International Journal of Electrical and Computer Engineering (IJECE) Vol.
No.
December 2024, pp.
ISSN: 2088-8708.
DOI: 10.
11591/ijece.
Hybrid digital and analog beamforming design using genetic Sidi Mohammed Bahri.
Abdelhafid Bouacha Laboratory of Telecommunications.
Faculty of Technology.
Abou-BekrBelkayd University.
Tlemcen.
Algeria
Article Info
ABSTRACT
Article history:
Hybrid analog and digital beamforming is gaining attention for its practical application in large-scale antenna systems.
It offers significant cost savings, reduced complexity, and lower power consumption compared to entirely digital beamforming, all while maintaining comparable performance.
This article proposes a hybrid beamforming architecture aimed at addressing these challenges by using a reduced number of radio frequency (RF) chains while achieving performance comparable to entirely digital schemes.
The study demonstrates that matching the number of RF chains to the total number of data streams enables hybrid beamforming to compete effectively with entirely digital beamformers.
The adopted approach focuses on computing analog and digital precoders and combiners using the metaheuristic method of genetic algorithms, in a point-to-point multiple input multiple output (MIMO) system scenario.
The objective is to simplify the system and reduce costs by optimizing the number of antennas.
RF chains, and data streams, all while maintaining comparable performance to entirely digital beamforming.
The study's results show that increasing the number of antennas significantly impacts the quality and capacity of the hybrid massive MIMO beamforming system.
Conversely, reducing the number of RF chains has a negligible effect on quality and capacity, but simplifies the design and minimizes costs Received Apr 23, 2024 Revised Jul 25, 2024 Accepted Aug 6, 2024 Keywords:
Genetic algorithm Hybrid beamforming Massive multiple input multiple Meta-heuristic method Millimeter wave This is an open access article under the CC BY-SA license.
Corresponding Author:
Sidi Mohammed Bahri Laboratory of Telecommunications.
Faculty of Technology.
Abou-BekrBelkayd University Tlemcen.
Algeria Email: sidimohammed.
bahri@univ-tlemcen.
INTRODUCTION
The exponential increase in data usage on mobile devices and the increasing demand for high data rate applications have motivated the development of millimeter wave .
mWav.
communication systems .
Ae.
The mmWave communication systems offer a large bandwidth and are capable of providing high data rates.
However, the high frequency and high path loss of mmWave signals present significant challenges in the design of efficient communication systems .
Nonetheless, the reduced wavelength associated with mmWave frequencies also facilitates the denser arrangement of antennas within a given physical space.
This phenomenon paves the way for extensive spatial multiplexing and the implementation of markedly focused beamforming strategies.
Consequently, the emergence of the massive multiple input multiple output (MIMO) concept becomes as a defining feature within the domain of mmWave communications.
However, the implementation of efficient beamforming techniques for mmWave communications is not without challenges.
Traditional approaches to beamforming, including both digital and analog methods, encounter limitations when applied to mmWave communications.
The utilization of digital beamforming in mmWave systems is hindered by the exorbitant expenses and power consumption associated with requiring a dedicated Journal homepage: http://ijece.
ISSN: 2088-8708
radio frequency (RF) chain for each antenna element .
Ae.
Analog beamforming, while more energyefficient, suffers from limitations in adaptability and flexibility, particularly in handling dynamic channel Addressing these challenges, researchers have turned their focus towards hybrid beamforming architectures, which combine the strengths of both digital and analog techniques.
Within the literature, various hybrid beamforming architectures have been proposed, each with its own advantages and limitations.
Among these, the utilization of analog or RF beamforming methodologies, implemented through analog circuitry, has been introduced .
Ae.
These methodologies predominantly rely on analog phase shifters, which enforce a constant modulus constraint on the beamformer's constituent elements.
Consequently, analog beamforming displays inferior performance when compared to entirely digital beamforming designs.
alternate avenue for addressing the RF chain limitation involves antenna subset selection, realized through the application of uncomplicated analog switches .
Ae.
However, these methods fall short of achieving complete diversity gains in correlated channels, as the antenna selection scheme exclusively engages a subset of channels .
