New Algorithm for Structured OFDM Channel Estimation using Subgroup Duality

This paper presents a group-theoretic framework for structured channel estimation in Orthogonal Frequency Division Multiplexing (OFDM). By modeling subcarriers as the cyclic group $\mathbb{Z}_N$, we show that nulling a subgroup $H \subseteq \mathbb{Z}_N$ constrains the channel impulse response to its annihilator $H^\perp$ in the dual domain. A low-complexity estimator is proposed that detects such structure by evaluating energy concentration across candidate annihilators. Simulations demonstrate consistent gains in mean squared error, bit error rate, and throughput compared with least-squares and linear minimum mean square error baselines, achieving competitive performance with substantially lower complexity and preserved interpretability.