Matrix Differential Calculus with Applications in Statistics and Econometrics

The remarkable promise of multiple-input multiple-output (MIMO) wireless channels has motivated an intense research activity to characterize the theoretical and practical issues associated with the design of transmit (source) and receive (destination) processing matrices under different operating conditions. This activity was primarily focused on point-to-point (single-hop) communications but more recently there has been an extensive work on two-hop or multi-hop settings in which single or multiple relays are used to deliver the information from the source to the destination. The aim of this tutorial is to provide an up-to-date overview of the fundamental results and practical implementation issues in designing amplify-and-forward MIMO relay systems.

A Tutorial on the Optimization of Amplify-and-Forward MIMO Relay Systems

Interference is traditionally viewed as a performance limiting factor in wireless communication systems, which is to be minimized or mitigated. Nevertheless, a recent line of work has shown that by manipulating the interfering signals such that they add up constructively at the receiver side, known interference can be made beneficial and further improve the system performance in a variety of wireless scenarios, achieved by symbol-level precoding (SLP). This paper aims to provide a tutorial on interference exploitation techniques from the perspective of precoding design in a multi-antenna wireless communication system, by beginning with the classification of constructive interference (CI) and destructive interference (DI). The definition for CI is presented and the corresponding mathematical characterization is formulated for popular modulation types, based on which optimization-based precoding techniques are discussed. In addition, the extension of CI precoding to other application scenarios as well as for hardware efficiency is also described. Proof-of-concept testbeds are demonstrated for the potential practical implementation of CI precoding, and finally a list of open problems and practical challenges are presented to inspire and motivate further research directions in this area.

/pdf/a-tutorial-on-interference-exploitation-via-symbol-level-3h4ot5avtv.pdf

A Tutorial on Interference Exploitation via Symbol-Level Precoding: Overview, State-of-the-Art and Future Directions

This paper considers a multipair massive multiple-input–multiple-output two-way relay network, in which multiple pairs of users are served by a relay station with a large number of antennas, which uses maximum ratio combining/maximum ratio transmission and a fixed amplification factor for reception/transmission. First, the users' ergodic rates are derived for the case with a finite number of antennas, and then, the rate gain is analyzed when the transmit power of the senders and the relay is sufficiently large. We show that the ergodic rates increase with the number of antennas at the relay, i.e., $N$ , but decrease with the number of user pairs, i.e., $K$ , both logarithmically. The energy efficiency for the network is also investigated when the number of antennas grows to infinity. It is further revealed that the ergodic sum-rate can be maintained while the users' transmit power is scaled down by a factor of $1/N$ or the relay power by a factor of $2K/N$ . This indicates that users obtain an energy efficiency gain of $N$ , but the relay has an energy efficiency gain of $N$ divided by the number of users, i.e., $2K$ .

Ergodic Rate Analysis for Multipair Massive MIMO Two-Way Relay Networks

Driven by the recent advancement in unmanned aerial vehicle (UAV) technology, this paper proposes a new wireless network architecture of coordinate multipoint (CoMP) in the sky to harness both the benefits of interference mitigation via CoMP and high mobility of UAVs. Specifically, we consider uplink communications in a multi-UAV enabled multi-user system, where each UAV forwards its received signals from all ground users to a central processor (CP) for joint decoding. Moreover, we consider the case where the users may move on the ground, thus the UAVs need to adjust their locations in accordance with the user locations over time to maximize the network throughput. Utilizing random matrix theory, we first characterize, in closed form, a set of approximated upper and lower bounds of the user’s achievable rate in each time epoch under the practical Rician fading channel model, which is shown to be very tight, both analytically and numerically. UAV placement and movement over different epochs are then optimized based on the derived bounds to maximize the minimum of user average achievable rates over all epochs for both cases of full information (of current and future epochs) and current information on the user’s movement. Interestingly, it is shown that the optimized location of each UAV at any particular epoch is the weighted average of the ground user locations at the current epoch as well as its own location at the previous and/or next epoch. Finally, simulation results are provided to validate and compare the performance of the proposed UAV placement and movement designs under different practical application scenarios.