, .
Despite the progress in this field, certain critical questions remain.
One such question pertains to the relationship between the number of RF chains and data streams in a hybrid beamforming architecture.
Interestingly, research has shown that the number of RF chains needs only to scale linearly with twice the total number of data streams to achieve performance comparable to entirely digital schemes.
However, challenges arise when the number of RF chains falls short of this threshold, warranting the exploration of heuristic algorithms proposed in .
The problem this paper addresses is the design and implementation of efficient beamforming techniques for mmWave massive MIMO systems that can overcome the inherent limitations of both digital and analog beamforming methods.
Specifically, it tackles the challenges posed by the high costs and power requirements of digital beamforming, the limited flexibility and adaptability of analog beamforming, and the limitations of heuristic methods.
Heuristic methods, while useful, often fail to achieve global optima and can be trapped in local minima, leading to suboptimal performance in dynamic and complex channel conditions.
To address these challenges, recent advancements in optimization techniques have introduced metaheuristic and global methods, which offer the promise of attaining global optima without succumbing to local These methods, though computationally intensive, provide robust solutions to ill-conditioned problems and constraints .
It is within this context that we propose the application of the genetic algorithm to the design of hybrid beamformers.
In this paper, the suggested approach involves utilizing a genetic algorithm to develop hybrid beamformers specifically designed for point-to-point massive MIMO systems.
The genetic algorithm is employed to optimize both analog and digital precoders and combiners, aiming to maximize spectral efficiency under the assumption of perfect knowledge of channel information (CSI) at both the base station and user level while minimizing implementation costs.
This approach leverages the genetic algorithm's robust global optimization capabilities to address the limitations of traditional heuristic methods and improve system performance in diverse scenarios.
Employing a genetic algorithm enables the design of hybrid beamformers that demonstrate commendable performance under the following conditions: .
when the number of RF chains is no less than the number of data streams, and i.
in scenarios where an uncorrelated channel matrix assumption holds true.
The results achieved with this approach are significant improvements in spectral efficiency and bit error rate (BER) compared to existing hybrid methods and close to the performance of entirely digital beamforming systems.
Detailed simulations and numerical analyses validate the efficacy of the genetic algorithm-based approach, showing superior performance in various configurations, including different numbers of antennas.
RF chains, and data streams.
For example, the results indicate that spectral efficiency increases as the signal-to-noise ratio (SNR) improves, and an increase in the number of antennas for transmission and reception enhances spectral efficiency and reduces BER.
Additionally, the genetic algorithm demonstrates notable efficiency gains, surpassing heuristic methods and achieving near-optimal performance in several key metrics.
SYSTEM MODEL AND PROBLEM FORMULATION
Consider a massive MIMO hybrid beamforming multi-user system operating in millimeter-wave frequencies, as depicted in Figure 1.
In this setup, a transmitter utilizes an array of ycAyc antenna elements and ycAycycIya RF transmission chains to communicate concurrently with ya users.
Each user employs an array of ycAyc antenna elements and ycAycycIya RF chains for transmitting ycc data streams.
To facilitate multi-stream communication, the system must satisfy the following conditions: ycc O ycAycycIya O ycAyc and ycAyc O ycAycycIya O ycAyc where ycAyc = ycoycc .
Int J Elec & Comp Eng.
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Int J Elec & Comp Eng
ISSN: 2088-8708
Figure 1.
System diagram for the downlink of a multiuser massive MIMO system with hybrid The baseband data streams undergo sequential precoding in a hybrid beamforming system operating at millimeter-wave frequencies.
Initially, digital precoding ycOya is applied, followed by analog precoding ycOycIya through corresponding RF chains.
The analog precoder ycOycIya consists of phase shifters satisfying:
cOycIya .
co, yc.
| = 1/OoycAyc OAyco, ycu.
