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**1 - 4**of**4**### ACHIEVING QOS AND EFFICIENCY IN THE MIMO DOWNLINK WITH LIMITED POWER

"... In this paper we study the problem of maximizing a weighted sum of rates under a sum power constraint in the multiple input multiple output (MIMO) downlink while rate require-ments have to be met for a subset of users. This setting reflects a more sophisticated problem of resource allocation combini ..."

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In this paper we study the problem of maximizing a weighted sum of rates under a sum power constraint in the multiple input multiple output (MIMO) downlink while rate require-ments have to be met for a subset of users. This setting reflects a more sophisticated problem of resource allocation combining an efficiency objective with strict Quality of Ser-vice (QoS) constraints. It is shown that the problem can be formulated as a convex optimization problem. Unlike in the case of pure weighted rate-sum maximization (WRSM), the question of feasibility arises. Moreover, the optimum Dirty-Paper Coding (DPC) order is not given by the ordering of the initial weights, but can be derived from the Lagrangian multipliers combined with the initial weights. An efficient algorithm based on primal-dual optimization is proposed which provably converges to the global optimum. The con-vergence properties are illustrated by means of numerical simulations. 1.

### SUM THROUGHPUT MAXIMIZATION IN QUALITY OF SERVICE CONSTRAINED MULTIUSER MIMO SYSTEMS BASED ON PERTURBATION ANALYSIS

"... Sum throughput maximization under a power constraint con-stitutes an important optimization problem for designing phys-ical layer algorithms. However it often leads to an unfair dis-tribution of resources to the users. On the other hand, due to the nature of the capacity region of the multiuser MIMO ..."

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Sum throughput maximization under a power constraint con-stitutes an important optimization problem for designing phys-ical layer algorithms. However it often leads to an unfair dis-tribution of resources to the users. On the other hand, due to the nature of the capacity region of the multiuser MIMO broadcast channel, strict Quality of Service (QoS) constraints such as rate ratios might lead to severe losses in sum capac-ity compared to the maximum possible sum capacity given a power constraint. For this reason minimum rates for each user are introduced and an algorithm is presented which di-vides the users into two groups: in one group all users are served with their required minimum rates as providing them with further resources will lead to decreases in sum capac-ity. Putting these further resources into the users of the other group instead is more beneficial for sum capacity. That is why these users will be served with higher rates than their re-quired minimum. This user classification is conducted based on perturbation analysis of convex optimization problems. 1.

### Transmitter and Precoding Order Optimization for Nonlinear Downlink Beamforming

, 2007

"... Abstract — The downlink of a multiple-input multiple output (MIMO) broadcast channel (BC) is considered, where each receiver is equipped with a single antenna and the transmitter performs nonlinear Dirty-Paper Coding (DPC). We present an efficient algorithm that finds the optimum transmit filters an ..."

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Abstract — The downlink of a multiple-input multiple output (MIMO) broadcast channel (BC) is considered, where each receiver is equipped with a single antenna and the transmitter performs nonlinear Dirty-Paper Coding (DPC). We present an efficient algorithm that finds the optimum transmit filters and power allocation as well as the optimum precoding order(s) possibly affording time-sharing between individual DPC orders. Subsequently necessary and sufficient conditions for the optimality of an arbitrary precoding order are derived. Based on these we propose a suboptimal algorithm showing excellent performance and having low complexity. I.

### QoS Feasibility for the MIMO Broadcast Channel: Robust Formulation and Multi-Carrier Systems

, 2010

"... Abstract—Based on recent results for the multiple-input multiple-output (MIMO) broadcast channel (BC), the feasibility of the quality of service (QoS) requirements of multi-carrier systems is investigated. Allowing for a precoding operation with arbitrary structure, the feasibility test for multi-ca ..."

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Abstract—Based on recent results for the multiple-input multiple-output (MIMO) broadcast channel (BC), the feasibility of the quality of service (QoS) requirements of multi-carrier systems is investigated. Allowing for a precoding operation with arbitrary structure, the feasibility test for multi-carrier systems is analogous to that for MIMO systems with linear transceivers. However, if the precoder is restricted to be applied separately to the different carriers, additional conditions must be fulfilled for feasibility. After stating these conditions, we propose a simple test which is sufficient, but not necessary for feasibility. For a robustQoSformulation that isappropriate for erroneous channel state information, the feasibility results for the MIMO BC can be reused as long as all possible channel realizations fulfill a regularity condition. I.