Guido Dartmann

On the Duality of the Max–Min Beamforming Problem With Per-Antenna and Per-Antenna-Array Power Constraints

This paper considers a downlink unicast transmission in a multicell network with multiple users. In a network with frequency reuse factor of one, intercell interference is a limiting factor. The max-min beamforming technique enables a balancing of the signal-to-interference-plus-noise ratio (SINR) among all users in a network under a power budget. Thus, a fair distribution of the achievable rate can be achieved. The max-min beamforming problem (MBP) is nonconvex in general. However, if instantaneous channel-state information (CSI) is available, the MBP has an equivalent quasiconvex form and can optimally be solved with an efficient algorithm based on a convex solver. In addition to this convex-solver-based solution, this paper considers the so-called surrogate dual problem of the MBP with per-antenna and per-antenna-array power constraints. The surrogate dual problem combines multiple power constraints to a single power constraint. Furthermore, the surrogate dual problem can efficiently be solved for long-term CSI in the form of spatial correlation matrices. Strong duality is proved for instantaneous and long-term CSI in the form of higher rank spatial correlation matrices. With the surrogate dual problem, a fast algorithm for the MBP is presented. The convergence issue is discussed. Numerical results verify the convergence and the performance of the proposed algorithm.

Power Allocation and Performance Analysis in Spectrum Sharing Systems with Statistical CSI

\boldmath This paper investigates power allocation strategies for secondary users (SUs) in cross-interfering spectrum sharing systems. Addressing limited cooperation between primary users (PUs) and SUs, only instantaneous channel state information (CSI) of the secondary link and statistical CSI of the other links is assumed to be available at the secondary transmitters (STs). We aim at maximizing the secondary achievable rate subject to both a peak power constraint at the ST and an average interference power constraint at the primary receiver. First, the optimal power control strategy is developed. In order to reduce the complexity, two suboptimal optimization strategies are proposed. The first one, named double threshold waterfilling (DT-WF), is based on an approximation of the optimal solution. The second strategy, named double threshold constant-power waterfilling (DTCP-WF), further simplifies DT-WF. Additionally, the achievable performance is derived in closed form for both suboptimal strategies. We also discuss the algorithm design in the multiple primary links scenario. Numerical results show the effectiveness of the proposed strategies and validate the accuracy of the closed-form analysis.

Outage-Constrained Power Allocation in Spectrum Sharing Systems with Partial CSI

Due to limited cooperation between the primary users and the secondary users (SUs) in practical spectrum sharing systems, the secondary transmitters and receivers are assumed to have partial channel state information related to the primary receiver. Under such an assumption, this work investigates power allocation strategies for the SUs subject to an outage probability constraint on the primary transmission and a peak transmit power constraint on the secondary transmission. The challenge lies in the non-convexity of the outage probability constraint. Firstly, we prove that strong duality holds and that the Karush-Kuhn-Tucker (KKT) conditions are necessary for optimality. The optimal solution is then derived by addressing the optimality issues of the KKT solutions. Secondly, in order to further reduce the algorithmic complexity, two suboptimal strategies are proposed. The first one is designed based on several simplifications of the optimal strategy. The second one is derived from the convex relaxation of the non-convex primal problem, which corresponds to the problem with the conventional interference temperature constraint. The performance for both suboptimal strategies is derived in closed form. All proposed strategies are shown to outperform non-adaptive power transmission. The near-optimality of the two suboptimal strategies is also validated, in particular for the first one.

Max-min beamforming for multicell downlink systems using long-term channel statistics

This paper investigates max-min beamforming for the multicell downlink transmission, where multiple base stations (BSs) cooperatively optimize their transmit beamforming vectors using long-term channel statistics. Based on Lagrangian duality, we reformulate the original problem into a dual uplink problem, which is expected to achieve the same optimal signal to interference plus noise ratio (SINR) as the primal downlink problem. The normalized dual uplink beamformer is the dominant eigenvector of a generalized eigenvalue decomposition (GEVD) problem, and the dual uplink transmit power can be solved iteratively. According to the duality theory, we develop an iterative algorithm and compare it with the beamformer-power iterative algorithm extended from [1]. Simulation results verify the computational efficiency of the proposed algorithm.

