Hiba A. Alsawaf
| Saad A. Ayoob*
© 2026 The authors. This article is published by IIETA and is licensed under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/).
OPEN ACCESS
The development of sixth generation (6G) wireless Networks has increased the demand for efficient and reliable channel estimation techniques in Intelligent Reflecting Surface (IRS) aided massive MIMO systems. However, accurate estimation of cascaded channels remains challenging due to dynamic propagation conditions and high computational complexity. This paper proposes a lightweight deep learning (DL) framework based on Convolutional Neural Networks (CNNs) for efficient channel estimation in IRS-aided massive MIMO environments. The proposed approach introduces two low-complexity CNN architectures designed to improve cascaded channel estimation accuracy while supporting multi-user communication through a shared Network structure. The developed models are evaluated against conventional estimation techniques, including Least Squares (LS), Orthogonal Matching Pursuit (OMP), and Minimum Mean Square Error (MMSE), as well as recent DL approaches such as Denoising CNN and Iterative Shrinking-Thresholding Algorithm Network (DnCNN-ISTANET). Simulation results demonstrate that the proposed framework achieves superior estimation accuracy with reduced computational complexity across different signal-to-noise ratio (SNR)conditions. Among the proposed models, the second architecture consistently provides the best overall performance, outperforming existing benchmark methods, particularly at high SNR levels.
channel estimation, intelligent reflecting surface, deep learning, massive MIMO
Massive MIMO is an integral part of 5G communication systems, ensuring spectral efficiency at high rates by leveraging spatial diversity. Hybrid beamforming can be utilized in such applications, yet it is difficult to integrate it in mm-wave transmission systems because of the challenges posed by high power consumption and hardware architecture complexity employed [1-3]. Therefore, Intelligent Reflecting Surface (IRS) are an appealing option that combines high efficiency, low physical complexity, and economic cost [4-6]. A reconfigurable intelligent surface (RIS) is a two-dimensional electromagNetic surface that consists of an array of reconfigurable passive reflecting elements, which are manufactured using metamaterials [7, 8]. IRS are programmable meta-surfaces whose operational properties can be adjusted via a backhaul control link to the base station (BS). The control allows for real-time manipulation of the phase and amplitude of the reflected signal, and thus the RIS can be utilized as a reflective surface in wireless communication systems to improve received signal power, extend coverage, and suppress interference [4, 9, 10]. Although RISs offer a low-cost and architecturally simple architecture, they pose additional challenges, most notably the need to address two wireless paths: the direct path between the BS and the user, and the composite path resulting from reflections across the RIS surface between the BS and the user [11, 12]. For channel estimation IRS systems, a transmission method based on Orthogonal Frequency Division Multiplexing (OFDM) was proposed by Zheng and Zhang [13], while a sparse matrix factorization approach was proposed by Alsawaf and Ayoob [14] for channel estimation. The significant increase in the difficulty of channel estimation is one of the most critical technical challenges in wireless Networks with IRS, due to the high number of elements in the surfaces. Deep learning (DL) techniques can be leveraged to reduce this complexity, which provides computationally efficient solutions and reduces the burden associated with the traditional estimation process [14]. Training a DL Network with a heterogeneous and diverse set of channel properties enables the Network to learn to react to environmental variation, such as user mobility, in a more robust and stable manner. Moreover, channel update frequency is reduced, which reduces the system's computational expense [15]. It is worth noting that in large intelligent surface-enhanced communication systems within massive MIMO environments, DL techniques have been employed in the design of reflected beamforming [16] as well as in the signal detection process [17]. Conventional estimation techniques such as Least Squares (LS) and Minimum Mean Square Error (MMSE) often suffer from excessive pilot overhead and degraded estimation accuracy in dynamic propagation environments. Moreover, traditional DL architectures, including Convolutional Neural Network (CNN) and Deep Neural Network (DNN) based models, exhibit limited capability to capture long-range spatial dependencies and adapt to rapidly varying IRS configurations, particularly in large-scale deployments [18]. Several recent studies have explored optimization-based DL frameworks and hybrid frameworks to improve channel estimation performance in IRS. Deep Unfolding Networks and hybrid architectures combining CNNs and Transformers have shown promising results in reducing the additional load of directional data and improving estimation efficiency in large MIMO and IRS-supported millimeter-wave systems. Despite these advances, current methods still face practical limitations related to training complexity, computational load, and robustness under imperfect channel state information (CSI) conditions [19]. Therefore, developing computationally efficient, highly reliable frameworks that can adapt to dynamic wireless environments supported by IRS remains an open research challenge and an important focus in future 6G communication systems.
In this paper, a DL-based approach for channel estimation in mm-Wave systems with massive multiple-input multiple-output (massive MIMO) assisted by IRS is proposed. It proposes two Networks for the estimation of the direct and cascaded channels in the DL scheme and assumes the availability of a deep Network at each user for the estimation of its channel. The received pilot signals feed the CNN with them, which establishes a nonlinear association between received signals and channel data.
This paper presented the estimation of both cascaded and direct channels in a downlink transmission scenario. Here, each user employs the received pilot signals as input to a DNN for estimating its respective channel. The Network is trained using diverse channel realizations for enhancing the robustness and accuracy of the estimation process. During the inference phase, the model's performance is evaluated with the help of test data that is statistically independent of the training set and hence gives an unbiased estimate of the accuracy of the channel estimation and the effectiveness of the proposed methods (proposed Net1 and proposed Net2).
