Regularized Zero-forcing Beamforming Research Articles

Regularized Zero-Forcing Aided Hybrid Beamforming for Millimeter-Wave Multiuser MIMO Systems

This paper considers hybrid beamforming consisting of analog beamforming (ABF) coupled with digital baseband beamforming (DBF) which is designed for multi-user (MU) multiple input multiple output (MIMO) millimeter-wave (mmWave) communications. ABF uses a limited number of radio frequency (RF) chains and finite-resolution phase-shifters to alleviate the power consumption at the base station (BS), while DBF uses either zero-forcing beamforming (ZFB) or regularized zero forcing beamforming (RZFB) to restrain MU interference. The joint design of ABF and DBF constitutes a computationally challenging mixed discrete continuous optimization problem. The paper develops efficient algorithms for its solution, which iterate scalable-complex expressions. Furthermore, we conceive a new class of MU RZFB for attaining higher rates. Simulations are provided to demonstrate the viability of the proposed algorithms and the advantages of the conceived RZFB.

New generalized zero forcing beamforming for serving more users in energy-harvesting enabled networks

This paper considers a multi-user wireless communication network supported by a multiple-antenna base station (BS), where the users who are located sufficiently close to the BS employ wireless energy harvesting (EH) to replenish their energy needs. The objective of this work is to design an efficient beamforming to maximize the minimum throughput among all the information users (IUs), subject to EH constraints. In this regard, transmit time-switching approach is employed, where energy and information are transmitted over different fractions of a time-slot. To achieve efficient EH, a conjugate beamforming (matched filtering) is applied. To design efficient information beamforming for max–min throughput optimization, conventional zero-forcing (ZF) beamforming can be adopted, however, it will not suppress multi-user interference if the number of users is greater than the number of antennas at the BS. To this end, different from the existing works which employ regularized zero-forcing (RZF) beamforming, this work proposes a new generalized zero-forcing (GZF) beamforming, which promises better max–min throughput compared to that achieved by the RZF beamforming. A new path-following algorithm is developed to achieve max–min throughput optimization by GZF beamforming, which is based on a simple convex quadratic program over each iteration.

A New Class of Structured Beamforming for Content-Centric Fog Radio Access Networks

A multi-user fog radio access network (F-RAN) is designed for supporting content-centric services. The requested contents are partitioned into sub-contents, which are then 'beam- formed' by the remote radio heads (RRHs) for transmission to the users. Since a large number of beamformers must be designed, this poses a computational challenge. We tackle this challenge by proposing a new class of regularized zero forcing beamforming (RZFB) for directly mitigating the inter-content interferences, while the 'intra-content interference' is mitigated by successive interference cancellation at the user end. Thus each beamformer is decided by a single real variable (for proper Gaus- sian signaling) or by a pair of complex variables (for improper Gaussian signaling). Hence the total number of decision variables is substantially reduced to facilitate tractable computation. To address the problem of energy efficiency optimization subject to multiple constraints, such as individual user-rate requirement and the fronthauling constraint of the links between the RRHs and the centralized baseband signal processing unit, as well as the total transmit power budget, we develop low-complexity path- following algorithms. Finally, we actualize their performance by simulations.

Downlink Training Design for FDD Massive MIMO Systems in the Presence of Colored Noise

Massive multiple-input multiple-output (MaMi) systems have attracted much research attention during the last few years. This is because MaMi systems are able to achieve a remarkable improvement in data rate and thus meet the immensely ongoing traffic demands required by the future wireless networks. To date, the downlink training sequence (DTS) for the frequency division duplex (FDD) MaMi communications systems have been designed based on the idealistic assumption of white noise environments. However, it is essential and more practical to consider the colored noise environments when designing an efficient DTS for channel estimation. To this end, this paper proposes a new DTS design by exploring the joint use of spatial channel and noise covariance matrices, when the channel is not reciprocal but the coherence block length remains limited. We derive an analytical solution for the mean square error (MSE) based on the proposed training design with colored noise. In addition, this paper exploits the method of random matrix theory to provide an analytical solution for the downlink (DL) achievable sum rate of the regularized zero forcing beamforming (RZFBF) precoder. Numerical results demonstrate that using the proposed DTS design, the MSE of the channel estimate is significantly reduced compared with the conventional training designs with white noise. Furthermore, the results show that the proposed pilot design markedly improves the DL achievable SR over the conventional training designs, especially at relatively low signal-to-noise-ratio (SNR) levels. This enables FDD MaMi systems to operate under more practical scenarios of colored noise and limited coherence time environments.

Large-Scale Beamforming for Massive MIMO via Randomized Sketching

Massive MIMO system yields significant improvements in spectral and energy efficiency for future wireless communication systems. The regularized zero-forcing (RZF) beamforming is able to provide good performance with the capability of achieving numerical stability and robustness to the channel uncertainty. However, in massive MIMO systems, the matrix inversion operation in RZF beamforming becomes computationally expensive. To address this computational issue, we shall propose a novel randomized sketching based RZF beamforming approach with low computational complexity. This is achieved by solving a linear system via randomized sketching based on the preconditioned Richard iteration, which guarantees high quality approximations to the optimal solution. We theoretically prove that the sequence of approximations obtained iteratively converges to the exact RZF beamforming matrix linearly fast as the number of iterations increases. Also, it turns out that the system sum-rate for such sequence of approximations converges to the exact one at a linear convergence rate. Our simulation results verify our theoretical findings.

