Optimized CNN and Adaptive RBFNN for channel Estimation and Hybrid Precoding approaches for Multi User Millimeter wave Massive MIMO

The Millimetre Wave (mmWave) communication satisfy the demand for high data rates due to the characteristic of wide bandwidth. Using massive Multiple-Input Multiple-Output (MIMO) technology, significant propagation loss of mmWave communication is effectively compensated. However, it is challenging to provide a specialised Radio Frequency (RF) chain for each antenna due to constrained physical area with closely spaced antennas and prohibitive power consumption in mmWave massive MIMO systems. This paper presents novel approaches for effective channel estimation and hybrid precoding in mmWave communication systems. To address the challenges of channel estimation, a Convolutional Neural Network (CNN) is utilized, and network parameters are optimized using Enhanced Whale Optimization Algorithm (EWOA). The proposed CNN-based channel estimation method aims to accurately estimate the channel in mmWave systems with enhanced efficiency and reduced complexity. By training CNN using EWOA optimization algorithm, the network parameters are fine-tuned to improve accuracy and generalization capability of channel estimation process. Furthermore, hybrid precoding is achieved using Adaptive Radial Basis Function Neural Networks (Adaptive RBFNN) which enables efficient precoding while minimizing complexity. Moreover, the Adaptive RBFNN approach determines the optimal precoding weights based on Channel State Information (CSI), resulting in improved performance and reduced computational overhead. The performance analysis is validated using MATLAB/Simulink software and offers in providing effectual and reliable mmWave communication systems, facilitating the realization of high-speed and high-capacity wireless networks.


I INTRODUCTION
Millimetre-wave technology, specifically MIMO wireless transmission, plays a crucial role in the advancement of sixth-generation (6G) wireless communication by offering a compelling solution for expanding available spectrum resources and achieving substantially higher wireless transmission speeds [1][2][3].Conversely, mmWave operates in the highfrequency band, characterized by a narrow beam and noticeable attenuation, resulting in significant path loss compared to lower frequency bands.To mitigate this, the use of large antenna arrays helps improve coverage and concentrate power towards the receiver.Furthermore, the wide bandwidth associated with mmWave necessitates higher hardware requirements for Analog-To-Digital Converters (ADCs) [4][5][6].
Existing literature presents two primary approaches to address this issue.The first solution involves adopting a hybrid precoding architecture, which integrates digital precoding with analog precoding.This entails utilizing an analog beamformer for signal processing purposes.By implementing the aforementioned hybrid precoding structure, it becomes possible to lessen overall number of ADCs and RF chains within the system.This reduction in hardware components helps achieve a more favorable balance in terms of cost [7][8][9].Another alternative solution involves substituting high-resolution ADCs with low-resolution ones for the quantization process, which directly contributes to minimizing power loss and lowering the hardware cost.However, it is important to note that the utilization of low-resolution ADCs [10][11][12] does introduce the challenge of quantization noise, which needs to be addressed accordingly.Signal processing in mmWave systems is susceptible to a number of significant practical constraints, despite the fact that principles of beamforming are similar irrespective of frequency used as the carrier [13][14][15].Hence in the proposed work introduced adaptive RBFNN overcoming the challenges of RBFNN [16] for hybrid precoding owing to its efficiency to allocate resources for multiple users, enhancing the overall capacity and quality of service.
Channel estimation in mmWave MIMO systems offers advantage of enabling adaptable design of hybrid analog/digital precoders and combiners, tailored to different optimization objectives [17][18][19].However, the hybrid nature of these systems presents a challenge when it comes to directly estimating the channels.This difficulty arises because of the analog beamforming and combining stage, which is employed to reduce power consumption compared to all-digital solutions commonly used at lower frequencies [20].Moreover, the operation at mmWave frequencies adds another layer of complexity to channel estimation.This is primarily due to low Signal to Noise Ratio (SNR) before beamforming and larger dimensions of channel matrices associated with mmWave arrays [21][22][23][24].Conventional, kalman [25] Least Square (LS) channel estimation neglects the impact of noise, rendering it inadequate for practical wireless systems that encounter noise imperfections and unknown effects [26].In contrast, Minimum Mean Square Error (MMSE) channel estimation offers improved performance, but its high computational complexity limits its practicality [27].Furthermore, MMSE relies on accurate knowledge of channel and noise second-order statistics, making it applicable only in specific scenarios.While mmWave channel estimation has received considerable attention, previous research has primarily concentrated on narrowband models.However, the wide bandwidth of mmWave systems necessitates development of efficient techniques for frequency-selective channels.
Compared to traditional methods, deep learning (DL) [28] has arisen as a promising technology for enhancing channel estimation in communication systems augmented with Intelligent Reflecting Surfaces (IRS) [29].In [30], a twin CNN is proposed, which utilizes received pilot signals to estimate both direct and cascaded channel matrices using an elementby-element approach.Another approach described in [31] involves the development of a deep denoising neural network to aid compressive sensing-based channel estimation.However, both methods suffer from long delays or high computational complexity.Consequently, there is still a need to devise a channel estimation scheme that balances low overhead and high accuracy, as there exists a general trade-off between channel estimation overhead and data transmission.
Accordingly, the proposed work introduces, EWOA-CNN for robust and accurate estimation of channel parameters.
Millimetre Wave communication offers wide bandwidth to meet high data rate demands, but deploying individual RF chains for each antenna in massive MIMO systems poses challenges due to limited space and high power consumption.This paper proposes novel solutions for channel estimation and hybrid precoding to overcome these constraints.The proposed approaches effectively address the challenges associated with mmWave communication, enabling efficient utilization of resources.The contributions of this work involve: • Implementation of EWOA-CNN for effective estimation of mmWave channel.
• Utilization of Adaptive RBFNN for hybrid precoding aims to achieve improved efficiency while minimizing complexity.
The rest of this paper is organized as Section II details the description of proposed system with modelling of system in Section III.Consequently, Section IV entails the validation outcome of proposed work and Section V offers the conclusion.