It has been considered an IRS-assisted millimeter-wave massive MIMO system. The system consisted of a BS with B antennas, serving Q single-antenna users, and an IRS with N passive reflecting elements, as illustrated in Figure 1. Each element of the IRS creates a phase shift in the signal received from the BS before redirecting it to the user. The phase of every element of the IRS can be controlled by the PIN diodes, which are commanded by the backhaul link [20, 21].
Figure 1. Intelligent reflecting surfaces (IRS) assisted mm-Wave massive MIMO scenario
The BS employs a baseband precoder $r=\left[r_1, \ldots, r_Q\right] \in$ $\mathbb{C}^{B \times Q}$ to transmit data symbols $s_q \in \mathbb{C}$. Thus, the downlink $B \times 1$ transmitted signal becomes $\bar{s}=\sum_{q=1}^Q \sqrt{\gamma_q} \bar{r}_q s_q$, where $\bar{r}_q=\frac{r_q}{\left\|r_q\right\|_2}$, and $\gamma_q$ refers the power allocated at $q^{\text {th}}$ user. The user's signal reaches the receiver through two channels: a direct channel from the BS, and another channel through the IRS. The following mathematical formula can express the received signal from the $q^{\text {th}}$:
$\mathscr{Y}_q=\left(h_q^H+v_q^H \Psi^H G^H\right) \bar{s}+n_q$ (1)
where, $n_q \sim \mathcal{C} \mathcal{N}\left(0, \sigma_n\right), h_q \in \mathbb{C}^B$: represented the direct channel from BS to $q^{\text {th }}$ user. $v_q^H \in \mathbb{C}^B$ refers IRS-assisted channel between the IRS and $q^{\text {th }}$ user, the diagonal matrix is $\Psi \in \mathbb{C}^{N \times N}, \Psi=\operatorname{diag}\left(\beta_1 e^{j \emptyset_1}, \ldots, \beta_N e^{j \emptyset_N}\right), n=1, \ldots, N$, and $\beta_n \in\{0,1\}$ represented the on/off state of IRS elements. Since the IRS elements cannot be completely switched on or off in actuality, they can be represented as $\beta_n=\left\{\begin{array}{ll}1-\epsilon_1 & O N \\ 0-\epsilon_0 & O F F\end{array}\right.$ for $\epsilon_0, \epsilon_1 \geq 0~[22], \emptyset_n \in(0,2 \pi)$ represents the phase shift caused by the reflective elements in the IRS system, and $G \in \mathbb{C}^{B \times N}$ is the channel between BS and IRS.
In the mm-Wave transmission, the Saleh-Valenzuela model has been used to model the channel using the geometric channel model with finite dispersion [13, 21]. The $N_h, N_v$, and $N_G$ paths are also assumed to be included in the mm-Wave channels $h_q, v_q$ and $G$. So, it can represent the channels $h_q$ and $v_q$ as:
$h_q=\sqrt{\frac{B}{h_q}} \sum_{n_h=1}^{N_h} \alpha_h \mathbb{a}_h\left(\theta_h\right)$ (2)
$v_q=\sqrt{\frac{N}{v_q}} \sum_{n_p=1}^{N_v} \alpha_v \mathbb{a}_v\left(\theta_v\right)$ (3)
where, $\left\{\alpha_h, \alpha_v\right\}$ are the gains of complex channel and $\left\{\theta_h\right.$, $\left.\theta_v\right\}$ represented the received path angles for corresponding channels. $\mathbb{a}_h(\theta)$ and $\mathbb{a}_v(\theta)$ are steering vectors associated with the angles of the paths, and can be expressed as follows [23]:
$\begin{aligned} & \mathbb{a}_h(\theta)=\frac{1}{\sqrt{B}}\left[e^{j \omega_o}, \ldots \ldots, e^{j \omega_{B-1}}\right]^T, \\ & \mathbb{a}_v(\theta)=\frac{1}{\sqrt{N}}\left[e^{j \omega_o}, \ldots \ldots, e^{j \omega_{N-1}}\right]^T\end{aligned}$ (4)
where, $\omega_{\ell}=\ell \frac{2 \pi d}{\lambda} \pi \sin (\theta), d=\frac{\lambda}{2}$ represent array spacing for wavelength $\lambda$. The BS-IRS channel is expressed as [24-26]:
$G=\sqrt{\frac{B N}{N_G}} \sum_{n_G=1}^{N_G} \alpha \mathbb{a}_{B S}\left(\theta_{B S}\right) \mathbb{a}_{I R S}^H\left(\theta_{I R S}\right)$ (5)
where, $\alpha \in \mathbb{C}$ refers the complex gain, $\left\{\theta_{B S}, \theta_{I R S}\right\}$ are the angle of arrival (AOA) and the angle of departure (AOD) of the paths. $\mathbb{a}_{B S}\left(\theta_{B S}\right)$ and $\mathbb{a}_{I R S}\left(\theta_{I R S}\right)$ are the steering vectors. The cascaded channel matrix between BS and $q^{\text {th }}$ user is represented by $G_q \in \mathbb{C}^{B \times N}$ and given $G_q=G \Gamma_q, \Gamma_q=$ $\operatorname{diag}\left\{v_q\right\}$. Consequently, it can write $G \Psi v_q=G_q \psi, \Psi=$ $\operatorname{diag}(\psi)$ [27].
