Decoupling Rainfall and Surface Runoff Effects Based on Spatio-Temporal Spectra of Wireless Channel State Information

Abstract

Leveraging ubiquitous wireless signals for environmental sensing provides a highly promising pathway toward constructing low-cost and high-density flood monitoring systems. However, in real-world flood scenarios, the wireless channel is simultaneously affected by rainfall-induced signal attenuation and complex multipath effects caused by surface runoff (water accumulation). These two physical phenomena become intertwined in the received signals, resulting in severe feature ambiguity. This not only greatly limits the accuracy of environmental sensing but also hinders communication systems from performing effective channel compensation. How to disentangle these combined effects from a single wireless link represents a fundamental scientific challenge for achieving high-precision wireless environmental sensing and ensuring communication reliability under harsh conditions. To address this challenge, we propose a novel signal processing framework that aims to effectively decouple the effects of rainfall and surface runoff from Channel State Information (CSI) collected using commercial Wi-Fi devices. The core idea of our method lies in first constructing a two-dimensional CSI spatiotemporal spectrogram from continuously captured multicarrier CSI data. This spectrogram enables high-resolution visualization of the unique “fingerprints” of different physical effects—rainfall manifests as smooth background attenuation, whereas surface runoff appears as sparse high-frequency textures. Building upon this representation, we design and implement a Dual-Decoder Convolutional Autoencoder deep learning model. The model employs a shared encoder to learn the mixed CSI features, while two distinct decoder branches are responsible for reconstructing the global background component attributed to rainfall and the local texture component associated with surface runoff, respectively. Based on the decoupled signal components, we achieve simultaneous and highly accurate estimation of rainfall intensity (mean absolute error below 1.5 mm/h) and surface water accumulation (detection accuracy of 98%). Furthermore, when the decoupled and refined channel estimates are applied to a communication receiver for channel equalization, the Bit Error Rate (BER) is reduced by more than one order of magnitude compared to conventional equalization methods.

1. Introduction

The evolution towards 6G is driving a paradigm shift from conventional terrestrial communication to integrated heterogeneous networks that span space–air–ground–sea domains. This deep integration is essential for unlocking transformative applications in vertical industries such as smart grid digitalization, the low-altitude economy (e.g., UAV traffic management), and maritime Internet Of Things (IOT) [1,2]. A recent comprehensive survey in 2025 [3] emphasized that ensuring security in ISAC systems is increasingly critical, especially when leveraging technologies like reconfigurable intelligent surfaces to address vulnerabilities in heterogeneous network environments. In these complex, multi-domain scenarios, wireless systems must transcend their traditional role of data transmission. They are increasingly expected to perform high-precision, real-time environmental sensing to enable intelligent decision-making and autonomous operation. This has given rise to Integrated Sensing and Communication (ISAC), a key enabling technology for 6G that aims to achieve synergistic benefits by sharing hardware, spectrum, and signal processing pipelines for dual functions [4,5].

However, as ISAC moves from controlled laboratory settings to the chaotic and dynamic environments inherent in heterogeneous networks, it confronts a fundamental and often overlooked challenge: the entanglement of signal features caused by multiple, co-existing physical phenomena. In real-world deployments, a single Radio Frequency (RF) signal is simultaneously affected by a variety of environmental factors—what can be termed physical-layer multimodal effects. For instance, a signal in a coastal area might be affected by both atmospheric rain and sea-surface scattering, while a signal for a low-altitude UAV network could be distorted by both building-induced multipath and weather conditions. These combined effects become intertwined in the received Channel State Information (CSI), creating severe feature ambiguity. This ambiguity not only cripples the accuracy of the ’sensing’ function but also severely compromises the ’communication’ function by preventing the receiver from performing effective channel estimation and equalization. Resolving this entanglement is a critical bottleneck for deploying robust and reliable ISAC systems in the wild.

To address this fundamental ISAC challenge, this paper focuses on a particularly demanding yet critical application scenario: flood monitoring. This scenario serves as a perfect microcosm of the complexities faced in integrated heterogeneous networks. In a typical flood event, a fixed wireless link—which could be a terrestrial segment of a larger space–air–ground emergency network—is simultaneously impacted by at least two distinct physical processes. The first is rainfall attenuation, arising from the absorption and scattering of electromagnetic waves by raindrops in the atmosphere. According to the Mie scattering theory, this effect is significant in the commonly used Wi-Fi frequency bands and manifests as a global, smooth decrease in CSI amplitude across all subcarriers, correlated with rainfall intensity [6]. The second is the severe multipath effect induced by surface water accumulation (runoff), which creates new, highly reflective surfaces. This drastically alters the propagation geometry, introducing new signal paths and resulting in sharp, frequency-selective fading across different subcarriers [7].

The simultaneous presence of these two physical modalities—atmospheric attenuation and ground-level reflection—in the received signals leads to severe ambiguity. For example, a 10 dB drop in signal power could be interpreted as a surge in rainfall from 5 mm/h to 50 mm/h. However, the same drop could also be caused by the formation of a shallow water layer under constant light rain, which introduces a destructive reflection path. This “different causes, same effect” problem makes it nearly impossible to accurately estimate either environmental parameter from the raw, mixed signal. More critically from an ISAC perspective, it masks the true channel response, hindering the communication receiver’s ability to perform reliable channel equalization. Consequently, the transmission of vital early-warning data over the link is severely threatened precisely when it is needed most [8].

