Intelligent Automation & Soft Computing DOI:10.32604/iasc.2022.021779 | |

Article |

Massive MIMO Codebook Design Using Gaussian Mixture Model Based Clustering

1Department of ECE, SRM TRP Engineering College, Tamil Nadu, 621105, India

2Dhanalakshmi College of Engineering, Chennai, 601301, Tamil Nadu, India

3Department of Information Technology, Rajagiri School of Engineering and Technology, Kerala, India

4Department of CSE, Bapatla Engineering College, Bapatla, 522102, India

5Department of ECE, Saveetha Engineering College, Tamil Nadu, India

6Gojan School of Business and Technology, Tamil Nadu, India

*Corresponding Author: S. Markkandan. Email: markkandan@gmail.com

Received: 14 July 2021; Accepted: 26 August 2021

Abstract: The codebook design is the most essential core technique in constrained feedback massive multi-input multi-output (MIMO) system communications. MIMO vectors have been generally isotropic or evenly distributed in traditional codebook designs. In this paper, Gaussian mixture model (GMM) based clustering codebook design is proposed, which is inspired by the strong classification and analytical abilities of clustering techniques. Huge quantities of channel state information (CSI) are initially saved as entry data of the clustering process. Further, split into N number of clusters based on the shortest distance. The centroids part of clustering has been utilized for constructing a codebook with statistic channel information, with an average distance that is the shortest towards the true channel data. The enhanced GMM based clustering codebook design outperforms traditional methods, particularly in the situations of non-uniform distribution of channels as demonstrated via simulation results which match theoretical analyses concerning achievable rate. The proposed GMM based clustering codebook design is compared with DFT-based clustering codebook design and k-means based clustering codebook design.

Keywords: Gaussian Mixture Model (GMM) based clustering; Massive MIMO; Codebook design; DFT

Massive multiple-input multiple-output (MIMO) is becoming the major driver for 5th generation wireless communication as well as transmission systems to enhance data speeds [1]. The precision of channel state information (CSI) has been important for beam development and spatial multiplexing improvements in transceivers with a huge number of antenna components [2]. The most popular approach for acquiring CSI is restricted feedback dependent on codebook, in which the receiver exclusively transmits return to the transmission index of the optimal weight vector of MIMO from a predefined codebook.

A significant study has been dedicated to the construction of a codebook in recent decades. To optimize the lowest gap between the codebook of MIMO vectors, a codebook namely the Grassmannian quantization codebook is developed. The independent channel is considered and involved in performing an identical distribution that its dominating acute singular vectors are uniformly distributed in space [3,4]. The alternative method namely random vector quantization (RVQ) produced the codebook randomly using MIMO vectors as isotropic assumption [5,6]. Furthermore, the DFT codebook technique evenly split the whole angular domain further into two B accelerated portions as well as created the codebook solely depending on the acceleration of the angle of arrival or departure [7,8], wherein the amount of feedback bits is denoted as B. The Multi-input multi-output (MIMO) channel is isotropic or distributed uniformly, which is a frequent assumption. This assumption is mostly not met in the real-world wireless environment. Thus, the MIMO channel being limited in the angular zone [9], and its multiple directions are focused on a specific angle limit. This prompted [10] to investigate a non-uniform codebook model that surpassed the uniform codebook approach. The propagation atmosphere is either uniform or not, it must be adopted by the codebook design.

By employing a machine learning approach, it is possible to design a wireless physical layer [11–13], feedback method of CSI depending on deep learning technique for massive MIMO has been implemented, where convolutional neural networks convert the indices of the channels to receiver's compressed expressions and then inverse transformation is performed on transmitter side [14,15]. Comparable to mentioned techniques, the channel is considered sparse, which isn't a universal assumption; for example, it's not appropriate for a dynamic dispersed ecosystem. The K-means algorithmic approach is well-known as it is often utilized as a clustering technique. It is utilized in MIMO identification [16,17], and NOMA client clustering [18] due to its capacity to classify and analyze huge volumes of data. It's essential mentioning that channel data may be divided into several groups, where each can be defined using clustering centroids.

A Gaussian mixture is a multiple distributions probability of a convex combination, often termed as mixture components [19]. Since finite mixture methods have been more popular in recent times are utilized as a combination of two distinct normal distributions to evaluate measurements of a large dataset containing 1000 crab. In diverse fields including medicine [20], sociology [21], physics [22], and several others application fields, Gaussian finite mixture models having proved effective for modeling complicated data.

