Design Analysis of Adaptive Beamforming in a MIMO-millimeter Wave 5G Heterogeneous Wireless Network using Machine Learning Models

Beamforming (BF) is a smart antenna technique to provide a summation of the weighted signal over multi-users to produce the more concentrated transmitted signal from massive MIMO antenna arrays deployed in a Millimeter-Wave (mm-Wave) 5G heterogeneous wireless network . It adjusts the amplitudes and phases of the signals received over different antennas in an optimum manner in the form of directional radiation. This paper will help in the installation of 5G and 6G mm-Wave heterogeneous wireless networks. Here, adaptive BF is designed and being implemented on the Machine Learning (ML) platform using Signal-to-Noise-Interference Ratio (SINR). The four ML methods having six BF properties to estimate the SINR of Multiple-Input-Multiple-Output (MIMO) - mm-Wave 5G wireless network are explored. The proposed algorithm suppresses noise plus interference and can reduce the power consumption. The python package pyArgus focusing on the BF and direction finding algorithms has been used for 20,000 simulations. The BF features namely noise variance, number of antenna elements, distance between antenna elements, azimuth angular range of receiving array, elevation angular range of receiving array and Direction of Arrival (DOA) of signal i.e. incident angle of Signal-of-Interest (SOI) are used in predicting the SINR. The 10-fold cross-validation experiment is performed to assess the robustness of the best

radiation pattern of the antenna array is built in the direction of desired user while minimizing the interference for nearby users. The inter-cell interference are suppressed using linear processing schemes in a coordinated BF fashion. The result of appropriate BF is that the links become isolated in direction, and intercellular interference plays a negligible role than in current small cellular networks. This fact implies that capacity gain in these systems is achieved by point-to-point technologies. Fixed BF is applied to the sources having fixed Angles-of-Arrival (AoAs) and helps in the network planning as well as antenna deployment schemes [7]. In adaptive BF, the weights of the array used are adapted to the changing signal environment in a continuous manner. The fixed or adaptive BF pattern plays an important role in achieving the spatial selectivity [8]. The reliable Channel State Information (CSI) analysis is necessary in mm-Wave massive MIMO systems for near-optimal BF performance. However, acquiring this analysis becomes very cumbersome practically due to much variation in the used channel and the significant numbers of transceiver antenna elements. Since, in a currently smart antenna array structure having an interface as Digital Signal Processing (DSP), BF technique needs a fairly accurate estimate of DOA. High frequency (HF) communication signals received by the array are passed on to Receiver (RX) front end and then to Analog to Digital Converter (ADC) system. The DOA estimation algorithm is applied to analog to digital converted signal samples. The antenna array calculates and optimizes the BF weights so that the output beam will adapt itself to the DOA of SOI. Fig. 1 depicts the general block diagram of the smart antenna array system.

Fig. 1 -General Smart Antenna Array System
The MIMO capability includes several techniques, falling into the categories of BF, diversity, and spatial multiplexing. BF and diversity techniques can reduce the effects of multipath fading, which benefits other communications metrics. Spatial multiplexing can allow multiple independent, parallel data streams to be transmitted, increasing the overall throughput of a system. The availability of large bandwidth in mm-Wave range provides very high frequencies for 5G mobile communication networks as a promising candidate enabler. To tackle the signal propagation challenge through various paths, mm-Wave systems employ large antenna arrays that are expected to implement highly directional BF and provide higher link-level gains. BF with an antenna array of typically 64 to 512 elements per system within small form factors will reduce interference to adjacent users using a Multi-user (MU)-MIMO system and provides more directivity. In addition to more capacity in the MU-MIMO system, BF has other advantages like reduced energy consumption and the abundant mm-wave spectrum utilization. Its lower energy consumption brings a reduction in overall network operating costs by targeting individual user equipment's with their assigned signals. Full digital baseband precoding is not preferred as it has extremely high hardware cost, space and energy utilization in a MIMO system, for the sake of the same number of Radio Frequency (RF) chains. The hybrid analogdigital precoding is a low-cost alternative solution to minimize the number of RF chains as it divides the precoding operations between the analog and digital domains [5,9]. The digital weights of each RF chain are controlled in digital BF. The phase of the signal transmitted at each antenna is adjusted using analog phase shifters in analog BF.
Therefore, the hardware-constrained mm-Wave massive MIMO communication system exploits both multiplexing gain and spatial diversity [5].

