The Interference-Conjugate Transform: The Tightest Interference-Linear Surrogate for Power Control, Scheduling and Beamforming in Wireless Networks
Abstract
Closed-form fractional programming (FP), weighted MMSE (WMMSE), and the 2026 surrogate-enhanced methods SEFP and XMMSE all maximize the weighted sum rate by iteratively maximizing a surrogate linear in the interference power. We show that this family admits a unique best member: the interference-conjugate transform (ICT), which replaces each rate term log(1+a/b) by maxκ≥0[Ω(κa)−κb], where Ω is the closed-form partial convex conjugate of the rate in the interference variable and the optimal multiplier is the interference price a/(b(a+b)). We prove that, for any fixed price, Ω(κ ·) is the pointwise largest own-signal function compatible with a valid interference-linear lower bound, and that tightness at an anchor forces the price. Hence all four benchmark surrogates, which share this price and differ only in their own-signal term, are dominated pointwise by ICT. At SINR γ, the benchmarks' own-signal curvature exceeds the true curvature by factors behaving as γ/2 (FP/WMMSE) and (logγ)/2 (SEFP/XMMSE), against 1+1/(γ(γ+2)) for ICT, and this ordering carries over to the certified ascent per iteration and the asymptotic linear convergence rate. ICT yields closed-form updates at the benchmarks' per-iteration cost for single-antenna power control, uplink joint scheduling and power control, and multi-cell MISO beamforming, and the first solver-free algorithm for sum-least-qth-percentile rate maximization, via a K-dimensional convex dual with closed-form gradient and Hessian and a certified duality gap. In uplink scheduling, ICT improves proportional-fairness utility over FP by +7.03 and over SEFP by +3.35 (60/60 drops) using 18.7 iterations per slot vs. 49.7 and 38.0; in MISO beamforming with M=8, it reaches 99.9% of its final value in a median of 9 iterations vs. 16 (XMMSE) and 1160 (FP/WMMSE).
Related
- Surrogate-Enhanced Fractional Programming for MIMO Device-to-Device Interference Networks
- Deep Reinforcement Learning for Blind Passive Beamforming in RIS-Assisted MIMO Systems
- Microwave Linear Analog Computer (MiLAC) for Simultaneous Active and Passive Beamforming
- A Smaller Subspace is All You Need: Efficient ISAC Beamforming via Dimensionality Reduction
- GSBF: Gaussian Splatting for Environment-Aware Beamforming
BibTeX
@misc{khan2026interferenceconjugate,
title = {{The Interference-Conjugate Transform: The Tightest Interference-Linear Surrogate for Power Control, Scheduling and Beamforming in Wireless Networks}},
author = {Ahmad Khan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37794},
eprint = {2610.37794},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37794},
}
RIS
TY - UNPB
TI - The Interference-Conjugate Transform: The Tightest Interference-Linear Surrogate for Power Control, Scheduling and Beamforming in Wireless Networks
AU - Ahmad Khan
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37794
UR - https://arxiv.org/abs/2610.37794
AB - Closed-form fractional programming (FP), weighted MMSE (WMMSE), and the 2026 surrogate-enhanced methods SEFP and XMMSE all maximize the weighted sum rate by iteratively maximizing a surrogate linear in the interference power. We show that this family admits a unique best member: the interference-conjugate transform (ICT), which replaces each rate term log(1+a/b) by max_κ≥0[Ω(κa)−κb], where Ω is the closed-form partial convex conjugate of the rate in the interference variable and the optimal multiplier is the interference price a/(b(a+b)). We prove that, for any fixed price, Ω(κ ·) is the pointwise largest own-signal function compatible with a valid interference-linear lower bound, and that tightness at an anchor forces the price. Hence all four benchmark surrogates, which share this price and differ only in their own-signal term, are dominated pointwise by ICT. At SINR γ, the benchmarks' own-signal curvature exceeds the true curvature by factors behaving as γ/2 (FP/WMMSE) and (logγ)/2 (SEFP/XMMSE), against 1+1/(γ(γ+2)) for ICT, and this ordering carries over to the certified ascent per iteration and the asymptotic linear convergence rate. ICT yields closed-form updates at the benchmarks' per-iteration cost for single-antenna power control, uplink joint scheduling and power control, and multi-cell MISO beamforming, and the first solver-free algorithm for sum-least-qth-percentile rate maximization, via a K-dimensional convex dual with closed-form gradient and Hessian and a certified duality gap. In uplink scheduling, ICT improves proportional-fairness utility over FP by +7.03 and over SEFP by +3.35 (60/60 drops) using 18.7 iterations per slot vs. 49.7 and 38.0; in MISO beamforming with M=8, it reaches 99.9% of its final value in a median of 9 iterations vs. 16 (XMMSE) and 1160 (FP/WMMSE).
ER -