Introduction

The rapid development of mobile communication technology has put forward higher requirements for the efficiency and quality of signal transmission. As an emerging technology, the Intelligent Metasurface-Assisted Communication (IMAC) system can enhance communication performance by dynamically adjusting the electromagnetic wave propagation environment1. It is a digitally controlled array surface that can programmatically adjust the electromagnetic characteristics, such as phase shift and amplitude of the incident signal2. This communication method only controls the reflected signal through a controller and does not require additional RF links, thus significantly reducing hardware costs and energy consumption. It has become one of the important candidate technologies for future green communication networks3,4. At present, the IMAC system is restricted by factors such as beamforming accuracy and channel estimation error in signal transmission. If the beamforming accuracy is not high, it may lead to a decline in signal transmission quality. The results of channel estimation can help optimize the beamforming strategy and improve the efficiency and stability of signal transmission. However, the existing methods still have deficiencies in these aspects, such as high computational complexity and slow convergence speed, which limit their practical application effects in dynamic environments. In response to this, the study proposes an optimization scheme for signal transmission in an IMAC system based on improved Deep Quantum Neural Networks (DQNN). This scheme starts from the two aspects of channel estimation and beamforming to jointly optimize the signal transmission process. By introducing the Improved DQNN (I-DQNN) model and fully leveraging its advantages in nonlinear approximation and high-dimensional data analysis, the accuracy of channel estimation and the efficiency of beamforming can be enhanced. The study aims to enhance the transmission efficiency and stability of signals in complex environments by optimizing the communication transmission performance of the IMAC system. The innovation of the research lies in introducing Squeeze-and-Excitation Networks (SENet) to improve the Ghost Convolutional Neural Network (GCNN), further enhancing its feature extraction ability and computational efficiency, and effectively suppressing the interference of redundant information. In addition, the study combines it with Quantum Neural Networks (QNNs) to construct a hybrid architecture model, achieving precise prediction of channel state information and rapid optimization of beam direction.

Related works

With the development of modern technology, an increasing number of scholars have begun to pay attention to the application potential and optimization strategies of intelligent metasurfaces in different communication scenarios. M. Di Renzo et al. proposed a planar structure for dynamically controlling electromagnetic waves to address the issue of poor communication control performance in IMAC systems. This structure has been improved in terms of surface power efficiency and radiation power flux through the slope imprint vector. After the application of this structure, the communication efficiency has been improved by more than 10%5. M. Ahmed et al. found that metasurface elements exhibit dual fading in wireless communication systems, which leads to a decrease in communication quality. Therefore, it proposed to introduce an active reconfigurable strategy to enhance signal transmission stability. This strategy could effectively suppress double fading, improve signal reception quality, and reduce system error rate by about 15%6. Z. Li et al. proposed a new uplink communication system to achieve high-quality wireless communication. The system was implemented by an intelligent metasurface transceiver, which applied orthogonal frequency division multiple access to multiple users. The system adopted an alternating optimization algorithm to jointly optimize the phase shift matrix of the intelligent metasurface and the power allocation of users, resulting in a 20% increase in efficiency7. W. Mei et al. found that the current signal transmission optimization methods for intelligent metasurfaces mainly focus on wireless links that enhance single-type reflection through only one or more reflective surfaces, resulting in propagation obstruction. For this reason, it proposed a multi-intelligent hypersurface cooperative transmission scheme, which realized signal coverage enhancement by constructing multiple reflection paths. This solution could effectively solve the problem of limited signal propagation and enhance system coverage capability8. The above research results indicate that the current IMAC system has problems such as limited signal reflection paths and low energy utilization, especially in complex dynamic environments where it is difficult to achieve stable and efficient communication performance.

QNNs have strong information processing capabilities and nonlinear mapping advantages, and have broad application prospects in various fields9. Z. Qu et al. designed a diagnostic method built on QNN to accurately identify abnormal electrocardiogram data. This method was based on a quantum arrhythmia detection model, which effectively improved the feature extraction and classification accuracy of electrocardiogram data by introducing the parallelism and superposition of quantum computing. The recognition accuracy of this method on the arrhythmia database reached 98.6%10. J. Shi et al. proposed an adversarial testing framework built on QNN for complex communication environments. This framework enhanced the robustness to noise interference through quantum entanglement guidance and generated diverse test samples using quantum superposition states. After applying this method, the error rate in complex noise environments was reduced by about 35%11. T. Mahmood et al. found that the activity at the microtubule level in the brain conforms to the concept of quantum mechanics and proposed a circuit-based QNN method. This method achieved efficient modeling of neuronal activity by simulating the superposition and entanglement characteristics of quantum states in microtubules, thereby demonstrating better generalization ability and computational efficiency than traditional neural networks in EEG signal recognition tasks12. C. Wang et al. proposed an intelligent model based on QNN and PSO algorithms to improve the efficiency and reduce costs of customized tubular parts for aviation. This model predicted cross-sectional distortion, optimized processing parameters, and significantly improved the accuracy of pipe forming. This method has increased the forming qualification rate by 17.5% in practical applications, effectively shortened the product development cycle, and reduced trial and error costs13.