Low complexity cooperative downlink beamforming in multiuser multicell networks

In a network with frequency reuse-1, especially cell edge users are subject to strong intercell interference. This paper presents a low complexity downlink beamforming technique with multipoint transmission to a scheduled user to improve its signal to noise plus interference ratio. The dual problem for the max-min beamforming problem with a per base station (BS) power constraint and multi-BS assignment is derived and a low complexity algorithm based on the simple power iteration method for the generalized eigenvector decomposition is presented. Especially cell edge users gain from the presented technique and, therefore, an improved sum rate can be achieved, because of the max-min approach. The presented algorithm has a very low complexity and a fast convergence and is, therefore, promising for practical approaches for fast beam switching combined with optimized scheduling based on multiple base station assignment.

A Novel Low-Complexity Numerical Localization Method for Dynamic Wireless Sensor Networks

The localization of distributed and wirelessly connected sensor system is of decisive importance for many applications. This paper focuses on the range-based localization and tracking problem for very large dynamic, i.e., moving sensor networks. We study the explorability of underwater systems with massive swarms of tiny sensors with reduced and restricted capabilities. In this context, we propose a least-squares based localization algorithm which shows superior performance and lower computational complexity than other methods, based, e.g., on unscented Kalman-filtering or semidefinite programming. The new and existing algorithms are evaluated using two different system models, derived from real fluid dynamics. We also compare our algorithm to other least-squares based methods, determine the computational overhead of the new method and investigate its performance gain in terms of estimation accuracy.

Equivalent Quasi-Convex Form of the Multicast Max–Min Beamforming Problem

Multicast downlink transmission in a multicell network with multiple users is investigated. Max-min beamforming (MB) enables a fair distribution of the signal-to-interference-plus-noise ratio (SINR) among all users in a network for given power constraints at the base stations (BSs) of the network. The multicast MB problem (MBP) is proven to be NP-hard and nonconvex in general. However, the MBP has an equivalent quasi-convex (QC) form and can be optimally solved with an efficient algorithm for special instances, depending on the structure of the available channel state information (CSI). This paper derives the equivalent QC form of the MBP for the practically relevant scenario of long-term CSI in the form of Hermitian positive semi-definite Toeplitz (HPST) matrices and per-antenna array power constraints. The optimization problem is then given by a convex feasibility check problem with finite autocorrelation sequences (FASs) as optimization variables. Using FASs, the MBP can be expressed as a QC fractional program (FP). Based on the theory of QC programming, this paper proposes a fast root-finding algorithm with superlinear convergence.

Joint optimization of beamforming, user scheduling, and multiple base station assignment in a multicell network

This paper presents a practice oriented approach for an optimization of user scheduling, base stations assignment and beamforming with multipoint transmission in a multiuser multicell scenario using statistical channel knowledge. Especially the cell edge users gain if they are served by multiple base stations (BSs). The max-min beamforming optimization balances the signal to interference and noise ratio of all scheduled users. An additional optimization of the scheduling decisions and the assignment of BSs to users can additionally improve the individual rates of the users. A multiuser multicell simulation based on the WINNER II channel model proves the enhanced performance of the presented low complexity algorithm for the network-wide optimization of the three degrees of freedom: optimal transmit beamforming, temporal user scheduling and base station to user assignment.

Intercell Interference Mitigation with Long-Term Beamforming and Low SINR Feedback Rate in a Multiuser Multicell Unicast Scenario

This paper considers downlink transmit beamform- ing for a unicast transmission to a multitude of users with the goal of a joint optimization of the beamforming weights from multitude of basestations. In wireless systems, bandwidth is a limited resource. Therefore in this paper, a frequency reuse-1 is applied at the expense of intercell interference. The optimization of the beamforming weights is done with semidefinite program- ming with the knowledge of long term channel state information (CSI). This paper presents a fair beamforming technique that results in a very low signal to interference and noise rate (SINR) feedback rate. An improvement of the throughput for users in the cell edge region with a constrained transmit power is achieved.

Jointly optimized transmit beamforming and temporal user scheduling in multiuser multicell scenarios based on correlation knowledge

This paper presents a new approach for a joint optimization of beamforming and temporal user scheduling for intercell interference mitigation in a multiuser multicell scenario using statistical channel knowledge. In general, the resource allocation problem considers two optimization criterions: fairness among the users in the network and a maximized sum rate of all users. The first one is achieved by a network-wide conventional multiuser transmit beamforming and the second one is achieved by an optimal assignment of users to scheduling slots. The resulting optimization problem is proven to be NP-hard, because of its equivalence to the well-known multidimensional assignment problem. A new low complexity algorithm is proposed to find good solutions with respect to the problem complexity. Regarding the performance and complexity, the new algorithm outperforms the simulated annealing technique, which is a well-known technique to overcome local optima.