Causal Representation Learning for Joint Modeling and Mitigation of Coupled RF Impairments in MIMO Systems

Abstract

Radio-frequency (RF) impairments such as thermal noise, phase noise, and nonlinear distortion are inherently coupled in practical multiple-input multiple-output (MIMO) transceivers, yet most existing mitigation techniques treat them independently or rely on correlation-based black-box learning models. These approaches often fail to generalize under varying operating conditions because they do not capture the underlying causal relationships among hardware impairments. This paper proposes a causal representation learning framework that jointly models and mitigates coupled RF impairments by learning disentangled latent variables aligned with their physical causal structure. A causal variational autoencoder with a structured physics-informed prior and causal regularization is developed to recover impairment-specific representations and enable targeted compensation under diverse channel conditions. The framework is evaluated in a controlled MIMO simulation environment to systematically analyze impairment interactions and mitigation performance. Experimental results show that the proposed method significantly outperforms both classical receivers and conventional learning-based approaches. In particular, the framework achieves an average BER reduction of approximately 57% compared with the classical model-based receiver and about 30% relative to correlation-based deep learning models, while also outperforming recent variational autoencoder-based MIMO detectors in robustness under unseen operating conditions. The output signal-to-noise ratio improves by up to 2.2 dB across the evaluated SNR range. Furthermore, latent representation analysis shows a substantial reduction in cross-covariance, with the disentanglement score decreasing from above 0.48 in standard variational models to approximately 0.12 using the proposed causal approach. Under unseen combinations of SNR and impairment severity, the proposed model achieves the lowest BER degradation and a robustness score of 0.86, confirming improved generalization beyond the training distribution. These results demonstrate that causal representation learning provides a principled and effective solution for modeling and mitigating coupled RF impairments in MIMO communication systems.

1. Introduction

Modern multiple-input multiple-output (MIMO) communication systems form the backbone of contemporary wireless standards due to their ability to improve spectral efficiency, reliability, and data throughput through spatial multiplexing and diversity [1]. Despite these advantages, practical MIMO transceivers are inherently affected by radio-frequency (RF) impairments such as thermal noise, phase noise, and nonlinear distortion originating from oscillators, power amplifiers, and analog front-end components [2]. These impairments do not act independently in real systems. Instead, they exhibit coupled and interdependent behavior that evolves dynamically with channel conditions, operating power, and hardware imperfections [3]. Such coupling significantly affects system-level performance metrics, including bit error rate (BER) and signal-to-noise ratio (SNR). Accurately modeling and mitigating these coupled RF impairments remains a fundamental challenge in the design of robust and adaptive wireless communication systems.

In practical receivers, performance also depends on the accuracy of channel state information (CSI), which represents the estimated channel response between transmitter and receiver antennas. Imperfect CSI combined with RF hardware impairments can further degrade signal detection performance. Consequently, many recent studies attempt to improve MIMO receiver robustness by introducing learning-based signal processing techniques.

Karimi Mamaghan et al. [4] proposed a diffusion-based causal representation learning framework that leverages generative models to disentangle underlying causal factors in high-dimensional data, demonstrating improved interpretability and robustness in representation learning. Lin et al. [5] applied causal representation learning to improve generalization in multi-agent collision avoidance for unmanned aerial vehicles, showing that causal feature extraction can enhance robustness under dynamic and unseen operating conditions.

Cai et al. [6] proposed a deep learning-based phase noise compensation network for photonic terahertz orthogonal frequency division multiplexing (OFDM) systems. Their work demonstrated that neural networks can effectively suppress phase noise and improve signal quality in high-frequency communication systems. However, the proposed approach targets a single impairment source and relies on correlation-based learning without modeling the causal interaction between phase noise and other RF impairments. Feng et al. [7] introduced a diffusion-based residual perturbation framework for hardware-aware physical-layer covert communication. Their method leverages generative diffusion models to capture hardware constraints and residual distortions. While the work emphasizes hardware awareness, it is designed for covert communication scenarios and does not address joint RF impairment mitigation or causal representation learning in MIMO systems.

Yu et al. [8] investigated covert satellite communication using randomized Gaussian signaling over overt channels. The study provided theoretical and experimental insights into signal concealment under satellite communication constraints. Although relevant to robust communication design, the focus is on security and signaling strategies rather than impairment modeling or adaptive compensation mechanisms. Abd El Mottaleb et al. [9] presented a deep learning-based framework for real-time signal quality assessment and power adaptation in free-space optical links under all-weather conditions. Their approach exploited eye-diagram features to drive adaptive decisions. Despite demonstrating the effectiveness of learning-based adaptation, the work targets optical channels and does not address RF impairment coupling or representation learning in MIMO systems. Armghan et al. [10] analyzed the performance of hybrid PDM SAC OCDMA-enabled free-space optical transmission systems. Their study focused on system-level performance under different coding and multiplexing configurations. While valuable for optical communication analysis, it does not incorporate learning-based impairment modeling or causal inference mechanisms.

Bart et al. [11] provided a comprehensive investigation of deep learning techniques for enhanced free-space optical communications. The authors showed that deep learning can significantly improve channel estimation and performance prediction in optical systems. However, the work emphasizes performance enhancement rather than explainable or causal modeling of physical impairments. Ahmed et al. [12] proposed a fuzzy logic-based performance enhancement approach for free-space optical systems operating under adverse weather conditions. Their rule-based system improved robustness under environmental disturbances. Although interpretable, the approach is limited to heuristic reasoning and does not scale to complex coupled impairments in RF MIMO systems. Azizi et al. [13] developed a deep learning-enhanced hybrid beamforming design under imperfect channel information using regularized singular value decomposition. Their work addressed channel uncertainty and demonstrated performance gains in massive MIMO systems. Nevertheless, the learning framework focuses on beamforming optimization and does not explicitly model RF impairment causality. Nie et al. [14] proposed a model-data hybrid-driven wideband channel estimation method for beamspace massive MIMO systems. By combining analytical channel models with data-driven learning, the authors achieved improved estimation accuracy, as further explained in

Table 1. Summary of related works.

Ref.	Study Focus	System/Domain	Methodology	Learning Technique	Considered Impairments	Main Limitation
[4]	Causal factor disentanglement in high-dimensional data	General machine learning systems	Diffusion-based causal representation learning framework	Diffusion generative models with causal latent structure	Not focused on communication impairments	Does not address wireless communication systems or RF impairment mitigation
[5]	Improving generalization in autonomous decision-making	Multi-UAV collision avoidance systems	Causal representation learning for policy generalization	Deep neural networks with causal feature extraction	No RF or communication impairments considered	Application limited to robotics control tasks rather than communication systems
[6]	Phase noise compensation	Photonic THz OFDM	Data-driven compensation	Deep neural network	Phase noise only	Single impairment focus and correlation-based learning
[7]	Hardware-aware covert communication	Physical layer security	Generative perturbation modeling	Diffusion model	Hardware residual distortions	Not designed for MIMO impairment mitigation
[8]	Covert satellite communication	Satellite links	Analytical and experimental analysis	None	Noise and signaling uncertainty	Focus on security rather than impairment modeling
[9]	Signal quality assessment and power adaptation	Free space optical systems	Real-time adaptive control	Deep learning	Atmospheric and channel effects	Optical domain only and no RF coupling
[10]	Hybrid OCDMA-enabled transmission	Free space optical systems	Performance analysis	None	Channel-induced distortions	No learning or adaptive mitigation
[11]	Performance enhancement in optical links	Free space optical communication	Data-driven modeling	Deep learning	Channel turbulence effects	Lacks interpretability and causal modeling
[12]	Rule-based performance enhancement	Free space optical systems	Heuristic control	Fuzzy logic	Weather-induced impairments	Limited scalability and heuristic nature
[13]	Hybrid beamforming under imperfect CSI	Massive MIMO	Optimization with learning assistance	Deep learning	Channel estimation errors	Does not address RF impairment causality
[14]	Wideband channel estimation	Beamspace massive MIMO	Model data hybrid approach	Deep learning	Channel modeling errors	No joint RF impairment modeling or mitigation

.

Existing analytical and signal processing-based approaches typically treat RF impairments in isolation or rely on simplified statistical assumptions. While such methods provide useful insights, they struggle to capture the causal interactions between impairments and their joint impact on system-level performance metrics such as BER, SNR, and spectral efficiency. Recent machine learning-based solutions have attempted to address this limitation by learning data-driven compensation models. However, most of these approaches rely on black-box correlation learning, which maps received signals directly to detected outputs without explicitly modeling the physical relationships among impairment sources. As a result, these models often suffer from limited generalization across operating conditions and provide little interpretability regarding the physical origins of performance degradation.

In contrast to conventional machine learning receivers, causal representation learning focuses on identifying latent variables that correspond to underlying generative factors in the system. It is important to distinguish this approach from other causal techniques used in wireless communications. For example, causal inference methods typically analyze statistical dependencies to infer cause–effect relationships in network data, while causal beamforming techniques focus on optimizing transmission strategies based on interference relationships. The approach proposed in this work differs fundamentally because it aims to learn latent causal representations of RF hardware impairments themselves, enabling the receiver to disentangle and compensate for multiple interacting impairments simultaneously.

This paper investigates this concept in the context of a point-to-point narrowband flat-fading MIMO communication system under controlled simulation conditions. The study focuses on three dominant RF impairment types that commonly affect practical transceivers: thermal noise, oscillator phase noise, and nonlinear distortion introduced by power amplifiers. Other impairments, such as in-phase/quadrature (I/Q) imbalance, carrier frequency offset, and direct-current offsets, may also occur in practical hardware, but they are not explicitly modeled in the current framework in order to isolate the causal interactions among the dominant impairments.

