Weighted Minimum Mean Square Error Research Articles

Tchebycheff Metric 기반 가중평균제곱오차 최소화법을 활용한 다중반응표면 최적화

Abstract Multiresponse optimization (MRO) seeks to find the setting of input variables, which optimizes the multipleresponses simultaneously. The approach of weighted mean squared error (WMSE) minimization for MRO imposesa different weight on the squared bias and variance, which are the two components of the mean squared error (MSE).To date, a weighted sum-based method has been proposed for WMSE minimization. On the other hand, this methodhas a limitation in that it cannot find the most preferred solution located in a nonconvex region in objective functionspace. This paper proposes a Tchebycheff metric-based method to overcome the limitations of the weighted sum-basedmethod. Key Words : Multiresponse Optimization, Weighted Mean Squared Error, Tchebycheff Metric, Weighted Sum 이 논문은 2012학년도 대구대학교 학술연구비 지원에 의한 논문임. * Corresponding Author : In-Junx Jeong (Daegu Univ.)Tel: +82-53-850-6275 email: ijjeong@daegu.ac.krReceived August 20, 2014 Revised October 13, 2014 Accepted January 8, 2015

Cross-Layer Provision of Future Cellular Networks: A WMMSE-based approach

To cope with the growing demand for wireless data and to extend service coverage, future fifth-generation (5G) networks will increasingly rely on the use of low-power nodes to support massive connectivity in a diverse set of applications and services [1]. To this end, virtualized and mass-scale cloud architectures are proposed as promising technologies for 5G in which all the nodes are connected via a backhaul network and managed centrally by such cloud centers. The significant computing power made available by the cloud technologies has enabled the implementation of sophisticated signal processing algorithms, especially by way of parallel processing, for both interference management and network provision. The latter two are among the major signal processing tasks for 5G due to an increased level of frequency sharing, node density, interference, and network congestion. This article outlines several theoretical and practical aspects of joint interference management and network provisioning for future 5G networks. A cross-layer optimization framework is proposed for joint user admission, user-base station (BS) association, power control, user grouping, transceiver design, as well as routing and flow control. We show that many of these cross-layer tasks can be treated in a unified way and implemented in a parallel manner using an efficient algorithmic framework called weighted minimum mean squared error (WMMSE). Some recent developments in this area are highlighted and future research directions are identified.

Filter-And-Forward Relay Design for MIMO-OFDM Systems

In this paper, the filter-and-forward (FF) relay design for multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems is investigated. Due to the considered MIMO structure, the FF relay design is investigated in the framework of joint design together with the linear MIMO transceiver. As the design criterion, first, the minimization of weighted sum mean square error (MSE) is considered. The joint design in this case is approached based on alternating optimization that iterates between the optimal design of the FF relay for given MIMO precoding and decoding matrices and the optimal design of MIMO precoding and decoding matrices for a given FF relay filter. Second, a more advanced problem of joint design for rate maximization is considered. The second problem is approached based on the obtained result regarding the first problem of weighted sum MSE minimization and the existing result regarding the relationship between weighted MSE minimization and rate maximization. Numerical results show the effectiveness of the proposed FF relay design method and significant performance improvement by the proposed FF relay over widely considered simple AF relays for MIMO-OFDM systems.

MMSE precoding for multiuser MISO downlink transmission with non-homogeneous user SNR conditions

This paper is concerned with linear precoding designs for multiuser downlink transmissions. We consider a multiple-input single-output (MISO) system with multiple single-antenna user equipment (UE) experiencing non-homogeneous average signal-to-noise ratio (SNR) conditions. The first part of this work examines different precoding schemes with perfect channel state information (CSI) and average SNR at the base-station (eNB). We then propose a weighted minimum mean squared error (WMMSE) precoder, which takes advantage of the non-homogeneous SNR conditions. Given in a closed-form solution, the proposed WMMSE precoder outperforms other well-known linear precoders, such as zero-forcing (ZF), regularized ZF (RZF), while achieving a close performance to the locally optimal iterative WMMSE (IWMMSE) precoder, in terms of the achievable network sum-rate. In the second part of this work, we consider the non-homogeneous multiuser system with limited and quantized channel quality indicator (CQI) and channel direction indicator (CDI) feedbacks. Based on the CQI and CDI feedback models proposed for the Long-Term Evolution Advanced standard, we then propose a robust WMMSE precoder in a closed-form solution which takes into account the quantization errors. Simulation shows a significant improvement in the achievable network sum-rate by the proposed robust WMMSE precoder, compared to non-robust linear precoder designs.