CoMP in the Sky: UAV Placement and Movement Optimization for Multi-User Communications

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

In this paper, we propose new algorithms to determine the antenna location for downlink distributed antenna systems (DASs) in single-cell and two-cell environments. We consider the composite fading channel which includes small and large scale fadings. First, for the single-cell DAS, we formulate the optimization problem of distributed antenna (DA) port locations by maximizing the lower bound of the expected signal to noise ratio (SNR). In comparison to the conventional algorithm based on the squared distance criterion which requires an iterative method, our problem generates a closed form solution. Next, for the two-cell DAS, we propose a gradient ascent algorithm which determines the optimum DA locations by maximizing the lower bound of the expected signal to leakage ratio (SLR). In our work, we consider selection transmission, maximal ratio transmission and zero-forcing beamforming (ZFBF) under sum power constraint and study equal gain transmission and scaled ZFBF under per-antenna power constraint. Simulation results show that our proposed algorithms based on both the SNR and the SLR criteria offer a capacity gain over the conventional centralized antenna systems.

Antenna Placement Optimization for Distributed Antenna Systems

In this paper, we present a beamforming and power allocation algorithm for a downlink multiple-input single-output distributed antenna system which maximizes energy efficiency (EE). To reduce the computational complexity of conventional joint optimization approaches relying on an iterative method, we propose a near optimal scheme based on a closed-form solution. Employing the decomposition property of the joint optimization problem, the EE problem is solved in two steps. First, we determine the beamforming strategy for the EE maximization exposing the structure of beamforming vectors. Then, the optimal power allocation is presented as a closed-form solution by solving Karush-Kuhn-Tucker conditions. Through numerical simulations, we confirm that the proposed solution shows the performance almost identical to the jointly optimum method with much reduced complexity.

Beamforming and Power Allocation Designs for Energy Efficiency Maximization in MISO Distributed Antenna Systems

In this paper we propose new algorithms to determine the antenna location for downlink distributed antenna systems (DAS) with selection transmission (ST). ST has some advantages for DAS since the feedback overhead is quite small and other-cell interference can be reduced compared to other transmission schemes. For the single-cell case, we consider a circular antenna layout with or without a center antenna and divide a cell into regions with the same physical area. Then, we formulate the optimization problem of distributed antenna (DA) port locations which maximizes the lower bound of the expected signal to noise ratio in each region. Also, for the two-cell DAS, we maximize the lower bound of the expected signal to leakage ratio to identify the optimum DA positions. In order to solve the problem, we propose an iterative method by deriving the gradient of the cost function for a gradient ascent algorithm. The DA locations obtained from our proposed method are compared with conventional solutions. Simulation results show that the proposed algorithms offer a large capacity gain over the centralized antenna systems in single-cell and two-cell environments.

Antenna Placement for Downlink Distributed Antenna Systems with Selection Transmission

In this paper, we propose a feedback bit allocation algorithm for multi-user downlink distributed antenna systems with limited feedback. We consider a composite fading channel with small scale fadings and path loss, and assume the case where each user is served by only one distributed antenna (DA) port while each DA port can support any number of users. In order to efficiently determine bit allocation, we propose an iterative algorithm which minimizes an upper bound of a mean rate loss. Compared to conventional bit allocation methods, the proposed algorithm can be applied to more general system configurations. Simulation results show that our proposed algorithm offers a performance gain of 20% over an equal bit allocation scheme.

Eunsung Park

Papers

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

Antenna Placement Optimization for Distributed Antenna Systems

Beamforming and Power Allocation Designs for Energy Efficiency Maximization in MISO Distributed Antenna Systems

Antenna Placement for Downlink Distributed Antenna Systems with Selection Transmission

Feedback Bit Allocation Schemes for Multi-User Distributed Antenna Systems