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High energy consumption at mobile devices is a critical issue for end users to access and enjoy high data-rate multimedia applications and services in Wireless Local Area Networks (WLANs). This paper develops an analytical framework for analyzing and comparing the energy efficiency performance of IEEE 802.11n Medium Access Control (MAC) protocol and a Busy Tone Based Cooperative MAC Protocol(namely BTAC) in multi-rate WLANs. Our proposed analytical model considers the impact of dynamic radio channel conditions and multi-rate transmission scenarios. Analytical and simulation results show that BTAC can achieve up to 50% energy saving, comparing to the IEEE 802.11n MAC protocol, under different radio channel conditions, network sizes and traffic loads.