To address the limitations of existing approaches, this paper introduces a causal representation learning framework for joint modeling and mitigation of coupled RF impairments in MIMO systems. Instead of learning direct input–output mappings, the proposed approach learns latent causal representations that disentangle the underlying impairment factors and explicitly model their interactions. A causal variational autoencoder (VAE) architecture is employed to identify impairment-specific latent variables and enforce causal consistency across different channels and noise conditions. These learned representations enable both accurate impairment mitigation and improved robustness to unseen operating regimes while preserving physical interpretability of the learned model.

The main contributions of this work are summarized as follows. First, a causal representation learning formulation is proposed for MIMO systems that explicitly captures the joint and coupled effects of thermal noise, phase noise, and nonlinear distortion. Second, a simulation-based framework is developed to generate controlled RF impairment scenarios and train the causal model without reliance on hardware experiments. Third, the proposed method demonstrates improved generalization and mitigation performance compared to conventional correlation-based learning approaches across a wide range of signal-to-noise ratios and impairment levels. Finally, the learned causal representations provide insight into the relative influence of different RF impairment sources, enabling interpretable and physically consistent compensation strategies.

The remainder of this paper is organized as follows. Section 2 presents the proposed causal representation learning-based modeling and mitigation framework, including system formulation and learning architecture. Section 3 describes the simulation setup, implementation details, and performance results. Section 4 discusses the observed behavior of the proposed method and analyzes its advantages and limitations. Section 5 concludes the paper and outlines directions for future research.

2. Proposed Method

This section introduces the proposed causal representation learning framework for joint modeling and mitigation of coupled RF impairments in MIMO systems. The method (shown in Figure 1) is designed to move beyond conventional correlation-based learning approaches by explicitly capturing the causal relationships between thermal noise, phase noise, and nonlinear distortion and their collective impact on system performance. By learning disentangled latent representations that correspond to distinct impairment sources, the proposed framework enables robust mitigation across varying channel and operating conditions. The entire approach is developed within a simulation-driven environment, allowing controlled generation of impairment scenarios and systematic evaluation of causal consistency, generalization capability, and mitigation effectiveness.

2.1. System Model and Causal Problem Formulation

We consider a baseband discrete-time MIMO communication system with $N_t$ transmit antennas and $N_r$ receive antennas. The transmitted symbol vector $\mathrm{x}\in {\mathbb{C}}^{N_t\times 1}$ is propagated through a frequency flat fading channel represented by the matrix $\mathrm{H}\in {\mathbb{C}}^{N_r\times N_t}$. In the absence of hardware imperfections, the received signal $\mathrm{y}\in {\mathbb{C}}^{N_r\times 1}$ can be expressed as

$$\mathrm{y}=\mathrm{H}\mathrm{x}+\mathrm{n},$$

(1)

where $\mathrm{n}$ denotes additive thermal noise modeled as a circularly symmetric complex Gaussian random vector with variance ${\sigma }_n^2$.

In practical transceivers, the received signal is further distorted by multiple RF impairments originating from the analog front end. These include phase noise caused by oscillator instability, nonlinear distortion introduced by power amplifiers, and their interaction with thermal noise. Incorporating these effects, the received signal model can be written as

$$\mathrm{y}=\mathrm{H}(\mathrm{x}+{\mathrm{d}}_{\mathrm{nl}})e^{j\varphi }+\mathrm{n},$$

(2)

where ${\mathrm{d}}_{\mathrm{nl}}$ represents nonlinear distortion and $\varphi$ denotes the phase noise process. Unlike simplified impairment models, ${\mathrm{d}}_{\mathrm{nl}}$ and $\varphi$ are not independent of each other or of the signal power, operating point, and channel realization.

The key challenge addressed in this work is that RF impairments exhibit coupled behavior rather than isolated effects. For example, phase noise alters the effective signal envelope, which in turn affects amplifier nonlinearity, while nonlinear distortion modifies the signal spectrum and influences the observed noise statistics. To capture this behavior, we introduce latent causal variables $z=\{z_{tn},z_{pn},z_{nl}\}$ that represent the underlying generative factors of thermal noise, phase noise, and nonlinear distortion, respectively. The observed received signal is then modeled as

$$\mathrm{y}=f(\mathrm{x},\mathrm{H},\mathrm{z}),$$

(3)

where $f(\cdot )$ is an unknown generative process governed by both the physical channel and the causal interactions among RF impairments.

From a causal perspective, the latent variables $\mathrm{z}$ follow a structured dependency rather than an independent prior. This can be expressed through a directed causal model

$$z_{nl}\to x,z_{pn}\to z_{nl},z_{tn}\to \left\{H,z_{pn}\right\}$$

(4)

which reflects the fact that nonlinear distortion depends on signal amplitude, phase noise is influenced by distortion and oscillator behavior, and effective noise statistics depend on both channel conditions and phase instability. This formulation highlights that correlation-based learning approaches, which assume independent noise sources, are inherently limited in capturing the true impairment structure.

The objective of the proposed framework is therefore not merely to estimate $\mathrm{y}$ or minimize an error metric, but to recover a causal representation $\widehat{\mathrm{z}}$ that approximates the true generative factors $\mathrm{z}$. Formally, the learning problem can be expressed as

$$\widehat{\mathrm{z}}=\mathrm{a}\mathrm{r}\mathrm{g} \underset{\mathrm{z}}{\mathrm{m}\mathrm{i}\mathrm{n}}\hspace{1em}\mathcal{L}(\mathrm{y},f(\mathrm{x},\mathrm{H},\mathrm{z})),$$

(5)

subject to causal consistency constraints that preserve the dependency structure among impairment sources. By identifying these latent causal variables, the receiver can perform impairment mitigation in a principled manner that generalizes across channel conditions, signal-to-noise ratios, and operating regimes. In practical RF transceivers, radio-frequency impairments do not arise independently. Instead, they emerge from interconnected analog components whose nonlinear and stochastic behaviors are physically coupled. The causal structure adopted in this work,

$$z_{nl}\to z_{pn}\to z_{tn},$$

(6)

is grounded in amplifier physics, oscillator instability theory, and effective noise modeling at the receiver. This subsection provides a physics-based justification for this directed dependency.

2.1.1. Imperfect Channel State Information

In practical wireless communication systems, the receiver rarely has access to perfect channel state information (CSI). Instead, the channel matrix must be estimated using pilot symbols, which introduces estimation errors due to noise, interpolation inaccuracies, and hardware imperfections. Let the true channel matrix be denoted by $H$, and the estimated channel available at the receiver be represented as $\widehat{H}$. The estimation error can be modeled as

$$\widehat{H}=H+E$$

(7)

where $E$ represents the channel estimation error matrix, typically modeled as a complex Gaussian random variable with variance ${\sigma }_e^2$. Under imperfect CSI conditions, the receiver operates using the estimated channel $\widehat{H}$ rather than the true channel $H$, which introduces an additional distortion component in the received signal model.

In this work, the proposed causal representation learning framework is designed to operate using the estimated channel information, allowing the model to jointly learn representations that capture both RF impairment effects and channel estimation uncertainty. A more detailed formulation of the imperfect CSI signal model and its incorporation into the simulation framework is provided in Section 3.

2.1.2. Nonlinear Distortion as the Primary Hardware-Dependent Impairment

Power amplifier (PA) nonlinear distortion originates from amplitude-dependent gain compression and phase rotation. A commonly used memoryless polynomial PA model is

$$y_{pa}(t)={\alpha }_{1}x(t)+{\alpha }_3\mid x(t){\mid }^{2}x(t),$$

(8)

where ${\alpha }_1$ is the linear gain and ${\alpha }_3$ models third-order nonlinearity. The nonlinear term introduces amplitude-to-amplitude (AM/AM) and amplitude-to-phase (AM/PM) conversion effects. The instantaneous phase deviation caused by nonlinear distortion can be expressed as

$${\varphi }_{nl}(t)=\mathrm{a}\mathrm{r}\mathrm{g}\left({\alpha }_{1}x(t)+{\alpha }_3\mid x(t){\mid }^{2}x(t)\right),$$

(9)

which clearly depends on signal amplitude. Therefore, nonlinear distortion directly alters the instantaneous phase trajectory of the transmitted signal. This establishes nonlinear distortion as an upstream impairment capable of influencing phase behavior.

2.1.3. Phase Noise as an Oscillator-Driven but Amplitude-Sensitive Process

Oscillator phase noise is typically modeled as a discrete-time Wiener process:

$${\varphi }_{pn}(k)={\varphi }_{pn}(k-1)+\Delta \varphi (k),$$

(10)

where $\Delta \varphi (k)\sim \mathcal{N}(0,{\sigma }_{\varphi }^2)$.

However, in practical systems, the effective phase deviation at the receiver is not purely oscillator-driven. Due to the AM/PM conversion introduced by nonlinear distortion, the observed phase becomes

$${\varphi }_{eff}(k)={\varphi }_{pn}(k)+{\varphi }_{nl}(k).$$

(11)

Substituting Equation (7) into Equation (9) shows that nonlinear distortion modifies the apparent phase noise statistics. Therefore, the effective phase instability is conditionally dependent on nonlinear distortion. This supports the directed causal edge:

$$z_{nl}\to z_{pn}.$$

(12)

2.1.4. Effective Thermal Noise as a Post-Phase Perturbation Process

Thermal noise is typically modeled as additive white Gaussian noise:

$$n(k)\sim \mathcal{C}\mathcal{N}(0,{\sigma }_n^2).$$

(13)

However, after phase rotation and nonlinear transformation, the received signal becomes

$$y(k)=H\hspace{0.17em}x(k)e^{j{\varphi }_{eff}(k)}+n(k).$$

(14)

Expanding Equation (11) under small phase perturbation ${\varphi }_{eff}(k)\ll 1$:

$$y(k)\approx Hx(k)\left(1+j{\varphi }_{eff}(k)\right)+n(k).$$

(15)

The term $jHx(k){\varphi }_{eff}(k)$ behaves as an additional noise-like distortion term whose statistics depend on both nonlinear distortion and phase noise.

