Least Square Estimation-Based Different Fast Fading Channel Models in MIMO-OFDM Systems

In cellular wireless communication systems, channel estimation (CE) plays a pivotal role as a crucial technique applied in orthogonal frequency division multiplexing (OFDM) modulation. CE utilizes a variety of methods, including decision-directed channel estimation, pilot-assisted channel estimation (PACE)

Channel estimation serves as the foundation for various functionalities, including precoding, signal detection, resource allocation, indoor positioning, and physical layer security. Channel estimation can be categorized into two methods: blind channel estimation and pilot-based channel estimation. Te choice between these methods determines the approach used. In blind channel estimation, summary statistics, such as second-order or high-order statistics, from the received signal are utilized to estimate the channel without requiring dedicated pilot signals. On the other hand, pilot-based channel estimation relies on dedicated pilot signals to perform the estimation [1]. In [2], the authors introduce a blind channel estimation method that utilizes statistical information related to the received signal's average power. Tis approach converts the average estimation into a quadratic equation that incorporates the channel gain, providing a way for user terminals to estimate the downlink channel gain in MIMO systems without requiring dedicated downlink pilot resources. Nevertheless, it should be emphasized that this method is tailored for time division duplex (TDD) systems and does not take advantage of sparse channel characteristics, potentially leading to suboptimal estimation accuracy.
In [3], researchers present an alternative blind channel estimation technique tailored for massive MIMO systems, leveraging the expectation proft-maximizing (EM) algorithm. Utilizing the sparseness of the channel in the angular domain, this method improves channel estimation precision. Although the EM-based approach ofers improved accuracy, it comes with the drawback of being computationally intensive, potentially posing challenges in real-world implementations. Te benefts of blind channel estimation include low dependence on known parameters and excellent spectral efciency. It is more complex and has reduced realtime performance, among other drawbacks, including less accurate channel estimates. However, in pilot-based channel estimation, pilot symbols are included in transmissions so that the receiver can make channel estimates based on the pilot signals it receives. In [4], in comparison to blind channel estimation, this method does reduce spectral efciency, but it is often preferred due to its ease of use. LS as well as MMSE methods are common methods of pilot-based techniques. Despite using a relatively straightforward method of interpolation, the LS algorithm's performance is hindered by poor attention to noise.
MMSE algorithm provides enhanced estimation accuracy when compared to LS methods. Te MMSE algorithm provides better estimation accuracy because it takes into account the full channel statistical data and noise variance. In spite of this, it emphasizes inverting the channel correlation matrix, which adds a signifcant amount of complexity to the computation and necessarily requires having prior channel statistics. To address this issue, the authors in [5][6][7] propose ALMMSE, a linearized version of MMSE that is optimized for fast-fading channels. Te ALMMSE technique reduces complexity by fltering and minimizing correlation matrices. Many channel parameters must be estimated in MIMO-OFDM systems because of the extremely high density of transceiver antenna pairs and the large number of subcarrier channels involved. Traditional pilot-based channel estimation methods, on the other hand, reduce spectral efciency and increase system complexity, making them impractical for use in massive MIMO systems. To address this challenge, researchers have put forth timedomain sparse channel estimation algorithms, particularly compressed sensing (CS) algorithms. CS ofers the advantage of concurrently estimating relevant tap positions and their corresponding channel coefcients, making it a preferred choice as it requires fewer pilots while achieving superior estimation performance. Te success of the CSbased reconstruction algorithm for MIMO-OFDM channel estimation depends on the pilot positions, which in turn afect the recovery matrix. Traditional algorithms struggle to fully exploit the block-sparse essence of the channel to jointly maximize pilot locations and symbols for precise reconstruction, despite progress in the study of massive MIMO-OFDM channels. Existing optimization methods, which heavily rely on ideal assumptions and model approximations, may encounter limitations in handling more complex scenarios. To overcome this challenge, a promising and efcient approach involves using deep learning-based channel estimation. Deep learning leverages ofine big data training and online real-time data updating, enabling more robust and adaptive channel estimation in dynamic and evolving wireless environments [8].
Deep learning demonstrates remarkable capabilities in extracting features and performing nonlinear mapping, thereby ofering substantial enhancements to channel estimation performance in difcult scenarios. Te goal is to strike a balance between the high complexity of online testing and the complexity of ofine training, leading to enhanced operational efciency. In tackling Intercarrier Interference (ICI) mitigation, the authors in [9] introduce a distinctive pilot pattern and channel estimation approach. Tis design combines comb-type and clustered patterns, efectively mitigating ICI while minimizing the pilot density. However, this method involves FFT operations and an iterative procedure for data extraction, as well as identifying the most important routes of the channel impulse response (CIR), making it mathematically complex. Another approach, iterative interference cancellation [10][11][12][13][14][15], has been extensively studied to exploit enhancing performance by considering the temporal variation of the time-varying channel. Te disadvantage of this approach is its increased computational complexity when compared to linear equalizers like MMSE and LS.
In conclusion, the self-mitigation of Intercarrier Interference (ICI) has become a highly promising strategy, attracting considerable research attention in recent times. Certain studies [16][17][18] have explored applying a time-domain window to the received OFDM signals, leading to the concentration of ICI power on the principal diagonal of the coupling matrix. In addition, a recent innovative approach introduced in [19,20] involves adaptive windowing, achieving its goals with linear complexity. Tis technique directly monitors an ideal receiver window to optimize the average SNR.

