Effect of Cell-Selection on the Effective Fading Distribution in a Downlink K-tier HetNet

This paper characterizes the statistics of effective fading gain in multi-tier cellular networks with strongest base station (BS) cell association policy. First, we derive the probability of association with the $n$-th nearest BS in the $k$-th tier. Next, we use this result to derive the probability density function (PDF) of the channel fading gain (effective fading) experienced by the user when associating with the strongest BS. Interestingly, our results show that the effective channel gain distribution solely depends upon the original channel fading and the path-loss exponent. Moreover, we show that in the case of Nakagami-$m$ fading channels (Gamma distribution), the distribution of the effective fading is also Gamma but with a gain of $\frac{\alpha}{2}$ in the shape parameter, where $\alpha$ is the path-loss exponent.