Advances in Wavelet Denoising for Communication Signals: From Parameter Selection Toward Data-Driven Optimization

Abstract

Wavelet denoising suppresses nonstationary, impulsive, and interference-like disturbances in communication signals, but efficacy depends on coupled choices of transform, mother wavelet, decomposition level, thresholding rule, and shrinkage function. Pairing communication experiments with a PRISMA-aligned synthesis of 2020-2025 studies from ten sources, coded by parameter focus and domain (biomedical, industrial, geophysical, communication), this review traces a shift from defaults to similarity-, sparsity-, entropy-, energy-, sub-band-SNR-, and task-loss-driven selection, but finds communication evidence scarce. We benchmark DWT, SWT, and WPT on an impulsive-noise OFDM channel under SNR gain, MSE, BER, EVM, and real-time feasibility, with Friedman and Wilcoxon tests, efficiency-index ranking, and assessment of embedded DSP/FPGA constraints. As waveform-fidelity gains need not improve hard-decision performance, the Unified Decision Framework prioritises receiver-level validation over fidelity surrogates, validated on synthetic pilot-aided OFDM and measured IEEE 802.11n channels. On the synthetic link, the configuration attains the lowest channel-estimation NMSE, significantly outperforms a fixed-parameter wavelet $(p<10^{-11})$, and is statistically indistinguishable from the strongest classical baseline in BER; on measured channels it attains the lowest BER and EVM. The supported claim is the lowest estimation error at statistically equivalent bit-error performance, and it is conditional on the disturbance being structured or impulsive, since under AWGN alone wavelet thresholding yields no systematic BER improvement. Within these limits the framework generalises to held-out data and adapts to the observed channel, recasting wavelet denoising into a reproducible, communication-aware design methodology extensible to deep-unfolding architectures.

arXiv comment44 pages,14 figures, 14 tables. This version is submitted and accepted for publication