Fig. 2 -Working Principle of Beamformer
The BF adjusts the weights of the antenna elements of the array, which were employed adaptively to optimize the quality of signals under certain performance metrics [10].
From the fig. 2, the BF signal output is calculated using the following equation (1.1):  [11]. The Quality of Service (QoS) for the receive SNR is given by equation 2) which is as follows: where temporal variations of H ∈ C N are the realization of an underlying distribution, but in stochastic approximation case, the analysis of channel distribution is not required; rather most recent channel realization is used. This approximation is well suited for Frequency-Division Duplexing (FDD) systems.
For each receiver k, SINR is calculated using the equation (1.3) which is as follows: where hjk are the elements of the channel matrix H, pk is the power allocated to the k-th link, σ 2 is the noise power at the k-th receiver. The large value of SINR is essential in the cases of multi-user and multi-relay networks [12].

Related Work
The  [15]. Fixed BF used a fixed set of weights and time delays to combine the signals using the information mainly about the locations of the sensors in space and the wave direction of interest, received from the sensors employed in the array pattern [16]. Adaptive BF or phased array was based upon the maximization signal at of the desired the main lobe provided by the maximum output SINR of beamformer and minimization of the interference signal [17][18][19]. It was observed that it was a flexible approach to find and estimate the SOI at the output of sensor array using data adaptive spatial or spatio-temporal filtering and interference cancellation. Its performance degradation could also take place, even if the SOI steering vector was precisely known, but the sample size during the training stage was small. Another reason for performance degradation was the environmental non-stationarities because of the fast variations of the propagation channel and rapid motion of interfering sources or antenna arrays. Fangxiao Jin et al. [20] proposed Maximum Correntropy Criterion (MCC) based vigorous cyclic array adaptive BF method to estimate DOA for cyclostationary signals to tackle against the Cycle Frequency Error (CFE) in impulsive noise as well as Gaussian noise environments. Practically, the impulsive noise often shows non-Gaussian properties. It was characterized by sudden bursts and frequently present in wireless systems [21,22]. Due to this, a number of adaptive BF methods such as the Fractional Lower Order Moments-based Beamformer algorithms [23,24], Linearly Constrained Minimum-'Normalized Variance' based Beamformer algorithms [25,26], MCC based Beamformer algorithms [27][28][29], and Correntropy based Beamformer [30,31] proposed to avoid the mismatch of DOA by adaptive beamformer and hence, to optimize its weights using the analog phase alignment by linear searching [36]. Hedi Khammari et al. provided an algorithm for allocating the resources as well as for designing the hybrid BF, and discussed K-mean unsupervised ML algorithm for optimal users grouping to reduce the feedback overhead. The proposed ML based analog BF along with zeroforcing digital precoding and user scheduling was used for better performance in terms of sum-rate [37]. Ahmet M. Elbir discussed the hybrid beamformer design in the mm-Wave -MIMO system. It used two Convolutional Neural Networks (CNNs) using the input of channel matrix based upon an optimization problem for the joint design of precoder and combiner. This technique utilized an algorithm for generating the training data for both networks [38]. Lorenzo Combi et al. designed an efficient algorithm for hybrid BF based on the matching-pursuit for a limited-size dictionary of analog beamformers, which was built on the statistical characteristics of the users' distribution. This dictionary was based upon the knowledge of spatial correlation of few DOAs and DODs representing the few radio front-haul channels at mm-Wave frequencies. Since the narrowband processing at the Resource Allocation Unit (RAU) was affected by the beam squint errors, the broadband analog processing with optical delay lines was adopted for HBF [39]. wide range of noise environments using ML to our best belief. Conventional featurebased approaches mainly depend upon the expert's knowledge, which may perform well on specialized solutions, but poor in generality and encounter high complexity and timeconsuming. To solve these problems, ML classifiers were shown great advantages.
Although ML methods have the advantage of solving classification problems efficiently and good performance, the feature engineering still depends on expert experience to some extent, resulting in degradation of accuracy rate. Therefore, self-learning ability is very important in case of an unknown environment. Moreover, ML has a potential to solve the complex problems without explicit programming. Both the research community and industry have advocated the various applications of ML in the field of wireless communication for resource management such as beamformer design, due to its successful applications to many practical tasks like image recognition. To optimize beamformer vectors in a scenario of MIMO broadcast channel, the Weighted Minimum Mean Square Error (WMMSE) algorithm was designed, which transformed the weighted sum-rate maximization problem into a higher dimensional space to make the problem more tractable [45][46][47].