The hybrid precoder configuration includes ycOya = .
cOya,1 o ycOya,yco o ycOya,ya ] OO ycIya yycA ECycAyc ycAyc yycAycycIya ycIya yycc where ycOya,yco OO ECycAyc represents the digital precoder matrix for the yco -th user, and ycOycIya OO Assuming the initial signal is ycI, the transmitted signal ycU is given by .
ycU = ycOycIya ycOya ycI = Ocya yco=1 ycOycIya ycOyayco ycIyco where ycI = .
cI1ycN , ycI2ycN ,a , ycIyaycN ]ycN OO ECycAyc y1 , where ycyaycN OO ECyccy1 denoting the symbols for the yco-th user, satisfying ya.
cyc ya ] = yaycAyc , ycU OO ECycAyc y1 and AnycOycIya ycOya An2 = ycEycN represents the total transmitted power.
For simplification, we assume a block fading narrowband propagation channel, resulting in the received signal vector ycyco OO ECycAyc y1 for the k-th user:
ycyco = yayco ycOycIya ycOyayco ycIyco yayco Ocyayco=1 ycOycIya ycOyayco ycIyco ycsyco ycoOyco The channel matrix yayco OO ECycAyc yycAyc represents the communication channel for the k-th user, while ycsyco OO ECycAyc y1 denotes the noise vector with independent and identically distributed complex Gaussian entries, having zero mean and covariance yuaycu2 yaycAyc .
Each user k initially processes received signals using an RF combiner ycOycIyayco OO ycIya ECycAyc yycAyc , implemented with phase shifters ensuring .
cOycIya .
co, yc.
| = 1/OoycAyc OAyco, yc.
Subsequently, the signals are down converted to baseband using ycAycycIya RF chains.
Finally, a low-dimensional digital combiner ycIya ycOyayco OO ECycAyc yycc processes the signals to produce the final processed signals.
ya ya ya ycUyco = a ycOycyco yayco ycOycyco ycIyco a ycOycyco yayco OcycoOyco ycOycyco ycIyco ycO aycyco ycsyco where ycOycyco = ycOycIya ycOyayco and ycOycyco = ycOycIyayco ycOyayco .
The combined multiuser channel is defined as: ya = .
a1ycN , ya2ycN ,A A A , yayaycN ]ycN .
Given Gaussian symbols are transmitted, the achieved spectral efficiency is determined as per reference .
ya ya ya ycIyco =ycoycuyci2 .
aNyc ycOycyco yaycoOe1 ycOycyco yayco ycOycyco ycOycyco yayco | .
ya ya The interference plus noise covariance matrix is given by yayco = ycOycyco yayco (OcycoOyco ycOycyco ycOycycoya ) yaycoya ycOycyco yua 2 ycOycyco ycOycyco .
Hybrid digital and analog beamforming design using genetic algorithms (Sidi Mohammed Bahr.
A ISSN: 2088-8708 This paper aims to maximize total Bandwidth efficiency while respecting total transmit power We assume perfect knowledge of yayco , focusing on solving the following problem: finding the optimal hybrid precoders at the base station (BS) and optimal hybrid combiners for each user.
maximize OcKk=1 k R k
VRF ,VD ,WRF ,WD
ycNyc .
cOycIya ycOya ycOyaya ycOycIya O ycEycN .
cOycIya .
cn, y.
= 1.
OAycn, yc .
cOycIyayco .
cn, y.
| = 1.
OA ycn, yc, yco .
yu where ycEycN is the power at the base station, and the weight yuyco represents the priority of user yco, i.
Ocyco yco yco=1 yuyco larger it is, the higher the priority of user yco.
Hybrid beamformer design for massive MIMO systems with single user This section centers on the development of hybrid beamformers.
We start by examining a massive MIMO system where a base station equipped with ycAyc antennas transmit ycAyc data symbols to a user with ycAyc To simplify notation, we assume an equal number of RF transmission and reception chains, denoted as ycAycycIya = ycAycycIya = ycAycIya .
In this hybrid system configuration, the bandwidth efficiency expression in .
can be simplified as .
R = log 2 .
aNyc yua2 ycOyc .
cOycya ycOyc )Oe1 ycOycya yaycOyc ycOycya yaya | .
where ycOyc = ycOycIya ycOya and ycOyc = ycOycIya ycOya .
