In the sensor array signal reception system, improving the accuracy of weak-signal detection is crucial. Traditional fixed-step algorithms struggle to balance the convergence rate (CR) and low steady-state error (SSE) owing to their inherent trade-off limitations. To address this limitation, we propose a novel variable-step-size least-mean-square (VSS-LMS) algorithm based on a modified versoria function, specifically redesigned to enhance curvature characteristics. This approach establishes dynamic coupling between error statistics and step-size factors through nonlinear mapping. It derives closed-loop equations governing parameters ($\alpha$, $\beta$, and $\gamma$) relative to the smoothed instantaneous error correlation function. Consequently, an adaptive feedback system is constructed to achieve real-time adjustment through optimal step-size generation. The optimal parameters ($\alpha$, $\beta$, and $\gamma$) are determined through empirical enumeration and analysis of their impact on algorithmic performance. Comparative evaluations against established VSS-LMS algorithms confirm performance: the proposed algorithm accelerates convergence while maintaining a low SSE, and exhibits robust signal recovery capabilities under low-SNR conditions with diverse interference types.

Index-modulated orthogonal frequency division multiplexing (OFDM-IM) has been recognized as a promising multicarrier transmission scheme due to its flexibility and favorable bit error rate (BER) performance. However, for future wireless communication systems requiring high reliability, high spectral efficiency, and low complexity, existing OFDM-IM schemes still face challenges in simultaneously improving spectral efficiency, maintaining diversity gain, and controlling detection complexity at the receiver. To address these issues, this paper proposes a joint-mode and repeated-index modulation-based coordinate interleaved OFDM scheme (MRIM-CI-OFDM). Building upon the shared subcarrier activation pattern (SAP) and coordinate interleaving structure, the proposed scheme introduces cross-cluster mode-pair indexing, enabling information bits to be jointly carried by the SAP domain, mode domain, and constellation symbol domain. This design enhances spectral efficiency while preserving the diversity advantages of coordinate interleaving. Furthermore, a rotated multi-mode constellation construction method based on inter-constellation minimum product distance is developed to improve mode separability. By exploiting the equivalent real-valued orthogonal structure introduced by coordinate interleaving, low-complexity maximum likelihood (ML) and three-stage Max-Log detectors are constructed. Simulation results demonstrate that the proposed low-complexity detectors achieve near-ML detection performance. Additionally, at a spectral efficiency of 1.25 bps/Hz, MRIM-CI-OFDM achieves approximately 3 dB SNR gain over the coordinate-interleaved/repeated-index benchmarks and more than 5 dB gain over conventional OFDM-IM.