Cluster analysis is a method of classifying information flows into various groups or clusters, and hence, the group containing the data points is comparable with one another rather than data points available in other clusters. The various types of clustering process can be categorized into divisive algorithms or hierarchical agglomerative with distinct linkages, partition optimization methods including model-based clustering [23], K-mean, Kmedoids, and density-based clustering. The connection among clustering and Gaussian mixture models is used in the latter. It is assumed that every mixture component oversees simulating a certain data set. Whereas this assumption is broken and requires a specific treatment, including combining mixture components [24–26], may be necessary, and concentrate mainly on the one-to-one connection among clusters as well as mixture components.

In this paper, Section 2 includes the literature review related to massive MIMO codebook design. Section 3 includes the proposed Gaussian mixture model (GMM) based clustering for designing a massive MIMO codebook. Section 4 compares the performance of the proposed system model with DFT, and k-means based clustering method concerning achievable rate and Section 5 includes the conclusion.

Depending on the MIMO channel properties, certain codebook designs for large MIMO systems have been studied. The codebooks for massive MIMO systems are generated by the compression of channel matrices to a smaller dimension through sparsity leveraging of channel descriptions in the domain of angle [27–30]. The construct the MIMO channel description into overfitted dictionaries because the departure angle, as well as the arrival angle, are non-uniform inside the angle-domain. With the premise that the departure angle information stays invariant in a departure angle coherence period, the departure angle adaptive subspace codebook formulated the channel profits very accurately [31]. An adaptive codebook depending on instantaneous CSI is proposed with the codebook scaling size only proportionally with the channel correlation matrix's ranking [32]. Thus, the statistical property is heavily reliant on these traditional codebook designs.

The antenna arrays have been customizable, as well as the transmission methods are more adaptable, according to developing wireless transmission systems. The azimuth codebook of Kronecker-product as well as the elevation codebook derived from 2 unique feedback mechanisms produces a codebook for 2D antenna arrays [33]. A novel double codebook is presented for the rectangular array construction in a uniform co-polarized. The correlation matrices of the 2 orthogonal directions based on Kronecker-product [34] represent the entire long-term characteristics. To summarize, the codebook design must account for a wide range of wireless situations as well as antenna array topologies in large MIMO systems.

Deep learning (DL) methods are preferred mainly for prediction for successfully tackle the CSI feedback issue [35–39]. In [40], a deep neural network (DNN) understands the characteristics of the wireless communication channel as well as the geographical features in the angle zone using training to provide channel estimate and departure angle estimation. At the receiver site, Conventional neural networks (CNNs) understand the structural channel sparsity acquired from training sampling data then converted CSI into a relatively optimum amount of codewords in [41–43].

The massive MIMO system communication is provided with one downlink cell is considered wherein base station (BS) is linked with both

The signal power generally assumed to be normalized is given as E

Here,

As illustrated in Fig. 1, the codebook with

The receiver returns the matching codeword index to the transmitting side using a limited feedback method. The transmitting side selects pre-coding matrix w acquired from the codebook C depending on the index followed by the transmitted signals using the chosen w is produced. Unlike conventional codebook design approaches, Gaussian mixture model-based clustering codebook design will use the GMM based clustering processing unit to evaluate CSI statistical characteristics and create a codebook depending on representation values of the statistical characteristics.

At the BS, the antennas including a uniform rectangular array (URA) as well as uniform linear array (ULA) configurations have been considered. ULA offers better performance in terms of capacity than URA due to azimuthal orientation of the array. The traditional channel model depending on narrowband ray is used. The antennas with ULA consist of downlink channel sequence may be written as

Here,

Here, BS’s antenna spacing is denoted as d, and the carrier with wave-length is denoted as λ. Angle of Departure (AoD) of the k-th users in i-th path is represented using θ(k,i). The number of users simulated is from 1 to 100 for antenna size of 10 to 100.

The channel matrix of downlink for a URA of antennas comprising horizontal antennas is denoted as

Here,

The AoD’s elevation as well as the azimuth of the k-th users in i-th route are

Assuming, overhead to remain constant is

Here, the precoding matrix chosen from codebook C is denoted as w, and the transmitting power is denoted as

The function achievable rate is given as

The above equation is rewritten and expressed as,

The difference among statistics channel information is denoted as

As a result, the proposed efficient codebook design reduces the sum distance between actual as well as statistics channel information.