The proposed two DL architectures use the received pilot symbols as input features to facilitate the estimation of both direct and cascaded channel.
3.1 Channel estimation of direct and cascaded channels
For the downlink transmission scenario, the BS transmits a set of orthogonal pilots denoted by $x_p \in \mathbb{C}^B$, and each pilot is transmitted over one coherence interval, with $p=1, \ldots, P$ and $P \geq B$. Consequently, $P$ is the total number of channels needed to estimate the direct channel. The received signal at $q^{\text {th}}$ is given by:
$y_q=\left(h_q^H+\psi^H G_q^H\right) \mathrm{X}+\mathrm{n}_q$ (6)
This equation represents the pilot signal reception model for channel estimation using DL or traditional estimation algorithms. Where the matrix of pilot signal $\mathrm{X}=$ $\left[\mathrm{x}_1, \ldots, \mathrm{x}_P\right] \in \mathbb{C}^{B \times P} \quad, \quad y_q=\left[y_{q, 1}, \ldots, y_{q, P}\right] \quad$ and $\quad \mathrm{n}_q=$ $\left[n_{q, 1}, \ldots, n_{q, P}\right]$ are $1 \times P$ row vectors and $\mathrm{n}_q \sim \mathcal{C} \mathcal{N}\left(0, \sigma_n I_P\right)$. Pilot training consists of two stages: direct channel estimation $\left(h_q\right)$ and cascade channel estimation $\left(G_q\right)$. The direct channel is estimated in the first training stage, with all IRS elements disabled. When the PIN diodes are disabled in the IRS elements, the elements become nearly transparent, meaning that the insertion loss is almost zero. Thus, the signal passes directly without significant IRS influence. This approach allows for step-by-step channel estimation using training data used in DNN hence positively contributing to the improvement of channel estimation accuracy. Therefore, the equation of received signal at $q^{t h}$ user is given by [20, 28]:
$y_{\text {direct}}=h_q^H \mathrm{X}+\mathrm{n}_q$ (7)
The label of the deep Network was chosen to be the direct channel $h_q$, and the corresponding input data is $y_{\text {direct}}$. After estimating the direct channel, the cascaded channel ($G_q$) is estimated in the second stage of training. $\mathrm{P}=\mathrm{B}$ pilot signals are sent when a single IRS element at a time is turned on. Here, the BS utilizes the microcontroller device in the backhaul link to ask the IRS to switch on one IRS element at a time. The vector of reflect beamforming for the $n^{\text {th}}$ frame becomes $\psi^{(n)}=\left[0, \ldots, 0, \psi_n, 0, \ldots, 0\right]^T, \beta_{\bar{n}}=\{0: \bar{n}=1, \ldots, N, \bar{n} \neq n\}$, this means that all elements $\bar{n}$ that are not equal to $n$ are set to zero, i.e., the other elements are disabled. At $q^{\text {th}}$ user, the received signal from cascaded channel is given by [14, 27]:
$y_C^{(q, N)}=\left(h_q^H+g_{q, n}^H\right) \mathrm{X}+\mathrm{n}_{q, n}$ (8)
where, $y_C{ }^{(q, N)}=\left[\mathscr{Y}_{C, 1}, \ldots, \mathscr{Y}_{C, P}\right]$, and $\mathrm{n}_{q, n}=\left[n_{q, 1}, \ldots, \mathrm{n}_{q, P}\right]$ are $1 \times P$ row vectors. The $\mathrm{n}^{\text {th}}$ column of $G_q$ is represented in Eq. (8) by $g_{q, n}$, which is $g_{q, n}=G_q \psi^{(n)}$. Consequently, the $g_{q, n}$ LS estimate becomes into [28-30]:
$\hat{g}_{q, n}=\left(y_C \mathrm{X}^H\left(\mathrm{XX}^H\right)^{-1}\right)^H-h_q$ (9)
With $\hat{h}_q$, the Eq. (9) can be solved for $n=1, \ldots, N$. The estimated cascaded matrix is then formed as $\hat{G}_q=$ $\left[\hat{g}_{q, 1}, \ldots, \hat{g}_{q, P}\right]$.
