Transmit Beamforming Vectors Research Articles

Robust Smart-Grid-Powered Cooperative Multipoint Systems

A framework is introduced to integrate renewable energy sources (RES) and dynamic pricing capabilities of the smart grid into beamforming designs for coordinated multi-point (CoMP) downlink communication systems. To this end, novel models are put forth to account for harvesting, storage of nondispatchable RES, time-varying energy pricing, as well as stochastic wireless channels. Building on these models, robust energy management and transmit-beamforming designs are developed to minimize the worst-case energy cost subject to the worst-case user QoS guarantees for the CoMP downlink. Leveraging pertinent tools, this task is formulated as a convex problem. A Lagrange dual based subgradient iteration is then employed to find the desired optimal energy-management strategy and transmit-beamforming vectors. Numerical results are provided to demonstrate the merits of the proposed robust designs.

On Transmit Beamforming for MISO-OFDM Channels With Finite-Rate Feedback

With finite-rate feedback, we propose two feedback methods for transmit beamforming in a point-to-point MISO-OFDM channel. For the first method, a receiver with perfect channel information, quantizes and feeds back the optimal transmit beamforming vectors of a few selected subcarriers, which are equally spaced. Based on those quantized vectors, the transmitter applies either constant, linear, or higher-order interpolation with the remaining beamforming vectors. With constant interpolation, we derive the approximate sum achievable rate and the optimal cluster size that maximizes the approximate rate. For linear interpolation, we derive a closed-form expression for the phase rotation by utilizing the correlation between OFDM subcarriers. We also propose a higher-order interpolation that requires more than two quantized vectors to interpolate transmit beamformers, and is based on existing channel estimation methods. Numerical results show that interpolation with the optimized cluster size can perform significantly better than that with an arbitrary cluster size. For the second proposed method, a channel impulse response is quantized with a uniform scalar quantizer. With channel quantization, we also derive the approximate sum achievable rate. We show that switching between the two methods for different feedback-rate requirements can perform better than the existing schemes.

Secure Beamforming for SWIPT in Multiuser MISO Broadcast Channel With Confidential Messages

In this letter, we consider simultaneous wireless information and power transfer (SWIPT) in multiuser multiple-input single-output (MISO) broadcast channel with confidential messages, where each receiver adopts the power splitting (PS) approach to decode information and harvest energy simultaneously. Our goal is to minimize the total transmit power while guaranteeing the secrecy rate and harvested energy constraints at each receiver by jointly optimizing the transmit beamforming vectors, artificial noise vector, and PS ratios. To solve this non-convex problem, a two-stage optimization approach is proposed. In addition, we also propose a low-complexity suboptimal algorithm based on the genetic algorithm to solve the original problem. Simulation results are finally presented to illustrate the effectiveness of our proposed algorithm.

다중안테나 다중셀 네트워크에서 간섭인지 기반 전력제어 기술을 이용한 사용자 스케쥴링

In this paper, we propose a distributed user scheduling with transmit power control based on the amount of generating interference to other base stations (BSs) in multi-cell multi-input multi-output (MIMO) networks. Assuming that the time-division duplexing (TDD) system is used, the interference channel from users to other cell BSs is obtained at each user. In the proposed scheduling, each user first generates a transmit beamforming vector by using singular value decompositon (SVD) over MIMO channels and reduces the transmit power if its generating interference to other BSs is larger than a predetermined threshold. Each BS selects the user with the largest effective channel gains among users, which reflects the adjusted power of users. Simulation results show that the proposed technique significantly outperforms the existing user scheduling algorithms.