Problem Statement:
The suitable BF method increases the signal strength so that it may propagate a large distance through combining various scattered beam components into a single beam in a particular direction with the least affection of environmental conditions. The various researchers had worked on various BF methods, but no one tried to implement any of these methods on the ML platform. The novelty of the proposed work is that we are designing an adaptive or phased array BF system, and implementing as well as analyzing it on the ML platform.

Main Contributions of this paper:
1. The proposed algorithm is implemented on a ML platform and is analyzed by the four ML methods.

It works in Maximum
Signal-to-Noise-Interference Ratio (MSINR) sense by the way of optimal adaptive BF and is capable of reducing power consumption as well as operational cost in a mm-Wave massive MIMO heterogeneous network by deploying suitable BF method.
3. The SINR responsible for the adaptive BF under a wide range of noise environments is predicted and maximized against target SINR using the various ML models.
The structure of this paper is as follows: The introduction along with the related work is presented in section 1. The types, proposed work flowchart, and data set and methodology of BF are described in section 2.
where hk is the Ntx1 channel vector between the transmitting array and the receiver antenna. The quantity in the denominator is the absolute magnitude of the channel vector, which is the square root of the sum of the square magnitudes of each of the complex elements of the channel vector. This weighting matrix maximizes the beam to the specific receiver antenna, which is entirely based on the channel vector, scaling both magnitude and phase to form an optimal beam. This beam will likely not represent a specific direction in an environment with a great deal of multipath, and it may include multiple lobes taking advantage of the multipath for the specific transmitter-receiver element combination. When the receiver has more than one element, MRT was applied to form an optimal beam to the first element, and receiver diversity techniques were applied to further enhance the gain using the additional receiver elements.

Transmit Precoding for BF
This technique uses a precoding table to specify a collection of predefined beams. The model also provides a mechanism for defining a table of precoding weights that can be applied to the H-matrix to perform transmit BF or diversity. The precoding weights provided by Alamouti and pseudo-Alamouti codes increased the probability that a receiver employing MIMO techniques will receive a signal with spatial diversity as an advantage. Precoding tables were used to define codebooks or collections of BF weights that can be used to support a BF method. When the precoding table is used to define multiple sets of precoding weights for each of a number of beams for a massive MIMO antenna array, it is attempted to use each set of weights and will select the set that provides the desired SINR. During a simulation, for each receiver, the model will attempt to use each beam and select the beam that provides the best SINR. This simulates a base station that has a fixed set of beams to choose from, which uses reference signals and feedback from each User Equipment (UE) to select the best beam for transmission to that UE.

