Linear Zero-forcing Beamforming Research Articles

Artificial-Noise-Aided Secure Multi-User Multi-Antenna Transmission With Quantized CSIT: A Comprehensive Design and Analysis

We present a secure multi-user multi-antenna transmission framework based on artificial-noise-aided linear zero-forcing beamforming, with limited channel state information feedback from multiple distributed legitimate users (LUs). The secrecy performance of the proposed scheme is analytically investigated and optimized. We develop a new accurate closed-form expression of a lower bound on the ergodic secrecy rate (ESR) of each LU without assuming asymptotes for any system parameter. To make system design tractable, we develop another lower bound on ESR which is so analytically amenable that it enables one to not only extend the results of the previous related works but also explore some untouched aspects of the well known artificial-noise-aided scheme. We derive the optimized power allocation coefficient to message-bearing signals which maximizes the latter ESR lower bound. Furthermore, we theoretically study respectively the impacts of the two main parameters, i.e., transmit power $P$ and the number of feedback bits of each LU $B$ , on the power allocation coefficient, and show the asymptotic results for the high-power and high-quantization-resolution systems. We also develop a sufficient condition on $P$ and $B$ under which a positive ESR of each LU can be achieved. We study some important parameters called the minimum required transmit power (MRTP) and the minimum required number of feedback bits (MRFBs) for each LU to achieve a positive ESR or to achieve a target ESR, which have rarely been touched before. Besides, we propose the algorithms to obtain the MRTP and MRFBs. Numerical results are also provided to verify our theoretical results.

Energy Efficiency Optimization for CoMP-SWIPT Heterogeneous Networks

In this paper, a fundamental study of energy efficiency (EE) optimization for coordinated multi-point (CoMP) simultaneous wireless information and power transfer (SWIPT) heterogeneous networks (HetNets) is provided. We aim to optimize the EE while satisfying certain quality-of-service requirements in regard to transmission rate and energy harvesting at both the macro cell and small cells. The corresponding joint beamforming and power allocation in the presence of intra- and inter-cell interference constitutes an EE maximization problem that is non-convex, and hence, very challenging to solve. In order to solve this problem, we propose to separate the beamforming design and power allocation processes. First, we adopt linear zero-forcing (ZF) beamforming to suppress the multi-user interference from both the energy harvesting users (EH-UEs) as well as the information decoding UEs (ID-UEs), thus transforming the HetNet under consideration to a virtual point-to-point system. An efficient power allocation algorithm is then developed to maximize the corresponding EE. On the other hand, the ZF strategy does not utilize the notion that interference benefits the EH-UEs. As a result, we propose a partial ZF approach by differentiating the EH-UEs and ID-UEs in order to further improve the EE. Our findings show that the EE can be significantly improved through the integration of CoMP-SWIPT in HetNets.

Full-Duplex Small-Cell Networks: A Physical-Layer Security Perspective

We provide a theoretical study of physical (PHY)-layer security performance in full-duplex (FD) small-cell networks. Here, the multi-antenna base stations (BSs) and user equipments (UEs) follow from the homogeneous Poisson point process-based abstraction model. To facilitate FD communications, we take into account: 1) successive interference cancellation capability at the UE side via guard regions of arbitrary radii and 2) residual self-interference at the BS side using Rician fading distribution with arbitrary statistics. We investigate the small-cell network PHY-layer security performance in the presence of a Poisson field of eavesdroppers, under the different scenarios of passive and colluding eavesdropping. Considering linear zero-forcing beamforming, we characterize the downlink and the uplink ergodic secrecy rates and derive closed-form expressions for the different useful and interference signals statistics. In certain special cases of interest, we apply non-linear curve-fitting techniques to large sets of (exact) theoretical data in order to obtain closed-form approximations for the different ergodic rates and ergodic secrecy rates under consideration. Our findings indicate that the FD functionality, in addition to enhancing the spectral efficiency, can significantly improve the PHY-layer security performance, especially with the aid of multi-antenna communications and interference cancellation schemes.