To overcome this critical bottleneck and unlock the true potential of ISAC in harsh environments, we propose a systematic and innovative signal processing framework based on deep learning. Our framework is designed to effectively decouple the compound effects of rainfall and surface runoff from CSI data collected via a single commercial Wi-Fi link. The core idea is to first transform the multicarrier CSI time-series data into a two-dimensional CSI spatiotemporal spectrogram. This novel representation converts the signal analysis problem into an image processing task, making the smooth background variations from rainfall structurally distinguishable from the sparse, high-frequency textures caused by runoff. Building on this, we design a Dual-Decoder Convolutional Autoencoder model that learns, in an end-to-end unsupervised manner, to separate these entangled components. This data-driven approach, which requires no prior physical models, is crucial for its adaptability and scalability within dynamic and unpredictable heterogeneous network environments.

The main contributions of this paper, framed within the context of this special issue, are summarized as follows:

1.

A Novel Framework for Robust ISAC in Complex Environments: We are the first to systematically define and address the fundamental challenge of physical-layer multimodal effect entanglement in ISAC systems. We propose an innovative decoupling framework based on CSI spatiotemporal spectrograms that enables robust sensing and communication in harsh, real-world conditions.

2.

Data-Driven Decoupling of Physical Modalities: We design and implement a Dual-Decoder Autoencoder model capable of disentangling the effects of two distinct physical phenomena (atmospheric attenuation and surface reflection) from a single RF signal. This demonstrates a powerful, model-free approach for signal source separation in multimodal communication and sensing scenarios.

3.

Experimental Validation of ISAC Synergy for Cross-Domain Orchestration: We provide the first comprehensive experimental validation of the profound synergy between sensing and communication enhancement enabled by our decoupling framework. We demonstrate not only high-precision, simultaneous environmental sensing but also a greater than one-order-of-magnitude reduction in communication Bit Error Rate (BER). This proves that our method provides the reliable, high-quality data and robust link integrity that are prerequisites for effective cross-domain orchestration in integrated heterogeneous networks.

The remainder of this paper is organized as follows: Section 2 reviews related work. Section 3 presents the proposed methodology. Section 4 reports and analyzes the experimental results. Finally, Section 5 concludes the paper and discusses future work.

2. Related Work

This section reviews related research from two perspectives: traditional flood monitoring techniques and wireless signal-based environmental sensing approaches. On this basis, we clarify the entry point of our study and highlight its novelty.

2.1. Traditional Flood Monitoring Techniques

Traditional flood monitoring primarily relies on direct measurements obtained from physical sensors. Hydrological station networks, equipped with professional instruments such as rain gauges, water level meters, and flow velocity sensors, provide high-precision point measurements and serve as the main data sources for current hydrological forecasting and flood management decision-making [9]. In recent years, with the development of the Internet Of Things (IOT), low-power and compact wireless sensor nodes have emerged, which can be more flexibly deployed to improve monitoring density [4]. In addition, remote sensing technologies, particularly Synthetic Aperture Radar (SAR) satellites, are capable of penetrating cloud cover over large areas to effectively map flood-inundated regions, providing important support for post-disaster assessment [10]. Nevertheless, these methods have inherent limitations. Physical sensor networks are constrained by high deployment and maintenance costs and are highly vulnerable to failure during disasters. Remote sensing technologies, on the other hand, are limited by satellite revisit cycles and spatial resolution, making it difficult to meet the stringent real-time requirements of flood early warning systems.

2.2. Wireless Signal-Based Environmental Sensing

Wireless signal-based environmental sensing, also known as device-free sensing, is a rapidly growing research area. The core idea is that objects and media in the environment alter the propagation paths of wireless signals, and by analyzing variations in the received signals, one can infer the state of the environment. Early studies primarily relied on the Received Signal Strength Indicator (RSSI) for sensing; however, the RSSI is highly susceptible to multipath effects, suffers from poor stability, and thus provides limited sensing accuracy [11].

The emergence of Channel State Information (CSI) has brought about a revolutionary breakthrough. CSI is a fine-grained physical-layer parameter that characterizes the amplitude and phase information of signals across multiple subcarriers, thereby providing a multidimensional perspective of the channel’s frequency response. Leveraging CSI, researchers have achieved a wide range of high-precision sensing applications in indoor scenarios, including intrusion detection, human activity recognition [12], vital sign monitoring [13], gesture recognition, and even through-wall imaging [14]. The success of these studies demonstrates the exceptional sensitivity of CSI to environmental changes. Advanced preprocessing algorithms [15] have been developed to correct CSI gain and phase errors for cleaner sensing signals, but they only address signal purification without resolving feature entanglement. Recent work has generalized deep learning-based CSI feedback via ID-photo-inspired preprocessing, using standardized input formatting to boost cross-environment adaptability [16], yet it still focuses on communication-oriented feedback rather than sensing feature decoupling.

In recent years, several studies have attempted to extend wireless sensing technologies to outdoor environments. For example, the attenuation of cellular network signal links has been exploited to estimate rainfall intensity [17]. This approach, known as opportunistic remote sensing, demonstrates the great potential of utilizing existing communication infrastructure for large-scale environmental monitoring. Similarly, other studies have explored the use of Wi-Fi or LoRa signals to monitor rainfall [18] and snow depth [19]. However, these works typically focus on single, slowly varying environmental factors. In contrast, floods involve multiple intense physical processes—such as heavy rainfall and surface runoff—that occur simultaneously and interact in complex ways. Existing wireless sensing methods have rarely addressed such scenarios. Even state-of-the-art CSI disentanglement frameworks for FDD systems leverage implicit channel reciprocity [20] but lack designs for distinguishing dynamic, flood-related texture variations like runoff-induced multipath effects. Notably, disentanglement has also been applied to dual-polarized CSI for communication compression by separating polarization-related components [21], yet it ignores environmental effect decoupling. Even 2025 research on wireless environment information-aided CSI prediction for massive MIMO systems has improved reconstruction accuracy [22], but it fails to distinguish mixed physical effects in dynamic flood scenarios. Reference [8] first suggested the feasibility of using Wi-Fi for flood monitoring, but the analysis was limited to the RSSI level and failed to resolve the entanglement of different physical effects.