In summary, the existing IMAC system has made certain progress in enhancing signal coverage, but still faces bottlenecks such as path restrictions and low energy utilization efficiency in complex dynamic environments. QNNs, with their advantages in feature extraction, nonlinear mapping, and parallel computing, have demonstrated outstanding performance in biomedical recognition, communication in complex environments, and intelligent manufacturing. Therefore, the study integrates QNNs with intelligent metasurfaces and proposes a new communication optimization method.

The organization of this paper consists of five sections, namely introduction, Related Works, methodological totals, Experimental Analysis, and conclusion. The introduction part summarizes the research background, research objectives and research content. Related Works summarizes, analyzes and discusses the current research status in related fields. In the method design stage, a QNN-driven intelligent metasurface beamforming architecture was proposed, and the phase configuration of surface units was optimized through quantum state coding. During the experimental stage, the performance of the research method was experimentally verified and the results were analyzed. The conclusion section further summarizes the research content and presents the conclusion. Finally, the prospects for future research work were presented.

Method design

To improve the signal transmission efficiency and quality of IMAC, this paper proposes a signal transmission optimization model based on DQNN. This model combines DQNN and the beamforming mechanism of intelligent metasurfaces to construct an end-to-end joint optimization framework.

Design of communication signal transmission optimization model framework based on I-DQNN

To achieve efficient optimization of IMAC system signal transmission, this study designs an IMAC signal transmission optimization model framework. This framework consists of three core components: channel estimation module, beamforming optimization module, and joint optimization control module14,15,16. Among them, the channel estimation module extracts environmental features by receiving pilot signals and uses GCNN to denoise and enhance channel state information to improve estimation accuracy. The beamforming optimization module generates the optimal beam direction based on the estimation results. The joint improvement of DQNN for beamforming design enhances the network’s ability to express high-dimensional channel features by introducing a quantum neuron encoding mechanism and an adaptive entanglement strategy. The joint optimization control module coordinates the collaborative work of the two through a feedback mechanism, enhancing the system’s adaptability in time-varying channels. The framework of the IMAC signal transmission optimization model is shown in Fig 1.

Fig. 1
figure 1

The framework of the IMAC signal transmission optimization model.

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In Fig. 1, channel state information is collected through pilot signals and input into the channel estimation module. After GCNN processing, the denoised channel characteristics are output. This feature is fed into an I-DQNN model, which maps high-dimensional channel parameters into quantum state representations through quantum neuron encoding, and strengthens critical path weights using adaptive entanglement strategies. The beamforming optimization module generates a dynamic beam pattern based on this. The joint optimization control module provides real-time feedback on link quality indicators and dynamically adjusts network hyperparameters. Dual-Intelligent Metasurfaces (DIMS) are currently a key technological path for improving system capacity and coverage, demonstrating enormous potential in scenarios where communication demands are increasing. Compared to single intelligent metasurface systems, DIMS further enhances signal focusing capability and spatial multiplexing gain through collaborative beamforming and joint optimization control17,18. Therefore, this study chooses the DIMS collaborative architecture as the research object and constructs a DIMS joint beamforming optimization model. The DIMS collaborative architecture consists of two parallel deployed intelligent metasurfaces, denoted as \({\text{RIS - 1}}\) and \({\text{RIS - 2}}\), respectively. The signal at the transmitting end is set to be Mathbf, reaching \({\text{RIS - 1}}\) via wireless channel \({\text{TR1}}\), and reaching \({\text{RIS - 2}}\) via \({\text{TR2}}\). Two intelligent metasurfaces are respectively applied with independent programmable phase matrices \({\text{F1}}\) and \({\text{F2}}\) to modulate the incident signal. The modulated signal is then transmitted to the receiving end respectively through channels \({\text{R1R}}\) and \({\text{R2R}}\). Therefore, the receiving end signal \({\text{MSM}}\) can be expressed as the superposition of two reflection path signals. Specific calculation is shown in equation (1).

$${\text{MSM}} = \left( {R1R \cdot F1 \cdot TR1 + R2R \cdot F2 \cdot TR2} \right)s^{\prime\prime} + {\text{Mathbf}}$$
(1)

In equation (1), \(n^{\prime\prime}\) represents additive Gaussian white noise. The core of this model lies in jointly optimizing the two phase matrices \({\text{F1}}\) and \({\text{F2}}\) to maximize the received signal power and effectively suppress multipath interference and interference between users. The objective function of optimization is defined as maximizing the Signal-to-Noise Ratio (SNR) at the receiving end while satisfying the phase constraint, that is, each reflection unit only changes the phase without altering the amplitude. The DIMS collaborative architecture is shown in Fig. 2.

Fig. 2
figure 2

DIMS collaborative architecture.

