Robust Downlink Beamforming Research Articles

A Data and Model-Driven Deep Learning Approach to Robust Downlink Beamforming Optimization

A Data and Model-Driven Deep Learning Approach to Robust Downlink Beamforming Optimization

Max–min fair robust beamforming design for underlay device‐to‐device communications in cellular networks

SummaryThis paper investigates the robust downlink beamforming designs based on max–min fairness and base station (BS) power consumption constraint for device‐to‐device (D2D) communications underlaying cellular network, under the assumption of imperfect channel state information (CSI) at the BS. Our objective is to maximize the minimum signal‐to‐interference‐plus‐noise ratio (SINR) or non‐outage probability of users while guaranteeing that the consumed power at the BS is less than a threshold. In particular, three max–min fairness scenarios are considered. In the first scenario, the worst‐case SINR of cellular users (CUs) is maximized where the D2D SINR is guaranteed to be above a specified predetermined threshold. In the second scenario, we extend the first scenario and maximized D2D SINR while maximizing CUs' SINR. In these two scenarios, it is assumed that the errors are upper bounded in their Frobenius norms. In the third scenario, the minimum non‐outage probability of users is maximized, while a probabilistic model is considered for the uncertainty of channel covariance matrices. Although such optimization problems are not convex, the semidefinite relaxation (SDR) approach is used to obtain the optimal beamforming matrix, which always complies the rank‐one constraint. Simulation results show that significant improvement in terms of minimum SINR of CUs, the minimum non‐outage probability of CUs, and the probability of feasibility and the fairness index can be achieved with our proposed algorithms in comparison with other beamforming schemes.

Worst case fair beamforming for multiple multicast groups in multicell networks

The design problem associated with robust downlink beamforming in multicast, multigroup, multicell wireless systems is addressed. The channel state information (CSI) of users is assumed to be imperfect and the uncertainty of CSI is modelled using the Frobenius norm. The objective is to optimise the signal-to-interference-plus-noise ratio over all users with a constraint on the maximum total transmitted power. This was achieved through a robust solution using the successive convex approximation (SCA) method. The beamforming problem is treated as a bi-convex problem, which is solved using the iterate-alternative convex technique. Here, the CSI uncertainty is addressed using a convex package through the non-monotone spectral projected gradient method and the beamforming vector is extracted using the SCA method. Also, the authors offer the required condition to extract the beamform vector using the SCA method through a suboptimal solution that always addressed before using different beamforming methods. Their simulation results examine all proposed system parameters in order to show convergence and feasibility of the solution. They also compare the solution with a suboptimal solution and the quality of service method for imperfect CSI in downlink beamforming. Numerical results show that the robust solution achieves the best power efficiency for practical solutions.

Robust Downlink Beamforming for BDMA Massive MIMO System

In this paper, we design robust downlink beamforming against the imperfect channel state information (CSI) for beam division multiple access (BDMA) massive multiple-input multiple output (MIMO) systems. Following a worst-case deterministic model, the proposed design is formulated as minimizing the power consumption of base station (BS) under different signal-to-interference-plus-noise ratio (SINR) constraints. The S-Procedure and semi-definite relaxation (SDR) are used to convert the initial non-convex optimization to a convex semi-definite programming problem. Then the optimality of SDR is strictly proved by showing the rank-one property of the optimal beamforming thanks to the orthogonal channels under BDMA scheme. More importantly, we make one step further by deriving the optimal beamforming directions and optimal beamforming power allocation of the SDR in closed-form, which greatly reduces the optimization complexity and makes the proposed design practical for a real word massive MIMO system. Simulation results are then provided to verify the efficiency of the proposed robust beamforming algorithm.

Optimal downlink beamforming for statistical CSI with robustness to estimation errors

We consider the problem of worst-case robust downlink beamforming in a multiuser Multiple-input–single-output (MISO) network with statistical channel state information (CSI) that is erroneous. In previous beamforming techniques, robustness is usually incorporated by employing generic error models, in which the mismatch between the presumed and the true instantaneous channel vectors, or the corresponding channel covariance matrices, is bounded by the Frobenius norm. A shortcoming of these methods is that these strongly rely on the assumption that the exact noise variance of the terminals and bounds on the channel mismatch are available. If this assumption is violated, then the beamforming approach may result in either insufficient robustness or overly conservative solutions. This assumption is particularly difficult as different sources of CSI error are generally not considered. In our proposed robust approach, we consider CSI mismatch from estimation errors in the noise power and the channel plus noise covariance matrix. Addressing both estimation errors separately allows us to derive meaningful threshold values for the uncertainty sets. In contrast to previous robust approaches based on Frobenius norm, we propose to use confidence intervals with given confidence levels to model the uncertainty sets. The simulation results verify the effectiveness of the proposed techniques.

Chance Constrained Robust Downlink Beamforming in Multicell Networks

We introduce a downlink robust optimization approach that minimizes a combination of total transmit power by a multiple antenna base station (BS) within a cell and the resulting aggregate inter-cell interference (ICI) power on the users of the other cells. This optimization is constrained to assure that a set of signal-to-interference-plus-noise ratio (SINR) targets are met at user terminals with certain outage probabilities. The outages are due to the uncertainties that naturally emerge in the estimation of channel covariance matrices between a BS and its intra-cell local users as well as the other users of the other cells. We model these uncertainties using random matrices, analyze their statistical behavior, and formulate a tractable probabilistic approach to the design of optimal robust downlink beamforming vectors. The proposed approach reformulates the original intractable non-convex problem in a semidefinite programming (SDP) form with linear matrix inequality (LMI) constraints. The resulting SDP formulation is convex and numerically tractable under the standard rank relaxation. We compare the proposed chance-constrained approach against two different robust design schemes as well as the worst-case robustness. The simulation results confirm better power efficiency and higher resilience against channel uncertainties of the proposed approach in realistic scenarios.