2.3. Research Gap and Contributions

In summary, existing studies reveal a clear research gap: the lack of a wireless sensing method capable of effectively handling the entanglement of compound physical effects in complex outdoor scenarios. The core contribution of this work is to fill this gap. To the best of our knowledge, we are the first to systematically investigate the combined impact of rainfall and surface runoff on wireless channels and to propose a deep learning-based signal processing framework. This framework aims to decouple these two independent physical effects from CSI data, thereby enabling simultaneous and high-precision sensing of flood-related environmental parameters.

3. Methodology

To address the complex entanglement of rainfall and surface runoff effects in the CSI of commercial Wi-Fi links, we designed and implemented a systematic signal processing and analysis framework. This framework follows a clear pipeline: first, the raw CSI data extracted directly from the hardware are rigorously preprocessed to eliminate noise and hardware-induced artifacts; second, the processed high-dimensional time-series data are innovatively reconstructed into a two-dimensional CSI spatiotemporal spectrogram, making them suitable for advanced image analysis techniques; finally, a specially designed Dual-Decoder Convolutional Autoencoder model is applied to the spectrogram to decouple the signal, separating the components attributable to different physical effects. Figure 1 illustrates the overall workflow of the proposed framework and the interconnections among its stages in detail.

The raw CSI stream extracted from a Wi-Fi Network Interface Card is first processed through a preprocessing stage, including outlier removal and phase sanitization. The processed data are then reconstructed into a two-dimensional CSI spatiotemporal spectrogram. This spectrogram is fed into the Dual-Decoder Autoencoder model, which outputs two independent spectrograms, representing the decoupled effects of rainfall and surface runoff, respectively.

3.1. CSI Data Preprocessing and Sanitization

The raw CSI data extracted from commercial Wi-Fi Network Interface Cards (NICs), such as the Intel 5300 NIC or the Atheros AR93xx series, contain rich channel information but are inevitably contaminated by hardware imperfections and environmental noise. Without proper processing, these artifacts can severely interfere with subsequent analyses and even mask meaningful environmental features. Therefore, a rigorous preprocessing pipeline is indispensable to ensure the reliability and effectiveness of the proposed framework.

1.

Amplitude Data Processing and Calibration: The raw CSI amplitude data often contain extreme outliers caused by sudden electromagnetic interference or internal hardware errors. To address this issue, we first apply a Hampel filter, a median-based robust filtering technique, to identify and remove these outliers. In addition, the Automatic Gain Control (AGC) mechanism of Wi-Fi receivers introduces synchronous, step-like variations in the amplitudes of all subcarriers, which are unrelated to environmental changes. To eliminate this artifact, we normalize the amplitudes of all subcarriers within each frame to a common scale, thereby focusing solely on the relative amplitude variations induced by changes in the wireless channel itself.

2.

Phase Data Sanitization and Linearization: Compared with amplitude, the CSI phase is more sensitive to environmental changes but also inherently less stable. The raw-phase data are primarily contaminated by two types of hardware-induced errors: Carrier Frequency Offset (CFO) and Sampling Frequency Offset (SFO). CFO introduces a random phase shift that is identical across all subcarriers, whereas SFO introduces a phase shift that varies linearly with the subcarrier index. These random offsets render the direct use of raw-phase information meaningless.To address this issue, we adopt a widely validated linear fitting method for phase sanitization [14]. For the raw phase ${\widehat{\varphi }}_{k,i}$ of the i-th subcarrier in the k-th frame, it can be modeled as:

$${\widehat{\varphi }}_{k,i}={\varphi }_{k,i}+2\pi {\displaystyle \frac{\mathrm{\Delta }f}{N}}i{\tau }_k+{\beta }_k+Z,$$

(1)

where ${\varphi }_{k,i}$ is the true phase, $\mathrm{\Delta }f$ is the subcarrier spacing, N is the FFT size, ${\tau }_k$ represents the timing error caused by SFO, ${\beta }_k$ denotes the random phase offset induced by CFO, and Z is Gaussian white noise. By performing linear regression across all subcarriers within each frame, we can estimate the slope (associated with SFO) and the intercept (associated with CFO). Subtracting these linear components from the raw phase yields a clean relative phase sequence that reflects only multipath propagation effects. The processed CSI can thus be expressed as

$$H_i\left(t\right)=\left|H_i\left(t\right)\right|e^{j\angle H_i\left(t\right)},$$

(2)

where i denotes the subcarrier index and t represents time.

3.

Subcarrier selection: In the IEEE 802.11n standard [23], not all subcarriers are utilized for data transmission. For example, under a 40 MHz channel bandwidth, a total of 114 subcarriers are available, but these include DC subcarriers, guard subcarriers, and pilot subcarriers. Since these subcarriers either do not carry valid channel information or are subject to special modulation, they can introduce interference into the analysis. Therefore, we retain only the subcarriers used for data transmission (e.g., 108 out of 114 subcarriers) for subsequent processing.