Proposed Work Flowchart of adaptive BF
The BF technique is mainly used in radar and sonar systems. Its task is to adjust the array weights to maximize SINR in its output as the source moves, while maintaining a constant gain for the SOI. In BF array, noise and interference are minimized in the output and the beam pattern is optimized by the processor incorporated by adjusting the control weights with respect to a prescribed criterion. BF algorithms were based upon certain criteria like minimizing the variance, maximizing the SINR ratio, minimizing the Mean Square Error (MSE) [49][50][51], and were used to optimize the smart antenna patterns. The Generate data using pyArgus antenna array pattern, and perform data pre-processing and cleaning in the form of a vector z n

Data set and its features having qualitative assessment
The required data is generated for the work using modeling and simulation. The python package pyArgus [1] has been used for 20,000 simulations. The noise variance, Pnoise is More number of radiating elements of the antenna is, more focused of the main lobe of beam is. Table 1 shows a brief description of the features, namely as Pnoise, N, d, a, b and Theta_soi using RF in terms of % Inc MSE and Inc Node Purity used for the generation of BF beam in this study. The higher value of any feature plays a more significant role in the generation of BF beams.  Description of the features using RF Table 1

Methodology used
The methodology of the proposed system, which is used for predicting the target SINR in terms of model evaluation parameters, consists of six steps. These steps as mentioned in Fig. 4 are described as follows: In step 1, the data is collected through modeling and simulation, and its pre-processing and cleaning is carried out to enhance its accuracy, validity, completeness, consistency and uniformity in step 2.

3.1Machine Learning (ML) Methods
The four ML methods (shown in Table 3) used for prediction of SINR of the received signal are present in R open source software, which is licensed under GNU GPL. A lot of ML methods are available, but only four methods, namely as rpart, RF, lm and neuralnet are applicable because the proposed model supports only regression and classification data, and output of the proposed model is a numeric value. These methods are explained briefly as:

(a) Decision Tree (rpart):
This method is an extension of C4.5 classification algorithms described by Quinlan [53]. It does not support online learning and suffers from easy overfitting problem. Therefore, it is not well suited for the proposed model. When all weights are trained, it is used to predict the class or quantity. hlayers, maxNwts.
and maxit are the number of hidden layers, maximum network weights and maximum number of iterations, respectively. The neuralnet used is 6-10-1 network. The tuning parameters used in each method minimize the error.

Model Evaluation
Adaptive beamformers are evaluated in terms of the beamformer response, the output SINR, the array gain, the array sensitivity, and the white noise gain.
The output SINR is determined by the equation (3.1) which is as follows: where Rss is sample covariance matrix of the source observed at the array beamformer, Ri+n is the covariance matrix of the interference and noise considered together. The adaptive beamformer is evaluated by the output SINR only, which provides a measure of the quality of communication, and estimates the ratio between the SOI and noise plus interference. It is optimized under wide range of noise environments by optimizing the value of spacing between elements, element tapering, lattice structure between elements and increasing the number of elements in antenna array used. The BF model is evaluated in terms of the following 4 performance analysis parameters given by equations (3.2) -(3.4) [57], which are not derived here:

Mean Absolute Error (MAE)
It measures the error rate of a regression model. However, it can only be compared between models having errors in the same units [57]. It is calculated by the equation where is ℎ actual SINR target value and is ℎ predicted SINR target value. It is calculated for all ML methods, which are shown in table 4.

Correlation (R)
It provides the statistical relationships between true and predicted values. It is defined by the equation ( Correlation is present between 0 and 1, and is considered as good if its value approaches 1 [57]. It is calculated for all ML methods, which are shown in table 4.

Coefficient of Determination (R 2 )
It evaluates the proportion of variance of the dependent variable, provided by the regression model and provides its explanatory power [57]. For perfectness of the model R 2 is 1, and for its failure, R 2 is zero. It is calculated by taking the square of the R − value between the predicted and observed values for all ML methods, which are shown in table 4.

Accuracy
Training Loss and accuracy give overall measures of the model's performance. The accuracy is improved by preprocessing the data. It is calculated by the following equation where a is the true target, p is the predicted target, n is the total number of iterations and e is the acceptable error [57]. It is calculated for all ML methods, which are shown in table 4.