In this section, our initial focus is on designing hybrid beamforming systems where the number of RF chains equals the number of data streams, i.
ycA ycIya = ycAyc .
We propose a meta-heuristic algorithm that achieves near-capacity rates under this condition.
Extending our approach, we demonstrate that the algorithm developed for ycA ycIya = ycAyc can also be applied when ycAyc < ycA ycIya < 2ycAyc .
The efficiency maximization problem in .
requires joint optimization of precoders and hybrid However, simultaneously optimizing the transmit-receive matrix for such constrained problems is generally challenging .
Additionally, constraints on the elements of analog beamformers in .
suggest that developing a low-complexity algorithm for finding the exact optimal solution remains difficult .
Therefore, this section adopts the following strategy: we initially focus on creating hybrid precoders assuming an optimal receiver design.
Subsequently, our objective shifts to designing the hybrid transmitter The problem of hybrid precoder design can be broken down into two steps as follows .
ycoycaycu ycoycuyci2 .
aycAyc ycOycIya ,ycOya yua2 ya ya yaycOycIya ycOya ycOyaya ycOycIya ya | .
cNyc .
cOycIya ycOya ycOyaya ycOycIya )OycE .
cOycIya .
cn, y.
= 1.
OAycn, yc .
This section introduces a genetic algorithm aimed at finding an effective solution to problem .
Initially, we derive the solution for the digital precoder given a fixed RF precoder, ycOycIya , as outlined in problem .
Subsequently, with the digital precoder established, we propose using the genetic algorithm to identify an optimal global RF precoder.
Design of a digital precoder for ycAycyc = ycAyei The initial step of the algorithm focuses on the design of ycOya , assuming that ycOycIya remains constant.
When the RF precoder is fixed, the effective channel yayceyceyce = yaycOycIya can be treated as the channel of interest.
Consequently, the task of designing the digital precoder can be formulated in the following manner:
ycoycaycu ycoycuyci2 .
aycAyc ycOya yua2 ya yayceyceyce ycOya ycOyaya yayceyceyce Int J Elec & Comp Eng.
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ycNyc .
cEycOya ycOyaya O ycE) A .
ya where ycE = ycOycIya ycOycIya - Genetic algorithm optimization In combinatorial optimization, genetic algorithms are employed to solve problems by introducing random variations in the chromosomes of the population.
Chromosomes with higher fitness values are more likely to survive and propagate to the next generation .
As generations pass, the chromosomes that remain in the population tend to have high fitness values, representing sub-optimal solutions.
Three basic operations of genetic algorithmsAiselection, crossover, and mutationAiwill be described in later sections.
The genetic algorithm requires defining a function that assesses the relevance of potential solutions based on the quantities to be optimized.
This is known as the objective function .
r cost function or fitness functio.
, which establishes a link between the physical problem and the optimization process.
The fitness function is a tool used to express the optimization goal and serves as a means to develop chromosomes.
The fitness function must mathematically translate the user's objectives.
Mathematically, the problem involves searching for the digital encoding law ycOya applied to the system input to maximize the spectral efficiency, given by .
ycI1 = log 2 .
aNyc yua2 ya yayceyceyce ycOya ycOyaya yayceyceyce .
In the context of the genetic algorithm, the digital encoding law ycOya is likened to a chromosome, with genes representing the values of this vector .
cOyaycn in this cas.
The initial phase of the genetic algorithm involves creating a population of individuals randomly in the form of a binary matrix, which contains an ya y ya number of 0s and 1s as follows: C denotes the number of columns, which is the product of the number of parameters in vector ycOya and the number of bits in the binary code used.
ya represents the number of rows, corresponding to the total number of individuals in the Following this, the fitness of individuals within the population is assessed by computing the fitness function for each individual.
This process includes decoding the chromosome associated with each individual in the population, which reverses the encoding operation.
The formula .
is utilized to decode N-bit genes for this purpose:
OeycE ycE = ycoycaycu ycA ycoycnycu OcycAOe1 ycn=0 2 ycaycn ycEycoycnycu ycEycoycaycu and ycEycoycnycu denote the maximum and minimum limits of the parameter value range, respectively, while ycaycn represents the i-th bit within the gene associated with parameter P .
here P may include one or more parameters, such as ycOyaycn ).
