative relaying systems, the source or the destination only needs to know the CSI corresponding to its own link such as the source-to-relay or the relay-to-destination in view of the MMSE. Simulation results show that the proposed design gives about 7.5 dB gains at a bit error rate of 10-4 over existing relay-destination joint MMSE schemes and we can get close to the optimal unquantized schemes with only a few feedback bits.

MMSE Based Transceiver Designs in Closed-Loop Non-Regenerative MIMO Relaying Systems

This paper investigates multiuser multiple-input–multiple-output (MIMO) wireless powered communication networks where a multiantenna hybrid access point (H-AP) transfers wireless energy to multiantenna users in a downlink phase, and the users utilize the harvested energy for their information transmission to the H-AP in an uplink phase. By employing space-division multiple-access techniques, we propose an optimal algorithm that jointly computes the downlink energy precoding matrices, the uplink information precoding matrices, and time allocation between the downlink and the uplink phases for maximizing the uplink sum-rate performance. To this end, we first obtain the optimal energy and information transmit covariance matrices with given time allocation. Then, the optimal time allocation can be efficiently identified by a simple line search method. Simulation results verify that the proposed joint optimal algorithm significantly improves the average sum-rate performance, compared with a conventional scheme that determines time allocation and precoding matrices separately.

Kyoung-Jae Lee

Papers

Linear precoder designs for K-user interference channels

Joint Optimization for One and Two-Way MIMO AF Multiple-Relay Systems

Resource Allocation Techniques for Wireless Powered Communication Networks With Energy Storage Constraint

MMSE Based Transceiver Designs in Closed-Loop Non-Regenerative MIMO Relaying Systems

Sum-Rate Maximization for Multiuser MIMO Wireless Powered Communication Networks