3.2. Construction and Representation of CSI Spatiotemporal Spectrogram

To fully exploit the powerful capability of Convolutional Neural Networks (CNNs) in processing image-like grid-structured data, we innovatively transform the preprocessed one-dimensional CSI time-series data into a two-dimensional image representation, referred to as the CSI spatiotemporal spectrogram. This transformation serves as a bridge between wireless signal analysis and image-based techniques, with its core idea being to map the intrinsic physical properties of the signal into visual structural features.

We arrange all the CSI frames collected within a fixed time window T (e.g., 10 s) in chronological order to form a matrix (i.e., a spectrogram). The construction of this spectrogram is as follows:

1.

The vertical axis (Y-axis) of the spectrogram represents the time dimension, ranging from the beginning $t_0$ to the end $t_0+T$ of the window. Each row of the spectrogram corresponds to one CSI frame.

2.

The horizontal axis (X-axis) represents the frequency dimension, corresponding to the indices of the N effective subcarriers selected. Each column of the spectrogram corresponds to a specific subcarrier.

3.

The pixel value of the spectrogram can be either the CSI amplitude or the denoised phase of the corresponding subcarrier at the given time. In our study, we found that amplitude and phase spectrograms capture complementary information; therefore, we treat them as two independent channels (similar to the R and G channels in an RGB image) and feed them jointly into the subsequent deep learning model.

To map signed phase values and high-dynamic-range amplitude values into unsigned 8-bit pixel values suitable for image representation, we adopt the following separate normalization methods for the pixel values of the two channels:

1.

Phase Channel Processing: All phase estimates are first sanitized and wrapped into the interval $(-\pi ,\pi ]$. A dataset-level linear transformation is then applied, with the specific formula as follows:

$$P_{pixel}=255\times {\displaystyle \frac{phase+\pi }{2\pi }},$$

(3)

This transformation monotonically maps the wrapped phase values to the pixel value range of 0–255 while preserving the circular continuity of the phase.

2.

Amplitude Channel Processing: Raw CSI amplitude values (denoted as $\left|H\right|$) are first converted to the logarithmic (dB) domain using the formula:

$$A_{dB}=20{log}_{10}\left|H\right|,$$

(4)

Subsequently, the global minimum $A_{min}$ and global maximum $A_{max}$ of $A_{dB}$ are calculated across the entire training and test sets. Each dB value is then mapped to a pixel value via the following linear scaling formula:

$$A_{pixel}=255\times {\displaystyle \frac{A_{dB}-A_{min}}{A_{max}-A_{min}}},$$

(5)

Here, $A_{min}$ and $A_{max}$ are fixed values applicable to all samples, ensuring consistent contrast across different samples and avoiding sample-dependent bias.

In this way, we obtain a three-dimensional tensor $T\times N\times 2$. The strength of this representation lies in its ability to explicitly visualize complex channel dynamics. As shown in Figure 2, different physical effects exhibit distinct and structured visual patterns in the spectrogram. The overall attenuation caused by rainfall, due to its similar impact on all subcarriers, appears as a smooth and large-scale variation in the background brightness of the spectrogram. In contrast, the multipath effect induced by surface runoff, owing to its frequency selectivity, manifests as sharp and sparse stripe-like textures along the subcarrier axis (X-axis) that vary over time (Y-axis). This remarkable structural distinctiveness provides a solid foundation for automated feature learning and disentanglement through deep learning models.

3.3. Decoupling Model Based on Dual-Decoder Autoencoder

The core of our problem is to decouple a CSI spectrogram containing mixed features into two spectrograms, each representing a single physical effect. Conceptually, this task is similar to foreground—background separation in image processing. To achieve this, we design a specialized autoencoder structure—namely, a Dual-Decoder Convolutional Autoencoder—whose detailed architecture is illustrated in Figure 3. Without relying on any prior physical channel models, this model learns to perform effect decoupling in a purely data-driven manner.

The input CSI spectrogram ($T\times N\times 2$) is processed by a shared encoder, composed of multiple convolutional and pooling layers, and compressed into a low-dimensional latent vector z. Subsequently, z is fed into two parallel, structurally asymmetric decoders. The rainfall decoder reconstructs a smooth background spectrogram, $I_{rain}$, while the runoff decoder reconstructs a sparse texture spectrogram, $I_{runoff}$.

1.

Shared Encoder: The encoder consists of a series of standard convolutional layers (we use 3 × 3 kernels to capture local time–frequency correlations), ReLU activation functions, and max-pooling layers. Specifically, these layers form 2 consecutive blocks, and the number of blocks is a well-defined hyperparameter determined by grid search on the validation set, rather than an optional choice. Its role is to progressively extract features from the input CSI spectrogram $I_{csi}$ and compress them into a compact, low-dimensional latent representation z. The encoder is designed to efficiently capture the core information of all variations present in the spectrogram, without making any prior distinction regarding their sources.

2.

Dual Decoders: This is the core innovation of our model design. Unlike conventional autoencoders that employ a single decoder, our approach introduces two parallel decoder branches originating from the shared latent vector z. These branches are asymmetric in both structure and reconstruction objectives.