II PROPOSED SYSTEM DESCRIPTION
In the proposed system, power allocation stage determines the optimal power distribution among the users or channels based on various criteria such as channel conditions or user requirements.The allocated power is then passed to the baseband beamforming stage, where the signal is processed in digital domain to generate beamforming weights.The digital signal in baseband beam former is converted to analog using a DAC and then passed through the RF chain, which includes components like amplifiers and filters, to prepare the signal for transmission.In the proposed work optimized CNN is adopted for effective channel estimation which leverages its ability to learn complex patterns and features from the received signals, enabling accurate estimation of mmWave channel.In order to optimize the network parameters, EWOA is employed, which effectively searches the parameter space to find reliable CSI.This CSI is then utilized to design adaptive RBFNN based hybrid precoders.The hybrid precoders combine analog and digital precoders to optimize the transmission beamforming.Analog precoders perform beamforming in the analog domain, while digital precoders operate in the digital domain.The analog precoders shape and steer the transmitted signals in analog domain, while the digital precoders perform additional beamforming and signal processing in digital domain.This combined operation enables efficient resource utilization and optimal beamforming based on estimated CSI.At the receiver side, RF combinier is utilized to combine individual user signals, reducing interference and improving system performance.The combined signal is then processed through RF chain and converted back to digital using an ADC.In the baseband combiner, signals from different users are combined to reconstruct the original transmitted data.Henceforth, the proposed system leads to improved transmission performance, increased spectral efficiency, and enhanced system capacity in wireless communication systems.