3.3 Key Propagation Characteristics

The DNN is particularly designed to determine critical propagation properties including delay, elevation angle, channel gains, and azimuth angle. A formula

The fully connected ‘L’ layers in DNN, comprising a single input layer, L-2 hidden layers followed by a single output layer, are chosen Fig. 2. The channel sequence H with the nonlinear cascaded transformation is the output

The q-th characteristic

Every data object is linked with the nearby centroid as per the nearest neighbor principle. The data item

Here,

Following the assignment of all data items, the centroids are upgraded using the centroid criterion, which selects the things with the smallest mean distance of each cluster as the fresh centroid. The q-th characteristic’s l-th cluster

Here,

Continue GMM based clustering procedure still items, as well as centroids of every cluster, remain the same. Lastly, the

In the massive MIMO, we examine several codebook designs approaches to enhance the resilience of the proposed model designing. The codebook construction technique will be shown using a variety of important propagation properties.

Both in correlated and uncorrelated channel environments, the angle features are critical for codebook design. The structural codebook only requires angle features in the event of substantial channel correlation. Therefore, we use the angle features to understand a unique propagation feature’s codebook design. The method of codebook building will be illustrated in detail using DFT codebook design depending on centroids.

The angle characteristic with centroid generates every individual codeword

Angle-based codebooks are expressed as follows as per the centroids:

In codebook design, the gain, as well as angular features, is employed once the channel is uncorrelated. Each codeword is formed using the x-axis component as well as the y-axis component depending on the valid space

The double-polarized channel codebook construction is done initially utilizing horizontal as well as elevation angles; later k-means clustering is used to get the final codebook.

Here, the horizontal angles are represented as

3.5 Algorithm of the Proposed Codebook Design

STEP 1: As the beginning centroids provide N sample data of the q-th propagation feature, expressed as a

STEP 2: The ‘d’ distance is estimated using

STEP 3:

STEP 4: Depending on the centroid criterion, every individual cluster are upgraded with the centroid

STEP 5: If the q-th characteristic’s centroid is constant, then step 3 as well as step 4 as to be recurrently used still acquiring the final centroid output

STEP 6: The propagation characteristics of every centroid have to be recurrently performed still acquiring

STEP 7: The valid space is obtained using

STEP 8: For various circumstances, generate the codeword that corresponds to

The proposed Gaussian mixture model (GMM) based clustering codebook design approach performs in massive MIMO systems. The difference rate is estimated among the perfect CSI as well as enhanced codebook-based feedback method. In an ideal world, the optimal pre-coding vector is represented as

The rate difference, which is determined by

Eq. (20), can be recast as for the 2nd codebook design technique discussed in the previous subsection.

The reduction in minimizing rate interest as,

Using the above-mentioned expression because of the channel model,

The aggregate rate of the GMM-based clustering codebook technique has been provided in this section under a variety of situations and with distinct antenna array configurations. The aggregate rate of proposed GMM-based clustering models is also compared to the traditional DFT method and K-means for

Fig. 5 shows the achievable rates for the corresponding SNR for k-means based clustering codebook method for various numbers of antennas

The Symbol-error-rate (SER) of proposed GMM based clustering with DFT and k-means based clustering is plotted in Fig. 7. The SER is defined using

We presented a Gaussian mixture model (GMM) based codebook approach for massive MIMO in this paper. It combines GMM with clustering methods that were used to create the codebook. The DNN learns the important CSI characteristics whereas the GMM based clustering algorithms obtain the statistic information for the associated characteristics. By utilizing DNN frameworks, the proposed GMM based clustering codebook approach can reduce channel parameters. Furthermore, because the clustering algorithmic approach can understand characteristics of the wireless channel, it ensures CSI feedback's performance in a variety of changing wireless settings. The proposed GMM based clustering codebook design outperforms existing methods, as demonstrated by simulation results as well as theoretical analysis concerning achievable rate. Fortunately, by upgrading the clustering processes regularly, the suggested codebook architecture may understand and adapts to the real world.

Funding Statement: The authors received no specific funding for this research.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present research.

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