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In Fig. 2, the DIMSs are respectively deployed near the transmitting end and the receiving end. This architecture includes a base station equipped with multiple transmitting antennas, two intelligent metasurface units, and multiple user terminals. When users send signals to blocking objects, it will lead to signal blocking and intensified resource competition, thereby affecting the overall communication efficiency. Through the coordinated beam regulation of DIMS, active suppression of interference paths and dynamic enhancement of main link gain can be achieved, thereby maintaining stable transmission in complex electromagnetic environments. The effective channel from the user to the base station is shown in equation (2).

$$h_{k} = \sum\limits_{n = 1}^{N} {N_{2} diag\left( {d_{k,n} } \right)\theta_{2} \theta_{1,n} } + H_{2k} \theta_{2} + {\text{H}}_{{1{\text{k}}}} \theta_{1}$$
(2)

In equation (2), \({\text{k}}\) is the user serial number. \({\text{N}}_{2}\) denotes the Channel Matrix (CM) from the second intelligent metasurface to the base station. \({\text{diag}}\left( \cdot \right)\) means a diagonal matrix operation, with its diagonal elements being the reflection coefficient vector of the first intelligent metasurface. \({\text{d}}_{{\text{k,n}}}\) is the CM between the \({\text{k}}\)-th user and the \({\text{n}}\)-th intelligent metasurface in the set of channel matrices. \(\theta_{1}\) and \(\theta_{2}\) are the reflection angles of two intelligent metasurfaces. \({\text{H}}_{{1{\text{k}}}}\) and \({\text{H}}_{{2{\text{k}}}}\) are the phase modulation matrices of two intelligent metasurfaces. \(\theta_{1,n}\) refers to the reflection phase shift matrix of the first intelligent metasurface. \({\text{N}}\) is the number of channel matrices. \({\text{h}}_{{\text{k}}}\) is the effective channel. The base station signal is transmitted to the intelligent metasurface unit through a frequency transmission link, and the reflection direction is optimized through a phase modulation matrix to achieve precise coverage of user terminals. The signal transmission process of the base station is shown in Fig. 3.

Fig. 3
figure 3

The process of base station signal transmission.

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In Fig. 3, digital precoding is first performed to obtain the RF chain, and then analog precoding is applied to distribute the signal to each antenna port. Subsequently, the intelligent metasurface receives the pilot signal from the base station, senses the incident angle, and adjusts the reflection phase shift matrix in real time to reflect the signal along the optimal path to the target user. The signal received by the user is shown in equation (3).

$${\text{y}} = {\text{W}}^{{\text{H}}} {\text{R}} \cdot {\text{diag}}\left( {{\text{d}}_{{\text{k,n}}} } \right) \cdot {\text{N}}_{{\text{i}}} {\text{F}}_{{{\text{RF}}}} + {\text{W}}^{{\text{H}}} n^{\prime}$$
(3)

In equation (3), \({\text{y}}\) is the received signal after all digital merging processing. \({\text{W}}^{{\text{H}}}\) is the all digital merge matrix. \({\text{R}}\) is the CM between the intelligent metasurface and the user device. \({\text{F}}_{{{\text{RF}}}}\) is the simulation precoding matrix, which needs to satisfy the constant modulus constraint. \(n^{\prime}\) is the number of intelligent metasurface units. This study considers the hardware limitations of actual systems and adopts a simulation precoding scheme based on discrete Fourier transform codebook, combined with reflection elements with finite discrete phase shift values to approximate the ideal beamforming performance. The precoding vectors in the discrete Fourier transform codebook are shown in equation (4).

$${\text{W}}_{{\text{k}}} = \left[ {1,e^{{\frac{ - 1j\pi k}{{2^{b} }}}} ,...,e^{{\frac{{ - 1j\pi k\left( {n - 1} \right)}}{{2^{b} }}}} } \right]^{T} ,k = 1,2,....,2^{b - 1}$$
(4)

In equation (4), \({\text{W}}_{{\text{k}}}\) is the \({\text{k}}\)-th precoding vector in the codebook. The imaginary unit of j \({2}^{{\text{b}}}\) is the number of pre-encoded vectors. This study chooses maximizing channel gain as the codeword criterion, and the optimal result is shown in equation (5).

$$f_{opt} = \arg \mathop {\max }\limits_{{f_{i} \in F}} \left\| {Hf_{i} } \right\|$$
(5)

In equation (5), \(f_{opt}\) is the optimal codeword function. \(f_{i}\) is the \(i\)-th column of the codebook. \(H\) is the CM. \(F\) is the codebook matrix. Afterwards, the specific process of simulating the pre-coded transmission signal through the pre-encoder is shown in equation (6).

$$X = f_{opt} \cdot s$$
(6)

In equation (6), \(s\) is the original signal vector, and \(X\) is the pre-encoded transmission signal.