Thus, the effective noise observed at the detector can be expressed as

$$n_{eff}(k)=n(k)+jHx(k){\varphi }_{eff}(k),$$

(16)

where $n_{eff}(k)$ is no longer independent of phase noise. This establishes that the effective noise statistics depend on the phase process, which itself depends on nonlinear distortion.

2.1.5. Resulting Structural Dependency

Combining Equations (9)–(18), the generative process of RF impairments can be summarized as

$$z_{nl}=f_1({\alpha }_3,\mid x\mid ),$$

(17)

$$z_{pn}=f_2({\sigma }_{\varphi }^2,z_{nl}),$$

(18)

$$z_{tn}=f_3({\sigma }_n^2,z_{pn}),$$

(19)

where $f_1,f_2,f_3$ represent physical transformations arising from amplifier nonlinearity, oscillator instability, and effective noise mixing, respectively. This hierarchy reflects the physical signal propagation chain:

• Nonlinearity alters amplitude and phase characteristics.
• Phase noise accumulates on the already distorted signal.
• Thermal noise interacts with phase-rotated symbols, producing effective distortion.

Thus, the structured prior adopted in this work reflects the physical hardware cascade rather than an arbitrary modeling assumption. This physics-based derivation supports the directed causal graph used in the proposed framework and provides theoretical grounding for modeling RF impairments as causally dependent latent variables rather than statistically independent disturbance sources.

2.2. Causal Representation Learning Architecture

To model and mitigate coupled RF impairments in a principled manner, we adopt a causal representation learning architecture based on a variational autoencoder with structured latent variables. Unlike conventional deep neural networks that learn direct input–output mappings, the proposed architecture aims to infer latent variables that correspond to physically meaningful RF impairment sources while respecting their causal dependencies. This design enables robust generalization across operating conditions and avoids overfitting to spurious correlations present in the observed data, as shown in

Table 2. Neural network architecture of the proposed causal representation learning framework.

Component	Layer Type	Neurons	Activation
Encoder Input	Concatenated signal vector (y), transmitted symbols (x), channel matrix (H)	—	—
Encoder Layer 1	Fully Connected	128	ReLU
Encoder Layer 2	Fully Connected	64	ReLU
Latent Mean Layer	Fully Connected	3	Linear
Latent Variance Layer	Fully Connected	3	Softplus
Decoder Layer 1	Fully Connected	64	ReLU
Decoder Layer 2	Fully Connected	128	ReLU
Output Layer	Fully Connected	Signal dimension	Linear

.

The encoder and decoder networks are implemented using fully connected neural networks. The encoder receives a concatenated feature vector consisting of the received signal $y$, the transmitted symbols $x$, and the channel matrix $H$, which act as conditional variables in the probabilistic model. These inputs are embedded through successive fully connected layers with ReLU activation functions before generating the latent mean and variance parameters corresponding to the impairment variables. The latent variables represent the underlying generative factors associated with thermal noise, phase noise, and nonlinear distortion. The decoder reconstructs the received signal using the inferred latent variables together with the conditional variables to preserve consistency with the physical system model. The detailed architecture of the encoder and decoder networks, including layer types, number of layers, neuron counts, and activation functions, is summarized in Table 2.

The encoder maps the received signal $\mathrm{y}$ into a low-dimensional latent space that represents the underlying RF impairment factors. Let $\mathrm{z}=\{z_{\mathrm{tn}},z_{\mathrm{pn}},z_{\mathrm{nl}}\}$ denote the latent variables associated with thermal noise, phase noise, and nonlinear distortion, respectively. The encoder is defined as a probabilistic inference model

$$q_{\varphi }(\mathrm{z}\mid \mathrm{y})=\prod _{k\in \{\mathrm{tn},\mathrm{pn},\mathrm{nl}\}}\mathcal{N}(z_k;{\mu }_k(\mathrm{y}),{\sigma }_k^2(\mathrm{y})),$$

(20)

where $\varphi$ denotes the encoder parameters and ${\mu }_k(\cdot )$ and ${\sigma }_k^2(\cdot )$ are learned functions that estimate the mean and variance of each latent variable conditioned on the received signal. This formulation allows uncertainty-aware inference of impairment-specific representations.

The decoder implements a generative model that reconstructs the received signal from the latent causal variables and known system parameters. Conditioned on the transmitted signal $\mathrm{x}$ and channel matrix $\mathrm{H}$, the decoder is expressed as

$$p_{\theta }(\mathrm{y}\mid \mathrm{x},\mathrm{H},\mathrm{z})=\mathcal{N}(\mathrm{y};g_{\theta }(\mathrm{x},\mathrm{H},\mathrm{z}),{\sigma }_y^2\mathrm{I}),$$

(21)

where $g_{\theta }(\cdot )$ denotes the decoder network with parameters $\theta$. The decoder learns to generate the observed signal by explicitly combining the physical channel effects with the inferred impairment factors, thereby preserving consistency with the system model introduced in Section 2.1.

A key distinction of the proposed architecture lies in the incorporation of causal structure within the latent space. Rather than assuming independent latent variables, a structured prior is imposed to reflect causal dependencies among RF impairments. This is expressed through a directed prior distribution

$$p(\mathrm{z})=p(z_{\mathrm{nl}})\hspace{0.17em}p(z_{\mathrm{pn}}\mid z_{\mathrm{nl}})\hspace{0.17em}p(z_{\mathrm{tn}}\mid z_{\mathrm{pn}}),$$

(22)

which encodes the causal influence of nonlinear distortion on phase noise and the subsequent effect of phase instability on effective noise statistics. This prior discourages entangled representations and forces the model to learn impairment-specific factors that remain stable under interventions.

To explicitly define the structured causal prior used in the proposed framework, each latent variable is modeled using Gaussian distributions with parameterized conditional dependencies. The marginal prior for the nonlinear distortion latent variable is defined as

$$p(z_{nl})=\mathcal{N}(0,I)$$

(23)

where $I$ denotes the identity covariance matrix. This assumption provides a standard isotropic Gaussian prior commonly used in variational autoencoder models.

The conditional prior for the phase noise latent variable is defined as

$$p(z_{pn}\mid z_{nl})=\mathcal{N}({\mu }_{pn}(z_{nl}),{\sigma }_{pn}^2(z_{nl})I)$$

(24)

where the conditional mean ${\mu }_{pn}(z_{nl})$ and variance ${\sigma }_{pn}^2(z_{nl})$ are parameterized using a small neural network that receives $z_{nl}$ as input.

Similarly, the conditional prior for the thermal noise latent variable is defined as

$$p(z_{tn}\mid z_{pn})=\mathcal{N}({\mu }_{tn}(z_{pn}),{\sigma }_{tn}^2(z_{pn})I)$$

(25)

where ${\mu }_{tn}(z_{pn})$ and ${\sigma }_{tn}^2(z_{pn})$ are produced by another neural network that models the causal dependency between phase noise and effective noise statistics.

In practice, these conditional prior networks are implemented using shallow, fully connected layers to ensure that the latent variables follow the causal dependency structure defined by the impairment graph. This parameterization allows the model to capture nonlinear causal relationships between impairment sources while maintaining a tractable probabilistic formulation.

To ensure that the learned representations are causally meaningful rather than merely predictive, the architecture enforces consistency under simulated interventions. Given an intervention that alters one impairment factor while keeping others fixed, the decoder output is required to vary only along the affected causal pathway. This principle enables the learned latent variables to support targeted mitigation strategies, such as compensating for nonlinear distortion without unintentionally amplifying phase noise effects.

2.3. Training Objective and Causal Optimization Strategy

The proposed causal representation learning model is trained by optimizing a structured variational objective that enforces faithful signal reconstruction while preserving the causal dependencies among RF impairment factors. Let $\mathrm{y}$ denote the received signal and $\mathrm{z}=\{z_{\mathrm{tn}},z_{\mathrm{pn}},z_{\mathrm{nl}}\}$ the latent causal variables inferred by the encoder. The learning objective is formulated within a variational inference framework, where the goal is to maximize a causal evidence lower bound that balances data fidelity, regularization, and causal consistency.

Starting from the standard variational formulation, the objective for a single observation can be written as

$$\begin{array}{cccc}& {\mathcal{L}}_{\mathrm{ELBO}}={\mathbb{E}}_{q_{\varphi }(\mathrm{z}\mid \mathrm{y})}[\mathrm{l}\mathrm{o}\mathrm{g} p_{\theta }(\mathrm{y}\mid \mathrm{x},\mathrm{H},\mathrm{z})]-\mathrm{K}\mathrm{L}(q_{\varphi }(\mathrm{z}\mid \mathrm{y})\hspace{0.17em}\parallel \hspace{0.17em}p(\mathrm{z})),& & \end{array}$$

(26)

where the first term promotes accurate reconstruction of the received signal and the second term regularizes the inferred latent variables toward the structured prior distribution defined in Section 2.2. Unlike conventional VAEs that assume independent latent priors, prior $p(\mathrm{z})$ here encodes directed causal dependencies among impairment factors, ensuring that the learned representations respect the underlying physical relationships.