Robust Transceiver Design for MISO Interference Channel With Energy Harvesting

In this paper, we consider multiuser multiple-input single-output (MISO) interference channel where the received signal is divided into two parts for information decoding and energy harvesting (EH), respectively. The transmit beamforming vectors and receive power splitting (PS) ratios are jointly designed in order to minimize the total transmission power subject to both signal-to-interference-plus-noise ratio (SINR) and EH constraints. Most joint beamforming and power splitting (JBPS) designs assume that perfect channel state information (CSI) is available; however CSI errors are inevitable in practice. To overcome this limitation, we study the robust JBPS design problem assuming a norm-bounded error (NBE) model for the CSI. Three different solution approaches are proposed for the robust JBPS problem, each one leading to a different computational algorithm. Firstly, an efficient semidefinite relaxation (SDR)-based approach is presented to solve the highly non-convex JBPS problem, where the latter can be formulated as a semidefinite programming (SDP) problem. A rank-one recovery method is provided to recover a robust feasible solution to the original problem. Secondly, based on second order cone programming (SOCP) relaxation, we propose a low complexity approach with the aid of a closed-form robust solution recovery method. Thirdly, a new iterative method is also provided which can achieve near-optimal performance when the SDR-based algorithm results in a higher-rank solution. We prove that this iterative algorithm monotonically converges to a Karush-Kuhn-Tucker (KKT) solution of the robust JBPS problem. Finally, simulation results are presented to validate the robustness and efficiency of the proposed algorithms.

Iterative Transceiver Design for Opportunistic Interference Alignment in MIMO Interfering Multiple-Access Channels

In this paper, we propose an iterative transceiver design algorithm for opportunistic interference alignment in MIMO interfering multiple-access channels. The proposed algorithm iteratively optimizes the transmit beamforming vectors, the receive matrices and the user selection set, which digs into the multiuser diversity gain. Specifically, data transmission can be operated in each iteration using the updated transceiver and the selected user set, which means that no additional processing delay is introduced. Simulation results demonstrate the improved average rate per cell performance of the proposed algorithm compared to the conventional ones. Index Terms—Interference alignment, OIA, user scheduling, iterative

Efficient beamforming method for downlink MU-MIMO broadcast channels

The sum rate maximization in multiuser MIMO broadcast channels is investigated in this paper. Due to the high computational complexity of non-linear dirty paper coding (DPC), zero-forcing dirty paper coding (ZF-DPC) is proposed as an alternative suboptimal approach. However, traditional ZF-DPC method requires that the number of total receive antennas is less than or equal to the number of transmit antennas. In this paper, we consider the scenario where the sum number of receive antennas may be more than the number of transmit antennas. It is shown that the optimal data stream allocation needs exhaustive search over all possibilities, and the complexity is significantly high. We propose a greedy transmit data allocation scheme that allocates one data stream at each step, the corresponding transmit beamforming vector and receive combining vector are designed to avoid interfering with the previous allocated data streams, and the pre-equalization Tomlinson–Harashima Precoder (THP) technique is adopted to pre-cancel the non-causally known interference caused by the previous allocated data streams. The proposed method is computationally efficient thanks to the low complexity. Simulation results show that this novel method outperforms the methods in the literature.

On the Bottleneck Users for Multiple-Antenna Physical-Layer Multicasting

Given the optimal transmit beamforming vector, the user who has the worst signal-to-noise ratio (SNR) is referred to as a bottleneck user for a single-group multicasting system with multiple antennas at the transmit side. In this paper, we present some interesting insights into the bottleneck users, such as the maximum number as well as the optimal beamformer when the transmitter has an arbitrary number of antenna elements. The max-min fair SNR problem is employed and the closed-form solutions are proposed from the weighted sum-SNR maximization perspective for different numbers of possible bottleneck users. A new heuristic beamforming algorithm based on the bottleneck users is also presented to improve the system performance in terms of the achievable rate for physical-layer multicasting.

