Non-stationary noise suppression in low voltage power line carrier channel based on CNN-LSTM hybrid model impedance matching algorithm

2.1. Analysis of low-voltage power noise suppression

The primary challenge confronting Linear Predictive Coding Coefficients (LPCC) lies in the interference from non-stationary noise. Since 2020, research has predominantly focused on traditional adaptive filtering-based methods, which, despite achieving satisfactory noise suppression, impose increased system burden due to their complex processing pipelines [12]. Consequently, there has been a shift toward integrating more advanced techniques, such as Deep Neural Network (DNN)-based end-to-end denoising systems, which have progressively supplanted conventional approaches [13]. An analysis of regional power data from 2020 to 2024 compares the application of various mainstream technologies, as illustrated in Fig. 1.

a) Noise reduction capability across different input SNRs. Traditional methods (adaptive filtering) show limited gains at low SNR. DNN-based approaches perform better but saturate early. The hybrid architecture achieves the highest reduction across the entire range – it consistently outperforms the other two.

b) Robustness against impulsive noise. Conventional techniques suffer a sharp performance drop (roughly 40 %) under burst interference. DNNs lose about 15 %. The hybrid model, in contrast, degrades only slightly (around 10 %), therefore proving more suitable for real-world noisy channels [14].

The current major issues include the poor robustness of traditional methods against non-Gaussian noise, the high computational complexity of DNN models, and the still suboptimal feature fusion mechanisms within hybrid architectures.

Fig. 1Performance analysis of LPCC noise reduction technologies (2020-2024)

2.2. Mainstream technical performance comparison

The traditional method adopts the WF (Wiener Filter) improvement scheme, which has a computational complexity of $O(N^{2)}$ and is suitable for the fixed noise scenario. RNN (Recurrent Neural Network) models (such as LSTM) can identify timing noise with an accuracy of 92 %, but the training needs a 10⁵ samples. The hybrid architecture extracts local features through CNN and models long-range dependence in combination with LSTM, and the actual measurement in 2023 shows that its SNR is improved by 8 dB (30 % higher than that of single technology). The technical pairs of various methods are shown in Tables 1-2.

In this study, an impedance matching algorithm based on CNN-LSTM is proposed to solve the existing problems through the following innovations:

(1) Double branch feature extraction (CNN processes time-frequency local features and LSTM captures noise timing dependence).

(2) Dynamic impedance matching module (adaptive adjustment of filter parameters to deal with non-stationary noise).

Therefore, the proposed scheme needs to maintain 12 dB noise reduction at SNR = 10 dB, and the inference delay is controlled within 15 ms.

3.1. CNN-LSTM technical framework and innovation

Designed in this study, the CNN-LSTM hybrid architecture adopts dual-branch feature extraction (CNN processes time-frequency local features, LSTM captures noise timing dependence) and a dynamic impedance matching module (adaptively adjusts filter parameters to deal with non-stationary noise).

The technical framework is shown in Fig. 2, including a preprocessing layer, a feature extraction layer, a dynamic matching layer and an output layer.

Fig. 2CNN-LSTM technical framework

Signal input, feature extraction, dynamic matching and noise reduction output modules are included in Fig. 2.

– Branch 1 (CNN – Local Time-Frequency Feature Extraction):

The input signal is first transformed into a two-dimensional time-frequency representation $T\in {\mathbb{R}}^{F\times T}$ using the STFT+WVD joint time-frequency analysis module, where $F$ denotes the number of frequency bins and $T$ the number of time frames. This time-frequency map is then fed into a lightweight CNN network. The CNN comprises three convolutional layers, each followed by batch normalization and a ReLU activation function. These layers progressively extract local spatial patterns and higher-level abstract features of the noise in the time-frequency domain. The CNN finally outputs a feature tensor $F_{cnn}\in {\mathbb{R}}^{C\times T\text{'}}$, where $C$ is the number of feature channels and $T\text{'}$ denotes the downsampled temporal dimension.

– Branch 2 (LSTM – Temporal Dependency Modeling):

The original one-dimensional time-domain signal $x\in {\mathbb{R}}^L$ (with $L$ being the sequence length) is directly input into a two-layer bidirectional LSTM network. This network processes the sequence in both forward and backward directions, effectively capturing long-term contextual dependencies and the dynamic evolution of noise. The final hidden states of the LSTM are extracted and linearly projected to form a temporal feature vector $F_{lstm}\in {\mathbb{R}}^D$.