3.2 Received pilot signals
The signal received at the preamble stage was used as the input to the deep Network. The input-output pairs are formed as follows: $y_{\text {direct }}, h_q$ for direct channel estimation and $y_C, g_{q, n}$. For cascaded channel estimation. To input data to a deep Network, real, imaginary, and absolute values are used for each element in the received signal. Although using only real or imaginary values is still possible, as noted in Dong et al. [31]. In the study [32] have shown that using a three-channel data representation significantly improves performance. This is because this representation increases the amount of information extracted from the signal, enhancing hidden features in the input data and thus helping the deep Network achieve more accurate channel estimation. The input matrix for the direct channel is formed by defining the input matrix $\mathrm{X}_{d c}$ as a real valued three channel matrix of size $\sqrt{B} \times \sqrt{B} \times 3$. To improve the use of 2D convolutional filters, the received signal $y_{\text {direct }}$ is divided into $\sqrt{B}$ sub vectors and then placed into $\sqrt{B}$ columns. The three channels of the $\mathrm{X}_{d c}$ matrix are defined as, channel $1 \rightarrow \operatorname{vec}\left\{\left[\mathrm{X}_{d c}\right]_1\right\}=$ $\operatorname{Re}\left\{y_{\text {direct }}\right\}$, channel $2 \rightarrow \operatorname{vec}\left\{\left[\mathrm{X}_{d c}\right]_2\right\}=\operatorname{Im}\left\{y_{\text {direct }}\right\}$ and channel $3 \rightarrow \operatorname{vec}\left\{\left[\mathrm{X}_{d c}\right]_3\right\}=\left|y_{\text {direct }}\right|$. In the same way, $X_{c c}$ is defined as a real valued three channel matrix of size $N \times B \times 3$. The three channels of the $X_{c c}$ matrix are defined as follows: channel $1 \rightarrow \operatorname{vec}\left\{\left[\mathrm{X}_{c c}\right]_1\right\}=\operatorname{Re}\left\{\tilde{y}_q\right\}$, channel $2 \rightarrow$ $\operatorname{vec}\left\{\left[\mathrm{X}_{c c}\right]_2\right\}=\operatorname{Im}\left\{\tilde{y}_q\right\}$ and channel $3 \rightarrow \operatorname{vec}\left\{\left[\mathrm{X}_{c c}\right]_3\right\}=\left|\tilde{y}_q\right|$, where $\tilde{y}_q=\left[y_C{ }^{(q, n)^T}, \ldots, y_C{ }^{(q, N)^T}\right]^T$ is a vector of size $L M \times 1$ containing the received pilot signals. After channel data is fed into the deep learning Network (DNN), a vector representation of the channels is output. The output is a simplified form of the channel matrices, so they can be easily analyzed by the Network. The direct channel output is $Out_{d c}=$ $\left[\operatorname{Re}\left\{y_{\text {direct }}\right\}^T, \operatorname{Im}\left\{y_{\text {direct }}\right\}^T\right]^T$, the real and imaginary values are combined into a vector of size $2 B \times 1$. The cascaded channel output is $Out_{c c}=$ $\left[\operatorname{Re}\left\{\operatorname{vec}\left\{G_q\right\}\right\}^T, \operatorname{Im}\left\{\operatorname{vec}\left\{G_q\right\}\right\}^T\right]^T$, the matrix $G_q$ is transformed into a vector using $\operatorname{vec}\left(G_q\right)$ so that its elements are arranged into a single vector. The real and imaginary parts are separated and then combined into a vector of size $2 M L \times 1$. Training data is generated by creating input-output pairs. The input can be represented by matrices $X_{d c}$ and $X_{c c}$, which represent the channels using three data channels (real, imaginary, and absolute magnitude). The output is represented by vectors $out_{d C}$ and $out_{C C}$, which represent the channel in vector form. Multiple simulations are performed to generate large numbers of these pairs, allowing the deep Network to learn different patterns to improve channel estimation. Algorithm 1 provides a description of how input-output pairs for different realizations should be created to obtain training data.
|
Algorithm 1: Intelligent Reflecting Surfaces assisted channel estimation with deep learning |
|
Input:
Output:
net $_{d c}^{\text {Net }_1}$, net $_{c c}^{\text {Net }_1}$, net $_{d c}^{\text {Net }_2}$, net $_{c c}^{\text {Net }_2}$.
1. System Initialization:
2. Channel Generation:
3. Training Data Generation:
4. Model Training:
5. Performance Evaluation:
6. CCDF analysis:
7. Robustness Analysis: Angle Mismatch Evaluation: $\theta^{\prime}=\theta+\Delta \theta$ |
The proposed Net1 (IRS-Aware Deep Residual Channel Estimation Network (IRS-DRCEN)) shows in Figure 2 consists of a Deep Convolutional Neural Network architecture optimized for the task of communication channel estimation. It relies on a series of successive convolutional layers with skip connections to enhance gradient flow through the Network. The Network starts with an input layer, followed by a preliminary convolutional layer with a 3 × 3 kernel and 128 filters.
Figure 2. Network1 (Net1) architecture
The Network contains three main residual blocks, each consisting of two paths: a main path containing two convolutional layers with batch normalization and PReLU activation, and a residual path that directly passes the input to the summation layer. The output is processed through final convolutional layers to reduce the dimension to two channels (representing the real and imaginary parts). The results are then flattened and concatenated with a fully connected layer to generate the final channel estimate. The Network relies on a regression loss function to optimize the weights during training, making it suitable for channel estimation in complex communication systems. The proposed Net2 architecture (IRS-Channel optimized residual Network (IRS-CorNet) in Figure 3 begins with a 3 × 3 convolutional layer (128 filters) with batch normalization and ReLU activation. Two sequential residual blocks follow, each consisting of two 3 × 3 convolutions (128 filters), batch normalization, and a residual connection added before ReLU activation. Then, after the residual blocks, it employs a 3 × 3 convolutional layer (64 filters) and another convolutional layer (2 filters). The output is flattened and passed to a fully connected layer and then a regression layer.