The resulting vector P is subsequently inputted into function ycI1 to to evaluate the fitness of this yaycnycycuyceycyc yaycycuycaycycnycuycu = ycI1 An elitist strategy that ensures the presence of the best individual in the future generation is utilized.
For this, a ranking-based selection method known as ranking is employed.
The crossover method used is the one-point Design of an RF precoder for ycAycyc = ycAyei Now, our objective is to design the RF precoder while assuming ycOya ycOyaya OO yu 2 ya.
The given assumption ensures that the transmitter power constraint in .
is automatically met regardless of the design of ycOycIya .
Consequently, the RF precoder can be acquired by resolving the subsequent problem:
ycoycaycu ycoycuyci2 .
a ycOycIya yu2 ya ycO ya ycO | yua 2 ycIya 1 ycIya yc.
cOycIya .
cn, y.
= 1.
OAycn, yc .
where ya1 = yaya y ya.
The problem of designing an analog precoder can be translated into an optimization problem that enhances the bandwidth efficiency ycI2 given by .
Hybrid digital and analog beamforming design using genetic algorithms (Sidi Mohammed Bahr.
A ISSN: 2088-8708
ycI2 = ycoycuyci2 .
a yu2 ya ycO ya ycO | yua 2 ycIya 1 ycIya In the genetic algorithm, the digital encoding law ycOycIya is like a chromosome, with genes representing its Initially, a population is created randomly as a binary matrix of size.
ya y ya, where ya is the number of individuals and ya is the product of the number of parameters in vector VRF and the number of bits in the binary code.
Each individual's fitness is evaluated by decoding their chromosome using a specific formula, which considers the bounds of the parameter value interval.
The decoded vector ycE is then used in function ycI2 to assess the individual's fitness.
yaycnycycuyceycyc yaycycuycaycycnycuycu = ycI2 An elitist strategy that ensures the presence of the best individual in the future generation is utilized.
For this, a ranking-based selection method known as ranking is employed.
The crossover method used is the one-point Design of hybrid combiners for ycAycyc = ycAyei Finally, our objective is to create hybrid combiners that optimize the total bandwidth efficiency in .
, given that hybrid precoders have already been designed.
When ycAycIya = ycAyc , the digital combiner becomes an unconstrained square matrix.
Hence, without compromising optimality, we can separate the design of ycOycIya and ycOya by initially designing the RF combiner assuming an optimal digital combiner.
Subsequently, we can determine the optimal digital combiner for this RF combiner.
Consequently, the problem of RF combiner design can be expressed as follows:
max log 2 .
a yua2 ycOycIya ya ya .
cOycIya ycOycIya )Oe1 ycOycIya ya2 ycOycIya | .
cOycIya .
cn, y.
= 1.
OAycn, yc .
where ya2 = H ycOyc ycOycya yaya .
This issue bears resemblance to the RF precoder design issue described in .
Consequently problem .
can be approximated by adopting the RF precoder design problem from .
To design ycOycIya , the genetic algorithm can be employed, substituting ya2 with ya1 and with yu2 .
ycAyc max log 2 .
a ycOycIya ycAyc yua 2 ya ycOycIya ya2 ycOycIya | yc.
cOycIya .
cn, y.
=1.
OAycn, yc .
The problem of designing an analog combiner can be translated into an optimization problem focused on maximizing spectral efficiency ycI3 given by .
R 3 = log 2 .
a ycAyc yua 2 ya ycOycIya ya2 ycOycIya | .
In the genetic algorithm, the digital encoding law ycOycIya functions like a chromosome with genes as its values.
A population is created randomly as a binary matrix of size ya y ya.
Each individual's fitness is assessed by decoding their chromosome and evaluating the resulting vector ycE using function R 3 .
yaycnycycuyceycyc yaycycuycaycycnycuycu = R 3 An elitist strategy that ensures the presence of the best individual in the future generation is utilized.