(a)

Rainfall Decoder: This decoder is composed of a series of transposed convolutional layers, with the objective of reconstructing only the background spectrogram $I_{rain}$ that represents the rainfall effect. It specifically includes 4 repeated upsampling convolution blocks, where each block uses transposed convolutional layers as its core. This block count is a well-defined hyperparameter determined by grid search on the validation set, not an optional setting. To encourage the generation of smooth, low-frequency outputs, we adopt relatively large convolutional kernels in its design and deliberately exclude any skip connections from the encoder to the decoder. This restriction limits the decoder’s ability to capture high-frequency details, thereby forcing it to focus on learning and reconstructing global, smooth background variations.

(b)

Runoff Decoder: This decoder is also composed of transposed convolutional layers, but its objective is to reconstruct only the texture spectrogram $I_{runoff}$ that represents the surface runoff effect. It contains 3 repeated upsampling convolution blocks, where each block uses transposed convolutional layers as its core. This block count is a well-defined hyperparameter determined by grid search on the validation set (not optional). To enable precise reconstruction of high-frequency and sparse details, its structure incorporates U-Net–like skip connections. These connections directly transfer feature maps from different levels of the encoder to the corresponding levels of the decoder, providing abundant high-resolution detail information. As a result, the decoder can focus on capturing local variations and fine textures within the spectrogram.

The final output of the model consists of two semantically separated spectrograms, $I_{rain}$ and $I_{runoff}$, whose sum should reconstruct the original input spectrogram $I_{csi}$ as accurately as possible.

3.4. Design of the Composite Loss Function

To successfully train the model without direct supervision (i.e., without pure rainfall or runoff spectrograms as ground-truth targets) and to guide the two decoders toward learning their intended, specialized behaviors, we designed a carefully crafted composite loss function, $L_{total}$. This loss function consists of three components, incorporating different regularization terms to constrain the output characteristics of the two decoders.

$$L_{total}=W_{rec}{L}_{rec}+W_{smooth}{L}_{smooth}+W_{sparse}{L}_{sparse}.$$

(6)

1.

Reconstruction Loss, $L_{rec}$: This is the fundamental loss term of the autoencoder, ensuring that the sum of the outputs from the two decoders can accurately reconstruct the original input. It guarantees information fidelity during the decoupling process. We adopt the widely used Mean Squared Error (MSE) to define this loss, as it is more sensitive to larger deviations:

$$L_{rec}={\displaystyle \frac{1}{T·N·C}}\sum _{c,t,i}{\left(I_{csi}(c,t,i)-\left(I_{rain}(c,t,i)+I_{runoff}(c,t,i)\right)\right)}^2,$$

(7)

where C denotes the number of channels (here, C = 2, representing amplitude and phase).

2.

Smoothness Loss, $L_{smooth}$: This loss term is applied to the output of the rainfall decoder $I_{rain}$ as a key regularization component. Its purpose is to penalize the presence of high-frequency components in the output, thereby enforcing the learning of a smooth background. We adopt the classical Total Variation (TV) from image processing as the smoothness loss. The TV loss computes the sum of gradients in both the temporal and frequency directions, with a smooth spectrogram yielding a very low TV value:

$$L_{smooth}=\sum _{c,t,i}\left(\left|{\nabla }_t{I}_{rain}(c,t,i)\right|+\left|{\nabla }_i{I}_{rain}(c,t,i)\right|\right),$$

(8)

where ${\nabla }_t$ and ${\nabla }_i$ denote the gradients along the temporal and frequency dimensions, respectively.

3.

Sparsity Loss, $L_{sparse}$: This loss term is a regularization applied to the output of the runoff decoder $I_{runoff}$, with the objective of encouraging sparsity in its output. This implies that most pixel values in the spectrogram should be close to zero, with nonzero values appearing only in regions where significant textures are induced by multipath effects. We employ the L1 norm to enforce this sparsity constraint, as it is the standard convex optimization method for inducing sparsity:

$$L_{sparse}=\sum _{c,t,i}\left|I_{runoff}(c,t,i)\right|,$$

(9)

During training, $W_{rec},W_{smooth},W_{sparse}$ are three predefined weighting hyperparameters used to balance reconstruction fidelity against the structural properties of the output components (smoothness and sparsity). By minimizing this composite loss function with the Adam optimizer, the model is able to learn, in a fully unsupervised manner, to effectively separate the mixed input CSI spectrogram into the desired background and texture components.

To determine these hyperparameters, We optimize the loss function weights via grid search on the validation set. The search grids are $W_{rec}\in \{1,0.5,0.1,0.05,0.01\}$, $W_{smooth}\in \{0.1,0.05,0.01,0.005,0.001\}$, and $W_{sparse}\in \{0.1,0.05,0.01,0.005,0.001\}$. The combination that yields the lowest reconstruction error on the validation set is selected: $W_{rec}=0.1$, $W_{smooth}=0.05$, and $W_{sparse}=0.05$.

4. Experimental Validation

This chapter aims to comprehensively and systematically validate the effectiveness of the proposed decoupling framework through a series of experiments conducted in controlled environments. We begin by providing a detailed description of the experimental platform, environmental design, and data collection protocol. Next, we define the quantitative metrics used to evaluate model performance. Finally, we present and thoroughly analyze the experimental results, assessing the performance of our approach from three perspectives: effect decoupling, environmental sensing, and communication enhancement.

4.1. Experimental Platform and Data Collection

To validate the effectiveness of our proposed decoupling framework and to provide high-quality training and testing data for the deep learning model, we designed and constructed a controllable outdoor experimental platform. This platform is capable of simulating rainfall with varying intensities and controllable surface runoff processes, while simultaneously collecting Wi-Fi CSI data along with corresponding environmental ground-truth data.