Figure 3. Network2 (Net2) architecture
The performance of the proposed framework for channel Network formation was also compared with a few DL techniques, i.e., MLP. In the simulation, B = P = 64, N = 64, and Q = 8. The simulation of the physical environment was created by the created by the $N_h=N_v=N_G=4$ paths, while user directions were randomly sampled within the interval $[-\pi, \pi]$.
Furthermore, to test Network robustness in extreme environments, the testing range was extended to include extreme noise levels from 0 dB to 30 dB in 5 dB increments.
Unless stated otherwise, default initial values $\epsilon_1=\epsilon_o=0$ were taken. 70% of all data generated was utilized for training and 30% for validation during training. After completing the training stage of the model on pilot training data, a new set of pilot signals, different from those used during the training phase, is generated in order to test the model's ability to generalize and accurately predict outside of the original data set. In this context, T = 100 Monte Carlo simulations are performed to evaluate the statistical performance of the model under different conditions. The Normalized Mean Square Error (NMSE) is a common and accurate criterion for evaluating the quality of Channel Estimation. The NMSE of the matrix $G_k$ is defined by the following relationship [33-35]:
$G_q=\frac{1}{T} \sum_{j=1}^J \frac{\left\|G_q-G_q^{(j)}\right\|_F^2}{\left\|G_q\right\|_F^2}$ (10)
NMSE measures the degree to accuracy the estimated values reflect compared to actual values, and the smaller NMSE values indicate higher channel estimation accuracy, showing the efficiency of the proposed model in extracting channel information from different test environments.
(a) Direct channel estimation
(b) Cascaded channel estimation
Figure 4. Normalized Mean Square Error (NMSE) Vs. signal-to-noise ratio (SNR) for two methods
Figure 4(a) shows the relationship between the signal-to-noise ratio (SNR) and the normalized mean square error (NMSE) to evaluate the performance of three channel estimation methods in a communication system supported by RISs. The compared methods included traditional LS estimation and two proposed neural Networks (Proposed Net1 and Proposed Net2). From the figure, the performance of all methods improves with increasing SNR, which is consistent with the theoretical nature of channel estimation, where the estimation accuracy increases as the relative noise level decreases. However, the two proposed neural Networks clearly outperform the LS method at all SNR values, demonstrating the effectiveness of DL-based models in capturing the structural characteristics of the channel and compensating for the effects of noise. On the other hand, it is shown that Proposed Net2 consistently outperforms Proposed Net1, especially in the medium and high SNR ranges (i.e., from 10 dB onwards). This indicates that the architectural or training improvements incorporated into Net2 have enhanced the model's ability to generalize and predict more accurately under different channel conditions. It also shows that the performance gap between traditional (LS) and neural Network-based methods increases with increasing SNR, indicating that traditional methods suffer from performance limitations that are difficult to overcome, while intelligent methods can better leverage the improved signal quality. Table 1 shows the comparison between Net1 and Net2.
Table 1. Compression between Net1 and Net2
|
Feature / Comparison Metric |
Net1 |
Net2 |
Impact on Channel Estimation Performance |
|
Primary activation function |
PReLU |
ReLU |
Net1 excels at phase tracking: the wireless channel parameters (H = Hreal + jHimag.) oscillate normally and symmetrically around zero. Net2's standard ReLU function reduces negative values to zero (causing the ReLU vanishing" problem) and ignores phase information. Net1's PReLU function preserves negative phase gradients through a learnable parameter ($\alpha$), significantly improving phase estimation accuracy in high-motion (Doppler) environments. |
|
Mathematical mapping |
Retains negative gradient dynamically: $\begin{aligned} & \sigma(x =\max (0, x)+\alpha \cdot \min (0, x)\end{aligned}$ |
Forces all negative values to zero: $\sigma(x)=\max (0, x)$ |
PReLU provides a continuous non-zero derivative for negative values, ensuring uninterrupted backpropagation during training. |
|
Dimensionality & compression |
Compresses features from 128⟶64⟶2 channels |
Maintains 128 full channels right before mapping to the 2 channels output |
Net1 for Noise Filtering; Net2 for Fine Details: The 64-channel bottleneck in NET1 acts as a low-rank spatial filter that strips out high-frequency noise (AWGN), yielding superior MSE in low-signal-to-noise ratio (SNR) regimes. Conversely, the 128-channel retention in NET2 expands model capacity, enabling it to reconstruct highly detailed multi-path components in high-SNR regimes. |
|
Final layer regularization |
Lacks a batch Normalization layer at its intermediate 64-channel compression stage |
It features an explicit batch normalization layer paired with a 128-channel block just before output |
Omitting BN in the bottleneck Net1 Network prevents the dispersion of subtle and weak signal characteristics at low signal-to-noise ratios. Including the BN equation in Net2 unifies the transformation of internal variables, accelerating Network convergence and improving training stability when processing large channel state information (CSI) arrays. |
|
Pre-flatten output stage |
Conv2D 3 × 3 mapping directly to a Flatten layer without a preceding local BN |
Conv2D 3 × 3,2 following a heavily regularized and nonlinear block (BN+ReLU) |
This dictates how the raw Real and Imaginary (I/Q) channel matrices are decoupled. Net1 maps aggregated, noise-filtered features, while Net2 maps deeply non-linear representations. |
Figure 4(b) compares the performance of three different methods for channel estimation in a wireless communication system using NMSE versus SNR curves. The LS algorithm maintains near-constant performance across all SNR values, with NMSE values around -3 dB, reflecting the method's limitations in leveraging improved signal quality. In contrast, both proposed neural Networks achieve significantly improved performance compared to LS, especially at SNRs above 0 dB, where NMSE decreases significantly with increasing SNR. Notably, proposed Net2 clearly outperforms Proposed Net1 at all SNR values, demonstrating its high efficiency in exploiting the statistical and structural properties of the signal and channel to improve estimation. For example, at SNR = 20 dB, Proposed Net2 achieves an NMSE of approximately -45 dB, compared to -38 dB for Proposed Net1, while the LS method remains at around -3 dB. These results indicate the effectiveness of DNN, particularly Proposed Net2, in improving channel estimation accuracy compared to traditional methods, especially in environments with high signal quality. This improvement is likely to be due to the use of more sophisticated learning mechanisms in Net2, such as residual layers, which make it better able to capture complex patterns in channel data.