III MODELLING OF PROPOSED SYSTEM A) SYSTEM MODELLING OF MULTI-USER MASSIVE MIMO
The system shown in Figure 1  |where | , | represent amplitude of (, ) − ℎ element of   .In addition to analog precoder, a digital precoder,  , is employed that allows for modifications in both amplitude and phase aspects of signal.In consideration   ∈    ×  is the ℎ user downlink channel matrix and signal received is expressed by, From aforesaid expression ℎ user signal vector is represented as  = [ Hence, the total spectral efficiency of  users is represented as follows: Where,   = From the expression above, signal wavelength is denoted as , separation between adjacent antenna elements as .
To accurately determine the channel conditions, account for variations caused by mobility and interference, and optimize transmission parameters, it enables adaptive techniques to enhance receiver design, and improves overall system performance.In the proposed work EWO-CNN is accomplished for accurate estimation of channel.

C) CHANNEL ESTIMATION USING EWOA-CNN
The CNN oriented estimation model utilizes a convolutional layer for initial and secondary layers, while the final layer employs a fully connected layer after converting the feature map of matrix data into a vector form.Figure 2 depicts channel estimation using CNN.The first layer employs 16 filters of size 4 × 1, the second layer has 32 filters of size 4 × 1, and last layer consists of 2 nodes.The convolutional layer extracts features from input data, generating a feature map, which is then transformed into the desired dimensions by the fully connected layer.Similar to neural network based estimation approach, input  is separated into its real and imaginary components, resulting in an input size of 2 × 1 × 1.
() =  3 .((((())))) +  3 (7) Where convolution layer operation is specified as (.).CNNs, in general, utilize the sliding convolutional filters to leverage the spatial local correlation.As previously mentioned, the input data in the form of estimated channels contains essential information like Angle of Arrivals (AoAs) and signal magnitudes.Hence, CNNs are effective in extracting these features from input elements and are anticipated to outperform neural network based estimation methods.While image processing typically employs smaller filters, our CNN-based estimation employs larger filter sizes compared to input size.This is due to the fact that input data, which is complex, is split into its real and imaginary components, requiring the inclusion of all 2 elements in feature extraction.However, CNNs are complex models with numerous parameters that need to be optimized for efficient and accurate performance.The EWOA is a met heuristic optimization algorithm inspired by social behavior of whales is accomplished in this work.

Whale Optimized Algorithm
The Whale Optimization Algorithm (WOA) is a unique metaheuristic algorithm designed to solve global optimization problems by emulating the social behavior of humpback whales.It stands out for its effective search capability, minimal controlling parameters, and straightforward implementation.The WOA algorithm employs three stages to update the positions of individuals: surrounding prey, searching for prey, and spiral position updating.These stages contribute to the iterative optimization process and enhance the algorithm's performance in finding optimal solutions.

Surrounding Prey
Searching Prey: Updating Position: If  ≥ 0.5,  ,+1 =  , +   .  .cos(2), From the expressions above solution of next generation and best generation is specified as  ,+1 and  , , best and random solution chosen is denoted as   and  , , and random number , maximum iteration as   .The value of 'a' is gradually decreased from 2 to 0 during successive iterations. represents a random number between 0 and 1.  is a constant that determines the characteristics of the logarithmic spiral, and  is a random real number within the range of -1 to 1.

Enhanced Whale Optimized Algorithm (EWOA)
Like other metaheuristic algorithms, the WOA face challenges in achieving high convergence accuracy and avoiding premature convergence when tackling complex optimization problems.The random initialization and population diversity can hinder the algorithm from escaping local optima.To enhance the search performance of the WOA, this study introduces the EWOA with two strategies.

Elite Opposition-Based Learning (EOBL)
The main objective of EOBL is to enhance population diversity by evaluating the fitness function of both the current and opposition solutions, selecting the superior solutions as initial individuals.Among the population, the individual with the lowest fitness value is considered the elite individual.The EOBL strategy can be represented as follows: From the expression mentioned above, current and opposition solution is specified as   and  ̅  , random number as  and value range is [0,1], lower and upper boundaries of scheduled area is represented as  and .