Feature fusion:

To fuse $F_{cnn}$ and $F_{lstm}$, global average pooling is first applied to $F_{cnn}$ along the time dimension $T\text{'}$, yielding a vector $F_{cnn}^{\text{'}}\in {\mathbb{R}}^C$ compatible in dimensionality with $F_{lstm}$. The two feature vectors are then concatenated, as shown in Eq. (1):

This fused feature $F_{fusion}$ integrates both local time-frequency structure and global temporal dynamics of the noise. It is subsequently fed into the dynamic impedance matching module to generate adaptive filter parameters.

Fig. 3 shows the data visualization processing analysis.

Fig. 3CNN-LSTM hybrid model for non-stationary noise suppression in LPCC

a) Noise suppression performance is shown as a function of both SNR and frequency. Higher SNR leads to better suppression, yet the effect varies across frequencies. Lower frequencies (around 100-200 kHz) benefit more; this is likely due to the CNN’s ability to extract local time-frequency patterns.

b) Temporal evolution of noise suppression is depicted here. The LSTM module captures dynamic variations (including vibration-like fluctuations) over time. Although suppression improves with SNR, it does not stabilize instantly – instead, it adapts gradually, which confirms the model’s responsiveness to non-stationary conditions.

3.2. Noise suppression model construction

(1) Dynamic impedance matching adjusts filter parameters to optimize signal transmission by estimating channel noise characteristics in real time. Its mathematical expression is, as shown in Eq. (2):

where $Z_{match}\left(t\right)$ is the matching impedance value at time $t$; $V_{sig}\left(t\right)$ is the signal voltage component; $I_{noise}\left(t\right)$ is the noise current component; $N\left(t\right)$ is the time-domain noise vector; and $\alpha$ is the attenuation coefficient (default value 0.05).

(2) The adaptive attenuation factor update is as follows, as shown in Eq. (3):

where ${\alpha }_{base}$ represents the basic attenuation coefficient (0.05); $\beta$ is the adjustment factor (0.1); and $\text{Var}(\cdot )$ is the variance calculation function.

(3) Mixed model loss function:

The loss function in Eq. (3) combines two objectives: signal reconstruction accuracy and impedance matching optimization, as shown in Eq. (4):

where, ${\mathcal{L}}_{recon}=|s-\widehat{s}|2^2$ quantifies the reconstruction error between the clean signal $s$ and the denoised output $\widehat{s}$. The term $\mathcal{L}imp=|Z-Z^{*}{|}_2^2$ penalizes deviations of the actual impedance $Z$ from the optimal matching impedance $Z^{*}$. The weighting coefficients $\alpha =$ 0.7 and $\beta =$ 0.3 were determined through ablation studies. This ratio achieves an optimal balance in preliminary experiments – preserving high signal fidelity (governed mainly by $\alpha$) while ensuring effective dynamic impedance adjustment (governed mainly by $\beta$). Experimental results show that as $\alpha$ increases from 0.5 to 0.8, the signal-to-noise ratio improvement ($\mathrm{\Delta }$SNR) first rises and then declines, peaking at $\alpha =\text{0.7}$. Setting $\beta =\text{0.3}$ effectively constrains impedance fluctuations without substantially degrading signal reconstruction.

(4) As for the model validation and performance analysis, we verify the model’s effectiveness through comparative experiments:

– Noise reduction effect: when SNR = 10 dB, the PSNR reaches 28.5 dB (12 dB higher than baseline).

– Real-time: single frame processing delay 15 ms (meeting LPCC real-time requirements).

– Robustness: performance fluctuation < 3 % in the temperature range of –40 ~ 85 ℃.

The noise reduction signal output equation is as follows, as shown in Eq. (5):

where $\otimes$ is the convolution operation; and $K_Z\left(t\right)$ is the kernel function generated based on $Z_{match}\left(t\right)$.

In this study, we propose a dual-branch feature extraction architecture, adopt the CNN-LSTM parallel structure to realize the joint modeling of spatio-temporal features, and design the dynamic impedance matching module to establish the real-time mapping relationship between noise intensity and filter parameters.

4.1. System architecture design

The flow of the dynamic impedance matching algorithm constructed in this study is shown in Fig. 4.

(1) Signal Acquisition and Preprocessing.

The low-voltage power line carrier signal is first acquired through a multi-rate sampling module with a frequency range from 10 kHz to 500 kHz. The raw signal then undergoes normalization and band-pass filtering. This step removes baseline drift and retains the effective communication frequency band.

(2) Joint Time-Frequency Analysis and Feature Extraction.

The preprocessed signal is fed in parallel into two branches. In the feature extraction branch, an improved STFT+WVD joint time-frequency analysis method (Equation 5) transforms the one-dimensional signal into a time-frequency image. This enhances the characterization of non-stationary noise. The resulting image is then passed to a CNN module, which extracts local spatial (time-frequency) features of the noise.

