Consider $n$ source-destination pairs randomly located in a shared wireless medium, resulting in interference between different transmissions. All wireless links are modeled by independently and identically distributed (i.i.d.) random variables, indicating that the dominant channel effect is the random fading phenomenon. We characterize the throughput of one-hop communication in such network. First, we present a closed-form expression for throughput scaling of a heuristic strategy, for a completely general channel power distribution. This heuristic strategy is based on activating the source-destination pairs with the best direct links, and forcing the others to be silent. Then, we present the results for several common examples, namely, Gamma (Nakagami-$m$ fading), Weibull, Pareto, and Log-normal channel power distributions. Finally -- by proposing an upper bound on throughput of all possible strategies for super-exponential distributions -- we prove that the aforementioned heuristic method is order-optimal for Nakagami-$m$ fading.