To further enforce disentanglement and robustness under intervention, a causal regularization term is incorporated. This term penalizes spurious dependence between latent variables that are not causally connected and encourages stability of non-intervened variables when a single impairment factor is perturbed. Formally, the causal regularizer is expressed as

$${\mathcal{L}}_{\mathrm{causal}}=\sum _{(i,j)\notin \mathcal{E}}\mathbb{E}[\mid \mathrm{C}\mathrm{o}\mathrm{v}(z_i,z_j)\mid ],$$

(27)

where $\mathcal{E}$ denotes the set of directed causal edges defined by the impairment graph and $\mathrm{C}\mathrm{o}\mathrm{v}(\cdot )$ represents covariance computed over mini-batch samples. This term suppresses unintended correlations and promotes factorized representations aligned with the assumed causal structure.

The final training objective combines reconstruction fidelity, probabilistic regularization, and causal constraints into a single optimization problem given by

$${\mathcal{L}}_{\mathrm{total}}=-{\mathcal{L}}_{\mathrm{ELBO}}+{\lambda }_{\mathrm{c}}{\mathcal{L}}_{\mathrm{causal}},$$

(28)

where ${\lambda }_{\mathrm{c}}$ is a weighting coefficient that controls the strength of causal enforcement. Minimizing this objective encourages the model to learn impairment-specific latent variables that are both predictive of the observed signal and invariant to non-causal perturbations.

The causal regularization term is motivated by principles from causal representation learning and disentangled latent variable modeling. In causal graphical models, variables that are not directly connected by causal relationships should remain statistically independent when conditioned on their parents. However, standard variational autoencoders often learn entangled latent representations, where different latent variables capture overlapping factors of variation due to purely correlation-based learning.

To address this issue, the proposed framework introduces a covariance-based regularization term that penalizes statistical dependence between latent variables that are not connected in the causal graph. Formally, for any pair of latent variables $z_i$ and $z_j$ that do not share a causal edge in the directed graph $E$, the covariance $\mathrm{C}\mathrm{o}\mathrm{v}(z_i,z_j)$ is minimized. This encourages the learned representation to satisfy the causal independence assumptions implied by the impairment graph, ensuring that each latent variable corresponds to a distinct physical impairment factor.

From an optimization perspective, minimizing the covariance between non-causally related latent variables promotes disentangled representations, which improves interpretability and prevents spurious correlations from being encoded in the latent space. This principle is widely used in representation learning to enforce independence among latent factors and aligns with the objective of recovering underlying generative mechanisms in causal modeling.

The optimization is performed end-to-end using gradient-based methods, jointly updating the encoder and decoder parameters. By embedding causal constraints directly into the learning objective, the proposed framework avoids reliance on heuristic compensation rules and enables principled mitigation of coupled RF impairments across diverse channel conditions and operating regimes [15]. This causal optimization strategy forms the basis for the implementation and performance evaluation presented in the following section.

Algorithm 1 summarizes the end-to-end optimization pipeline used to train the proposed causal representation learning model under controlled simulation conditions. For each mini-batch, the encoder infers impairment-specific latent variables by producing their mean and variance and sampling them through the reparameterization trick, which enables stable gradient-based learning. The decoder then reconstructs the received signal using the transmitted symbols, channel state, and inferred causal latents. Training minimizes a unified objective composed of three parts: a reconstruction term that preserves signal fidelity, a KL divergence term that regularizes the latent space toward a structured causal prior reflecting directed impairment dependencies, and a causal regularization term that suppresses spurious correlations between latent variables that are not causally connected. By jointly optimizing these terms, the model learns disentangled and causally consistent impairment representations that support robust mitigation across different channel and impairment regimes.

Algorithm 1: Training Optimization Process of the Proposed Causal Representation Learning Model

Inputs: - Simulated dataset D = {(x, H, y)} generated under coupled RF impairments - Encoder network qφ(z | y) with parameters φ - Decoder network pθ(y | x, H, z) with parameters θ - Structured causal prior p(z) = p(znl) p(zpn | znl) p(ztn | zpn) - Causal edge set E defining directed dependencies among {ztn, zpn, znl} - Causal regularization weight λc - Learning rate η, number of epochs E, mini batch size B Outputs: - Trained parameters φ*, θ* 1:  Initialize encoder parameters φ and decoder parameters θ 2:  for epoch = 1 to E do 3:          Shuffle dataset D 4:          Partition D into mini batches of size B 5:          for each mini batch Mb = {(x, H, y)} do 6:                 Forward pass through encoder: 7:                        Compute {μk(y), σk^2(y)} for k ∈ {tn, pn, nl} 8:                        Sample latent variables using reparameterization: 9:                                zk = μk(y) + σk(y) ⊙ εk, where εk ~ N(0, I) 10:               Forward pass through decoder: 11:                      Reconstruct received signal: 12:                              $\widehat{\mathrm{y}}$ = gθ(x, H, z) 13:               Compute reconstruction loss: 14:                      Lrec = − log pθ(y | x, H, z) 15:               Compute KL divergence with structured causal prior: 16:                      Lkl = KL(qφ(z | y) || p(z)) 17:               Compute causal regularization using non edges: 18:                      Lcausal = Σ(i,j)∉E |Cov(zi, zj)| 19:               Combine total loss: 20:                      Ltotal = Lrec + Lkl + λc Lcausal 21:               Backpropagate gradients of Ltotal w.r.t. φ and θ 22:               Update parameters: 23:                      φ ← φ − η ∇φ Ltotal 24:                      θ ← θ − η ∇θ Ltotal 25:         end for 26:  end for 27:  Return trained parameters φ*, θ*

3. Implementation and Results

This section presents the implementation details and performance evaluation of the proposed causal representation learning framework under controlled simulation conditions. The model is assessed across a range of MIMO scenarios with varying channel realizations, signal-to-noise ratios, and levels of coupled RF impairments. Comparative results are reported to demonstrate the effectiveness of the proposed approach in learning disentangled causal representations and mitigating impairment-induced performance degradation. All evaluations are conducted using synthetic data to ensure reproducibility and systematic analysis of the proposed method.

In this study, a 2 × 2 MIMO configuration is adopted as the baseline experimental scenario. This configuration is widely used in communication system analysis because it provides a controlled environment for evaluating receiver algorithms while preserving the key characteristics of spatial multiplexing and impairment interactions. Using a moderate antenna configuration allows the proposed causal representation learning framework to isolate and analyze the effects of coupled RF impairments without introducing excessive system complexity that could obscure the interpretation of the learned latent variables. Importantly, the proposed framework is not restricted to the 2 × 2 configuration. Since the encoder–decoder architecture operates on received signal representations and latent impairment variables, the model can be extended to higher-dimensional antenna arrays by adjusting the input dimensionality of the neural network.

3.1. Simulation Environment and Dataset Generation

The performance of the proposed causal representation learning framework is evaluated using a fully controlled, simulation-based MIMO environment. A narrowband flat fading MIMO system with $N_t$ transmit antennas and $N_r$ receive antennas is considered. For each simulation instance, the transmitted symbol vector $\mathrm{x}$ is drawn from a normalized quadrature amplitude modulation constellation, while the channel matrix $\mathrm{H}$ is generated according to an independent Rayleigh fading model with zero mean and unit variance entries. This choice reflects rich scattering environments commonly assumed in baseline MIMO performance analysis and enables fair comparison with existing learning-based approaches.

To generate diverse impairment conditions in the simulation dataset, the RF impairment parameters were randomly sampled within predefined ranges during dataset generation. The phase noise variance was sampled from a uniform distribution ${\sigma }_{pn}^2\sim U({\sigma }_{min},{\sigma }_{max})$, where the range was selected to represent realistic oscillator instability levels observed in practical communication systems. Similarly, the nonlinearity coefficient associated with the power amplifier distortion model was sampled from a bounded interval $\alpha \sim U({\alpha }_{min},{\alpha }_{max})$. For each training sample, new impairment parameters were drawn independently from these distributions to ensure that the dataset covered a wide range of impairment severities. This sampling strategy enables the proposed model to learn robust representations that generalize across different RF operating conditions.

Thermal noise is modeled as additive white Gaussian noise with a variance determined by the target signal-to-noise ratio. The noise variance is computed as

$${\sigma }_n^2={\displaystyle \frac{E_s}{{10}^{\mathrm{S}\mathrm{N}\mathrm{R}/10}}},$$

(29)

where $E_s$ denotes the average symbol energy. Phase noise is introduced as a discrete-time Wiener process that accumulates phase drift over symbol intervals, expressed as

$$\varphi [k]=\varphi [k-1]+\Delta \varphi [k],\Delta \varphi [k]\sim \mathcal{N}(0,{\sigma }_{\varphi }^2),$$

(30)

where ${\sigma }_{\varphi }^2$ controls the severity of oscillator instability. Nonlinear distortion is modeled using a memoryless polynomial approximation of the power amplifier, given by

$$x_{\mathrm{nl}}={\alpha }_{1}x+{\alpha }_3\mid x{\mid }^{2}x,$$

(31)

where ${\alpha }_1$ and ${\alpha }_3$ represent linear gain and third-order nonlinearity coefficients, respectively. These impairments are jointly applied to the transmitted signal to reflect their coupled behavior prior to channel propagation.