Performance Analysis of Optimal Beamforming in Fixed-Gain AF MIMO Relaying over Asymmetric Fading Channels

This paper analyzes the performance of an optimal single stream beamforming scheme for a multiple-input multiple-output (MIMO) relay network with dual-hop fixed-gain amplify-and-forward (AF) relaying. The source-relay and relay-destination channels undergo Rayleigh and Rician fading respectively. Different Rician fading scenarios are considered for relay-destination channel, depending on the rank of the Rician channel matrix. The channel state information is only available at the destination, and the destination computes the optimal transmit and receive beamforming vectors to maximize the instantaneous signal-to-noise ratio (SNR). The optimal transmit beamforming vector is sent back to the transmitter via a dedicated feedback link. We derive new analytical expressions for the cumulative distribution function, probability density function, and moments to statistically characterize the properties of the instantaneous SNR. These statistical properties are used to analyze the system performance in terms of the outage probability, average bit error rate, and the ergodic capacity. The performance analysis investigates the effects of the Rician factor, rank of the line-of-sight component, and number of antennas at the nodes on the system performance. The results reveal that the optimal single stream beamforming system provides better performance than an orthogonal space-time block coded based AF MIMO system.

A robust beamformer design for underlay cognitive radio networks using worst case optimization

We propose a robust beamforming design for underlay cognitive radio networks where multiple secondary transmitters communicate with corresponding secondary receivers and coexist with a primary network. We consider a scenario where all transmitters have multiple antennas and all primary and secondary receivers are equipped with a single antenna. The main focus is to design the optimal transmit beamforming vectors for secondary transmitters that maximize the minimum of the received signal-to-interference-plus-noise ratios of the cognitive users. The interference powers to the primary receivers are kept below a threshold to guarantee that the performance of the primary network does not degrade due to the secondary network. Imperfect channel state information (CSI) in all relevant channels are considered, and a bounded ellipsoidal uncertainty model is used to model the CSI errors. We recast the problem in the form of semidefinite program and an iterative algorithm based on the bisection method is proposed to achieve the optimal solution. Further, we propose upper and lower bounds for the optimal value of the considered problem, which provides better initialization for the algorithm. Numerical simulations are conducted to show the effectiveness of the proposed method against the non-robust design.

Joint Transmit Beamforming and Receive Power Splitting for MISO SWIPT Systems

This paper studies a multi-user multiple-input single-output (MISO) downlink system for simultaneous wireless information and power transfer (SWIPT), in which a set of single-antenna mobile stations (MSs) receive information and energy simultaneously via power splitting (PS) from the signal sent by a multi-antenna base station (BS). We aim to minimize the total transmission power at BS by jointly designing transmit beamforming vectors and receive PS ratios for all MSs under their given signal-to-interference-plus-noise ratio (SINR) constraints for information decoding and harvested power constraints for energy harvesting. First, we derive the sufficient and necessary condition for the feasibility of our formulated problem. Next, we solve this non-convex problem by applying the technique of semidefinite relaxation (SDR). We prove that SDR is indeed tight for our problem and thus achieves its global optimum. Finally, we propose two suboptimal solutions of lower complexity than the optimal solution based on the principle of separating the optimization of transmit beamforming and receive PS, where the zero-forcing (ZF) and the SINR-optimal based transmit beamforming schemes are applied, respectively.

Dual-based bounds for resource allocation in zero-forcing beamforming OFDMA-SDMA systems

We consider multi-antenna base stations using orthogonal frequency division multiple access and space division multiple access techniques to serve single-antenna users. Some users, called real-time users, have minimum rate requirements and must be served in the current time slot while others, called non real-time users, do not have strict timing constraints and are served on a best-effort basis. The resource allocation problem is to find the assignment of users to subcarriers and the transmit beamforming vectors that maximize the total user rates subject to power and minimum rate constraints. In general, this is a nonlinear and non-convex program and the zero-forcing technique used here makes it integer as well, exact optimal solutions cannot be computed in reasonable time for realistic cases. For this reason, we present a technique to compute both upper and lower bounds and show that these are quite close for some realistic cases. First, we formulate the dual problem whose optimum provides an upper bound to all feasible solutions. We then use a simple method to get a primal-feasible point starting from the dual optimal solution, which is a lower bound on the primal optimal solution. Numerical results for several cases show that the two bounds are close so that the dual method can be used to benchmark any heuristic used to solve this problem. As an example, we provide numerical results showing the performance gap of the well-known weight adjustment method and show that there is considerable room for improvement.

