Theoretical Bounds for Minimum Interference in Full Multi-Interface Multi-Channel Wireless Networks

This paper presents novel theoretical results for the channel assignment problem in full multi-interface multi-channel wireless networks (fM²WNs). We show that the minimum interference for a fM²WN with n routers each equipped with r radio interfaces can only be achieved with a certain number of channels and derive upper and lower bounds for that number as a function of r. Furthermore, exact values are obtained when certain relations between n and r are satisfied. These bounds are then employed to develop closed-form expressions for the minimum channel interference. Accordingly, a polynomial-time algorithm to find a near-optimal solution is developed. Theoretical bounds and the performance of the developed algorithm are validated through a comparison with exhaustive search results.