For this, a ranking-based selection method known as ranking is employed.
The crossover method used is the one-point Finally.
When every other beamformer has been fixed, the best digital combiner is found when presented in .
ya ycOya = yaOe1 ycOycIya yaycOyc ya ya where ya = ycOycIya yaycOyc ycOycya yaya ycOycIya yua 2 ycOycIya ycOycIya Int J Elec & Comp Eng.
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ISSN: 2088-8708
Design of hybrid beamforming for ycAyei < ycAycyc < yaycAyei In this section, we introduced a meta-heuristic algorithm for designing hybrid beamformers initially for ycAycIya = ycAyc .
We then shifted focus to cases where ycAyc < ycAycIya < 2ycAyc .
Even in scenarios with ycAyc < ycAycIya < 2ycAyc , the transmitter design problem remains defined by .
Given a fixed RF precoder, the optimal digital ya precoder is determined using .
, with the condition ycOycIya ycOycIya = yu 2 .
aycAyc .
The objective function from .
, aimed at maximizing over ycOycIya , is reformulated to handle all eigenvalues, approximating the function when ycAycIya is approximately ycAyc .
Thus, the RF precoder design problem is effectively represented by .
SIMULATION
In this section, we showcase the findings from our simulation study, aimed at evaluating the efficiency of our proposed algorithm in a massive MIMO system.
We will examine the impact of the SNR .
he ratio of signal power to noise powe.
on spectral efficiency and BER .
ate of errors in bit transmissio.
in hybrid MIMO beamforming systems.
Various configurations will be analyzed by varying the number of antennas, the number of RF channels, and the number of data streams.
Furthermore, we will conduct comprehensive comparisons with existing hybrid beamforming algorithms and a pure digital beamforming We consider a base station utilizing a massive MIMO system.
A linear antenna configuration within a Rayleigh multipath propagation environment is assumed .
, described by the following channel matrix:
ycAycA ya yayco = Oo yc yc Ocyayco=1 yuycoyco ycayc OIycoycyco ycayc (OIycoycyco ) .
ya The complex gain yuycoyco yeye.
represents the yco -th path's strength between the base station and the k-th user, with hase angles OIycoycyco OO .
, 2yuU] and OIycoycyco OO .
, 2yuU].
Additionally, ycayc (.
) and ycayc (.
)denote the response vectors of the antenna array on reception and transmission, respectively.
The response vectors of the array configuration with ycAyc uniform linear antenna elements are given as .
= OoycAyc , yce ycycoyccycycnycu.
U , yce ycycoycc.
cAycOe.
] ycN 2yuU where yco = , ycc represents the distance between antennas and yuI denotes the wavelength of the signal.
yuI At the receiving end, we also consider a single user equipped with a massive MIMO system.
In our simulation, we model an environment with 15 multipath components between the base station and each user.
These components have uniformly distributed arrival and departure angles, with a distance of yuI/2 separating each antenna element.
We evaluate the system's performance in terms of spectral efficiency and bit error rate.
Impact of varying the number of transmit and receive antennas We study a base station using hybrid MIMO beamforming technique with two RF channels .
cAycIya = .
for both transmission and reception, and two data streams .
cAyc = .
The optimization of precoders and combiners through the genetic algorithm can be easily accomplished by adjusting the input parameters of the The input parameters of the genetic algorithm .
fter several trial.
are listed:
- Population size: 20 individuals - Number of generations: 20 - Mutation rate: 0.
- Crossover rate: 0.
- Bit length: 16 We vary the number of antennas both in transmission and reception to evaluate performance based on spectral efficiency and bit error rate.
Spectral efficiency in terms of SNR with variation of ycAyc and ycAyc Based on the findings depicted in Figure 2, we observe the following points: Spectral efficiency increases as SNR increases.
An increase in the number of antennas used for transmission and reception also leads to improved spectral efficiency.
For example, in a massive MIMO beamforming system with 512y512 antennas compared to a 16y16 MIMO system, the bandwidth efficiency improves from 10 bits/s/Hz at an SNR of 10 dB.
