As corollaries, they get a strong l imit theorem of equitable ratios for countable nonhomogeneous Markov Chains and a strong lim it theorem of equitable ratios of the frequency of occurrence of the couple of s tates for countable nonhomogeneous Markov Chains.

A scheduling algorithm used for wireless sensor network(WSN) was proposed to realize the proportional fairness principle.

The new algorithm can guarantee the proportional fairness among users while achieving large system throughput by local search.

In order to overcome the high computing complexity of the existed PUURC algorithm, we propose the greedy proportional fairness scheduling algorithm, which tries to reduce the computing complexity while guarantying the system throughput and user fairness.

At receiver,the capacity threshold is obtained by using proportional fair parameter in each sub-channel on each user.

In this paper,we proposed a novel joint routing and proportional fair scheduling.

Compared with traditional proportional fair algorithm in 3G LTE(Long Term Evolution),the proposed algorithm fully considered the inter-cell interference,and improved both the system throughput and user throughput fairness performance.

This paper presents the implementation of semi-static LTE uplink system level simulator,including some details on simulation procedure,and introduction of cell and user distribution,modulation and coding schemes, Round Robin and Proportional Fairness scheduling schemes and fractional power control.