4.1.1. Hardware and Software Platform

Our experimental system consists of a Wi-Fi transceiver link, a data collection server, and a set of environmental ground-truth sensors, as illustrated in Figure 4.

1.

Wi-Fi Transceiver Links: We used two Mini PCs equipped with Intel 5300 802.11n wireless network cards as the transmitter (TX) and receiver (RX). Both PCs were installed with the Ubuntu 16.04 operating system, and modified iwlwifi drivers and a specially developed CSI Tool [24] were used to extract physical-layer CSI data. The TX and RX were configured in a peer-to-peer ad hoc mode, operating in the 5 GHz frequency band with a 40 MHz channel bandwidth. TX continuously transmitted UDP frames at a rate of 100 frames per second, and RX recorded the corresponding CSI matrix upon receiving each frame. Each CSI matrix contains complex channel response values of 3 antenna pairs and 114 subcarriers.

2.

Data Acquisition Server: The RX PC is connected to a data acquisition server via Ethernet. This server is responsible for real-time storage of the CSI data stream received from the RX and attaching accurate timestamps to it.

3.

Environmental Ground-Truth Sensors: To obtain the “ground truth” for verifying the accuracy of the algorithm, we deployed two types of professional sensors:

(a)

Tipping Bucket Rain Gauge: A high-precision tipping bucket rain gauge was placed at the midpoint of the transceiver link to accurately measure the rainfall intensity during the experiment (unit: mm/h).

(b)

Ultrasonic Water Level Sensor: An industrial-grade ultrasonic water level sensor was vertically installed directly above the simulated runoff area to monitor the depth of surface ponding in real time (unit: mm).

(c)

The data from these two sensors were collected by an Arduino microcontroller and also sent to the data acquisition server, where they were time-synchronized with the CSI data.

TX and RX are 6 m apart, with the middle area being a controllable experimental area. The rain gauge and water level sensor provide environmental ground truth, and all data are collected to the server for synchronous recording.

4.1.2. Design of Controllable Experimental Environment

We set up the experimental environment in an open outdoor field. The antennas of TX and RX were fixed on tripods 1.5 m above the ground, and they were 6 m apart. On the ground between them, we constructed a system for simulating rainfall and surface runoff.

1.

Rainfall Simulation System: We set up a sprinkler system composed of multiple adjustable nozzles directly above the link at a height of 2.5 m. Through a water pump and a precision flow control valve, we precisely controlled the water output of the sprinkler system, thereby simulating rainfall processes of different intensities, ranging from drizzle (~5 mm/h) to heavy rain (~60 mm/h).

2.

Surface Runoff Simulation System: On the ground below the link, we placed a shallow water basin with dimensions of 4 m × 2 m (depth 10 cm) to simulate surface ponding. Through an independent water inlet pipe and a drain valve, we precisely controlled the water level in the basin, simulating the formation and recession processes of surface runoff from no ponding to different depths.

This controllable design enables us to isolate and combine different environmental factors, thereby collecting datasets with clear physical significance for model training and validation.

4.1.3. Data Acquisition Protocol

To comprehensively evaluate the performance of our model, we designed four different experimental scenarios and conducted long-term data collection under each scenario.

1.

Scenario 1: Baseline Data (Baseline)

(a)

Conditions: Sunny day, no wind, no rainfall, and no surface ponding.

(b)

Purpose: To collect CSI data in a static environment, which serves as a reference benchmark for subsequent analyses.

2.

Scenario 2: Pure Rainfall (Rain-only)

(a)

Conditions: Keep the water basin empty, activate the sprinkler system, and gradually change the rainfall intensity (from 5 mm/h to 60 mm/h, then gradually decrease the intensity).

(b)

Purpose: To collect CSI data affected only by rainfall effects. These data will help us understand the influence pattern of rainfall on the “background” of the CSI spatiotemporal map.

3.

Scenario 3: Pure Runoff (Runoff-only)

(a)

Conditions: Keep the sprinkler system turned off, slowly fill the water basin with water to make the water level rise from 0 mm to 80 mm, and then slowly drain it.

(b)

Purpose: To collect CSI data affected only by surface runoff effects. These data will help us understand the influence pattern of ponding water on the “texture” of the CSI spatiotemporal map.

4.

Scenario 4: Combined Effects (Combined)

(a)

Conditions: Activate both the sprinkler system and the water injection system simultaneously to simulate real flood scenarios, that is, under rainfall of different intensities, surface ponding forms and changes simultaneously.

(b)

Purpose: To collect CSI data containing the aliasing effects of rainfall and runoff. This is the core data to be processed by our model and serves as the main test set to verify the effectiveness of our decoupling algorithm.

In each scenario, we continuously collected data for at least 2 h to ensure coverage of various changing states of the environment. The entire dataset contains more than 8 million CSI data frames, providing sufficient samples for the subsequent training of deep learning models.

4.1.4. Dataset Description

The dataset comprises $7.98\times {10}^6$ valid CSI frames acquired in four chronologically ordered outdoor scenarios (Baseline, Rain-only, Runoff-only, Combined); each frame contains 108 complex subcarrier responses and is time-synchronised with tipping bucket rain rate $0–60\mathrm{mm}{\mathrm{h}}^{-1}$ and ultrasonic water depth $0–80\mathrm{mm}$ labels. After Hampel outlier removal, samples are split as 70% training, 10% validation, 20% test by collection time to prevent data leakage.

4.2. Evaluation Metrics

To quantitatively evaluate the performance of our proposed decoupling framework, we define the following three types of evaluation metrics:

1.