Figure 5(a) displays the Complementary Cumulative Distribution Function (CCDF) of the Normalized Mean Squared Error (NMSE) for three channel estimation methods: LS, Proposed Net1, and Proposed Net2. CCDF estimates the statistical performance of these estimation methods across different channel realizations. The Figure clearly illustrates the improved performance of the proposed neural Network-based methods (Proposed Net1 and Proposed Net2) compared to the traditional LS estimation. For any probability on the y-axis, NMSE values of Proposed Net1 and Proposed Net2 are significantly lower than those of the LS method. What this implies is that the proposed Networks are less prone to noise and fluctuations in channels, which leads to better accuracy in channel estimation in more cases. Figure 5(b) shows the CCDF curves of the NMSE values for three different channel estimation algorithms. As shown, the traditional (LS) method performs poorly, with most samples concentrated at NMSE values above 0 dB. In contrast, the two proposed neural Networks achieve significant performance improvements. Proposed Net2 demonstrates a high error reduction capability, with its NMSE distribution concentrated in the negative region, demonstrating its estimation efficiency under complex channel conditions. These results confirm the feasibility of using DNNs to improve channel estimation accuracy compared to traditional methods. Figure 5(a) and (b) are important tool for evaluating the effectiveness of different channel estimation techniques and highlights the superiority of neural Networks in estimation accuracy within IRS systems.
Overall, the results demonstrate that incorporating DL techniques into the design of channel estimation systems in RIS-enabled communications environments can make a significant difference in performance, especially in millimeter wave (mm-Wave) systems, where channel characteristics are more complex and require more expressive and flexible estimation models.
(a) Direct channel estimation
(b) Cascaded channel estimation
Figure 5. Complementary Cumulative Distribution Function (CCDF) of the Normalized Mean Squared Error (NMSE) for three channel estimation methods
(a) Direct channel estimation
(b) Cascaded channel estimation
Figure 6. The performance of Normalized Mean Square Error (NMSE) Vs. Angle Mismatch standard deviation
Figure 6(a) illustrates the Normalized mean squared error (NMSE) performance of several channel estimation methods under various standard variations of angular mismatch for the direct channel. The traditional LS estimator exhibits the highest NMSE values compared to the other methods and exhibits low sensitivity to angular deviations, but with poor estimation accuracy. In contrast, the proposed DL-based estimators, denoted Net1 and Net2, perform significantly better than the LS method. In particular, the proposed Net2 model achieves the best performance, maintaining an NMSE of approximately -47 dB across all angular mismatch levels examined. These results highlight the model's ability to withstand angular estimation errors and confirm the effectiveness of DL techniques in overcoming typical shortcomings in practical systems supported by reflecting intelligent surfaces in massive MIMO environments. Figure 6(b) presents the NMSE performance of different channel estimation techniques vs. the standard deviation of angular mismatch over an angular range of 0° to 10°. The conventional LS method possesses relatively poor performance, with an NMSE of approximately 3 dB at all levels of angular error, indicating its high angular inaccuracy sensitivity. In contrast, the two proposed neural Networks (Net1 and Net2) perform much better with low and consistent NMSE values of approximately -47 dB and -53 dB, respectively, demonstrating high robustness against angular error. The stability of the curves of NMSE with changing angular error reflects the capability of the proposed models to generalize and adapt in the presence of spatial uncertainty.