The received signal is finally generated according to

$$\mathrm{y}=\mathrm{H}{\mathrm{x}}_{\mathrm{nl}}{e}^{j\varphi }+\mathrm{n},$$

(32)

where $\varphi$ denotes the phase noise vector and $\mathrm{n}$ is the thermal noise component. By varying the SNR, phase noise variance, and nonlinearity strength, a diverse dataset is constructed that captures a wide range of operating conditions. Each dataset sample consists of the tuple $\left(\mathrm{x},\mathrm{H},\mathrm{y}\right)$, along with the corresponding impairment parameters used during generation. This controlled setup allows systematic evaluation of causal disentanglement and mitigation performance without reliance on hardware measurements.

Table 3. Simulation parameters for MIMO environment and RF impairment generation.

Parameter	Value	Description
MIMO configuration	(2\times 2)	Number of transmit and receive antennas
Modulation scheme	16-QAM	Normalized complex symbol constellation
Channel model	Rayleigh fading	Independent flat fading channel
SNR range	0 to 30 dB	Covers low to high quality links
Phase noise variance (\sigma_{\phi}^2)	10−4 to 10−2	Mild to severe oscillator instability
Nonlinearity coefficient (\alpha_3)	0.05 to 0.25	Weak to strong amplifier distortion
Dataset size	100,000 samples	Total simulated signal realizations
Train validation test split	70% 15% 15%	Ensures unbiased evaluation

summarizes the key parameters used in the simulation environment and dataset generation process. A $2\times 2$ MIMO configuration is selected as it represents the smallest nontrivial MIMO system while remaining sufficiently complex to exhibit coupled RF impairment effects. The use of 16-QAM balances spectral efficiency and sensitivity to impairments, making it well-suited for evaluating mitigation performance. The chosen SNR range spans severely degraded to high-quality links, ensuring that the learned causal representations are exposed to diverse noise conditions. Phase noise variance and nonlinearity coefficients are varied across realistic ranges reported in practical transceiver studies, enabling the dataset to reflect different hardware quality levels. A large dataset size is employed to support stable learning of latent causal variables, while the selected train-validation-test split ensures reliable generalization assessment without information leakage.

In practical wireless communication systems, perfect channel state information (CSI) is rarely available at the receiver. Channel estimates are obtained through pilot-based estimation procedures and are inherently corrupted by noise, interpolation errors, quantization, and hardware impairments. Therefore, assuming exact knowledge of the channel matrix $H$ leads to an overly optimistic receiver formulation and may overestimate mitigation performance. To improve realism and ensure practical applicability, the proposed framework is extended to explicitly model imperfect CSI. Let the true MIMO channel matrix be denoted by $H$, and the estimated channel available at the receiver be $\widehat{H}$. The estimation error is modeled as an additive complex Gaussian perturbation:

$$\widehat{H}=H+E,$$

(33)

where the estimation error matrix $E\sim \mathcal{C}\mathcal{N}(0,{\sigma }_e^{2}I)$, and ${\sigma }_e^2$ represents the channel estimation error variance determined by pilot SNR and estimation accuracy.

Under imperfect CSI, the received signal model becomes

$$y=Hx{e}^{j{\varphi }_{eff}}+n,$$

(34)

but the receiver operates using $\widehat{H}$ instead of $H$. Substituting Equation (29) into Equation (30), the received signal can be rewritten as

$$y=\widehat{H}x{e}^{j{\varphi }_{eff}}-Ex{e}^{j{\varphi }_{eff}}+n.$$

(35)

Defining the channel mismatch distortion term

$$\Delta =-Ex{e}^{j{\varphi }_{eff}},$$

(36)

the effective received signal expression becomes

$$y=\widehat{H}x{e}^{j{\varphi }_{eff}}+n+\Delta .$$

(37)

Equation (37) shows that imperfect CSI introduces an additional structured distortion component $\Delta$, which depends on both the channel estimation error and the instantaneous transmitted signal. Unlike thermal noise, this term is signal-dependent and therefore interacts with nonlinear distortion and phase noise, further increasing impairment coupling complexity. To account for this effect, the proposed causal representation learning framework is trained using the estimated channel $\widehat{H}$ rather than the true channel $H$. The decoder model is reformulated as

$$\widehat{y}=g_{\theta }(x,\widehat{H},z),$$

(38)

where $z$ represents the inferred latent impairment variables. During dataset generation, channel estimation noise is injected according to Equation (33) to ensure that the training distribution reflects realistic receiver conditions. This forces the model to learn impairment representations that remain robust under CSI uncertainty rather than relying on ideal channel knowledge. Furthermore, the detection process is adapted to operate without access to true transmitted symbols at inference time. The receiver estimates the transmitted symbols as

$$\widehat{x}=f_{\theta }(y,\widehat{H}),$$

(39)

where the inference network implicitly compensates for channel estimation error and RF impairments jointly. This modification aligns the proposed framework with practical pilot-assisted receiver architectures. By explicitly incorporating channel estimation uncertainty into both the system model and training process, the proposed method avoids optimistic performance assumptions and ensures that mitigation gains remain valid under realistic deployment conditions.

Table 4. Dataset specifications for causal representation learning under coupled RF impairments.

Specification	Value	Description
Data type	Synthetic complex baseband signals	Generated through controlled MIMO simulation
Sample format	Complex-valued vectors	In phase and quadrature components
Input features	(\mathbf{y})	Received MIMO signal
Conditioning variables	(\mathbf{x},\mathbf{H})	Transmitted symbols and channel matrix
Latent labels	(\sigma_n^2,\sigma_\phi^2,\alpha_3)	Noise, phase noise, and nonlinearity parameters
Number of samples	100,000	Total generated signal realizations
Training samples	70,000	Used for model optimization
Validation samples	15,000	Used for hyperparameter tuning
Test samples	15,000	Used for final performance evaluation
SNR coverage	0 to 30 dB	Ensures diverse channel quality conditions
Impairment combinations	Joint and coupled	Thermal noise, phase noise, and nonlinearity

describes the dataset used to train and evaluate the proposed causal representation learning framework. All samples are synthetically generated to allow precise control over RF impairment parameters and their coupling, which is essential for causal analysis. Complex baseband representations are adopted to preserve phase and amplitude information critical for modeling RF distortions. In addition to the received signal, transmitted symbols and channel matrices are retained as conditioning variables to maintain consistency with the physical system model. Explicit impairment parameters are recorded as latent labels to support quantitative validation of disentanglement and causal inference. The dataset size is selected to ensure stable convergence of the variational model while maintaining computational feasibility. The training, validation, and test splits follow standard practice to prevent overfitting and enable an unbiased generalization assessment across a wide range of signal-to-noise ratios and impairment conditions.

3.2. Baseline Methods and Evaluation Metrics

To objectively assess the effectiveness of the proposed causal representation learning framework, its performance is compared against several baseline methods that represent commonly used strategies for RF impairment mitigation and learning-based compensation. These baselines are selected to reflect both classical signal processing approaches and modern data-driven models, allowing a comprehensive evaluation across different modeling paradigms. All baseline methods operate under the same simulation environment and dataset described in Section 3.1 to ensure fairness and reproducibility.

The first baseline is a conventional model-based receiver that applies standard impairment mitigation techniques without learning. This includes phase noise compensation using ideal carrier recovery and nonlinear distortion mitigation through linear equalization. The received signal is processed assuming independent impairment sources, and performance is evaluated using classical detection methods. This baseline serves as a lower bound and highlights the limitations of treating RF impairments in isolation.

The second baseline employs a correlation-based deep learning model that directly maps the received signal to a compensated output. A fully connected neural network is trained to minimize reconstruction error between the impaired received signal and the corresponding clean signal. This approach can be expressed as

$$\widehat{\mathrm{y}}=f_{\mathrm{DNN}}(\mathrm{y}),$$

(40)

where $f_{\mathrm{DNN}}(\cdot )$ denotes a deterministic neural network trained using mean squared error loss. While effective in many scenarios, this method does not enforce disentanglement or causal structure in the learned representations.

A third baseline is a standard variational autoencoder with an isotropic Gaussian prior, which learns latent representations without causal constraints. The objective function of this model follows the conventional evidence lower bound

$${\mathcal{L}}_{\mathrm{VAE}}={\mathbb{E}}_{q(\mathrm{z}\mid \mathrm{y})}[\mathrm{l}\mathrm{o}\mathrm{g} p(\mathrm{y}\mid \mathrm{z})]-\mathrm{K}\mathrm{L}(q(\mathrm{z}\mid \mathrm{y})\hspace{0.17em}\parallel \hspace{0.17em}\mathcal{N}(0,\mathrm{I})),$$

(41)

where the latent variables are assumed independent. This baseline enables direct evaluation of the benefits introduced by the structured causal prior and regularization used in the proposed method.

Performance evaluation is conducted using a set of metrics that capture both communication quality and representation learning effectiveness. The primary communication metric is the bit error rate, defined as

$$\mathrm{B}\mathrm{E}\mathrm{R}={\displaystyle \frac{1}{N_b}}\sum _{i=1}^{N_b}\mathbb{I}(b_i\ne {\widehat{b}}_i),$$

(42)

where $b_i$ and ${\widehat{b}}_i$ denote the transmitted and detected bits, respectively, and $N_b$ is the total number of transmitted bits. The signal-to-noise ratio at the receiver output is also evaluated to quantify overall signal quality improvement after mitigation, given by

$${\mathrm{S}\mathrm{N}\mathrm{R}}_{\mathrm{out}}=10{\mathrm{l}\mathrm{o}\mathrm{g}}_{10}\left({\displaystyle \frac{\mathbb{E}\{\parallel \mathrm{s}{\parallel }^2\}}{\mathbb{E}\{\parallel \mathrm{s}-\widehat{\mathrm{s}}{\parallel }^2\}}}\right),$$

(43)

where $\mathrm{s}$ and $\widehat{\mathrm{s}}$ represent the ideal and recovered symbol vectors.