Distributed Pricing-Based User Association for Downlink Heterogeneous Cellular Networks

This paper considers optimization of the user and base-station (BS) association in a wireless downlink heterogeneous cellular network under the proportional fairness criterion. We first consider the case where each BS has a single antenna and transmits at fixed power and propose a distributed price update strategy for a pricing-based user association scheme, in which the users are assigned to the BS based on the value of a utility function minus a price. The proposed price update algorithm is based on a coordinate descent method for solving the dual of the network utility maximization problem and it has a rigorous performance guarantee. The main advantage of the proposed algorithm as compared to an existing subgradient method for price update is that the proposed algorithm is independent of parameter choices and can be implemented asynchronously. Further, this paper considers the joint user association and BS power control problem and proposes an iterative dual coordinate descent and the power optimization algorithm that significantly outperforms existing approaches. Finally, this paper considers the joint user association and BS beamforming problem for the case where the BSs are equipped with multiple antennas and spatially multiplex multiple users. We incorporate dual coordinate descent with the weighted minimum mean-squared error (WMMSE) algorithm and show that it achieves nearly the same performance as a computationally more complex benchmark algorithm (which applies the WMMSE algorithm on the entire network for BS association) while avoiding excessive BS handover.

Joint Back-Pressure Power Control and Interference Cancellation in Wireless Multi-Hop Networks

Back-Pressure Power Control (BPPC) is a cross-layer network optimization policy that uses power control at the physical layer to facilitate efficient routing of packets at the network layer. The starting point of this paper is that interference cancellation can be judiciously employed together with power control to further enhance network throughput. Effective cancellation requires that the interfering signal can be reliably decoded, implying that power control and interference cancellation are tightly coupled. This leads to a joint Back-Pressure Power Control and Interference Cancellation (BPPC-IC) problem formulation, with the pragmatic constraint that each receiver can cancel at most one interfering signal. This problem is shown to be NP-hard, and two approximate solutions are proposed based on successive geometric programming approximation, and an extended weighted minimum mean squared error (WMMSE) reformulation, respectively. A simpler approximation based on stochastic exploration of the control space is also considered. Simulation results demonstrate that joint optimization of power control and interference cancellation pays off, enabling considerably higher network throughput, and lower average delay due to reduced backlogs.

Optimal Design of Spatial Source-and-Relay Matrices for a Non-Regenerative Two-Way MIMO Relay System

This paper considers a system where two users exchange information via a non-regenerative half-duplex two-way MIMO relay and each of the two users and the relay is equipped with multiple antennas. We study the design of the spatial source covariance matrices (or source matrices) at the two users and the spatial transformation matrix (or relay matrix) at the relay to maximize the achievable weighted sum rate of the system. The source matrices and the relay matrix are optimized alternately until convergence. If the relay matrix is given, we show that the optimal design of the source matrices (for uniformly weighted sum rate) follows a generalized water filling (GWF) algorithm. If the source matrices are given, we show two search algorithms to optimize the relay matrix. The first algorithm is a hybrid gradient method which adaptively switches between the (steepest) gradient descent and the Newton's search. The second is an iterative weighted minimum mean square error (WMMSE) method which alternately refines the MMSE equalizers at the users and the relay matrix. We compare the convergence behaviors of the two algorithms and demonstrate their advantage over prior algorithms. We also show an optimal structure of the relay matrix, which is useful to reduce the search complexity.

The design of optimal uniform filter banks with specified composite response

In this paper we prove that for suitable design specifications and a wide class of optimization criteria, the optimal complex filter bank with specifications on its composite response is composed of frequency translated versions of a prototype filter. In particular, this holds for the min-max and WMMSE (weighted minimum mean square error) criteria. As a result, a simplified design problem whose solution is an optimal prototype filter is formulated. This prototype is essentially an optimal FIR low-pass filter subject to linear constraints on its impulse response. For the WMMSE criterion, this characterization of the optimal filter bank results in a simplified version of the design method presented in [1]. For the min-max criterion, this characterization implies that there exists an optimal window, by which the window design method results in the optimal low-pass prototype. The optimal window design problem is formulated as a linear programming problem, and an approximate solution is derived using the Remez exchange algorithm. For real filter banks in which each filter is composed of a pair of complex filters, the optimal filter bank is no longer composed of frequency translated versions of prototype filter. However, for efficient implementation, the prototype translation property may be part of the design specifications. For this reason, the optimal WMMSE prototype for a class of real filter banks is derived as well.

WMMSE design of digital filter banks with specified composite response

A new method for designing uniform and nonuniform digital filter banks with a specified composite response is presented. The composite response of the filter bank can be met either exactly or to within a given tolerance. We focus on filter banks in which the individual filters are finite impulse response (FIR) digital filters of possibly nonequal length, although the new method is applicable even to more general structures as well. The new method minimizes the weighted sum of the mean square errors in the response of the individual filters, subject to the composite response specifications. Sufficient conditions for either real, ness or phase linearity of the optimal individual filters are presented. The new weighted minimum mean square error (WMMSE) design method is interpreted from a statistical viewpoint as a maximization of the harmonic mean of the output signal-to-noise ratio (SNR) of the individual filters. The complexity of the new method is analyzed, and the design process is demonstrated via a design example.