(3) Temporal Modeling and Dynamic Impedance Matching.

Simultaneously, in the temporal modeling branch, the signal is fed into an LSTM network to capture the dynamic time-correlated properties of the noise. The local features from the CNN and the temporal features from the LSTM are concatenated in a fusion layer. The fused feature vector serves as input to a dynamic impedance-matching module. This module employs a deep reinforcement learning agent based on Proximal Policy Optimization (PPO) (Eq. (7)). Using the real-time estimated noise characteristics – defined by the state space in Eq. (6) – the agent dynamically adjusts the parameters of the impedance-matching network (Eq. (1)). As a result, optimal noise-suppression filter coefficients are generated.

(4) Noise Suppression and Signal Reconstruction.

Finally, the generated filter is applied to the noisy signal to achieve noise suppression. The reconstructed signal undergoes post-processing before output. The entire process is optimized in an end-to-end manner, guided by the joint loss function defined in Eq. (3).

Fig. 4The STFT+WVD algorithm flow

The algorithmic framework employs a multirate sampling technique (with sampling frequencies ranging from 10 kHz to 500 kHz) in the signal acquisition module to ensure comprehensive capture of the full spectral characteristics of LPCC noise. The noise feature analysis module utilizes a joint time-frequency analysis method to achieve precise characterization of non-stationary acoustic signals. The corresponding processing results are displayed in Fig. 5.

a) Multi-rate signal acquisition is combined here with time-frequency joint noise analysis. Acquisition quality improves as frequency increases, yet analysis accuracy depends also on temporal resolution. The joint approach (STFT+WVD) characterizes non-stationary noise more precisely than either method alone.

b) Dynamic impedance matching efficiency and noise suppression output are shown together. Matching adapts to varying channel conditions in real time, therefore suppression performance remains stable across frequencies. Although some fluctuation persists (due to residual noise), the overall gain is substantial.

Fig. 5Dynamic impedance matching system for LPCC non-stationary noise suppression

4.2. Impedance matching algorithm based on DRL

(1) The time-frequency joint analysis adopts the improved STFT + WVD hybrid method, and the mathematical expression is as follows, as shown in Eq. (6):

where $TF\left(x,t\right)$ is the time-frequency joint distribution; $\alpha$ represents the weight coefficient ($0\le \alpha \le 1$); $STFT(\cdot )$ is the short-time Fourier transform; and $WVD(\cdot )$is the Wigner-Ville distribution. Balance time and frequency resolution with adaptive weighting factors ($\alpha$).

In this study, a DRL-based impedance parameter optimization algorithm is proposed, and the optimal matching strategy is learned through the interaction between Agent and Environment.

State space definition, as shown in Eq. (7):

where $S_t$ is the state vector at time $t$; $SNR\left(t\right)$ is the current signal-to-noise ratio; and $N\left(t\right)$ is the noise vector.

The training process uses PPO (Proximal Policy Optimization) algorithm. The PPO loss function is like this, as shown in Eq. (8):

where $r_t\left(\theta \right)$ is the probability ratio of the new and old strategies; ${\widehat{A}}_t$ is the estimated value of the dominance function; $H\left(\pi \right)$ represents the entropy of the strategy; and $c_1$ represents the regularization coefficient.

By establishing a dynamic impedance matching system based on deep reinforcement learning, the analysis of noise characteristics and the intelligent optimization of impedance parameters are realized. Through combining the time-frequency analysis method and PPO algorithm, the accuracy of impedance matching in a non-stationary noise environment is significantly improved, providing a new technical implementation path for power line carrier communication.

5.1. The experimental environment setup

To address the inherent limitations of purely simulated scenarios – such as the lack of unpredictable noise bursts and load transients – this study adopts a hybrid validation strategy. A combination of synthetic data generated from a standardized channel model and real-world field measurements is used for training and testing, ensuring both reproducibility and practical relevance. The specific parameters for both data sources are outlined below.

– Data Sources and Sampling Specifications:

Simulated Data: Synthetic signals are generated using the widely recognized IEEE 1901.2 standard channel model (Eq. (8)). The primary sampling rate is set to 500 kHz, covering typical low-voltage PLC frequency bands. Additional tests also apply sampling rates from 10 kHz to 200 kHz to evaluate robustness under varying bandwidth conditions.

Real-world Data: Field measurements are collected from a low-voltage distribution network under typical operating conditions. Signal acquisition is performed with a calibrated data logger, employing the same 500 kHz sampling rate to ensure compatibility. These measurements are conducted across different times of day and under varied load conditions to capture realistic channel and noise dynamics.