(a) Direct channel estimation
(b) Cascaded channel estimation
Figure 7. The Performance of Normalized Mean Square Error (NMSE) Vs. OFF state leakage ratio
(a) Direct channel estimation
(b) Cascaded channel estimation
Figure 8. The relationship between Normalized Mean Square Error (NMSE) and signal-to-noise ratio (SNR) for comparing channel estimation algorithms
Figure 7(a) illustrates the NMSE performance of the direct channel as a function of the inactive state leakage ratio ($\epsilon_o$). All curves are nearly horizontal, indicating that the estimation performance is stable and remarkably insensitive to changes in the leakage ratio within the studied range. The LS method registers a value of approximately −30 dB across all values, reflecting consistent but less efficient performance compared to the proposed methods. In contrast, Proposed Net2 achieves a significant improvement at -36 dB, while Proposed Net1 delivers the best performance at -37.5 dB. The difference between Net1 and LS is 7 dB, which translates to a reduction of the error capacity to more than half, according to the logarithmic relationship of the decibel scale. The consistent performance across variations in ($\epsilon_o$) indicates that the effect of inactive-state leakage on the direct channel is relatively limited. However, the DL-based models maintain their superiority due to their greater ability to represent the statistical structure of the channel. Overall, the results confirm the robustness of the proposed methods and their consistent superiority over traditional linear estimation. Figure 7(b) illustrates the performance of NMSE as a function of the inactive state leakage ratio ($\epsilon_o$) for cascaded channel estimation. We observe that the LS algorithm maintains a near-constant value of Δ2.5 dB across all values, indicating its poor sensitivity to changes in the leakage ratio and its inability to model the effects of nonlinearity or model mismatch. In contrast, the two proposed Networks achieve significantly superior performance; Proposed Net2 registers values between -39 and -42 dB, while Proposed Net1 achieves the best performance between -46 and -49 dB. A consistent downward trend is also observed in the NMSE as $\epsilon_o$ increases, reflecting the ability of deep models to learn the statistical structure of the leakage and compensate for its effects. Figure 8(a) shows a performance comparison between traditional methods and various DL techniques for channel estimation, using the normalized mean square error (NMSE) as a performance indicator across a variety of signal-to-noise ratios (SNRs). The traditional LS model exhibits relatively poor performance, with significantly higher NMSE values across all SNR levels. Although MMSE [34] and OMP [35] techniques achieve relative improvements, they fall short of the estimation accuracy provided by DL models. In contrast, the proposed Network, Proposed Net1, exhibits improved performance compared to traditional and hybrid methods such as MMPGA-LS [36], while Proposed Net2 outperforms all other models, achieving the lowest NMSE values at various SNR levels. Figure 8(b) compares the performance of a range of channel estimation techniques, including traditional methods, hybrid algorithms, and DL models, in terms of the normalized mean square error (NMSE) in dB versus the SNR for cascaded channel estimation. The results of the LS method show almost consistently poor performance across all SNR values, reflecting its high sensitivity to noise and inefficiency in modern communications environments.
In contrast, optimized traditional methods such as MMSE, OMP, and the MMPGA-LS combination offer better performance, but their improvement remains limited at high SNR values. On the other hand, DL-based models, particularly DnCNN-ISTANET [37] and the two proposed Networks (Proposed Net1 and Proposed Net2), demonstrated significantly superior performance. Proposed Net2 performed best among all models, with its NMSE value dropping below -50 dB at SNR = 30 dB, indicating high channel estimation accuracy. Proposed Net1 and Proposed Net2 algorithms were compared with traditional OMP, MMSE, and LS algorithms, as well as learning algorithms (DnCNN-ISTANET and MMPGA-LS), in terms of basic assumptions, architectural analysis, and techniques used, as shown in Table 2. The computational complexity is illustrated in Table 3.
Table 2. The comparison between Least Squares (LS), proposed Net1, proposed Net2, Minimum Mean Square Error (MMSE), OMP, MMPGA-LS, and DnCNN-ISTANET
|
Algorithm |
Basic Assumptions |
Architectural Analysis and Techniques Used |
|
LS |
Direct Linear Estimation |
LS: Direct estimation using $y_C \mathrm{X}^H\left(\mathrm{XX}^H\right)^{-1}$, low complexity but sensitive to noise and channel misfitting |
|
Proposed Net1 |
Deep Learning to Improve Estimation |
CNN with PReLU and two remaining blocks: ▪️ Initial feature extraction ▪️ Two blocks (Conv-BN-PReLU) with skip connections ▪️ Flatten and FC for final estimation |
|
Proposed Net2 |
Improving Estimation Accuracy and Deepening the Network |
Deeper CNN with ReLU and two residual blocks: ▪️ Each block: Conv → BN → ReLU twice ▪️ Skip connections between blocks ▪️ FC & Regression Layer for the output |
|
MMSE [36] |
Knowledge of Implicit Channel Statistics |
Minimum Mean Square Error: Uses channel and noise prior statistics to minimize the mean square error |
|
OMP [37] |
Symmetric and Compressed Channel (Sparse) |
Orthogonal Matching Pursuit: An algorithm based on extracting rare signals using recursive projections |
|
MMPGA-LS [38] |
LS Optimization Using a Genetic and Linear Algorithm |
ResNet based on LS inputs and MMPGA outputs: ▪️ Four residual blocks ▪️ Each block contains Conv → BN → ReLU twice ▪️ Skip connection adds the input to the block output ▪️ Deep learning based on MMPGA outputs |
|
DnCNN-ISTANET [39] |
Using Deep Learning and Denoising |
DnCNN-ISTANET: ▪️ ISTANET for recursive estimation of rare signals ▪️ DnCNN for denoising CNN ▪️ Combining the two Networks to achieve accurate estimation in noisy environments |
Aligning the model with different-dimensional IRS configurations can be efficiently achieved through Transfer Learning techniques, allowing the reuse of extracted features without the need for retraining from scratch, which is a key focus for future studies. To bridge the gap between theoretical gains and practical application, the performance benefits offered of Proposed Net2 model offer direct hardware and economic advantages. First, its high accuracy reduces the number of pilots required, providing greater bandwidth for actual data transmission without the need for additional radio frequency bands. Second, its high durability allows smart surfaces (L = 64) to be operated using low-cost hardware (such as 1-bit or 2-bit precision reflectors) instead of expensive, continuously oriented components. Finally, data processing occurs centrally at the broadcasting station, conserving battery power on the user equipment side.