Distributed user selection scheme for uplink multiuser MIMO systems in a multicell environment

Abstract We propose an interference-aware user selection scheme for uplink multiuser multiple-input multiple-output systems in a multicell environment. The proposed scheme works in a distributed manner. Each mobile station determines its transmit beamforming vector based on the locally available channel state information, and informs the associated base station (BS) of the amount of potential interference caused to adjacent cells along with the resulting beamforming vector. Then, the BS selects a set of users to be served simultaneously with consideration of intercell interference. The user selection scheme is devised either to maximize the sum rate or to achieve proportional fairness among users. For each case, we derive an optimal user selection criterion and propose a suboptimal distributed user selection algorithm with low complexity. Simulation results confirm that the proposed scheme offers significant throughput enhancement due to reduction of the intercell interference in a multicell environment.

Nonsmooth Optimization for Efficient Beamforming in Cognitive Radio Multicast Transmission

It is known that the design of optimal transmit beamforming vectors for cognitive radio multicast transmission can be formulated as indefinite quadratic optimization programs. Given the challenges of such nonconvex problems, the conventional approach in literature is to recast them as convex semidefinite programs (SDPs) together with rank-one constraints. Then, these nonconvex and discontinuous constraints are dropped allowing for the realization of a pool of relaxed candidate solutions, from which various randomization techniques are utilized with the hope to recover the optimal solutions. However, it has been shown that such approach fails to deliver satisfactory outcomes in many practical settings, wherein the determined solutions are found to be unacceptably far from the actual optimality. On the contrary, we in this contribution tackle the aforementioned optimal beamforming problems differently by representing them as SDPs with additional reverse convex (but continuous) constraints. Nonsmooth optimization algorithms are then proposed to locate the optimal solutions of such design problems in an efficient manner. Our thorough numerical examples verify that the proposed algorithms offer almost global optimality whilst requiring relatively low computational load.

Performance Analysis of Optimal Single Stream Beamforming in MIMO Dual-Hop AF Systems

This paper investigates the performance of optimal single stream beamforming schemes in multiple-input multiple-output (MIMO) dual-hop amplify-and-forward (AF) systems. Assuming channel state information is not available at the source and relay, the optimal transmit and receive beamforming vectors are computed at the destination, and the transmit beamforming vector is sent to the transmitter via a dedicated feedback link. Then, a set of new closed-form expressions for the statistical properties of the maximum eigenvalue of the resultant channel is derived, i.e., the cumulative density function (cdf), probability density function (pdf) and general moments, as well as the first order asymptotic expansion and asymptotic large dimension approximations. These analytical expressions are then applied to study three important performance metrics of the system, i.e., outage probability, average symbol error rate and ergodic capacity. In addition, more detailed treatments are provided for some important special cases, e.g., when the number of antennas at one of the nodes is one or large, simple and insightful expressions for the key parameters such as diversity order and array gain of the system are derived. With the analytical results, the joint impact of source, relay and destination antenna numbers on the system performance is addressed, and the performance of optimal beamforming schemes and orthogonal space-time block-coding (OSTBC) schemes are compared. Results reveal that the number of antennas at the relay has a great impact on how the numbers of antennas at the source and destination contribute to the system performance, and optimal beamforming not only achieves the same maximum diversity order as OSTBC, but also provides significant power gains over OSTBC.

Belief Propagation Methods for Intercell Interference Coordination in Femtocell Networks

Interference coordination is a fundamental challenge in emerging femtocellular deployments. This paper considers a broad class of interference coordination and resource allocation problems for wireless links based on utility maximization with a general linear mixing interference model suitable for complex femtocellular systems. The resulting optimization problems are typically hard to solve optimally even using centralized algorithms but are an essential computational step in implementing rate-fair and queue stabilizing scheduling policies in wireless networks. We consider a belief propagation framework to solve such problems approximately. In particular, we construct approximations to the belief propagation iterations to obtain computationally simple and distributed algorithms with low communication overhead. Notably, our methods are very general and apply to, semi-static and dynamic interference coordination problems including the optimization of transmit powers, transmit beamforming vectors, fractional frequency reuse (FFR) and sub-band allocations to maximize the above objective. Numerical results for femtocell deployments demonstrate that such algorithms compute a very good operating point in typically just a couple of iterations.

