Improved channel assignment algorithms for cellular networks were designed by modelling the interference constraints in terms of a hypergraph (Sarkar and Sivarajan). However these algorithms only considered cochannel reuse constraints. Receiver filter responses impose restrictions on simultaneous adjacent channel usage in the same cell or in neighbouring cells. An asymptotically tight upper bound for the traffic carried by the system in the presence of arbitrary cochannel and adjacent channel reuse constraints was developed in Deora (1995). However this bound is computationally intractable even for small systems like a regular hexagonal cellular system of 19 cells. We have obtained approximations to this bound using the optimal solutions for cochannel reuse constraints only, and a further graph theoretic approach. Our approximations are computationally much more efficient and have turned out to track very closely the exact performance bounds in most cases of interest. We also present some heuristics for designing fixed channel assignment algorithms with a minimum number of channels satisfying both cochannel and adjacent channel reuse constraints.
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