form $$\label{eq:preamble_trans_suc_prob}
    r_s(t) = a \log_2 \left (1 + \frac{{\rho_o {h_o}}}{{{\sigma ^2} + {{\cal I}_{s}}(t)}} \right ), \forall s \in {\mathcal{S}^I}$$ where $\sigma^2$ represents the noise power, ${{\cal I}_{s}}(t)$ denotes signal interference received at the RRH, the useful signal power equals to $\rho_o h_o$ due to the truncated channel inversion power control[^3] [@elsawy2014stochastic] with $h_o$ denoting the channel power gain between the IoT device and the RRH. It is noteworthy that the channel power gain experienced at a generic RRH is related to the spatial locations of both the RRH and its associated IoT devices. Nevertheless, we drop the spatial indices for notation lightening. Besides, just like [@elsawy2014stochastic], all channel gains are assumed to be known and be independent of each other, independent of the spatial locations, symmetric and are identically distributed (i.i.d.). Considering both the particular IoT device deployment environment and the convenience of theoretical analysis, the Rayleigh fading is assumed, and the channel power gain $h_o$ is assumed to be exponentially distributed with unit mean.

Based on the following five facts, we next present the analytical expression of signal interference

-   **Fact 1**: the average signal received from any single IoT device belonging to inter-cells is strictly less 