Channel estimation based on GCNN

This study divides the framework of the IMAC optimization model into three layers. The first two layers are responsible for channel estimation and beamforming, while the third layer is responsible for providing feedback information to adjust model parameters and beamforming strategies. This study uses GCNN to estimate the channel. This neural network maintains high feature extraction capability while reducing the number of parameters through a lightweight design. Prior to this, this study utilizes least squares for preliminary channel estimation, which is then input into GCNN for further processing. The specific process of the proposed channel estimation method is displayed in Fig. 4.

Fig. 4
figure 4

Channel estimation process based on GCNN.

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In Fig. 4, this study first uses the least squares method to perform preliminary channel estimation on the pilot signal and obtain the noisy channel response matrix. Subsequently, as the input of GCNN, it undergoes multi-layer convolution and nonlinear activation operations to effectively separate noise components from real channel features. The computational complexity of traditional convolution is closely related to the dimensions of input and output features. Ghost convolution generates cost feature maps through point by point convolution, and can use inexpensive operations to split and generate residual feature maps, reducing computational overhead. Therefore, this study adopts GCNN to reduce model complexity while ensuring channel estimation accuracy19,20. The output of the ghost module is shown in equation (7).

$$\left\{ {\begin{array}{*{20}c} {Y_{G} = \left[ {y_{11}^{\prime \prime } ,y_{12}^{\prime \prime } ,...,y_{ms}^{\prime \prime } } \right]} \\ {y_{ij}^{\prime \prime } = \Phi_{i,j} \left( {y^{\prime}} \right)\begin{array}{*{20}c} {} & {\forall i = 1,...,m,j = 1,...,d} \\ \end{array} } \\ \end{array} } \right.$$
(7)

In equation (7), \(\Phi_{i,j} \left( {y^{\prime}} \right)\) is a simple linear transformation of the \(i\)-th original feature map. \(m\) is the amount of feature maps. \(d\) is the large number of feature maps obtained by splitting and convolving phantoms. \(y_{ij}^{\prime \prime }\) is the phantom feature map. \(Y_{G}\) is the output of the ghost module. To further improve the efficiency of channel estimation and reduce model complexity, this study proposes a lightweight design for it. SENet is a typical lightweight attention mechanism that adaptively calibrates feature channels by introducing channel attention modules. The SENet module first performs global average pooling on the input feature map to obtain channel statistical information, and then generates channel weight vectors through Fully Connected Layers (FCLs) and activation layers to achieve adaptive recalibration of different channel features21,22,23. Finally, the Scale operation applies weight vectors to the original feature map to complete feature enhancement. In the process of channel estimation, this study first divides the least squares pre-estimated CM and the real CM into two parts: the real part and the imaginary part, forming a 2D matrix. This 2D matrix is fed into GCNN as input features to extract preliminary spatial features. Subsequently, the SENet lightweight attention module is introduced to adaptively weight the feature channels and enhance the expression ability of key channel features. Finally, 2D convolution operations are utilized to further explore spatial correlations and achieve refined feature extraction. Research has found that DIMS communication systems are susceptible to various environmental factors, leading to rapid changes in channel conditions and posing serious challenges to the accuracy of channel estimation. To address these challenges, this study introduces anti-interference strategies based on GCNN. This strategy utilizes the Subtraction operation to subtract the front and back feature maps element by element, extracting residual information to enhance the sensitivity of the network to weak channel changes. The proposed improved GCNN structure is shown in Fig. 5.

Fig. 5
figure 5

Structure of GCNN.

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In Fig. 5, this study sets the channel estimation model as a multi-layer stacked structure, which includes three improved ghost convolution modules and a fusion unit of Spectral Efficiency (SE) attention mechanism. Batch normalization and ReLu activation function are applied after each layer to stabilize the training process and enhance non-linear expression ability, and Subtraction operation is performed to extract residual features. In the ghost module, this study uses 1×1 convolution to channel condense input features, generate a small number of intrinsic feature maps, and generate a large number of derived features through a series of inexpensive layer by layer convolution operations. In summary, this study is based on an improved GCNN for channel estimation of dual IMAC systems, providing channel state information support for subsequent beamforming design.

Design and joint optimization control based on I-DQNN beamforming

On the basis of obtaining accurate channel state information, this study further proposes a beamforming design scheme based on I-DQNN. This scheme combines the superposition and entanglement characteristics of QNN to construct a high-dimensional quantum state weight space, improving the control accuracy of the beam pattern. The structure of DQNN is exhibited in Fig. 6.

Fig. 6
figure 6

Structure of DQNN.