Decoupling Accuracy: This metric is used to measure the degree of accuracy with which our model separates combined effects into independent components. We use the Structural Similarity Index (SSI) to compare the similarity between the rainfall component maps output by the model under Scenario 4 (combined effects) and the ground-truth maps collected under Scenario 2 (pure rainfall), as well as between the runoff component maps output by the model and the ground-truth maps collected under Scenario 3 (pure runoff). The closer the SSI value is to 1, the better the decoupling effect.

2.

Sensing Accuracy: This metric is used to evaluate the accuracy of sensing environmental parameters using the decoupled signal components.

(a)

Rainfall Intensity Estimation: We extract the average amplitude attenuation from the decoupled rainfall component map $I_{rain}$ as a feature and train a simple regression model (e.g., Support Vector Regression, SVR) to estimate the rainfall intensity. We use the Mean Absolute Error (MAE) to measure the gap between the estimated values and the ground truth from the rain gauge.

(b)

Surface Ponding Detection: We extract energy (sum of the squares of all pixel values) from the decoupled runoff component map $I_{runoff}$ as a feature. By setting an energy threshold, we can determine whether there is surface ponding. We use Accuracy, Precision, and Recall to evaluate the performance of ponding detection.

3.

Communication Improvement: This metric is used to verify the potential of our method in enhancing communication reliability. We apply the decoupled channel estimation ($I_{rain}$ + $I_{runoff}$) to channel equalization at the receiver and compare it with the traditional method that uses original mixed CSI for equalization. We quantify the improvement in communication performance by calculating and comparing the Bit Error Rate (BER) under the two methods.

4.3. Experimental Results and Analysis

This section presents and analyzes in detail the experimental results of our method and compares them with those of six baseline methods to highlight its superiority:

1.

Raw CSI: Directly uses raw, un-decoupled composite CSI data for subsequent sensing and channel equalization. This serves as the lower bound for performance evaluation.

2.

Filtering-based: Employs a simple signal processing method. A 2D Low-Pass Filter (LPF) is applied to the CSI spatiotemporal map to extract the background (rainfall), and then the texture (runoff) is obtained by subtracting the background from the original map.

3.

PCA-based: Adopts the Principal Component Analysis (PCA) method for separating CSI spatiotemporal maps. PCA is a classic linear dimensionality reduction technique; here, its first principal component is treated as the background (rainfall), and the remaining components are treated as the texture (runoff).

4.

ICA-based: Uses the Independent Component Analysis (ICA) method. ICA is another classic blind source separation technique, whose goal is to find statistically independent components.

5.

NMF-based: Applies the Non-Negative Matrix Factorization (NMF) method. This method requires both input and output to be non-negative, and it is used here for the separation of CSI amplitude maps.

6.

RPCA-based: Utilizes Robust Principal Component Analysis (RPCA). This method decomposes a matrix into a low-rank component (corresponding to the smooth background) and a sparse component (corresponding to the sparse texture), whose physical assumptions are highly consistent with our problem.

4.3.1. Quantification and Visualization Analysis of Decoupling Effect

The quality of decoupling is the foundation for all subsequent applications. We first evaluate the decoupling performance of our method (referred to as DDAE hereinafter, i.e., Dual-Decoder AutoEncoder) from both quantitative and visual perspectives.

Quantitative Analysis:

Table 1. Comparison of decoupling accuracy among different methods. All results are obtained under the combined-effects scenario.

Method	Rainfall Component SSI	Runoff Component SSI
Filtering-based	0.62	0.55
PCA-based	0.71	0.65
ICA-based	0.73	0.68
NMF-based	0.68	0.61
RPCA-based	0.89	0.85
DDAE (ours)	0.96	0.92

presents a comparison of SSI scores for decoupling accuracy between DDAE and various baseline methods under the combined-effects scenario. It can be observed that our DDAE model achieves the highest SSI values in reconstructing both the rainfall component and the runoff component (at 0.96 and 0.92, respectively). RPCA, as the strongest baseline method, also performs quite well but still lags behind DDAE, indicating that our deep learning-based nonlinear model can better capture complex signal dynamics. Traditional PCA, ICA, and NMF methods perform next best, while the simplest filtering method performs the worst. This indicates that DDAE can most accurately separate signal features corresponding to real physical processes.

Visualization Analysis: Figure 5 intuitively illustrates such differences. The input composite CSI map (Figure 5a) exhibits feature aliasing. Our DDAE model successfully separates it into a smooth rainfall background (Figure 5b) and a sparse runoff texture (Figure 5c), both of which are highly consistent with the real patterns in pure scenarios. In contrast, the rainfall component separated by the PCA method (Figure 5d) still retains obvious streaks, while its runoff component (Figure 5e) contains a large amount of undesired background noise. Visualization results of other baseline methods (not all shown in the figure) also confirm the conclusions of the quantitative analysis, i.e., traditional methods struggle to achieve clean and complete separation. This visualization result strongly demonstrates the superiority of our method.

4.3.2. Comparative Evaluation of Environmental Sensing Performance

More accurate decoupling should lead to more accurate environmental sensing. We have conducted detailed comparative validation on this.