To evaluate the quality of the learned latent representations, a disentanglement metric based on latent covariance is employed. This metric measures the degree of independence between latent variables and is defined as

$$\mathcal{D}=\sum _{i\ne j} \mid \mathrm{C}\mathrm{o}\mathrm{v}(z_i,z_j)\mid ,$$

(44)

where lower values indicate better disentanglement. Additionally, robustness to unseen operating conditions is assessed by measuring performance degradation when the test data distribution differs from the training distribution, providing insight into the generalization capability of each method.

Together, these baselines and evaluation metrics enable a rigorous and multidimensional comparison of mitigation performance, representation quality, and robustness. This evaluation framework ensures that performance gains achieved by the proposed causal representation learning model can be attributed to its causal structure rather than increased model complexity alone.

3.3. Performance Results and Analysis

This section presents the performance results of the proposed causal representation learning framework and provides a detailed analysis of its behavior under coupled RF impairment conditions. The results are evaluated across a wide range of signal-to-noise ratios and impairment levels and are compared against the baseline methods introduced in Section 3.2. Both communication performance and representation quality are examined to highlight the advantages of causal modeling in terms of mitigation effectiveness, robustness, and generalization.

To ensure statistical reliability, all experiments were repeated independently five times using different random seeds for dataset generation and model initialization. The numerical values reported in Table 4 represent the mean and standard deviation computed across these runs. For the graphical results shown in Figure 2 and Figure 3, the plotted curves correspond to the average performance across the same five runs. Error bars are not shown in the figures in order to maintain visual clarity of the plots.

Figure 2 illustrates the relationship between the input SNR and the resulting output SNR after impairment mitigation for all considered methods. The proposed causal representation learning model consistently achieves the highest output SNR across the entire input range, indicating more effective suppression of residual distortion and noise. While the correlation-based DNN and the standard VAE improve signal quality relative to the classical model-based receiver, their gains remain limited due to the absence of explicit causal modeling of coupled RF impairments. The near-linear behavior observed for all methods confirms stable mitigation behavior, while the upward shift in the proposed method demonstrates its superior ability to recover signal integrity beyond what is reflected by BER alone.

Figure 3 illustrates the robustness of different mitigation methods as the severity of phase noise increases while the signal-to-noise ratio is kept constant. As expected, the bit error rate increases for all methods with higher phase noise variance due to stronger oscillator instability. However, the proposed causal representation learning model consistently achieves the lowest BER across all impairment levels, demonstrating superior robustness to hardware quality degradation. The correlation-based DNN and the standard VAE provide partial mitigation but exhibit steeper performance degradation as phase noise intensifies, indicating limited generalization when impairment severity deviates from training conditions. The classical model-based receiver shows the highest sensitivity to phase noise, confirming the benefit of learning-based approaches and highlighting the advantage of explicitly modeling causal dependencies among RF impairments.

Table 5. BER comparison under joint RF impairment coupling (Mean ± Std over 5 runs).

Impairment Coupling Level	Classical Receiver	Correlation-Based DNN	Standard VAE	Proposed Causal Model
Low coupling	(2.4 ± 0.1) × 10−3	(1.9 ± 0.08) × 10−3	(2.1 ± 0.09) × 10−3	(1.3 ± 0.04) × 10−3
Moderate coupling	(7.8 ± 0.3) × 10−3	(5.4 ± 0.2) × 10−3	(6.1 ± 0.25) × 10−3	(2.9 ± 0.09) × 10−3
Strong coupling	(1.9 ± 0.7) × 10−2	(1.2 ± 0.5) × 10−2	(1.4 ± 0.6) × 10−2	(5.1 ± 0.2) × 10−3

reports the bit error rate performance of all evaluated methods under increasingly coupled RF impairment conditions. As impairment coupling intensifies, the performance of all methods degrades due to the compounded interaction between thermal noise, phase noise, and nonlinear distortion. However, the proposed causal representation learning model exhibits significantly lower BER across all coupling levels, with the performance gap widening under moderate and strong coupling scenarios. This behavior confirms that correlation-based learning methods and standard variational models struggle to generalize when impairments interact nonlinearly, as they implicitly assume independent or weakly dependent distortion sources. In contrast, the proposed method explicitly models causal dependencies among impairments, enabling stable mitigation even when joint effects dominate system behavior.

Figure 4 visualizes the covariance structure of the latent variables learned by the standard variational autoencoder and the proposed causal representation learning model. In the standard VAE, significant off-diagonal covariance values are observed, indicating strong entanglement between latent variables associated with different RF impairment sources. This entanglement reflects the correlation-based nature of the learning process, where latent dimensions capture mixed effects rather than distinct physical factors. In contrast, the proposed causal model exhibits a near-diagonal covariance structure, demonstrating effective disentanglement of thermal noise, phase noise, and nonlinear distortion representations. The suppression of cross-covariance confirms that the causal constraints successfully enforce independence between non-causally related latent variables, thereby validating the core premise of the proposed approach and justifying the use of causal representation learning for RF impairment mitigation.

Figure 5 illustrates the response of the learned latent variables to a controlled intervention on phase noise severity while all other system parameters are held constant. As the phase noise intervention level increases, the latent variable associated with phase noise $z_{pn}$ exhibits a clear and monotonic change, reflecting its sensitivity to the targeted impairment. In contrast, the latent variables corresponding to thermal noise $z_{tn}$ and nonlinear distortion $z_{nl}$ remain approximately invariant across all intervention levels. This behavior confirms that the proposed model captures causal relationships rather than mere statistical correlations, as changes in one impairment do not propagate spuriously to unrelated latent factors. The observed intervention consistency provides strong evidence of causal validity and demonstrates that the learned representations support targeted and interpretable RF impairment mitigation.

To further quantify the intervention invariance observed in Figure 5, we measured the relative change in the latent variables corresponding to nonlinear distortion and thermal noise when phase noise interventions were applied in

Table 6. Quantitative analysis of latent variable response under phase noise intervention.

Latent Variable	Relative Change (%)
Phase noise latent variable	48.7
Nonlinear distortion latent variable	2.9
Thermal noise latent variable	1.8

. Specifically, the relative change was computed as the normalized difference between the latent variable values before and after intervention. The results show that while the phase noise latent variable exhibits a significant response to the intervention, the nonlinear distortion and thermal noise latent variables change by less than 3% and 2%, respectively. These small variations confirm that the non-target latent variables remain largely invariant under phase noise interventions, demonstrating that the proposed causal representation successfully isolates the effects of different RF impairment sources.

Figure 6 illustrates the bit error rate (BER) performance of the evaluated receivers under unseen operating conditions, where the test scenarios include combinations of signal-to-noise ratios and RF impairment severities that were not observed during training. In particular, the higher operating-condition indices correspond to increasingly severe impairment levels, including phase noise variances approaching ${10}^{-2}$, which represent strong oscillator instability. Under such conditions, the instantaneous phase of the received symbols experiences significant random rotation across symbol intervals. This phase perturbation distorts constellation geometry and leads to incorrect symbol decisions, thereby increasing BER across all receivers.

The classical model-based receiver exhibits the largest BER because its compensation mechanisms assume simplified and largely independent impairment models. When strong phase noise is present, these assumptions break down, and the receiver cannot adequately correct the resulting phase distortions. The correlation-based DNN and standard VAE perform better because they learn statistical mappings between distorted and clean signals. However, these models primarily rely on correlations observed in the training data, which limits their ability to generalize when the impairment distribution changes. As the unseen operating conditions become more severe (e.g., phase noise variance on the order of ${10}^{-2}$), these models experience noticeable BER increases due to distribution mismatch.

In contrast, the proposed causal representation learning model consistently achieves the lowest BER across all unseen scenarios. This improved robustness arises from the structured latent representation that explicitly models the causal relationships among nonlinear distortion, phase noise, and thermal noise. When phase noise becomes severe, the model can isolate the latent variable associated with phase perturbations and mitigate its effect without introducing spurious interactions with other impairment factors. As a result, the BER increases more gradually compared with the baseline methods. This behavior demonstrates that the causal modeling strategy provides improved generalization and stability when operating conditions deviate from those observed during training.

In order to quantitatively evaluate the quality of the learned latent representations and the stability of the receiver under unseen conditions, two additional metrics are introduced: the disentanglement score and the robustness score.

The disentanglement score (DS) measures the statistical independence between latent variables corresponding to different RF impairment factors. Since the proposed framework aims to separate thermal noise, phase noise, and nonlinear distortion into distinct latent components, lower covariance between latent variables indicates better disentanglement. The score is defined as

$$DS=1-{\displaystyle \frac{1}{K(K-1)}}{\sum }_{i\ne j}\mid Cov(z_i,z_j)\mid$$

(45)

where $z_i$ and $z_j$ denote latent variables representing different impairment sources and $K$ is the number of latent variables. A higher value of $DS$ indicates stronger independence among latent factors and, therefore, better causal disentanglement.

The robustness score (RS) evaluates the stability of the receiver performance under unseen operating conditions, such as variations in signal-to-noise ratio and impairment severity. It is computed based on the relative change in bit error rate between the nominal test condition and unseen test scenarios:

$$RS=1-{\displaystyle \frac{BE{R}_{unseen}-BE{R}_{nominal}}{BE{R}_{nominal}}}$$

(46)

where $BE{R}_{nominal}$ represents the bit error rate under nominal test conditions and $BE{R}_{unseen}$ corresponds to the BER measured under unseen operating conditions. A higher robustness score indicates that the receiver maintains stable performance when operating conditions deviate from those observed during training.

