## Final Activity Report Summary - OPTIMISM (Efficient modelling algorithms for UMTS network optimisation)

The project concentrated on network models simple enough (but accurate) to ensure fast computations as well as on fast convergence optimisation algorithms. Existing UMTS network model (so called 'method of sums' further called cell based power control) was enhanced through algebraic study for taking into account multi-service environment as well as non-uniform orthogonality factor distribution within a cell. The model differs from widely known static simulation model and allows for much faster computations (at least 10x) without the loss of accuracy.

Selection of appropriate parameters for optimisation was made. Analysis took into account operators' needs as well as feasibility/costs of changing given parameter value. Mathematical model limitations were considered in parameter selection process and parameters like soft-handoff hysteresis, timers etc were rejected since any static approach doesn't take into account these parameters in realistic way. Reasonable parameters were selected for automated optimisation: antenna tilt, azimuth and pilot channel power.

It was decided to use simple cost function based on transmit power / receive interference power as most of network key performance indicators (KPI) are limited by finite power resources. Extensive cost function analysis was made to find its properties. It was discovered that sub-optimal solutions can represent completely different network configurations. It was also found that it is important to test each obtained solution for robustness to prevent having 'good' minima but with very narrow surroundings. As expected the cost function was very nonlinear particularly caused by vertical antenna characteristic.

A number of optimisation algorithms have been tested including: Linear Scan Solver (LSS fellow's own algorithm), genetic algorithms, pattern search algorithms, DIRECT algorithm as well as stochastic optimisation algorithms. They were implemented in both ways: whole network optimisation, iterative network optimisation in cell clusters. The conclusion was: LSS and stochastic optimizers require reasonable staring point, DIRECT algorithm gives excellent results but only if the cost function has less than 10 dimensions, genetic algorithms require large amount of cost function evaluations to converge for reasonable solution (but some solutions are excellent). Pattern search algorithms have quite nice convergence but it depends on starting point. The fastest convergence was reached by carefully tuned stochastic optimisation algorithms. Convergence rate was only a bit sensitive to increased number of dimensions. Summarising, it was discovered that the best trade-off between solution quality and computation time is obtained when using multi-start pattern search algorithm first and then use obtained solutions as an input to stochastic optimiser with use of simple to evaluate cost function (e.g. based on power). The method was also improved by using cell interference coupling matrix to guide both optimizers (especially the stochastic one).

The main conclusion from this project is as follows: static network models widely used for optimisation purposes are rough. Furthermore input propagation data is inaccurate compared to reality so, constructing complicated cost function is not essential, even more results obtained by the simulations will be inaccurate. Therefore it was proposed for future research to make static optimisation phase as a simple pre-optimisation activity with power based cost function and concentrate on autotuning of number of parameters (dynamic optimisation) as on-line adaptation to traffic changes.

Selection of appropriate parameters for optimisation was made. Analysis took into account operators' needs as well as feasibility/costs of changing given parameter value. Mathematical model limitations were considered in parameter selection process and parameters like soft-handoff hysteresis, timers etc were rejected since any static approach doesn't take into account these parameters in realistic way. Reasonable parameters were selected for automated optimisation: antenna tilt, azimuth and pilot channel power.

It was decided to use simple cost function based on transmit power / receive interference power as most of network key performance indicators (KPI) are limited by finite power resources. Extensive cost function analysis was made to find its properties. It was discovered that sub-optimal solutions can represent completely different network configurations. It was also found that it is important to test each obtained solution for robustness to prevent having 'good' minima but with very narrow surroundings. As expected the cost function was very nonlinear particularly caused by vertical antenna characteristic.

A number of optimisation algorithms have been tested including: Linear Scan Solver (LSS fellow's own algorithm), genetic algorithms, pattern search algorithms, DIRECT algorithm as well as stochastic optimisation algorithms. They were implemented in both ways: whole network optimisation, iterative network optimisation in cell clusters. The conclusion was: LSS and stochastic optimizers require reasonable staring point, DIRECT algorithm gives excellent results but only if the cost function has less than 10 dimensions, genetic algorithms require large amount of cost function evaluations to converge for reasonable solution (but some solutions are excellent). Pattern search algorithms have quite nice convergence but it depends on starting point. The fastest convergence was reached by carefully tuned stochastic optimisation algorithms. Convergence rate was only a bit sensitive to increased number of dimensions. Summarising, it was discovered that the best trade-off between solution quality and computation time is obtained when using multi-start pattern search algorithm first and then use obtained solutions as an input to stochastic optimiser with use of simple to evaluate cost function (e.g. based on power). The method was also improved by using cell interference coupling matrix to guide both optimizers (especially the stochastic one).

The main conclusion from this project is as follows: static network models widely used for optimisation purposes are rough. Furthermore input propagation data is inaccurate compared to reality so, constructing complicated cost function is not essential, even more results obtained by the simulations will be inaccurate. Therefore it was proposed for future research to make static optimisation phase as a simple pre-optimisation activity with power based cost function and concentrate on autotuning of number of parameters (dynamic optimisation) as on-line adaptation to traffic changes.