On the Throughput Maximization in Dencentralized Wireless Networks

A distributed single-hop wireless network with $K$ links is considered, where the links are partitioned into a fixed number ($M$) of clusters each operating in a subchannel with bandwidth $\frac{W}{M}$. The subchannels are assumed to be orthogonal to each other. A general shadow-fading model, described by parameters $(\alpha,\varpi)$, is considered where $\alpha$ denotes the probability of shadowing and $\varpi$ ($\varpi \leq 1$) represents the average cross-link gains. The main goal of this paper is to find the maximum network throughput in the asymptotic regime of $K \to \infty$, which is achieved by: i) proposing a distributed and non-iterative power allocation strategy, where the objective of each user is to maximize its best estimate (based on its local information, i.e., direct channel gain) of the average network throughput, and ii) choosing the optimum value for $M$. In the first part of the paper, the network hroughput is defined as the \textit{average sum-rate} of the network, which is shown to scale as $\Theta (\log K)$. Moreover, it is proved that in the strong interference scenario, the optimum power allocation strategy for each user is a threshold-based on-off scheme. In the second part, the network throughput is defined as the \textit{guaranteed sum-rate}, when the outage probability approaches zero. In this scenario, it is demonstrated that the on-off power allocation scheme maximizes the throughput, which scales as $\frac{W}{\alpha \varpi} \log K$. Moreover, the optimum spectrum sharing for maximizing the average sum-rate and the guaranteed sum-rate is achieved at M=1.

💡 Research Summary

This paper investigates throughput maximization in a large‑scale decentralized single‑hop wireless network comprising K transmitter‑receiver pairs. The links are partitioned into a fixed number M of clusters, each of which exclusively occupies a sub‑channel of bandwidth W/M; sub‑channels are orthogonal, eliminating inter‑cluster interference. The wireless environment is modeled with a general shadow‑fading framework characterized by two parameters: α, the probability that a link experiences shadowing, and ω (≤ 1), the average cross‑link gain that captures the strength of interference from other links within the same cluster.

The authors set two distinct performance objectives. First, they define the average sum‑rate, the long‑term expected total data rate across all links, and study its scaling behavior as K → ∞. Second, they introduce the guaranteed sum‑rate, which is the total rate that can be assured to all users when the outage probability tends to zero, thereby reflecting a quality‑of‑service (QoS) guarantee.

Distributed Power Allocation

Each user possesses only local channel state information (CSI), namely its direct channel gain h_ii. Based on this information, a non‑iterative, fully distributed power‑allocation rule is proposed: a user compares h_ii with a pre‑determined threshold τ. If h_ii ≥ τ the user transmits at a fixed power level; otherwise it remains silent. This on‑off (threshold‑based) scheme requires no exchange of CSI among users and incurs negligible computational overhead.

Analysis of the Average Sum‑Rate

Under the strong interference regime—where the aggregate interference from other links dominates the noise—the authors prove that the on‑off rule is optimal for maximizing the average sum‑rate. By employing stochastic geometry and large‑system asymptotics, they show that the average sum‑rate scales as Θ(log K). This logarithmic growth matches the well‑known capacity scaling of random access networks but is achieved with a dramatically simpler protocol.

Analysis of the Guaranteed Sum‑Rate

When the design criterion shifts to guaranteeing a minimum rate to every user with vanishing outage probability, the same on‑off policy again emerges as optimal. The guaranteed sum‑rate is shown to scale as

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