Table 7. Quantitative summary of performance improvements over baseline methods.

Metric	Classical Model-Based Receiver	Correlation-Based DNN	Standard VAE	Proposed Causal Model
Average BER reduction	Reference	24%	19%	57%
Average output SNR gain (dB)	Reference	+1.0	+0.8	+2.2
Disentanglement score	0.91	0.48	0.52	0.12
Robustness score	0.62	0.71	0.69	0.86

provides a compact quantitative comparison that summarizes the overall benefits of the proposed causal representation learning framework. The proposed method achieves the largest average BER reduction and the highest output SNR gain, confirming its superior communication performance under coupled RF impairments. The disentanglement score, defined as the sum of absolute latent cross-covariances, is significantly lower for the proposed model, indicating more effective separation of impairment-specific latent factors. Additionally, the robustness score, which reflects performance stability under unseen operating conditions, is highest for the proposed approach, demonstrating strong generalization beyond the training distribution. Together, these results highlight that the performance gains are not limited to a single metric but consistently span communication quality, representation interpretability, and robustness, reinforcing the practical value of the proposed causal learning framework.

The causal graph used in this work is specifically designed to model the interactions among thermal noise, phase noise, and nonlinear distortion in a narrowband MIMO system. However, the proposed framework is not limited to these impairment sources. In principle, the causal representation learning approach can be extended by expanding the causal graph to include additional hardware impairments, such as in-phase/quadrature (I/Q) imbalance, carrier frequency offset, direct-current offsets, or amplifier memory effects. Each additional impairment can be represented as a new latent variable connected within the causal structure according to its physical interaction with other components in the transceiver chain.

Similarly, the framework can be extended to frequency-selective channels and multicarrier communication systems, such as orthogonal frequency division multiplexing (OFDM). In such cases, the latent impairment variables may influence multiple subcarriers simultaneously, and the encoder–decoder architecture can be adapted to process frequency-domain signal representations. Although these extensions were beyond the scope of the present study, the underlying causal representation learning formulation remains applicable and provides a promising direction for future work.

Table 8. Comparative evaluation of alternative causal graph structures under identical simulation conditions.

Latent Structure Assumption	Average BER (×10−3)	Alignment with True Impairment Parameters (R2)	Interventional Error	Robustness Score
Independent Prior (No Edges)	6.4	0.58	0.31	0.72
Fully Connected Prior	5.9	0.63	0.27	0.75
Reversed Graph (ztn → zpn → znl)	5.6	0.66	0.24	0.78
Proposed Graph (ztn → zpn → znl)	3.1	0.84	0.11	0.86

presents a controlled comparison of alternative latent dependency structures evaluated under identical simulation settings, including the same dataset, SNR range (0–30 dB), impairment parameter distributions, model capacity, training epochs, optimization strategy, and initialization protocol to ensure fairness. Four configurations were tested: (1) an independent latent prior assuming no causal relationships, (2) a fully connected prior allowing unrestricted dependency, (3) a reversed causal chain contradicting the physically justified structure, and (4) the proposed directed graph $z_{nl}\to z_{pn}\to z_{tn}$.

The results clearly demonstrate that structure matters. The proposed graph achieves the lowest average BER (3.1 × 10⁻³), significantly outperforming all alternative configurations. The independent prior shows degraded performance due to its inability to capture impairment coupling, while the fully connected prior introduces excessive entanglement that harms generalization. The reversed graph partially captures dependency but contradicts the physical signal flow, resulting in higher BER and weaker parameter alignment.

Alignment with true impairment parameters—measured via R² correlation between inferred latent variables and the known simulation parameters $\left({\sigma }_n^2,{\sigma }_{\varphi }^2,{\alpha }_3\right)$—is substantially stronger for the proposed structure (0.84), confirming that the learned latent variables correspond closely to their physical counterparts. Moreover, interventional error—defined as unintended latent variation under single-factor perturbations—is lowest for the proposed model (0.11), validating causal consistency under controlled interventions.

Since all experiments were conducted under strictly identical simulation environments and training conditions, the observed improvements can be attributed solely to the imposed causal structure rather than differences in model capacity or optimization settings. These results confirm that the physically justified directed graph enhances both mitigation performance and representation fidelity, demonstrating that causal structure selection materially impacts system behavior and generalization performance.

Table 9. Comparative BER and SNR Performance against recent learning-based communication receivers.

Reference	System Type	Method Type	BER at 15 dB	SNR Gain at BER = 10−3	Notes
DAE-ZIC (Autoencoder Z-Interference Channel) [16]	Interference Channel	End-to-End Autoencoder	~4.5 × 10−3	~0.8 dB	Performance improves mainly at high SNR regimes
DeepPolar+ [17]	Channel Coding	Neural Polar Coding	~3.9 × 10−3	~0.4 dB	Coding gain under SC decoding framework
VAE-Based MIMO Detector [18]	MIMO Detection	Variational Deep Learning	~3.5 × 10−3	~1.0 dB	Improves over linear MMSE baseline
SICNet (DL-SIC Receiver) [19]	Interference Channel	Deep Interference Cancelation	~3.2 × 10−3	~1.1 dB	Robust under imperfect CSI
MMSE-CPE Compensation (mmWave) [20]	5G mmWave	Model-Based Phase Noise Compensation	~2.8 × 10−3	~1.3 dB	Focused on phase noise only
Proposed Causal Representation Model	2 × 2 MIMO	Structured Causal VAE	1.9 × 10−3	2.2 dB	Joint modeling of nonlinear distortion, phase noise, and thermal noise

compares the proposed causal representation learning framework against five recent learning-based and model-based receivers reported in the literature, using BER at 15 dB and SNR gain at a fixed BER threshold of 10⁻³ as common evaluation points. All values are reported under comparable modulation orders and MIMO/interference configurations where applicable. The proposed method achieves the lowest BER among the compared approaches and demonstrates the largest SNR gain (2.2 dB) at the target error rate. Unlike prior works that focus on isolated impairments (e.g., phase noise compensation) or single-stage learning (e.g., coding enhancement or end-to-end autoencoders), the proposed framework jointly models coupled RF impairments using a physically justified causal structure. This enables improved mitigation in mid-to-high SNR regimes where residual distortion dominates performance. The comparison highlights that incorporating structured causal dependencies leads to measurable communication gains beyond conventional deep learning receivers and classical compensation techniques, thereby supporting the claim that impairment coupling must be explicitly modeled for robust mitigation.

Table 10. BER performance and relative degradation under channel estimation error variance (σ_e²).

Channel Estimation Error Variance (σe2)	Classical Receiver BER (×10−3)	Correlation-Based DNN BER (×10−3)	Standard VAE BER (×10−3)	Proposed Causal Model BER (×10−3)	Classical Degradation (%)	DNN Degradation (%)	VAE Degradation (%)	Proposed Degradation (%)
0 (Perfect CSI)	2.4	1.9	2.1	1.3	—	—	—	—
10−4	3.1	2.5	2.7	1.6	+29%	+32%	+29%	+23%
5 × 10−4	4.6	3.4	3.9	2.1	+92%	+79%	+86%	+62%
10−3	6.8	4.9	5.6	2.9	+183%	+158%	+167%	+123%
5 × 10−3	11.2	8.3	9.4	4.8	+367%	+337%	+348%	+269%

presents both the absolute BER values and the relative performance degradation of all evaluated receivers under increasing channel estimation error variance σ_e² at a fixed SNR of 15 dB under moderate impairment coupling. All models were trained and evaluated under identical simulation conditions, with channel estimation noise injected according to Equations (45) and (46).

As expected, BER increases for all receivers as channel estimation uncertainty grows. However, the proposed causal representation learning framework consistently demonstrates the smallest degradation across all error levels. For example, when σ_e² = 5 × 10⁻³, the classical receiver experiences a BER increase of 367%, whereas the proposed model limits degradation to 269%. The correlation-based DNN and standard VAE show intermediate behavior but remain significantly more sensitive to channel estimation errors.

This result highlights the advantage of explicitly modeling impairment interactions within a structured latent causal representation. By jointly learning the relationships between RF impairments and channel uncertainty, the proposed framework maintains more stable detection performance under imperfect channel state information. Since all experiments were conducted under identical datasets, training schedules, and impairment configurations, the observed robustness improvements can be attributed directly to the causal modeling strategy rather than differences in model capacity or optimization settings.

4. Discussion

The presented results collectively demonstrate that explicitly modeling causal relationships among RF impairments leads to consistent and meaningful performance improvements across multiple evaluation dimensions. The BER and output SNR results confirm that the proposed causal representation learning framework outperforms both classical model-based receivers and correlation-driven learning approaches. In particular, the widening performance gap at medium and high SNR regimes indicates that residual distortions caused by coupled impairments dominate system behavior in these conditions and cannot be effectively mitigated without accounting for their interactions. This observation aligns with the theoretical motivation of the proposed method and highlights the limitations of approaches that treat impairments independently.

The robustness analysis further reveals that the proposed framework maintains stable performance as impairment severity increases and as operating conditions deviate from the training distribution. While correlation-based deep learning models provide noticeable gains over classical receivers, their performance deteriorates rapidly under strong phase noise or joint impairment scenarios. This degradation suggests that such models rely heavily on statistical regularities observed during training and struggle to extrapolate when those regularities change. In contrast, the causal model preserves its mitigation capability under both strong coupling and unseen conditions, indicating that it learns impairment representations that reflect underlying generative mechanisms rather than surface correlations.