Levy Flight
Levy flight is a stochastic search technique widely employed in numerous metaheuristic algorithms, known for its successful applications.By comparing the fitness values before and after performing the Levy flight, the superior solutions are chosen to advance to the next generation using a greedy strategy.The Levy flight strategy can be described as follows: ,+1 = {  ,1,  ( ,1 ) <  ( , )  ,,  ( ,1 ) <  ( , ) , From the above expression current solution after Levy flight  ,1 ,  determines constant value 1.5, random number obeying normal distribution is denoted as  and  and gamma function as Γ.Henceforth, the network parameters of CNN, are effectively tuned using EWOA, thereby accurate CSI are estimation which make the system efficient and reliable.To exploit CSI and optimize the precoding design, hybrid precoding is followed after channel estimation.

D) HYBRID PRECODING USING ADAPTIVE RBFNN
In order to optimize the performance of precoding system in a dynamic and adaptive manner, the proposed work adopts Adaptive RBFNN technique for hybrid precoding.The design of proposed hybrid modelling is described in Figure 3.The control input, denoted as , is composed of two components: state feedback control input  and input  ̂ generated by adaptive RBFNN.The input  ̂ is obtained by calculating error between actual and desired state variable   .The state feedback control, which is executed using PID control, contributes to overall control input.The Adaptive RBFNN estimates the disturbance and generates an equivalent compensation input to enhance control performance.From equation ( 24) state feedback control of weight matrix is denoted as , and the expression is written as The expression for error function is evaluated as Here, error between desired and real state variable   and () is represented as  =   - The function unknown , which is described below, includes the variables   and , and By leveraging the universal approximation capability of RBFNN, it is possible to indirectly estimate the value of  by estimating .Consequently, the estimation of the unknown function f can be accomplished in the following manner.
The weight of ideal matrix is signified as  ̅  , regression vector as ()and offset network at the output layer of neural network as  ̅ ().Henceforth the error expression (26) becomes Therefore, actual and ideal error value is expressed as In consideration with weight adaptive law of RBFNN and control law the expression is written as ̂() = (  ) By Substituting ( 31) and ( 32 Hence, due to the unbounded nature of , the system is globally stable for all  and  ̃ *  .Therefore, the adoption of adaptive RBFNN for hybrid precoding enables the system to achieve improved performance, adaptability, robustness, and efficiency in diverse and dynamic wireless communication scenarios.

IV RESULTS AND DISCUSSION
This section assesses the effectiveness of suggested approaches and parameters is found in Table 1.

Channel Estimation
This study investigates the proposed EWOA-CNN channel estimation technique in a mixed ADC architecture, along with other conventional techniques commonly used for channel estimation.To assess the effectiveness of proposed method, several traditional channel estimation techniques, including Linear Minimum Mean Square Estimator (LMMSE), Support Vector Machine (SVM), and Artificial Neural Network (ANN), are selected for comparison.In every dataset element, the channels are generated using different covariance matrices, along with corresponding received signals from pilot transmissions.This means that noise, channel, and covariance matrix of each sample vary.The channel Normalized Mean Square Error (NMSE) is used as metric to measure the accuracy of channel estimation.
From Expression (41) channels recovered by algorithm is represented as  ̂.

Figure 5: Analysis of NMSE for Channel Estimation Techniques
In Figure 5, a comparison is presented between various methods for channel estimation.The evaluation takes into account the ULA architectures and mixed-resolution ADC quantization.The results indicate that proposed EWOA-CNN method exhibits superior performance in comparison to conventional channel estimation techniques.Moreover, the precision of channel estimation is significantly higher with the EWOA-CNN network when compared to alternative approaches.The visual representation of complexity assessment for four different algorithms, including proposed EWOA-CNN channel estimation algorithm is provided in Figure 6.It is evident from the graph that the EWOA-CNN algorithm exhibits faster convergence, owing to the remarkable learning capabilities of CNN.As a result, the EWOA-CNN algorithm requires fewer complex multipliers contrasted to other techniques examined.The variation in estimated error for low-resolution ADCs ranging from 1-4 bits, as well as mixed resolution using EWOA-CNN, is depicted in Figure 8.The sparsity corresponds to the number of channel paths.It is evident from the graph that as resolution of ADC increases, the estimation error decreases.In other words, higher-resolution ADCs exhibit lower errors in estimating the channel.

