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This is Part II of a two-part paper series that studies the use of the proportional fairness (PF) utility function as the basis for capacity allocation and scheduling in multi-channel multi-rate wireless networks. The contributions of Part II are twofold. (i) First, we extend the problem formulation, theoretical results, and algorithms to the case of time-varying channels, where opportunistic capacity allocation and scheduling can be exploited to improve system performance. We lay down the theoretical foundation for optimization that “couples” the time-varying characteristic of channels with the requirements of the underlying applications into one consideration. In particular, the extent to which opportunistic optimization is possible is not just a function of how fast the channel characteristics vary, but also a function of the elasticity of the underlying applications for delayed capacity allocation. (ii) Second, building upon our theoretical framework and results, we study subcarrier allocation and scheduling in orthogonal frequency division multiplexing (OFDM) cellular wireless networks. We introduce the concept of a W-normalized Doppler frequency to capture the extent to which opportunistic scheduling can be exploited to achieve throughput-fairness performance gain. We show that a “look-back PF” scheduling can strike a good balance between system throughput and fairness while taking the underlying application requirements into account. Key words− Proportional fairness, Opportunistic scheduling, QoS, Subcarrier assignment, OFDM, Wireless networks Corresponding Author: Professor Soung Chang Liew Email: [email protected] Tel:/Fax: (852) 2609-8352/2603-5032 URL: http://www.ie.cuhk.edu.hk/soung _____________________________________ This work was supported under the Area of Excellence Scheme (Project Number AoE/E-01/99) and the Competitive Earmarked Research Grant (Project Number 414305 and Project Number 418506) established under the University Grant Committee of the Hong Kong Special Administrative Region, China. Proportional Fairness in Multi-channel Multi-rate ... Liew and Zhang