The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06) IMPROVED MODELING OF HIGHLY LOADED UMTS NETWORK WITH NONNEGATIVE CONSTRAINTS Rafal Zdunek Maciej J. Nawrocki Institute of Telecommunications, Teleinformatics, and Acoustics Wroclaw University of Technology, Poland E-mails: rafal.zdunek@pwr.wroc.pl maciej.nawrocki@pwr.wroc.pl ABSTRACT In this paper, we deal with the power control problem in a non-uniform and highly loaded UMTS network with omnidi- rectional and smart antennas. If the pole capacity limit in a cell is exceeded no reasonable solution to the power control problem can be obtained with the methods such as the Gaus- sian elimination, Jacobi, Gauss-Seidel, SOR, or some Krylov subspace projection methods. In such a case, some users are usually removed from the system. In our approach, we solve a non-negatively constrained least square problem with very efficient gradient based linear solvers. This allows us to ap- proximately estimate the powers of all the users even though a pole capacity is slightly affected in some cells. It can be implemented in Radio Resource Management as an effective solution for networks in overload state. Additionally, to reduce a complexity of computation, we extend the dimension reduc- tion technique proposed by Mendo and Hernando to the case of smart antennas. Our considerations are supported with some simulations based on a UMTS network model. I. I NTRODUCTION In UMTS network planning and optimization, static Monte Carlo simulations are usually performed to optimize power re- sources in the designed network [1, 2, 3, 4, 5, 12]. In each run (snapshot), powers of all the users can be numerically esti- mated from a large system of linear equations which describes target SIRs at the receiver. Then, such powers are used for evaluation of a cost function to be minimized. The computa- tion of the powers is the most computationally intensive task in an overall optimization problem. This task should be achieved with the lowest computational cost, which involves applying dimension reduction technique [6] and/or very efficient meth- ods for solving systems of linear equations [7, 8]. This issue has been also discussed, e.g. in [9], especially in the context of optimization of a UMTS network with smart antennas. The computation of powers has some restrictions. In a highly loaded network, some overloading effects occur quite often, what completely perturbs the power estimations. This is the case when a number of users in some cells is much greater than in their neighboring cells, and in consequence, many esti- mated powers in a whole system may have negative or positive extremely large values. The snapshots with this overloading effect must be removed from a Monte Carlo analysis. When smart antennas are applied [10], a cell capacity considerably in- creases but is still severely limited due to finite side-lobe level [11]. When looking at the problem from real system performance perspective potential negative power solutions would force Ra- dio Resource Managemet (RRM) algorithms [12] to remove unwanted users from the system (Congestion Control) or not allow the new user to be admitted to the system (Admission Control). To reduce a complexity of computation in simulations, the dimension reduction technique, which has been proposed by Mendo and Hernando [6] to analyze a network with traditional antennas (having a constant gain), is usually used. We extend this technique to the case with smart antennas. Then, to solve such a reduced system of linear equations, we formulate a lin- ear least square problem subjected to nonnegativity constraints, and then, we use very efficient projected gradient methods. The proposed method which avoids a negative solution can find an application not only in simulation software but can also have a direct implementation into RRM procedures and poli- cies. It can help to find an appropriate balance in power man- agement through smart decreasing of some users’ quality re- quirements in case of network overload. It leads to saved con- nections in extreme situations. The layout of the paper is organized as followed. In Section II., we introduce the model that describes an uplink transmis- sion. Section III. contains the methods that we propose to effi- ciently solve the model. Some related experiments are given in Section IV. Finally, a brief discussion is presented in Section V. II. MODEL Let us assume that in the system we have K users assigned to M base stations. For traditional antennas the uplink transmis- sion is described by the model ∀k ∈{1,...,K}: l(φ k ,k)p k ∑ j=k l(φ k ,j )p j + N (φ k ) = γ k , (1) where p k is unknown power of the k-th Mobile Station (MS), φ k is an index of the Base Station (BS) to which the k-th MS is assigned, l(φ k ,j ) is an attenuation path between the j -th MS and the φ k -th BS, γ k = R (k) b E B is a target SIR of the k-th MS, and N (φ k )= ( N0B G ) (k) is thermal noise of the φ k -th BS. Fol- lowing then, R (k) b is a data bit-rate of the k-th MS, E (k) is the required ratio of bit energy to noise and interference power spectral density, B is a channel bandwidth, N 0 is a spectral density of thermal noise power, G is a directional gain for a pair of BS-MS antennas that are assumed to be omni-directional. For smart antennas, the uplink transmission is modeled as 1-4244-0330-8/06/$20.00 c 2006 IEEE