– Signal Duration and Channel Conditions:

Each sample (both simulated and real) spans 0.1 seconds, sufficient to capture multiple power-frequency cycles and non-stationary noise characteristics. In simulations, frequency-selective fading is modeled with path attenuation coefficients ($a_i$), delays (${\tau }_i$), and Doppler spread parameters (${\nu }_i$) randomly drawn within typical ranges. The simulation temperature range is set from –40 °C to 85 °C to evaluate thermal adaptability.

– Noise Composition and Synthesis:

The hybrid dataset incorporates the following noise components:

a) Switching impulse noise, modeled using the Middleton Class A distribution in simulations and directly measured from load-switching events in field data.

b) Additive white Gaussian noise, representing background thermal noise in both sources.

c) Harmonic interference, simulated with adjustable total harmonic distortion (THD) and also extracted from real recordings of inverter-based equipment.

These noise types are superimposed onto clean carrier signals at varying signal-to-noise ratios (SNRs) and mixing proportions to create a diverse and challenging dataset.

– Dataset Construction and Partitioning:

A total of 20,000 samples are compiled: 10,000 from simulation and 10,000 from field measurements (including both noisy and clean segments). The combined dataset is randomly partitioned into training (70 %), validation (20 %), and test (10 %) subsets. Five-fold cross-validation is applied across the combined data to ensure statistical reliability and robustness of the results. The IEEE 1901.2 standard channel model [17] is adopted to accurately emulate frequency-selective fading across a temperature range of –40 to 85 ℃. Its mathematical representation is given by, as shown in Eq. (9):

where $H\left(f\right)$ is the frequency response function; ${\alpha }_i$ represents the attenuation coefficient of the $i$ path; $f_c$ represents the center frequency (10-500 kHz); ${\sigma }_i$ represents the Doppler spread parameter; and ${\tau }_i$ is the time delay.

A performance benchmarking is conducted among three approaches: conventional adaptive filtering (2020) [18], deep neural network (DNN)-based noise suppression (2023) [19], and a hybrid architecture [20]. The evaluation focuses on three key metrics: signal-to-noise ratio (SNR) improvement, computational latency, and thermal adaptability. All tests are performed under an identical noise dataset incorporating impulsive noise, white Gaussian noise, and power frequency interference, with 5-fold cross-validation applied to ensure statistical reliability.

The data set configuration is shown in Table 3.

The hardware and software configurations are shown in Table 4.

5.2. Experimental test and analysis

5.2.2. Arithmetic latency test

The experimental validation assesses the computational efficiency of the CNN-LSTM hybrid model for real-time noise suppression. A comparative evaluation of latency performance is conducted against conventional DnCNN, wavelet thresholding, and a recent attention-based method to determine the feasibility of deploying the model on embedded devices. The models compared include a one-dimensional adapted version of DnCNN [5], an adaptive wavelet thresholding method employing Daubechies 8 basis functions [21], and a multi-head attention mechanism (Patent CN120448698A).

Latency, defined as the model’s forward propagation time, is reported in milliseconds (ms), as shown in Eq. (12):

12

$T_{latency}=\frac{{\sum }_{i=1}^N{T}_i}{N},$

where $T_i$ is the single inference time, and the mean value is taken for ($N=$ 1000) tests.

The test results are shown in Table 7 and Fig. 7.

Table 7Arithmetic latency test

Methods	Average delay (ms)	Peak memory footprint (MB)
CNN-LSTM	12.3±0.8	245
DnCNN	8.7±0.5	180
Wavelet threshold	5.1±0.2	45
Multi-head attention	23.6±1.2	520

a) Latency distributions are compared across four methods via boxplots. Wavelet thresholding is the fastest but also the least powerful in noise reduction. DnCNN runs reasonably fast, whereas the multi-head attention mechanism suffers from high latency (over 20 ms on average). The proposed CNN-LSTM falls in between – slower than DnCNN, yet still acceptable for many real-time tasks.

b) Latency changes with SNR improvement are shown here. All methods exhibit slight delay increases when SNR rises, because more computation is required. The CNN-LSTM model stays below 15 ms across the tested range. After INT8 quantization, its latency drops to about 9.2 ms, therefore meeting the sub-10 ms real-time requirement.

The experimental results indicate that the latency of CNN-LSTM lies between that of traditional methods and the modern attention-based approach. However, it is 41.4 % higher than that of DnCNN, primarily due to the sequential processing overhead introduced by the LSTM module. Owing to the need for storing temporal features, the memory consumption of CNN-LSTM is 5.4 times that of the wavelet thresholding method, yet it remains lower than that of the attention mechanism. The latency can be reduced to 9.2 ms, meeting the real-time requirement (< 10 ms).

Fig. 6Computational latency test for real-time noise suppression algorithms