Joint Beamforming and Power Optimization with Per-Antenna Power Constraints in Cognitive MISO System

Joint Beamforming and power allocation schemes are considered for cognitive radio (CR) multiple input single output (MISO) system in this paper. We considered the robust downlink beamforming and power allocation problem with per-antenna power constraints which is more realistic in practice, instead of sum-power constraint, under the imperfect channel state information (CSI). Since the given optimization problem is a non-convex problem which is difficult to handle, we transformed it into second order cone program (SOCP) problem, which can be solved efficiently. Simulation shows that the proposed scheme indeed has a better performance in CR system.

Robust Downlink Beamforming With Partial Channel State Information for Conventional and Cognitive Radio Networks

We address the problem of robust multiuser downlink beamforming under the assumption that the transmitter has partial covariance-based channel state information (CSI). In our approach, the uncertainty on the channel covariance matrices is assumed to be confined in an ellipsoid of given size and shape, where prior knowledge about the statistical distribution of the CSI mismatch is taken into account. The goal is to minimize the transmitted power under the worst-case quality-of-service (QoS) constraints. We extend the developed robust problem to downlink beamforming in cognitive radio (CR) networks where QoS constraints apply to the users of the secondary network (SN) and interference leaked to the primary users (PUs) is required to be below a given interference threshold. We avoid the coarse approximations used by previous solutions and obtain exact reformulations for both worst-case problems based on Lagrange duality. The resulting problems can then be approximated using semidefinite relaxation (SDR). Further, we consider a popular alternative robust approach that is based on probabilistic QoS and interference constraints and show that both approaches are generally equivalent. Computer simulations show that the proposed techniques provide substantial performance improvements over earlier robust downlink beamforming techniques for both the conventional and the CR scenarios.

Robust Multicast Beamforming for Spectrum Sharing-Based Cognitive Radios

We consider a robust downlink beamforming optimization problem for secondary multicast transmission in a multiple-input multiple-output (MIMO) spectrum sharing cognitive radio (CR) network. The minimization of transmit power is formulated subject to both quality-of-service (QoS) constraints on the secondary receivers and interference temperature constraints on the primary users, under the assumption of imperfect channel state information (CSI). The problem is a nonconvex quadratically constrained quadratic program (QCQP), and in general it is hard to achieve the global optimality. As a compromise, we present two randomized approximation algorithms for the problem via convex optimization techniques. Apart from the general setting of the robust beamforming problem, we identify one interesting special case, the robust problem of which can be solved efficiently. Simulation results are presented to demonstrate the performance gains of the proposed algorithms over an existing robust design.

A SECOND-ORDER CONE PROGRAMMING APPROACH FOR ROBUST DOWNLINK BEAMFORMING WITH POWER CONTROL IN COGNITIVE RADIO NETWORKS

The downlink beamforiming technology plays a key role in a cognitive radio network (CR-Net). It can be used to reduce transmission power and interference to other users, etc. This paper presents a robust downlink beamforming method with power control for a multiuser multiple-input-single-output (MISO) CR-Net. In this proposed approach, the beamforming optimization problem is formulated as the second-order cone programming (SOCP). The presented method can not only minimize the transmitted power but also guarantee that the received signal-to-interference-plus-noise ratio (SINR) is strictly above the prescribed quality-of-service (Qos)- constrained threshold at each secondary user (SU) and the the interference power (IP) is strictly below the prescribed threshold at the primary user (PU). Simulation results are presented to verify the e-ciency of the proposed method.

Robust Downlink Beamforming in Multiuser MISO Cognitive Radio Networks With Imperfect Channel-State Information

This paper studies the problem of robust downlink beamforming design in a multiuser multiple-input-single-output (MISO) cognitive radio network (CR-Net) in which multiple secondary users (SUs) coexist with multiple primary users (PUs) of a single-cell primary radio network (PR-Net). It is assumed that the channel-state information (CSI) for all relevant channels is imperfectly known, and the imperfectness of the CSI is modeled using a Euclidean ball-shaped uncertainty set. Our design objective is to minimize the transmit power of the SU-Transmitter (SU-Tx) while simultaneously achieving a lower bound on the received signal-to-interference-plus-noise ratio (SINR) for the SUs and imposing an upper limit on the interference power (IP) at the PUs. The design parameters at the SU-Tx are the beamforming weights, and the proposed methodology to solve the problem is based on the worst-case design scenario through which the performance metrics of the design are immune to variations in the channels. The original problem is a separable homogeneous quadratically constrained quadratic problem (QCQP), which is an NP-hard problem, even for uncertain CSI. We reformulate our original design problem to a relaxed semidefinite program (SDP) and then investigate three different approaches based on convex programming. Finally, simulation results are provided to validate the robustness of the proposed methods.

Robust Downlink Beamforming Based on Outage Probability Specifications

A new approach to multi-antenna downlink beam- forming is proposed that provides an improved robustness against uncertainty in the downlink channel covariance matrices caused by errors between the actual and estimated channel values. The proposed method uses the knowledge of the statistical distribution of such a covariance uncertainty to minimize the total downlink transmit power under the constraint that the outage probability does not exceed a certain threshold value. Although our approach initially leads to a non-convex optimization problem, it can be reformulated in a convex form using the semidefinite relaxation technique. The resulting convex optimization problem can be solved efficiently using the well-established interior point methods. Computer simulations verify performance improvements of the proposed technique as compared to the robust transmit beamforming method based on the worst-case performance optimization with judicious selection of the upper bounds on channel covariance errors.