[Paper Review] A model for randomized resource allocation in decentralized wireless networks

Kamyar Moshksar, Alireza Bayesteh+1 more|ArXiv.org|Nov 29, 2009

Cooperative Communication and Network Coding23 references5 citations

TL;DR

This paper proposes a randomized frequency hopping (FH) scheme for decentralized wireless networks with random user activity, where transmitters hop over sub-bands without coordination. It derives tight bounds on mutual information at high SNR, showing that the sum multiplexing gain of FH approaches that of optimal systems, and demonstrates that FH significantly improves spectral efficiency over FD in terms of average sum and minimum per-user multiplexing gain, with a bounded loss in the worst-case gain of at most $1/e$. The scheme avoids cognitive radio complexity and enables efficient, low-complexity spectrum sharing in dynamic environments with unknown user counts.

ABSTRACT

In this paper, we consider a decentralized wireless communication network with a fixed number $u$ of frequency sub-bands to be shared among $N$ transmitter-receiver pairs. It is assumed that the number of active users is a random variable with a given probability mass function. Moreover, users are unaware of each other's codebooks and hence, no multiuser detection is possible. We propose a randomized Frequency Hopping (FH) scheme in which each transmitter randomly hops over a subset of $u$ sub-bands from transmission to transmission. We derive lower and upper bounds on the mutual information of each user and demonstrate that, for large Signal-to-Noise Ratio (SNR) values, the two bounds coincide. This observation enables us to compute the sum multiplexing gain of the system and obtain the optimum hopping strategy for maximizing this quantity. We compare the performance of the FH system with that of the Frequency Division (FD) system in terms of several performance measures and show that (depending on the probability mass function of the number of active users) the FH system can offer a significant improvement implying a more efficient usage of the spectrum.

Motivation & Objective

• To design a low-complexity, decentralized resource allocation scheme for wireless networks with unknown and random numbers of active users.
• To avoid the need for centralized control or spectrum sensing, which increases system complexity.
• To maximize spectral efficiency in the presence of mixed Gaussian interference due to random, non-cooperative transmissions.
• To compare the performance of the proposed FH scheme with traditional Frequency Division (FD) systems using multiple performance metrics.
• To derive tight bounds on mutual information and compute the sum multiplexing gain under high SNR conditions.

Proposed method

• Uses a randomized frequency hopping (FH) strategy where each transmitter independently selects a random subset of sub-bands for transmission.
• Models the interference-plus-noise as a mixed Gaussian distribution due to random user activity and non-cooperative signaling.
• Derives lower and upper bounds on mutual information per user, showing they converge at high SNR, enabling accurate multiplexing gain analysis.
• Applies Jensen’s inequality to the expectation of the interference term, leveraging convexity properties under specific conditions on the expected number of users.
• Computes the sum multiplexing gain $\eta_{\mathrm{FH}}^{(1)}$ and per-user gains $\eta_{\mathrm{FH}}^{(2)}$, $\eta_{\mathrm{FH}}^{(3)}$, and service capability $\eta_{\mathrm{FH}}^{(4)}$ for comparison with FD systems.
• Uses the function $v(1 - v/u)^{\mathbb{E}\{N\}-1}$ to optimize the hopping strategy and derive sufficient conditions for performance superiority over FD.

Experimental results

Research questions

• RQ1 Can a randomized frequency hopping scheme outperform traditional Frequency Division (FD) in terms of average sum multiplexing gain under random user activity?
• RQ2 What is the achievable sum multiplexing gain of a decentralized FH system with mixed Gaussian interference and no multiuser detection?
• RQ3 How does the minimum nonzero per-user multiplexing gain of the FH system compare to that of the FD system?
• RQ4 What is the optimal frequency hopping strategy that maximizes the sum multiplexing gain in a decentralized network with random user counts?
• RQ5 To what extent is the performance of the FH system limited in the worst-case scenario compared to FD?

Key findings

• The proposed FH scheme achieves a higher average sum multiplexing gain than FD when the expected number of active users satisfies $\mathbb{E}\{N\} < \frac{1}{2}\ln((e^2 - 1)n_{\max})$.
• The average minimum per-user multiplexing gain of FH exceeds that of FD when $\frac{1}{\mathbb{E}\{N\}}\left(1 - \frac{1}{\mathbb{E}\{N\}}\right)^{\mathbb{E}\{N\}-1} > \frac{1}{n_{\max}}$, which holds for $\mathbb{E}\{N\} \leq 1.1565$ or moderate $n_{\max}$.
• The worst-case per-user multiplexing gain of FH is bounded by $\frac{1}{e}$ of the FD gain, i.e., $\frac{\eta_{\mathrm{FH}}^{(3)}}{\eta_{\mathrm{FD}}^{(3)}} \geq \frac{1}{e}$, indicating a bounded performance loss.
• At high SNR, the mutual information bounds for each user converge, enabling accurate computation of the sum multiplexing gain and validating the analytical approach.
• The service capability $\eta^{(4)}$ of the FH system is shown to be superior to FD under the same random user activity model, indicating better scalability.
• The optimal hopping strategy is derived by maximizing $v\mathbb{E}\{N(1 - v/u)^{N-1}\}$, with performance gains dependent on the distribution of the number of active users.