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In Fig. 6, QNN is responsible for optimizing the phase matrix in high-dimensional quantum state space, utilizing quantum parallelism to quickly search for the optimal solution space. The deep learning layer processes traditional channel estimation and beam direction prediction. Both are trained end-to-end through a joint loss function. The QNN output serves as the phase configuration for intelligent metasurface units, while the deep neural network output serves as the beam weight for the base station24,25. In QNN, this study uses parameterized quantum circuits. This circuit achieves the evolution of quantum states through rotation gates and entanglement gates, and its parameters are updated through classical optimization algorithms. After being initialized by Hadamard gates, quantum bits enter a parameterization layer consisting of a single qubit rotation gate and a dual qubit Controlled-NOT gate (CNOT). Each layer contains trainable angle parameters for regulating the degree of superposition and entanglement of quantum states. By stacking multiple layers of parameterized quantum circuits, the mapping from the initial state to the target phase matrix can be achieved. QNN maps the input channel state information to Discrete Cosine Transform (DCT) coefficients of the intelligent metasurface phase matrix through quantum gate operations26,27,28. The phase distribution of intelligent metasurfaces is reconstructed based on the output DCT coefficients to achieve precise control of electromagnetic beams. The relationship between DCT coefficients and phase matrix is shown in equation (8).

$$\Phi^{\prime} = \zeta_{{{\text{DCT}}}}^{ - 1} \left( X \right)$$
(8)

In equation (8), \(\Phi^{\prime}\) is the intelligent metasurface phase matrix, \(\zeta_{{{\text{DCT}}}}\) is the DCT coefficient, and \({\text{X}}\) is the coefficient vector. The transformation formula of the coefficient vector is shown in equation (9).

$${\text{X}}\left( {\text{k}} \right) = \alpha \left( {\text{k}} \right) \cdot \sum\nolimits_{{{\text{n}} = 0}}^{{N^{\prime} - 1}} {x\left( n \right) \cdot \cos \left( {\frac{\pi }{N}\left( {n + 0.5} \right)k} \right)}$$
(9)

In equation (9), \({\text{k}}\) represents the input channel state information. \(\alpha \left( \cdot \right)\) is the normalization coefficient. \({y_{{ij}}}^{{\prime \prime }}\) is the number of Intelligent Metasurface Reflection Units (IMRUs), which is the dimension of the phase matrix. QNN calculates all possible phase combinations in parallel through quantum superposition to obtain DCT coefficient values. Subsequently, the coefficient vectors are substituted into the inverse DCT to reconstruct the complete phase distribution matrix. The deep learning layer adopts an improved residual network structure and introduces an attention mechanism in the convolutional blocks to enhance the ability to extract the delay characteristics of multipath channels. The joint loss function is composed of weighted quantum phase configuration error and beam direction prediction error, and synchronously optimizes the quantum circuit parameters and deep neural network weights through the backpropagation algorithm. The loss function is given by equation (10).

$${\text{L}} = \alpha \cdot {\text{L}}_{{{\text{phase}}}} + \beta \cdot {\text{L}}_{{{\text{bearm}}}}$$
(10)

In equation (10), \(\alpha\) and \(\beta\) are the weights of both. \(L_{phase}\) is the beam direction prediction error. \(L_{bearm}\) is the phase configuration error. \({\text{L}}\) is the joint loss function. Based on multiple cross validation results, this study sets the values of \(\alpha\) and \(\beta\) to 0.6 and 0.4. The quantum phase configuration error is measured by Mean Square Error (MSE), while the beam direction prediction error is calculated by the cross-entropy loss function to adapt to the task of discretized direction classification. During the optimization process, forward propagation calculates the joint loss value. When propagating gradients, the parameters of quantum circuits are updated through the chain rule of complex matrices. The weights of the neural network are iteratively optimized using real-number gradient descent to ensure a stable direction of parameter updates. To further enhance the generalization ability and robustness of the proposed DQNN in forming design, this study adds gradient-based constraints and applies regularization penalties to phase gradient changes to avoid severe phase jumps during quantum state collapse. This constraint is imposed in the loss function by introducing a phase smoothing term. The phase smoothing term is shown in equation (11).

$${\text{P}} = \lambda \nabla \varphi^{\prime}$$
(11)

In equation (11), \(\lambda\) is the regularization coefficient, \(\nabla \varphi^{\prime}\) is the magnitude of the phase gradient between adjacent qubits, and \({\text{P}}\) is the smoothing term. In addition, to further reduce the number of parameters and decrease the complexity, this study introduces a parameter sharing mechanism to bind the quantum gate parameters within the same layer. In this process, this study applies a parameter sharing mechanism to the quantum convolutional layer and quantum pooling layer to reduce redundant parameters and improve training efficiency. The I-DQNN proposed is shown in Fig. 7.

Fig. 7
figure 7

The I-DQNN structure.

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In Fig. 7, the I-DQNN consists of a Quantum Convolutional Layer (QCL), a Quantum Pooling Layer (QPL), and an FCL stacked in sequence. Each quantum convolution layer arranges quantum gates containing parameters in a 2D grid, sharing the same set of rotation angle parameters to reduce redundancy. Each layer is followed by a QPL, which achieves dimension compression through local measurements while preserving key quantum state information. The FCL is composed of classical neural networks, responsible for integrating the feature vectors output by the quantum layer and ultimately completing the beamforming prediction task. The output result continues to be input into the deep neural network model, and the predicted result is used for dynamic adjustment and optimization of beam direction, achieving adaptive response to complex electromagnetic environments. The structure of a deep neural network model includes an input layer, multiple hidden layers, and an output layer, which are connected by nonlinear activation functions to enhance the model’s expressive power. Two models are trained end-to-end using a joint loss function. In summary, this study first utilizes GCNN for channel estimation and inputs the estimation results into an I-DQNN model for beamforming design. By introducing phase smoothing constraints and parameter sharing mechanisms, the robustness and convergence speed in noisy environments are improved. In joint optimization control, this study introduces a feedback mechanism to dynamically adjust the parameter update strategy in QNN by monitoring the deviation between the beamforming output and the target direction in real-time. This feedback signal is used to correct the regularization strength of the phase smoothing term and adaptively adjust the parameter sharing range according to environmental changes.

