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An important issue in the widespread deployment of infrastructure based wireless local area networks (WLANs) is the network design. In this paper, we propose a new WLAN design approach that focuses on assuring sufficient data rate capacity to meet expected user demand in the coverage area, while still satisfying signal coverage and interference level requirements. Noting the low cost of WLAN access points, we formulate a novel mathematical network design model within the framework of constraint satisfaction problems. Our model is termed the capacity based WLAN constraint satisfaction problem (Cap-WLAN CSP). The solution of the Cap-WLAN CSP model yields a network design based on data rate demand by providing the access point locations, the frequency channel allocation, and power levels required for the WLAN to meet expected user demands. Our numerical results illustrate that the capacity based approach is more appropriate for the design of WLAN systems than those of traditional coverage based designs.