Spectral Efficiency
In this section, spectral efficiency of ULA based mmWave MIMO system is evaluated to assess the effectiveness of proposed algorithm.The recommended algorithm, which combines adaptive RBFNN with hybrid precoding, is compared with various precoding schemes including CNN, ANN and Least Mean Square (LMS) algorithm.The objective is to determine the performance superiority of suggested adaptive RBFNN hybrid precoding algorithm over other considered precoding schemes.The graph in Figure 12 shows the comparison of spectral efficiency among different precoding techniques with   = 36,   = 36,   = 4 &   = 1 for perfect CSI.According to the graph, the suggested Adaptive RBFNN-based solution performs comparably to complete digital precoding.This suggests that the proposed technique achieves a similar level of spectral efficiency as the more complex and computationally intensive digital precoding methods.The assessment of spectral efficiency in terms of bits per second per hertz (bps/Hz) for examining efficiency available frequency spectrum for transmitting information by approaches like RBFNN and Adaptive RBFNN is listed in Table 2.In comparison, adaptive RBFNN ranks better with superior performance.The data presented indicates that the system's spectral efficiency improves significantly when multiple data streams are transmitted compared to a single data stream.It is evident that spectral efficiency of conventional pre-coding techniques decreases in comparison to Adaptive RBFNN.This demonstrates the exceptional performance of proposed technique, particularly when dealing with multiple data streams.The comparison of accuracy among mentioned approaches, including proposed EWO-CNN based channel estimation technique, GNN, DLCS and OMP.The accuracy comparison likely refers to the ability of these approaches to accurately estimate the channel.Accordingly, the maximum accuracy obtained by EWO-CNN, among these approaches is reported as 98.75%.This ensures that the proposed EWO-CNN technique, achieves high level of accuracy in channel estimation, which is essential for reliable communication systems.

V CONCLUSION
This paper establishes an innovative approach combining adaptive RBFNN for hybrid precoding and EWOA-CNN for channel estimation to provide a comprehensive solution to limitations encountered in mmWave communication for massive MIMO systems.By integrating these advanced techniques, the system achieves enhanced spectral efficiency, increased data rates, and improved overall performance.By incorporating EWOA into training process, CNN effectively learns and estimate mmWave channel parameters, leading to improved accuracy and reduced computational complexity.The adaptive RBFNN-based hybrid precoding technique demonstrates exceptional performance in achieving high spectral efficiency.It outperforms traditional pre-coding methods, such as LMS and ANN, particularly when handling multiple data streams.The results highlight the advantages of proposed approaches in terms of accuracy, spectral efficiency, and losses compared to existing methods.Furthermore, the proposed research contributes to the advancement of mmWave communications and facilitates development of practical and efficient systems for highcapacity wireless networks.

Figure 1 :
Figure 1: Architecture of Proposed mmWave massive Multi User MIMO Channel

Figure 6 :
Figure 6: Antenna array size vs complex multiplications

Figure 8 :
Figure 8: NMSE versus number of paths with various ADC resolutions

Figure 9 :
Figure 9: Achievable Sum-Rate against (a) NMSE and (b) SNRThe relationship between NMSE and achievable sum rate for ULA with various CSI depending on channel model is illustrated in Figure9(a).The comparison is made across different ADC resolutions.The results clearly indicate that higher-resolution ADCs perform better in terms of achieving higher sum rates.Furthermore, Figure9(b) examines the impact of SNR on beam selection rate for both suboptimal and perfect CSI scenarios, with NMSE adjusted to 10..