The pseudo-code of the proposed algorithm is shown in Table 1.

Table 1 Pseudo-code.
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Results

A series of simulation experiments and practical tests are designed to verify the performance of the proposed IMAC optimization model. The experimental environment simulates multi-user, multi-path, and dynamic interference scenarios.

Analysis of channel estimation effect based on ghost convolution

To test the performance of the proposed channel estimation method (M1), this study compares its performance with the traditional least squares method (M2) and ordinary CNN-based method (M3) under different SNR conditions. The experimental parameters are as follows: the number of IMRUs is 20-100, the number of users is 8, the learning rate is 0.001, the training epochs are 200, the sample size is 10,000, the path loss is 30 dB, and the number of multipath paths is 6. The simulation parameters are shown in Table 2.

Table 2 Simulation parameters.
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Firstly, the complexity of M1 is analyzed. Under the same parameter configuration, the parameter count, trainable parameters, and single-sample training time of traditional CNN, Ghost Convolution (GC), and GC model with SENet introduction (GC-SENet) are shown in Fig.8.

Fig. 8
figure 8

The number of parameters for each model, trainable parameters, and single-sample training time.

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In Fig. 8 (a), the GC-SENet model has approximately 11% fewer parameters than the traditional CNN, and its trainable parameters have decreased by about 13%. This is attributed to the optimization of the channel attention mechanism of the feature map by the SENet module, which effectively suppresses the propagation of redundant features. Combined with the feature reuse strategy of GC, the model scale is further compressed. In Fig. 8 (b), its single-sample training time is nearly 28% shorter than that of CNN, and compared with GC, the increase in training time is not high. This indicates that the proposed model significantly reduces the computational overhead while ensuring performance, and is more suitable for resource-constrained intelligent metasurface systems. The situation may be due to that the research method can effectively compress redundant features and dynamically adjust the channel weights through the SENet module, thereby enhancing the efficiency of feature utilization.

To further analyze the performance of the research method, this study introduces Normalized Mean Squared Error (NMSE) as an evaluation metric. The smaller the NMSE, the higher the accuracy of channel estimation. This study first compares it with M2 and M3 under different SNR conditions. The NMSE and iterations of the three methods under different SNR conditions and different numbers of IMRUs are shown in Fig. 9.

Fig. 9
figure 9

The NMSE and iteration of three methods under different SNRs.

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In Fig. 9 (a), as the SNR increases, the NMSE values of each method gradually decrease. Among them, M1 is significantly better than M2 and M3 at all SNRs, especially in low SNR areas where the advantage is more pronounced. When the SNR reaches 20 dB, the NMSE of M1 has dropped to 10-2. This is because M1 effectively enhances the extraction ability of key features by introducing an attention mechanism and combining GC to reduce model redundancy, significantly improving estimation accuracy while maintaining a relatively light computational load. In Fig. 9 (b), M1 can converge to stable performance with a relatively small number of iterations, approaching convergence after 15 iterations. In contrast, M2 and M3 require more than 25 and 20 iterations, respectively, to achieve similar performance. This indicates that the proposed method has a faster convergence speed and stronger optimization stability, thanks to the gradient-directed propagation mechanism guided by SENet, which effectively alleviates the gradient dispersion problem in deep networks. Under different numbers of IMRUs, as shown in Figs. 9 (c) and (d), M1 maintains the lowest NMSE within the range of 0 to 120 reflection units, and the performance decline trend is the slowest as the number of units increases. These results indicate that the proposed method has higher and more stable channel estimation accuracy and is less affected by the number of reflection units, SNR, etc.

To test the online continuous estimation performance of this method, this study further tests the channel tracking ability of each method in a dynamic channel environment. Over time, the NMSE changes of each method under different SNR conditions are listed in Table 3.

