In cellular networks, each mobile station adjusts its power level under control of its base station, i.e., through uplink transmit power control, which is essential to reach desired signal-to-interference-plus-noise ratio (SINR) at the base station and to limit inter-cell interference. The optimal levels of transmit power in a network depend on path loss, shadowing, and multipath fading, as well as the network configuration. However, since path loss is distance dependent and the cell association distances are correlated due to the cell association policies, the performance analysis of the uplink transmit power control is very complicated. Consequently, the impact of a specific power control algorithm on network performance is hard to quantify. In this paper, we analyze three uplink transmit power control schemes. We assume the standard power-law path loss and composite Rayleigh-lognormal fading. Using stochastic geometry tools, we derive the cumulative distribution function and the probability density function of the uplink transmit power and the resulting network coverage probability. It is shown that the coverage is highly dependent on the severity of shadowing, the power control scheme, and its parameters, but invariant of the density of deployment of base stations when the shadowing is mild and power control is fractional. At low SINRs, compensation of both path loss and shadowing improves the coverage. However, at high SINRs, compensating for path loss only improves coverage. Increase in the severity of shadowing significantly reduces the coverage.

We propose a novel base stations (BSs) -mobile stations (MSs) association policy for cellular networks. In this policy, the BS which provides the highest signal-to-interference ratio (SIR) among those located within a predetermined maximum association distance of the MS is selected as the serving BS. This policy encompasses the conventional highest-SIR association as a special case. Application of the new policy in 2-and 3-dimensional single-tier (homogeneous) and 2-dimensional twotier (heterogeneous) networks is discussed. Coverage probability expressions are derived assuming BSs in each tier are distributed according to an independent homogeneous Poisson point process (PPP). Rayleigh fading and exponential path-loss radio channels are assumed. Analysis is validated by Monte-Carlo simulations. For single-tier networks, two methods are proposed for the selection of the maximum association distance. With such selection, the proposed association policy performs similarly to the highest-SIR association. It is shown that this policy can also be used to manage user offloading to small cells in two-tier heterogeneous networks.

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