Bit error rate (BER) in terms of SNR variation with ycAyc and ycAyc From the results in Figure 3, the following observations can be made: BER continuously decreases as SNR increases.
BER decreases as the number of antennas used for transmission and reception increases.
Hybrid digital and analog beamforming design using genetic algorithms (Sidi Mohammed Bahr.
A ISSN: 2088-8708 For example, for a BER of 10-2, the SNR improves by 20 dB when transitioning from a 16y16 MIMO system to a 512y512 MIMO system.
Thus, at an SNR of 0 dB, the minimal BER .
is achieved for the 512y512 MIMO system.
Figure 2.
Spectral efficiency as a function of SNR for various values of the number of transmitting and receiving antennas where ycAycIya = ycAyc = 2 Figure 3.
BER as a function of SNR for various values of the number of transmitting and receiving antennas where ycAycIya = ycAyc = 2 Impact of varying the number of RF chains In this part of the simulation, we analyze the bandwidth efficiency of hybrid precoding techniques in a MIMO beamforming system .
with two data streams .
cAyc = .
, based on SNR.
We vary the number of RF chains for both transmission and reception in each case studied.
Spectral efficiency in terms of SNR variation with ycAycIya Based on the findings depicted in Figure 4, several notable observations can be derived.
Spectral efficiency increases as SNR increases.
A slight increase in spectral efficiency is observed when the number of RF channels used for both transmission and reception increases from 6 to 10.
For example, at an SNR of 0 dB, spectral efficiency experiences an enhancement of 2.
5 bits/s/Hz in a hybrid MIMO beamforming system with ycAycIya = 10, compared to a system with ycAycIya = 8.
However, the number of RF channels does not significantly impact spectral efficiency.
rather, it helps minimize system implementation costs.
Bit error rate (BER) in terms of SNR variation with ycAycIya From the results in Figure 5, the following observations can be made: BER decreases as SNR Increasing the number of RF channels for both transmission and reception leads to a decrease in BER.
For instance, for a BER of 10-2, the SNR improves by 11 dB when increasing the number of RF channels from 6 to 10.
However, this improvement is modest, suggesting that the influence of RF channels on system performance is negligible.
Hence, reducing the number of RF channels is possible to cut costs.
Impact of variation in rf chains at transmission and reception with ycAycyc = ycAyei In this simulation section, we analyze the spectral efficiency of hybrid precoding techniques in a MIMO beamforming system .
, based on the SNR.
We vary the number of RF chains for both transmission and reception while maintaining ycAycIya = ycAyc .
Spectral efficiency in relation to SNR and ycAycIya variation According to the results presented in Figure 6, a notable trend emerges: Spectral efficiency increases as SNR increases.
With an increase in the number of RF chains, bandwidth efficiency also improves.
For example, at an SNR of -10 dB, spectral efficiency experiences an enhancement of 100 bits/s/Hz in a hybrid MIMO beamforming system with ycAycIya = ycAyc = 10 compared to a system with ycAycIya = ycAyc = 2.
Bit error rate in relation to SNR and ycAycIya variation The outcomes in Figure 7 highlight the direct correlation between increasing the number of RF channels for both transmission and reception and the reduction in bit error rate (BER).
For instance, for a BER of 10-2, an improvement of 8 dB in SNR is achieved by increasing the number of RF chains from 4 to 10.
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Figure 4.
Bandwidth efficiency as a function of SNR for various values of the number of RF chains in a 64y64 MIMO system where ycAyc = 2 Figure 5.
BER as a function of SNR for various values of the number of RF chains in a 64y64 MIMO system where ycAyc = 2 Figure 6.
Spectral efficiencies as a function of SNR for various values of the number of RF chains in a 64y64 MIMO system where ycAycIya = ycAyc Figure 7.
BER as a function of SNR for various values of the number of RF chains in a 64y64 MIMO system where ycAycIya = ycAyc Impact of varying the number of data streams In this section, we examine how spectral efficiency and bit error rate vary with SNR in a hybrid MIMO beamforming system .
with ycAycIya = 10.