Performance Improvement for Multi-User Millimeter-Wave Massive MIMO Systems

In this paper, we study the problem of optimizing the performance of multi-user millimeter-wave (mmWave) communications in three steps. The first one is given by the use of a new pilot mapping to reduce the inter-user interference effect and to perform more accurate channel estimation. In the second step, we designed a hybrid receiver that, based on the accuracy of the channel state information, chooses between the minimum mean square error (MMSE) and the multi-user regularized zero-forcing beamforming (RZFBF) receivers, to combine/precode the massive multiple-input multiple-output (MIMO) signal. In the third step, we propose to improve the beam direction with a slight change in the azimuth angle during the uplink communications to increase the multi-user efficiency and reduce inter-user interference. Numerical results show the performance increase using the proposed solutions in terms of the spectral efficiency by comparing the MMSE, RZFBF, and hybrid receivers.

Multi-User Regularized Zero-Forcing Beamforming

Regularized zero-forcing beamforming (RZFB) is an interesting class of linear signal processing problems, which is very attractive for use in large-scale communication networks due its simple visualization as a straightforward extension of the well-accepted zero-forcing beamforming (ZFB). However, unlike ZFB, which is multi-user interference free, RZFB must manage multi-user interference to achieve its high throughput performance. Most existing works focus on the performance analysis of particular RZBF schemes such as the equip-power allocated RZBF under a fixed regularization parameter. This paper is the first work to consider the joint design of power allocation and regularization parameter for RZFB to maximize the worst users' throughput or the quality-of-service awarded energy efficiency under a fixed transmit power constraint. Such designs pose very computationally challenging optimization problems, for which the paper proposes two-stage optimization algorithms of low computational complexity. Their computational and performance efficiencies are substantiated through numerical examples.

Message Passing Algorithm for Distributed Downlink Regularized Zero-Forcing Beamforming with Cooperative Base Stations

Base station (BS) cooperation can turn unwanted interference to useful signal energy for enhancing system performance. In the cooperative downlink, zero-forcing beamforming (ZFBF) with a simple scheduler is well known to obtain nearly the performance of the capacity-achieving dirty-paper coding. However, the centralized ZFBF approach is prohibitively complex as the network size grows. In this paper, we devise message passing algorithms for realizing the regularized ZFBF (RZFBF) in a distributed manner using belief propagation. In the proposed methods, the overall computational cost is decomposed into many smaller computation tasks carried out by groups of neighboring BSs and communication is only required between neighboring BSs. More importantly, some exchanged messages can be computed based on channel statistics rather than instantaneous channel state information, leading to significant reduction in computational complexity. Simulation results demonstrate that the proposed algorithms converge quickly to the exact RZFBF and much faster compared to conventional methods.

Sum Rate Maximization for Cognitive MISO Broadcast Channels: Beamforming Design and Large Systems Analysis

This paper considers the ergodic weighted sum rate maximization (WSRMax) problem for an underlay cognitive radio multiple input single output (MISO) broadcast channel. In this setting, a secondary network, consisting of a base-station with M transmit antennas and K single-antenna secondary users (SUs), is allowed to share the same spectrum with a primary user (PU), under an average total transmit power (ATTP) constraint and an average interference power (AIP) constraint at the PU receiver. We show that the ATTP constraint always remains active, and as the maximum ATTP P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">av</sub> → ∞, the ergodic WSR approaches infinity similar to conventional non-CR networks. We propose a novel low-complexity suboptimal beamforming scheme termed "Partially-Projected & Regularized Zero-Forcing Beamforming" (PP-RZFBF) with a close-form beamformer, by combining the regularized zero-forcing (RZF) with the channel projection idea, to achieve a tradeoff between maximizing secondary throughput and suppressing secondary multiuser interference as well as the interference on PU. In order to analyze and optimize the performance of this scheme, we employ the large system analysis technique, in the limit as M and K approach infinity with a fixed ratio r=K\M. This allows us to derive deterministic limiting approximations for the PP-RZFBF problem which enables us to determine asymptotically optimal beamformers for PP-RZFBF. In the large system limit, for the PP-RZFBF scheme, we also find that as P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">av</sub> → ∞, the interference on PU caused by the secondary transmission is asymptotically removed. A special suboptimal beamforming scheme called "CZFBF" is also considered, which involves zero forcing all the interference, including the secondary multiuser interference as well as the interference imposed on PU. Various interesting comparisons between PP-RZFBF and CZFBF are provided. Numerical simulations illustrate that the asymptotically optimal beamformers for the PP-RZFBF scheme provide an excellent performance even for finite-sized systems.

Regularized Zero-Forcing for Multiantenna Broadcast Channels with User Selection

A multiantenna multiuser broadcast channel with transmitter beamforming and user selection is considered. Different from the conventional works, we consider imperfect channel state information (CSI) which is a practical scenario for multiuser broadcast channels. We propose a robust regularized zero-forcing (RRZF) beamforming at the base station. Then we show that the RRZF outperforms zero-forcing (ZF) and regularized ZF (RZF) beamforming even as the number of users grows to infinity. Simulation results validate the advantage of the proposed robust RZF beamforming.