Joint Design of User Association and Power Allocation With Proportional Fairness in Massive MIMO HetNets

Although the massive MIMO enabled heterogeneous networks (HetNets) can intensify the spectral efficiency benefits, the proper user association and resource allocation are both crucial to achieve desirable performance since the power consumption of base station (BS) scales with the large number of antennas. This paper aims to investigate joint design of user association and power allocation with loads constraint and transmit power constraint for the massive MIMO HetNets by considering proportional fairness about the spectral efficiency under imperfect channel state information. First, we derive a closed-form lower bound on the ergodic spectral efficiency with linear zero-forcing beamforming, based on which, a mixed-integer nonlinear programming problem is formulated. It is difficult to efficiently obtain an exact solution since it is non-convex and combinational. To solve this NP-hard problem, an effective algorithm with guaranteed convergence is proposed, where the original problem is decomposed into the corresponding subproblems, which can be solved by low complexity approaches, respectively. Numerical results show that how the number of antennas and the number of BSs affect the spectral efficiency, and our proposed algorithm outperforms other algorithms in terms of the spectral efficiency and load balancing.

Sum Rate Analysis of MU-MISO Systems with ZF Beamforming over Composite Fading Channels

The performance of multiuser multiple-input single-output (MU-MISO) systems is not only affected by small-scale multipath fading but also by large-scale fading (i.e., shadowing) and path loss. In this paper, we concentrate on the sum rate distribution of MU-MISO systems employing linear zero-forcing beamforming, accounting for both multipath fading and shadowing effects, as well as spatial correlation at the transmit and receiver sides. In particular, we consider the classical spatially correlated lognormal model and propose closed-form bounds on the distribution of the achievable sum rates in MU-MISO systems. With the help of these bounds, we derive a relationship between the interuser distance and sum rate corresponding to 10% of the cumulative distribution function under different environmental conditions. A practical conclusion from our results based on the considered system is that the effect of spatially correlated shadowing can be considered to be independent when the interuser distance is approximately five times the shadowing correlation distance. Furthermore, a detailed analysis of the effects of composite channel attenuation consisting of multipath fading and shadowing is also provided.

Network MIMO With Linear Zero-Forcing Beamforming: Large System Analysis, Impact of Channel Estimation, and Reduced-Complexity Scheduling

We consider the downlink of a multicell system with multiantenna base stations and single-antenna user terminals, arbitrary base station cooperation clusters, distance-dependent propagation pathloss, and general “fairness” requirements. Base stations in the same cooperation cluster employ joint transmission with linear zero-forcing beamforming, subject to sum or per-base station power constraints. Intercluster interference is treated as noise at the user terminals. Analytic expressions for the system spectral efficiency are found in the large-system limit where both the numbers of users and antennas per base station tend to infinity with a given ratio. In particular, for the per-base station power constraint, we find new results in random matrix theory, yielding the squared Frobenius norm of submatrices of the Moore-Penrose pseudo-inverse for the structured non-i.i.d. channel matrix resulting from the cooperation cluster, user distribution, and path-loss coefficients. The analysis is extended to the case of nonideal Channel State Information at the Transmitters obtained through explicit downlink channel training and uplink feedback. Specifically, our results illuminate the trade-off between the benefit of a larger number of cooperating antennas and the cost of estimating higher-dimensional channel vectors. Furthermore, our analysis leads to a new simplified downlink scheduling scheme that preselects the users according to probabilities obtained from the large-system results, depending on the desired fairness criterion. The proposed scheme performs close to the optimal (finite-dimensional) opportunistic user selection while requiring significantly less channel state feedback, since only a small fraction of preselected users must feed back their channel state information.

Multiuser MISO Transmitter Optimization for Intercell Interference Mitigation

The transmitter optimization (i.e., steering vectors and power allocation) for a MISO Broadcast Channel (MISO-BC) subject to general linear constraints is considered. Such constraints include, as special cases, the sum power, the per-antenna or per-group-of-antennas power, and "forbidden interference direction" constraints. We consider both the optimal dirty-paper coding and the simple suboptimal linear zero-forcing beamforming strategies, and provide numerically efficient algorithms that solve the problem in its most general form. As an application, we consider a multi-cell scenario with partial cell cooperation, where each cell optimizes its precoder by taking into account interference constraints on specific users in adjacent cells. The effectiveness of the proposed methods is evaluated in a simple system scenario including two adjacent cells, under different fairness criteria that emphasize the bottleneck role of users near the cell "boundary". Our results show that "active" Inter-Cell Interference (ICI) mitigation outperforms the conventional "static" ICI mitigation based on fractional frequency reuse.