We also change the number of input data streams .
cAyc ) each time.
Spectral efficiency in terms of SNR variation with ycAyc From the results in Figure 8, we observe the following: Increasing the number of input data streams leads to improved spectral efficiency.
For example, at an SNR of 10 dB, the spectral efficiency improves by 80 bits/s/Hz when transitioning from 2 input data streams .
cAyc = .
to 10 input data streams .
cAyc = .
in a hybrid MIMO beamforming system.
Bit error rate (BER) in terms of SNR variation with ycAyc From the results in Figure 9, we observe the following: .
BER decreases as SNR increases and i.
BER decreases as the number of input data streams .
cAyc ) decreases.
Now, we analyze a massive MIMO system with 64 transmitting antennas and 16 receiving antennas, supporting ycAyc = 6 data streams.
For the hybrid beamforming MIMO system, we utilize ycAycIya = ycAyc = 6 RF chains for both transmission and reception.
Hybrid digital and analog beamforming design using genetic algorithms (Sidi Mohammed Bahr.
A Figure 8.
Spectral efficiencies as a function of SNR
for various values of the number of data streams in a 64y64 MIMO system where ycAycIya = 10
ISSN: 2088-8708
Figure 9.
BER as a function of SNR with varying numbers of data streams in a 64y64 MIMO system where ycAycIya = 2 As illustrated in Figure 10, the genetic algorithm exhibits commendable spectral efficiency performance compared to the heuristic algorithm presented in study .
As well as the hybrid beamforming algorithms introduced in studies .
The efficiency gains are 2 bits/s/Hz compared to the heuristic algorithm and 4 bits/s/Hz compared to the algorithms outlined in studies .
at an SNR of 0 dB.
Next, we analyze the performance of our algorithm in terms of spectral efficiency.
We consider a hybrid beamforming massive MIMO system with 10 antennas for both transmission and reception, and a corresponding number of RF chains in relation to the data streams: ycAycIya = ycAyc = 2.
The relatively limited antenna count is chosen to facilitate a comparison with the exhaustive search method.
Figure 11 reveals that our algorithm surpasses the heuristic algorithm and the exhaustive search method by 1 bit/s/Hz and outperforms the quantized hybrid beamforming algorithms in .
by 3 bits/s/Hz, thereby establishing its superior performance.
Figure 10.
Spectral efficiencies attained through various methods in a 64y16 MIMO system with N_RF=N_s=6 Figure 11.
Spectral efficiencies as a function of SNR for various methods in a 10y10 MIMO system where ycAycIya = ycAyc = 2 Int J Elec & Comp Eng.
Vol.
No.
December 2024: 6389-6400
Int J Elec & Comp Eng
ISSN: 2088-8708
CONCLUSION
In this article, we have examined the concept of hybrid beamforming in massive MIMO systems.
This approach employs two sets of weighting vectors for transmission and two sets for reception, with the aim of simplifying and reducing implementation costs by decreasing the required number of RF channels without compromising the performance that can be comparable with digital beamforming systems.
The necessary number of RF chains must be no more than double the number of data streams.
Furthermore, when the number of RF chains is identical to the number of data streams, this article presents a solution through a meta-heuristic algorithm .
enetic algorith.
to maximize overall spectral efficiency in the context of MIMO transmission over a downlink system.
Firstly, we analyzed the effect of varying antenna numbers for both transmission and reception on system performance.
Next, we investigated how varying the number of RF channels, for both transmission and reception, affects the bandwidth efficiency and BER of the system.
Finally, we examined the influence of the number of data streams on these performance metrics.
The numerical results demonstrate that the proposed meta-heuristic method achieves better performance than the heuristic methods and entirely digital beamforming schemes.
Through our observations, we noticed that increasing the number of antennas for transmission and reception significantly impacts the quality and capacity of the massive MIMO hybrid beamforming system.
Our observations have also shown that reducing the number of RF channels has a negligible effect on the quality and capacity of the massive MIMO system employing hybrid beamforming.
This finding confirms that employing this approach simplifies design and reduces costs without compromising system performance.
REFERENCES