Figure 10 :
Figure 10: Spectral Efficiency Analysis having Perfect CSI with   = 16,   = 16,   = 4 &   = 1To validate spectral efficiency of proposed algorithm, a comparison of sum spectral efficiency against SNR in mmWave channels with system   = 16,   = 16,   = 4 &   = 1 is considered.The graph shown in Figure10, clearly demonstrates that the proposed Adaptive RBFNN scheme exhibits significant superiority over other schemes in mmWave channels.The sum spectral efficiency accomplished by proposed Adaptive RBFNN algorithm surpasses that of alternative schemes by a considerable margin in channel scenarios.

Figure 11 :
Figure 11: Spectral Efficiency Analysis having Perfect CSI with   = 16,   = 16,   = 4 &   = 3Spectral efficiency comparison between proposed Adaptive RBFNN-based hybrid precoding technique and other similar methods is shown in Figure13.In this evaluation, the system is configured with   = 16,   = 16,   = 4 &   = 3.The graph shows that suggested Adaptive RBFNN-based solution performs comparably to complete digital precoding.Additionally, earlier LMS precoding method is similar to that of ANN approach, while the difference between CNN and RBFNN is only slight.These findings indicate that the proposed Adaptive RBFNN-based hybrid precoding technique exhibits competitive performance with respect to other comparable techniques.

Figure 13 : 3 In Figure 13 ,
Figure 13: Spectral Efficiency Analysis having imperfect CSI with   = 36,   = 36,   = 4 &   = 3In Figure13,      is increased to 36 for evaluating the performance of different hybrid precoding techniques.The evaluation is conducted under imperfect CSI.It is stated that Adaptive the RBFNN precoding technique demonstrates superior performance compared to other precoding schemes.Specifically, the Adaptive RBFNN precoding technique achieves high spectral efficiency, indicating efficient utilization of the available bandwidth.

Figure 14 :
Figure 14: Spectral Efficiency Comparison in accordance with (a) SNR and (b) Time Slot

Figure 15 :
Figure 15: Comparison of Accuracy

Figure 16 :
Figure 16: Loss Analysis for Training Vs Validation comprises a Base Station (BS) and  independent users.The BS is furnished with   transmission antennas and    chains, while each user has .This analog precoder is constructed using analog phase shifters, enabling it to manipulate the phase component of the signal.It is important to note that each entry of   is normalized to ensure that | , = 1 √ , average power transmitted by BS is specified as , the identity matrix   ×   is signified as    , . . specifies vector   ∈     denotes   ×    analog combiner matrix and   determines    ×   ℎ user's base band combiner.If  ̃ =        ,  = 1,2, … , signifies equivalent baseband channel matrix, then Equation (2) is rewritten as,  ̂ =     ̅      + ∑     ̅      +         ,  = 1,2, … (2), and Additive White Gaussian Noise (AWGN).The combined received signal at ℎ user is expressed as   .̂=+         ,  = 1,2, … (2)From Equation(2) The channel model incorporates   clusters, where each cluster consists of , the term "√  " represents the large-scale path fading, while " ̇" denotes the normalized channel matrix for k-th user, satisfying  [‖ ̇‖  2] =     .In the context of mmWave channels, a remarkable characteristic is the presence of a limited number of scattering clusters along propagation path.This limitation in scattering clusters is captured by adopting the Saleh-Valenzuela geometric model.More specifically, the channel   ∈    ×  , which describes the transmission from BS to ℎ user, is represented using this model.The expression becomes propagation paths.Within this model,    represents complex amplitude accompanying with the  − ℎ path in  − ℎ scattering cluster.Transmit and receive array vector response for user  is specified as    (   ) and    (   ), while azimuth angles arrival and departure is denoted as    and    of path (, ). Te truncation of Laplace Transform is implemented to engender    and    .The Uniform Linear Array (ULA) model is represented as () = [ 1 (),  2 (), ..,   ()]  and the exponential decay momentum factor, denoted as , is utilized to update the error loss.̇= −    + 2   ( ̂−  ̅  () −  ̅ ()) + 2 ∑  ̃ * , hidden node is denoted as ℎ, ℎ row of  as   * ,  *