Distributed Power Control and Coding-Modulation Adaptation in Wireless Networks using Annealed Gibbs Sampling

In wireless networks, the transmission rate of a link is determined by received signal strength, interference from simultaneous transmissions, and available coding-modulation schemes. Rate allocation is a key problem in wireless network design, but a very challenging problem because: (i) wireless interference is global, i.e., a transmission interferes all other simultaneous transmissions, and (ii) the rate-power relation is non-convex and non-continuous, where the discontinuity is due to limited number of coding-modulation choices in practical systems. In this paper, we propose a distributed power control and coding-modulation adaptation algorithm using annealed Gibbs sampling, which achieves throughput optimality in an arbitrary network topology. We consider a realistic Signal-to-Interference-and-Noise-Ratio (SINR) based interference model, and assume continuous power space and finite rate options (coding-modulation choices). Our algorithm first decomposes network-wide interference to local interference by properly choosing a “neighborhood” for each transmitter and bounding the interference from non-neighbor nodes. The power update policy is then carefully designed to emulate a Gibbs sampler over a Markov chain with a continuous state space. We further exploit the technique of simulated annealing to speed up the convergence of the algorithm to the optimal power and coding-modulation configuration. Finally, simulation results demonstrate the superior performance of the proposed algorithm.

💡 Research Summary

The paper tackles the challenging problem of jointly controlling transmit power and selecting coding‑modulation schemes in wireless ad‑hoc networks where interference is global (SINR‑based) and the rate‑power relationship is both non‑convex and discontinuous due to a finite set of modulation options. Existing works either assume a single, predetermined modulation for all links or treat the rate as a continuous function of SINR, thereby ignoring the practical step‑wise nature of real coding‑modulation choices. To bridge this gap, the authors propose a fully distributed algorithm that maximizes the weighted sum of link rates while penalizing total transmit power, achieving throughput‑optimality (stability for any arrival vector inside the network’s capacity region).

Key technical contributions are:

1. Localizing Global Interference – Each node defines a one‑hop neighbor set N₁(a) based on a channel‑gain threshold α and a two‑hop neighbor set N₂(a). An upper bound ξ_ab on interference from non‑neighbors is pre‑computed, allowing the SINR of link (a,b) to be expressed solely as a function of the powers of its neighbors plus a known constant. This “noise + partial‑interference” term Υ_ab enables a localized view of interference.

2. Decision Set Generation – In every time slot, nodes contend for inclusion in a decision set D using random back‑off and INTENT messages. The protocol guarantees that any two transmitters in D are neither one‑hop nor two‑hop neighbors, so simultaneous updates do not interfere with each other. This construction yields a reversible Markov chain over power configurations.

3. Continuous‑State Gibbs Sampling – Power for each selected link is treated as a continuous variable. For a given link, the algorithm computes a set of critical power levels: the highest power at which each possible modulation of neighboring links remains feasible. These critical points partition the power interval