Differentiable High-Order Markov Models for Spectrum Prediction

TL;DR

This work revisits spectrum prediction with high-order Markov models, proposing composite-state representations and a differentiable extension to fine-tune the transition dynamics when sensing length $M$ differs from model memory $M'$. It introduces an embedding-like interpretation and a fast, gradient-based fine-tuning strategy for the transition matrix $P$, yielding the FT Markov variant. Across real Wi-Fi traffic datasets, high-order Markov methods achieve competitive accuracy with neural networks, particularly under data-constrained conditions and in the presence of outliers, with FT Markov offering improved robustness to mis-specified memory or state-space choices and better generalization beyond the training horizon. The results support a practical, interpretable, and efficient hybrid approach for spectrum prediction in cognitive radio and multi-channel contexts, motivating further exploration of state-space design and probabilistic outputs for link adaptation.

Abstract

The advent of deep learning and recurrent neural networks revolutionized the field of time-series processing. Therefore, recent research on spectrum prediction has focused on the use of these tools. However, spectrum prediction, which involves forecasting wireless spectrum availability, is an older field where many "classical" tools were considered around the 2010s, such as Markov models. This work revisits high-order Markov models for spectrum prediction in dynamic wireless environments. We introduce a framework to address mismatches between sensing length and model order as well as state-space complexity arising with large order. Furthermore, we extend this Markov framework by enabling fine-tuning of the probability transition matrix through gradient-based supervised learning, offering a hybrid approach that bridges probabilistic modeling and modern machine learning. Simulations on real-world Wi-Fi traffic demonstrate the competitive performance of high-order Markov models compared to deep learning methods, particularly in scenarios with constrained datasets containing outliers.

Figures (13)

• Figure 1: Examples of measured energy levels (green and orange colors) and corresponding PU states (in blue).
• Figure 2: Simulation results for the toy example using deterministic PU traffic with blocks of size 3, to illustrate the need of $M'\geq M$.
• Figure 3: Representation of a Markov model as an embedding approach. Top: standard Markov, bottom: differentiable Markov.
• Figure 4: Prediction performance of the neural network and Markov models with different state-space choices and different model memory $M'$. Scenario 1: training on dataset 1 testing on dataset 3.
• Figure 5: Prediction performance of the neural network and smart-state Markov. Scenario 1: training on dataset 1 testing on dataset 4.