A New Multi-User Beamforming Algorithm

In R9 version of LTE system, the double multi-user beamforming is proposed. To suppress inter-user interference of multi-user multiple input multiple output (MU-MIMO) system, a new algorithm is presented in this paper: on condition that current user eliminates the interference to other users, it designs its own transmit beamforming vector; if all users take such measures, the interference that each user suffers from others will be reduced to a minimum, which improves the performance of the system. Simulation shows that, as the number of user increases, the algorithm used in this paper can reduce the bit error rate (BER) of the system more obviously than the traditional signal-to-leakage-and-noise ratio (SLNR) algorithm.

Tree-Structured Random Vector Quantization for Limited-Feedback Wireless Channels

We consider the quantization of a transmit beamforming vector in multiantenna channels and of a signature vector in code division multiple access (CDMA) systems. Assuming perfect channel knowledge, the receiver selects for a transmitter the vector that maximizes the performance from a random vector quantization (RVQ) codebook, which consists of independent isotropically distributed unit-norm vectors. The quantized vector is then relayed to the transmitter via a rate-limited feedback channel. The RVQ codebook requires an exhaustive search to locate the selected entry. To reduce the search complexity, we apply generalized Lloyd or $k$-dimensional (kd)-tree algorithms to organize RVQ entries into a tree. In examples shown, the search complexity of tree-structured (TS) RVQ can be a few orders of magnitude less than that of the unstructured RVQ for the same performance. We also derive the performance approximation for TS-RVQ in a large system limit, which predicts the performance of a moderate-size system very well.

Optimization of Training and Feedback Overhead for Beamforming Over Block Fading Channels

We examine the capacity of beamforming over a single-user, multiantenna link taking into account the overhead due to channel estimation and limited feedback of channel state information. Multi-input-single-output (MISO) and multi-input-multi-output (MIMO) channels are considered subject to block Rayleigh fading. Each coherence block contains L symbols, and is spanned by T training symbols, B feedback bits, and the data symbols. The training symbols are used to obtain a minimum mean squared error estimate of the channel matrix. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sup> i.i.d. random vectors, and sends the corresponding B bits back to the transmitter. We derive bounds on the beamforming capacity for MISO and MIMO channels and characterize the optimal (rate-maximizing) training and feedback overhead (T and B) as L and the number of transmit antennas N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> both become large. The optimal N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> is limited by the coherence time, and increases as L/logL. For the MISO channel the optimal T/L and B/L (fractional overhead due to training and feedback) are asymptotically the same, and tend to zero at the rate 1/log N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> . For the MIMO channel the optimal feedback overhead B/L tends to zero faster (as 1/log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> ).

Cooperative Interference Management With MISO Beamforming

In this correspondence, we study the downlink transmission in a multi-cell system, where multiple base stations (BSs) each with multiple antennas cooperatively design their respective transmit beamforming vectors to optimize the overall system performance. For simplicity, it is assumed that all mobile stations (MSs) are equipped with a single antenna each, and there is one active MS in each cell at one time. Accordingly, the system of interests can be modeled by a multiple-input single-output (MISO) Gaussian interference channel (IC), termed as MISO-IC, with interference treated as noise. We propose a new method to characterize different rate-tuples for active MSs on the Pareto boundary of the achievable rate region for the MISO-IC, by exploring the relationship between the MISO-IC and the cognitive radio (CR) MISO channel. We show that each Pareto-boundary rate-tuple of the MISO-IC can be achieved in a decentralized manner when each of the BSs attains its own channel capacity subject to a certain set of interference-power constraints (also known as interference-temperature constraints in the CR system) at the other MS receivers. Furthermore, we show that this result leads to a new decentralized algorithm for implementing the multi-cell cooperative downlink beamforming.