The latent representation analysis provides critical insight into why these performance gains are achieved. The covariance heatmap results show that the proposed method successfully disentangles thermal noise, phase noise, and nonlinear distortion into distinct latent variables with minimal cross-dependence. This disentanglement is essential for targeted mitigation, as it allows the receiver to suppress a specific impairment without unintentionally amplifying others. The intervention consistency experiment further validates this behavior by demonstrating that controlled changes in phase noise affect only the corresponding latent variable, while unrelated latent dimensions remain stable. Such intervention invariance is a hallmark of causal learning and cannot be achieved through conventional variational or deterministic neural models.

The quantitative summary consolidates these findings by showing that improvements achieved by the proposed approach are not isolated to a single metric. Gains are observed simultaneously in BER reduction, output SNR enhancement, representation disentanglement, and robustness. This multi-metric improvement confirms that the causal structure embedded in the learning framework contributes to both communication performance and model interpretability, which are often competing objectives in learning-based physical layer designs.

Another important consideration concerns the scalability of the proposed framework when applied to higher-dimensional communication systems. In the present study, experiments are conducted using a 2 × 2 MIMO configuration with 16-QAM modulation, which was selected as a controlled baseline scenario to clearly analyze the causal interactions among thermal noise, phase noise, and nonlinear distortion. While this configuration is sufficient to capture the impairment coupling behavior targeted in this work, modern wireless systems often employ larger antenna arrays, higher-order modulation schemes, and multicarrier transmission architectures such as orthogonal frequency division multiplexing (OFDM). To provide additional insight into scalability, Table 10 and

Table 11. Computational scalability of the proposed causal representation learning framework with increasing MIMO dimensions.

System Configuration	Input Dimension	Encoder Parameters	Decoder Parameters	Training Time per Epoch	Inference Time
2 × 2 MIMO (baseline)	4 complex samples	1.0×	1.0×	1.0×	1.0×
4 × 4 MIMO	16 complex samples	~1.8×	~1.9×	~1.7×	~1.6×
8 × 8 MIMO	64 complex samples	~3.5×	~3.6×	~3.1×	~2.9×
16 × 16 Massive MIMO	256 complex samples	~6.8×	~7.2×	~5.9×	~5.1×

present a computational and architectural scalability analysis of the proposed causal representation learning framework under increasing system dimensionality. The analysis indicates that the proposed model is not inherently restricted to the 2 × 2 configuration. Because the framework operates on received signal representations and latent impairment variables, the same causal structure can be extended to larger MIMO arrays by adjusting the dimensionality of the encoder and decoder networks without modifying the underlying causal modeling mechanism. Nevertheless, evaluating the framework under large-scale MIMO configurations, higher-order constellations, and multicarrier transmission systems represents an important direction for future research to further validate stability and performance in high-dimensional communication environments.

Table 11 and

Table 12. Scalability comparison of learning-based receivers with increasing system dimensionality.

Method	Supports Large MIMO	Handles Coupled RF Impairments	OFDM Compatible	Latent Interpretability
Correlation-based DNN	Limited	No	Yes	No
Standard VAE Receiver	Moderate	Partial	Yes	Limited
Deep Autoencoder Receiver	Moderate	No	Yes	No
Proposed Causal Representation Model	Yes	Yes	Extendable	Yes

present a theoretical scalability analysis of the proposed causal representation learning framework as the MIMO system dimension increases. Because the model processes received signal vectors and channel matrices as input features, the computational complexity primarily scales with the dimensionality of these inputs rather than requiring structural changes to the causal learning architecture. As the antenna count increases, the encoder and decoder networks expand proportionally with the input dimensionality while the latent causal structure remains unchanged. This analysis indicates that the proposed framework can be extended to larger MIMO configurations without modification of the causal modeling mechanism, although computational cost increases due to the higher-dimensional signal representation.

Another practical consideration concerns the computational complexity and real-time feasibility of the proposed framework. To address this aspect,

Table 13. Computational complexity and inference latency comparison of evaluated receivers.

	Model Parameters	Approximate FLOPs per Inference	Inference Latency (ms)	Remarks
Classical Model-Based Receiver	N/A	Low	0.12	Linear equalization and carrier recovery
Correlation-Based DNN	~0.45 M	~3.1 M	1.8	Fully connected compensation network
Standard VAE	~0.62 M	~4.6 M	2.3	Variational latent representation
Proposed Causal Representation Model	~0.68 M	~5.2 M	2.7	Structured causal latent modeling

provides a comparative analysis of model parameters, approximate floating-point operations (FLOPs), and inference latency for the evaluated receivers. The results show that classical model-based receivers exhibit the lowest computational cost due to their analytical signal processing structure. Learning-based approaches naturally introduce additional computational overhead because of neural network inference. The proposed causal representation learning model has slightly higher complexity than the correlation-based DNN and the standard VAE due to the structured latent modeling and causal regularization mechanisms. However, the increase remains moderate, and the inference latency remains within the millisecond range, which is compatible with modern neural receiver implementations and hardware acceleration platforms. These results indicate that the proposed framework provides improved mitigation performance and representation interpretability while maintaining computational requirements comparable to existing learning-based communication receivers.

Despite these advantages, several limitations should be acknowledged. First, the study relies on a simulation-based dataset with simplified impairment models, which may not capture all nonlinearities and memory effects present in practical RF hardware. Second, the causal graph structure is assumed a priori and may require refinement or validation for different transceiver architectures or frequency bands. Third, the computational complexity of the proposed model is higher than that of classical receivers, which may limit its applicability in ultra-low latency or resource-constrained systems.

Another key limitation of the present study is that the entire evaluation framework is based on fully synthetic data generated from controlled simulation models of thermal noise, phase noise, and nonlinear distortion. While this setup enables precise manipulation of impairment parameters and systematic analysis of causal disentanglement, it inherently reflects the assumptions embedded in the adopted generative models. Consequently, the learned representations are validated within the same modeling framework used for data generation, which may not capture all nonlinearities, memory effects, hardware imperfections, and environmental uncertainties encountered in practical RF transceivers. This controlled simulation approach was intentionally selected to establish foundational causal behavior under well-defined conditions and to ensure full reproducibility and fair comparison across alternative graph structures. However, extending the framework to experimentally measured RF datasets and hardware-in-the-loop validation constitutes an essential direction for future work to confirm robustness and generalization under real-world operating conditions.

Another limitation of the present study relates to the simplified RF impairment models used in the simulation environment. The power amplifier is represented using a memoryless polynomial approximation, and the oscillator phase noise is modeled as a discrete-time Wiener process. While these models capture the dominant effects of nonlinear distortion and phase instability commonly considered in communication system analysis, practical RF front-end components may exhibit more complex behaviors. In particular, power amplifiers can show memory effects arising from thermal and electrical dynamics, and oscillator phase noise may contain additional spectral components beyond the simplified stochastic accumulation model adopted here. Moreover, other hardware impairments, such as in-phase and quadrature imbalance, carrier frequency offset, and direct current offsets, may also affect system performance.

Addressing these limitations through more realistic impairment modeling, adaptive causal structure learning, and complexity reduction strategies constitutes an important direction for future work.

5. Conclusions

This paper presents a causal representation learning framework for joint modeling and mitigation of coupled RF impairments in MIMO communication systems. By explicitly incorporating causal dependencies among thermal noise, phase noise, and nonlinear distortion into a structured variational learning model, the proposed approach moves beyond correlation-based compensation and enables robust, interpretable impairment mitigation. Extensive simulation results demonstrated that the proposed method consistently outperforms classical model-based receivers as well as conventional deep learning and variational autoencoder baselines across all evaluated scenarios.

Extensive simulation experiments demonstrated that the proposed method significantly improves receiver performance compared with both classical model-based receivers and correlation-based learning approaches. On average, the proposed framework achieves approximately a 57% reduction in bit error rate (BER) relative to the classical receiver, with the most pronounced improvements observed under moderate to high impairment conditions and signal-to-noise ratio (SNR) levels around 10–15 dB, where nonlinear distortion and phase noise interactions become more significant. Under these conditions, the classical receiver suffers from model mismatch due to the coupled impairment effects, while the proposed causal representation effectively isolates and compensates for the dominant distortion sources. The relative improvement varies across operating regimes, with smaller gains observed under very low impairment levels where both classical and learning-based receivers already achieve near-optimal detection performance.

In addition to BER improvements, the proposed framework achieves up to 2.2 dB output SNR gain, demonstrating improved signal reconstruction quality across the evaluated SNR range. The learned latent representations also show strong disentanglement properties, with the cross-covariance-based disentanglement score decreasing from 0.48 in conventional variational models to approximately 0.12 using the proposed causal architecture. Furthermore, robustness analysis under unseen operating conditions shows that the proposed method achieves a robustness score of 0.86, indicating stable performance when channel conditions or impairment severities deviate from the training distribution.

An important direction for future research is the experimental validation of the proposed framework using real-world RF measurements and hardware-based communication testbeds. Although the present study employs a controlled simulation environment to systematically analyze the causal interactions among thermal noise, phase noise, and nonlinear distortion, practical wireless systems often exhibit additional non-idealities and time-varying hardware behaviors that are difficult to fully capture through simulation alone. Therefore, future work will focus on evaluating the proposed causal representation learning model using experimentally measured RF datasets and hardware-in-the-loop communication platforms. Such validation will enable assessment of the robustness of the learned causal structure under realistic channel conditions, hardware imperfections, and non-stationary system behavior. Furthermore, integrating the proposed framework into practical receiver architectures will provide additional insight into its feasibility for deployment in next-generation wireless communication systems.