Table 3 The NMSE changes of each method under different SNRs over time.
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In Table 3, as the SNR increases, the error values of all methods show a decreasing trend, especially M1, which has the most significant decrease. At 30 dB and 0 Ts, its error value is only 6.01×10-6. Over time, M1 exhibits the smallest increase in error, demonstrating good stability and noise resistance. This is because it adopts dual estimation in channel estimation, first using the least squares method for preliminary estimation, and then suppressing noise through iterative optimization, effectively improving estimation accuracy. This indicates that this method can still maintain a high estimation accuracy in a low SNR environment, providing a reliable guarantee for the stable operation of actual communication systems. In comparison, although M2 has certain stability, its error decline rate is relatively slow, indicating that its ability to suppress noise is limited. However, M3 has the smallest error reduction under a high SNR, and fluctuates greatly over time, indicating its weak anti-interference ability. This is because it only relies on single-linear interpolation for channel estimation and does not effectively model and suppress noise components, resulting in a significant reduction in estimation accuracy in high-noise environments. Especially at 30 dB, the error of M3 rapidly rises to 24.71×10-6 during the time extension process, which is much higher than that of the other two methods, further verifying its defect of insufficient robustness.

Performance evaluation of beamforming based on I-DQNN

To test the performance of the proposed I-DQNN beamforming algorithm (A1), this study compares it with the pre-I-DQNN and conventional QNN. The convergence of the loss function values during the training process is compared. The loss values include \({\text{L}}_{{{\text{phase}}}}\) and \({\text{L}}_{{{\text{bearm}}}}\), as shown in Fig. 10.

Fig. 10
figure 10

Comparison of the training conditions of DQNN before and after improvement.

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In Fig. 10 (a), the loss value of I-DQNN rapidly decreases in the early stage of training, and tends to converge after 45 iterations, with fewer iterations compared to before improvement, and its convergence value is lower, only 0.04. In Fig. 10 (b), the loss value of I-DQNN maintains a decreasing trend throughout the training process, and the convergence speed is significantly faster than QNN and the I-DQNN, approaching stability at the 60th iteration. The final convergence value is 0.03, which is about 42% lower than QNN. This indicates that I-DQNN has stronger learning ability and stability in the optimization process. This indicates that the I-DQNN can adjust the network parameters more efficiently, thereby approaching the optimal solution in a shorter time.

To further test the performance of this method, this study compares it with beamforming algorithms based on alternating optimization algorithm and spectral clustering algorithm (A2), and block coordinate descent algorithm (A3). Fig. 11 evaluates its performance as a function of the base station transmission power, the number of reflection units, and the Weighted Sum Rate (WSR) under channel error.

Fig. 11
figure 11

The WSR of each beamforming algorithm under the conditions of base station transmission power, the number of reflection units, and channel error.

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In Fig. 11 (a), with the increase of the transmission power of the base station, the WSR of each algorithm shows an upward trend, but the improvement of A1 is more significant. The average WSR is 5.8 bit/s/Hz, which is significantly higher than 4.6 bit/s/Hz of A2 and 4.9 bit/s/Hz of A3. This is attributed to the I-DQNN’s higher sensitivity to channel states, which enables it to optimize the beamforming matrix more precisely, thereby maintaining excellent performance at both low and high power levels. In Fig. 11 (b), all algorithms exhibit a trend of increased WSR when the number of reflection units increases, but the gain of A1 is more obvious. Its WSR value reaches up to 6.7 bit/s/Hz, which is approximately 32% and 28% higher than that of A2 and A3, respectively. This advantage is attributed to the refined modeling capability of the I-DQNN for the phase control of the reflection unit, enabling it to more efficiently explore the potential of reconfigurable intelligent surfaces in high-dimensional spaces. As the channel error increases, A1 can still maintain a relatively stable rate performance, further verifying its robustness advantage. In Fig. 11 (c), when the channel error gradually increases, A1 can still maintain a high rate stability, demonstrating stronger robustness and verifying its superior performance in complex environments. In summary, the I-DQNN demonstrates superior WSR and robustness under different base station powers, the number of reflection units, and channel errors. Its beamforming performance is significantly superior to other algorithms.

To further test the performance of several algorithms in beamforming design, Beamforming Gain (BG), Interference Suppression Ratio (ISR), SE, and MSE are introduced for comparison. The experiment uses two user devices and three interference sources for simulation testing, simulating the actual communication environment. The test scenarios include indoor and outdoor scenarios, as shown in Table 4.

Table 4 Performance comparison of various beamforming algorithms.
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In Table 4, in both indoor and outdoor scenarios, A1 significantly outperforms A2 and A3 in terms of BG, ISR, and SE, with the lowest MSE. Its BG reaches 17.65 dB indoors, an increase of nearly 69% compared to A2, ISR exceeds the latter by 7.81 dB, and SE increases by nearly 80%. Even if the environment is changed from indoor to outdoor, A1’s performance is slightly reduced, but all indicators remain leading, indicating that it has good adaptability and robustness to different transmission environments. This further proves the superior potential of the algorithm in practical deployment.

Application effect of communication optimization model based on I-DQNN and GC

To comprehensively test the practical application effect of the proposed communication optimization model based on I-DQNN and GC (Model 1), this study compares its performance with References29,30,31, and32 (Models 2-5). This study selects Symbol Error Rate (BER), System Throughput, Energy Efficiency (EE), and Average Delay (AD) as evaluation metrics. This study applies five models to the 5G base station network in a densely populated urban area of City A and the 5G private network in an industrial park for field testing. The data of the five models in different scenarios are listed in Table 5.