-Fold Cross Validation
It measures the robustness of the predictive method employed. The generated dataset is randomly divided into say k equal size subsamples as a first step. Thereafter, out of the k Sub-samples, a single subsample is retained as the validation data for testing the method, and the remaining k − 1 subsamples are used for carrying out the training of the generated data. The cross-validation process is then repeated K-fold of times, with each of the k subsamples used exactly once as the validation data. Then, all the results from Kfolds can be averaged to provide a single estimation. The 10-fold validation and crossvalidation in terms of true and predicted values of target SINR are shown in figs. 7 and 8.

Simulation Results and Discussion
The proposed adaptive BF system is hybrid in a sense that it is a combination of an analog part driven by a computer controlled system and a ML part. The prediction results of all employed ML methods on the training-testing data set are analyzed. All the models, which were discussed in section 4, have been run on a sample dataset (shown in Table 2) and evaluated on correlation, R 2 , MAE and % accuracy. The dataset is handling a smaller number of input features, which are larger in observation values. The 10-fold validation is used to assess the robustness of the best predictive method. The regression model suffers from overfitting problem as the criterion used for its training is not exactly the same as the criterion used to judge its efficacy. So, the validation experiment has been conducted on the generated dataset using best predictive model selected from training-testing experiment. The overfitting issue may have less chance, if the number of parameters in the employed network is much smaller as compared to the total number of data points in the training set. If the size of the training dataset is increased by collecting more data, techniques like regularization and early stopping are not feasible to prevent over-fitting.

Training-Testing Simulation Experiment
The generated data set is divided into two sets -one set is used for training first and thereafter; the second set is used to test the performance of the result. The generated data set is distributed to 70% and 30% respectively for all employed methods in trainingtesting experiment. Table 4 Table 4 presents the R value of the employed methods. It has been observed that the RF model has the largest R value of 0.92. The R 2 parameter is computed by taking the square of correlation and Table 4 presents the R 2 parameter of the employed methods. It has been found that the RF model has the largest R 2 of 0.85 in the prediction of target SINR on the training-testing dataset.
Accuracy is computed using equation (3.4) with some acceptable error and Table 4 depicts the % accuracy of the employed methods. It has been observed that the RF model has the largest accuracy of 86.40% having acceptable error in the prediction of target SINR on the training-testing dataset.

Validation and Cross-Validation Simulation Experiment
The 10-fold validation and cross-validation are used to measure the robustness of the RF model.

Conclusion
BF is a noise mitigation scheme to improve the SINR ratio of received signals, and focus transmitted signals in desired spatial directions. The parameters of each path of multipath propagation model are cleaved into the corresponding channel gain and the DOA information in the channel matrix. Here, the adaptive BF is used under low and high SINR regime using ML in MSINR sense, and is more suited to massive MIMO systems than switched BF due to its capability to suppress interference and power consumption reduction. The ML models, namely Decision Tree, Random Forest, Linear Model and Neural Network are used to predict the target SINR responsible for BF. The optimization of antenna combining weights is based on MSINR value. The ML models are evaluated and compared in terms of performance analysis parameters, namely correlation, R 2 , Mean Absolute Error and % Accuracy on a data set generated using the python package pyArgus. Random Forest ML model is the best among the four ML models used and has the best performance analysis features as follows: Correlation-0.92, R 2 -0.85, Mean Absolute Error-70.73 and % Accuracy-86.40.. The further research is required to improve the coding to enhance the performance analysis results shown in this paper. The proposed adaptive BF system may be applied in VSCs, which is to be explored in the next research. The more advanced antenna arrays can be used to overcome the optimum halfwavelength limit of arbitrary configured planar antenna systems.

Data Statement
Data will be submitted after manuscript acceptance so that the proper citation may be included in the final publication. The generated dataset will be provided in a file named dataset.csv to the journal, as I am facing difficulty in uploading the same.

Conflict of interests-No
Declarations-All sections are relevant to the manuscript.