Channel assignment using a subspace approach to neural networks

The problem of planning a mobile cellular network involves the allocation of channels to base stations so as to ensure the network can carry sufficient traffic whilst avoiding unacceptable levels of interference. A number of authors have considered energy minimising neural networks as a method of solving the channel assignment problem (CAP). These parallel algorithms rely on the minimum of the dynamic equation describing the neural network, known as the energy function, coinciding with the optimum solution of the channel assignment problem. Numerous studies of neural networks as a method of solving combinatorial optimisation problems have been undertaken. The travelling salesman problem (TSP) has been tackled in the context of a rigorous mathematical structure. With this approach the solution is confined to a subspace in which valid solutions are known to lie. A solution technique is then developed which resolves the conflict between minimising the energy and ensuring the final solution lies within the valid subspace. Previous has shown that this solution technique can be extended to the channel assignment problem by formulating it in terms of the valid subspace in which valid solutions to the traffic demand constraint must lie. The interference constraints are enforced by means of the energy function which is minimised whilst ensuring the solution remains within the valid subspace. The advantage of this formulation is the ability to independently control the traffic demand constraint which can be enforced without the need of a heuristically- derived energy function. The paper extends the algorithm to include adjacent channel interference from arbitrary base stations and presents the results for a channel assignment problem typical of densely populated areas