Rainfall Intensity Estimation: Figure 6 presents scatter plots of rainfall intensity estimation results from three representative methods (raw CSI, RPCA, DDAE), where the x-axis represents the ground truth measured by the rain gauge, and the y-axis represents the estimated values. Ideally, all points should lie on the diagonal line. It can be observed that the estimation results using raw CSI directly (Figure 6a) are highly scattered, barely reflecting the real trend (MAE = 7.23 mm/h). The RPCA method (Figure 6b) performs excellently, significantly outperforming traditional methods, but still has some errors (MAE = 2.85 mm/h). In contrast, the scatter plot obtained by our DDAE method (Figure 6c) is highly consistent with the diagonal line, with an MAE of only 1.48 mm/h, which demonstrates the necessity of decoupling for accurate rainfall intensity estimation and the advancement of our method.

Surface Ponding Sensing: We not only evaluated the performance of ponding detection but also further attempted to estimate the ponding depth.

Table 2. Comparison of surface ponding sensing performance.

Evaluation Task	Method	Performance Metrics
	Raw CSI	Accuracy: 81.5%
	Filtering-based	Accuracy: 85.3%
	PCA-based	Accuracy: 89.1%
Ponding Detection	ICA-based	Accuracy: 89.8%
	NMF-based	Accuracy: 87.2%
	RPCA-based	Accuracy: 95.4%
	DDAE (ours)	Accuracy: 98.2%
	Raw CSI	MAE: 18.7 mm
	Filtering-based	MAE: 15.1 mm
	PCA-based	MAE: 11.3 mm
Ponding Depth Estimation	ICA-based	MAE: 10.9 mm
	NMF-based	MAE: 12.5 mm
	RPCA-based	MAE: 6.2 mm
	DDAE (ours)	MAE: 4.1 mm

summarizes the detailed comparison results of all methods. In the ponding detection task, all metrics (Accuracy, Precision, Recall) of DDAE are significantly superior to those of all other methods, reaching a nearly perfect level. In the more challenging ponding depth estimation task, DDAE also performs the best, with an MAE of only 4.1 mm, which is much lower than that of all baseline methods. This indicates that the runoff component separated by DDAE contains purer feature information that is highly correlated with ponding depth.

4.3.3. Comparative Evaluation of Communication Performance Improvement

Finally, we verify the gain of the decoupling method on the communication system itself. Figure 7 shows the communication Bit Error Rate (BER) curves under different Signal-to-Noise Ratio (SNR) conditions in the combined-effects scenario. It can be observed that compared with the baseline method that uses raw mixed CSI for channel equalization, all decoupling methods can bring a certain degree of performance improvement. Equalization using channel estimation after decoupling by DDAE performs far better than baseline methods. Among them, the effect of DDAE is the most significant, achieving the lowest BER under all SNR conditions. Especially in the medium-to-low SNR range (5–15 dB), the BER improvement brought by DDAE exceeds an order of magnitude. This strongly demonstrates that the more accurate Channel State Information provided by our decoupling method can directly benefit the communication system itself, significantly enhancing its communication robustness in harsh environments.

4.3.4. Ablation Study

To verify the necessity of each component in our designed composite loss function, we conducted an ablation experiment. We trained three incomplete models, respectively: (1) using only the reconstruction loss $L_{rec}$; (2) using $L_{rec}+L_{smooth}$; (3) using $L_{rec}+L_{sparse}$.

Table 3. Results of the loss function ablation experiment.

Model (Loss Used)	Rainfall Component SSI	Runoff Component SSI
$L_{rec}$ only	0.53	0.48
$L_{rec}+L_{smooth}$	0.91	0.61
$L_{rec}+L_{sparse}$	0.68	0.89
$L_{rec}+L_{smooth}+L_{sparse}$ (Complete Model)	0.96	0.92

presents their performance in terms of decoupling accuracy. The results clearly show that the absence of any regularization term leads to a sharp decline in decoupling performance. With only the reconstruction loss, the model cannot effectively separate the two effects. The lack of smoothness loss causes the background component to incorporate a large amount of textures, while the lack of sparsity loss results in the texture component containing a large amount of background noise. This demonstrates that our designed $L_{smooth}$ and $L_{sparse}$ are indispensable for guiding the two decoders to fulfill their respective roles and achieve successful decoupling.

5. Conclusions

This study addresses the core challenge of mixed composite effects caused by rainfall and surface runoff on wireless channels in flood scenarios. For the first time, we systematically propose and validate an end-to-end decoupling framework based on CSI spatiotemporal spectrograms and a Dual-Decoder Convolutional Autoencoder. By constructing high-resolution CSI spatiotemporal spectrograms, one-dimensional time-series signals are transformed into two-dimensional image representations, thereby successfully revealing the structural distinction between the smooth background attenuation induced by rainfall and the high-frequency sparse textures generated by surface runoff. Building on this, our Dual-Decoder model achieves precise separation of the two physical effects under unsupervised conditions by employing the composite loss function. Experimental results demonstrate that, in the task of rainfall intensity estimation, the proposed method attains a mean absolute error of only 1.48 mm/h, while achieving a surface water detection accuracy as high as 98.2%. These results significantly outperform traditional signal separation methods such as RPCA and ICA. In addition, applying the decoupled clean channel responses to receiver-side equalization reduces the Bit Error Rate by more than one order of magnitude under low-to-medium SNR conditions, providing the first experimental validation of the synergistic gain between environmental sensing and communication enhancement. Furthermore, ablation studies confirm that both the smoothness loss and the sparsity loss are indispensable to the overall performance of the model. In summary, this study not only overcomes the application bottlenecks of wireless sensing in complex real-world scenarios but also provides a feasible technical pathway and theoretical foundation for building future flood monitoring networks that are low-cost, high-density, and resilient.