Table 5 Test results of five models in different scenarios.
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In Table 5, Model 1 demonstrates optimal performance in both test scenarios. Its BER is the lowest, throughput exceeds other models by more than 20%, EE reaches 4.32 and 4.58 bit/Hz/J, and AD compression is 3.20 ms and 2.83 ms, significantly better than the comparison model. Especially in densely populated urban 5G base station networks, the throughput reaches 987.62 Mbps, an increase of 166.27 Mbps compared to Model 3. It indicates that this model has a stronger adaptability in high-concurrency and complex interference environments, and can effectively improve network quality and user experience. This indicates that Model 1 has significant advantages in dealing with high-density user access and complex electromagnetic environments, and its algorithm optimization effectively improves the signal demodulation accuracy and resource scheduling efficiency. This is because it introduces adaptive modulation and coding technology, combined with a dynamic resource allocation mechanism driven by deep reinforcement learning, to maximize spectrum utilization while ensuring link stability.

To further verify the stability and robustness of the research method in long-term operation, this study records a 3-month continuous operation test. The communication system failure rate and communication interruption frequency of each model application are shown in Fig. 12.

Fig. 12
figure 12

The continuous operation test results of each model.

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In Fig. 12 (a), Model 1 maintains a stable failure rate below 0.17% and significantly lower than other models during 3 months of continuous operation. The other four models all show varying degrees of fluctuations, with peak failure rates reaching 0.45%, 0.38%, 0.52%, and 0.61%. In Fig. 12 (b), the total number of communication interruptions for Model 1 is only 17, while the rest of the models have more than 20 interruptions. The average interruption interval time for the model is 18.3 days, which is longer compared to other models. Model 1 has excellent stability and reliability in long-term operation, ensuring continuous and efficient communication in different scenarios and reducing operation and maintenance costs.

To verify the computational overhead and performance trade-off under RIS of different scales, the experiment measures the number of Floating-Point Operations (FLOPs), memory usage, and forward latency of each configuration. The equivalent simulation of a 16-qubit DQNN on NISQ devices consumes approximately 3.2 GPU hours, verifying its feasibility under current hardware conditions. As the number of RIS units increases to 256, the FLOPs of the traditional channel estimation method reach 8.7×106, the memory usage increases to 1.2GB, and the latency significantly increases to 46 ms. However, the proposed GC architecture reduces the computational complexity and memory overhead by 42% and 57%, and the latency is compressed to 19 ms. It demonstrates stronger scalability and real-time performance advantages. Under 64 and 128 unit configurations, this solution also demonstrates significant advantages, with FLOPs reduced by 39% and 41%, respectively, memory usage decreased by 51% and 55%, and latency controlled at the 17 ms and 18 ms levels. The experimental results show that GC, through depth-separable feature extraction and sparse connection mechanisms, significantly reduces the consumption of computing resources while ensuring estimation accuracy, and is particularly suitable for high-density RIS deployment scenarios.

Conclusion

To enhance the communication reliability and stability of the communication system, this study proposed an IMAC optimization model based on I-DQNN. This study aimed to improve the combination of GCNN and I-DQNN to obtain a hybrid neural network architecture for channel estimation and beamforming design in communication systems. As a result, the communication efficiency and robustness of the communication system have been improved. In the experiment, the GC-SENet model reduced the number of parameters by about 11% compared to the CNN, and its trainable parameters decreased by about 13%. The single-sample training time was shortened by nearly 28%. When SNR=20 dB, the NMSE of M1 has decreased to 10-2. As the number of IMRUs increased, the NMSE values of each method gradually decreased, and M1 always maintained a low NMSE level. The average WSR of M1 was 5.8 bit/s/Hz, significantly higher than A2’s 4.6 bit/s/Hz and A3’s 4.9 bit/s/Hz. The BG of M1 reached 17.65 dB indoors, an increase of nearly 69% compared to A2, with ISR exceeding the latter by 7.81 dB and SE increasing by nearly 80%. In two testing scenarios, Model 1 had the lowest BER, with a Throughput exceeding other models by more than 20%. The EE reached 4.32 and 4.58 bit/Hz/J, and the AD was compressed to 3.20 ms and 2.83 ms. Especially in densely populated urban 5G base station networks, the throughput reached 987.62 Mbps, an increase of 166.27 Mbps compared to Model 3. Model 1 maintained a stable failure rate of 0.17% or below and significantly lower than other models, during three months of continuous operation. The total number of communication interruptions was only 17 times. Research models can effectively improve the reliability and energy efficiency of communication systems, significantly reducing bit error rates and system latency. However, there are still limitations in current research, specifically manifested in the insufficient adaptability of dynamic environments during data transmission. Subsequent research will consider further integrating dynamic environment perception mechanisms with adaptive learning strategies to enhance the model’s generalization ability under complex time-varying channel conditions.