Table 3. Computational complextity
|
Algorithm |
Computational Complextity |
|
MMSE |
$\mathcal{O}\left(M^3\right)$ |
|
OMP |
$\mathcal{O}(K . N . M)$ |
|
MMPGA-LS |
$\mathcal{O}\left(G . P . M^3\right)+\operatorname{ResNet}$ |
|
DnCNN-ISTANET |
$\mathcal{O}($ iterative Steps $\times$ CNN FLOPs $)$ |
|
Net1 |
$\mathcal{O}($ Forward FLOPs $)$ |
|
Net2 |
$\mathcal{O}($ Forward FLOPs $)$ |
This paper presented a DL-based framework for channel estimation in IRS aided massive MIMO systems through the development of two lightweight CNN architectures designed to improve the estimation accuracy of both direct and cascaded channels. The simulation results demonstrated that the proposed models consistently outperform conventional estimation methods aa well as recent DL-based approaches, achieving significant improvements in NMSE performance while reducing computational complexity, particularly at high SNR levels. Among the developed models, the second architecture achieved the best overall performance, confirming the effectiveness and robustness of the proposed framework in dynamic wireless environments.
The practical significance of this work lies in its potential applicability to future 6G wireless Networks, which require intelligent and efficient solutions capable of supporting ultra-reliable communications, massive connectivity, and low latency services. In this context, DL-based channel estimation techniques can substantially enhance spectral efficiency and communication reliability in IRS-aided wireless systems, making them a promising candidate for next generation wireless infrastructures.
Despite the promising results achieved by the proposed model in estimating IRS channels, there are some limitations to consider. First, the performance of the current model depends on the stability of the trained reflective surface dimensions. Second, the simulation assumes channel stability during the estimation period. Therefore, future directions aim to develop hybrid models combining CNN and LSTM to enhance predictive capabilities in highly dynamic environments, as well as explore architecture-agnostic learning techniques to ensure system resilience to structural changes in IRS arrays.
From a practical implementation perspective, the proposed models are designed to be scalable for large-scale deployments of IRS. The model's convolutional architecture enables efficient processing of high-dimensional channel data, making it suitable for integration into CPUs such as cloud-RAN. In dynamic urban or industrial environments, the model's robustness, demonstrated through intensive Monte Carlo simulations, exhibits high adaptability to varying multipath conditions and SNRs. Furthermore, the high-resolution channel estimates provided by this model can be directly integrated with existing beamforming techniques. The near-instantaneous provision of CSI eliminates the need for extensive codebook searches, significantly reducing overhead and latency in real-time 6G communication systems.
|
aBS |
BS steering vector |
|
ah |
Steering vector for direct channel |
|
aIRS |
IRS steering vector |
|
av |
Steering vector for IRS-assisted channel |
|
B |
Number of antennas at the base station |
|
BW |
Bandwidth (Hz) |
|
d |
Array spacing (m) |
|
fc |
Carrier frequency (Hz) |
|
G |
Channel matrix between BS and IRS |
|
Gq |
Cascaded channel matrix for qth user |
|
gq,n |
nth column of the cascaded channel matrix |
|
hq |
Direct channel vector from BS to qth user |
|
N |
Number of IRS passive reflecting elements |
|
nq |
Additive white Gaussian noise vector |
|
NG |
Number of paths in the BS-IRS channel |
|
Nh |
Number of paths in the direct channel |
|
Nv |
Number of paths in the IRS-user channel |
|
P |
Total number of pilot symbols |
|
Q |
Number of single-antenna users |
|
rq |
Baseband precoder for qth user |
|
sq |
Transmitted data symbol for qth user |
|
vq |
IRS-assisted channel vector between IRS - qth user |
|
X |
Matrix of pilot signals |
|
yq |
Received signal at qth user |
|
Greek symbols |
|
|
α |
Complex gain of the BS-IRS channel |
|
αh |
Complex gain of the direct channel |
|
αv |
Complex gain of the IRS-assisted channel |
|
βn |
Amplitude reflection coefficient of nth IRS element |
|
γq |
Power allocated to qth user (W) |
|
ϵ0 |
OFF-state leakage ratio |
|
ϵ1 |
ON-state insertion loss |
|
θ |
Path angle (rad) |
|
λ |
Wavelength (m) |
|
σn |
Noise variance |
|
ϕn |
Phase shift caused by nth IRS element (rad) |
|
Ψ |
IRS reflection phase shift matrix |
|
ψ |
Reflect beamforming vector |
|
ω |
Spatial frequency (rad/m) |
|
Subscripts |
|
|
c |
Cascaded channel (indirect path) |
|
d |
Direct channel (path without IRS) |
|
q |
Index of the user |
|
n |
Index of the IRS element |
|
Superscripts |
|
|
H |
Conjugate transpose operator |
|
T |
Transpose operator |
|
-1 |
Matrix inverse operator |
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