2
International Transactions on Electrical Energy Systems Te key fndings and contribution of this research can be outlined as follows: (1) A MIMO-OFDM system has been devised, tailored for 5G and future communication systems, utilizing the pedestrian A channel profle model to account for mobility and frequency selective fading efects. Te design assumes that the receiver lacks knowledge of instantaneous channels, necessitating the inclusion of pilot signals in the transmitted data symbols for channel estimation. (2) Modeling the channel time-frequency response by generating a new dataset with 5G specifcations as a 2D image using the PedA model using the MATLAB simulator [21]. Te structure of this paper is as follows: In Section 2, a comprehensive review of the relevant literature is provided. Section 3 explains the OFDM system, while Section 4 explores multipath fading channels. State-of-the-art channel estimators, including LS for fast fading, are discussed in Section 5. Section 6 presents the proposed system model for the fast-fading channel estimator. Te channel model is described in Section 7, and in Section 8, the performance of the channel estimators is evaluated in terms of physical layer data throughput and mean square error (MSE). Finally, the paper is concluded in Section 9.

Related Works
Several methods have been developed to estimate the channel variance in OFDM systems, either across multiple OFDM symbols or within a single OFDM signal. Most of these approaches are based on pilot symbols [22][23][24]. In situations where channels experience rapid changes, a signifcant number of unknown channel coefcients need estimation due to the high-order variations observed within a single OFDM symbol cycle [25,26]. Several approaches have been put forward to address this, such as the base development model (BDM) [27,28], block-sparse Bayesian learning (BSBL) [29,30], and the piecewise linear model (PLM) [31,32], aimed at reducing the number of coefcients that require estimation, which approximate the channel variation.
Tis study proposes the use of the least square (LS) technique for channel variance estimation in multipath fading channel OFDM-MIMO systems. Te method includes zero-padding an OFDM symbol with a cyclic prefx and inserting an impulse signal among these zeros. Te obtained impulse signal is used by the LS estimation method in the receiver to create a channel estimate at the OFDM symbol's pilot sample. After that, we use a linear model to predict the channel shifts over the course of an OFDM symbol.

OFDM System
Within an OFDM system, multiple-input bits are aggregated and combined to create a single data symbol. Tese data symbols, denoted as X(0) to X(N − 1), undergo modulation using a digital modulation technique. Subsequently, in the process of inverse fast Fourier transform (IFFT), the serial data symbols are converted into their parallel counterparts [33]. Te IFFT process ensures the orthogonality of each subcarrier and maps the N data symbols onto N subcarriers. Data symbols handled by IFFT are represented by x(0), x(1), . . ... . .. x(N − 1) and mathematically expressed as [34] x(n) (1) Te OFDM system uses N-point IFFT samples as it is in Figure 1. For each OFDM symbol, "n" is varying between zero (0) and (N − 1) and x(n) represents the n th sample. Each OFDM symbol is comprised of N IFFT samples. However, when these symbols meet the multipath channel, they are overcomplicated with channel taps, resulting in the presence of OFDM symbol samples from the preceding symbol. Tis occurrence results in Interblock Interference (IBI). In order to counter IBI, a longer cyclic prefx than the number of channel taps (L) is added to the commencement of each OFDM signal. Te length of the cyclic prefx (G) needs to be greater than L (i.e., G > L). Once the cyclic prefx is added, a serial stream is generated from the parallel samples. Tese transmitted samples, which are received as x(n -G + 1). . . x(N − 1), are subject to AWGN. Te samples received are depicted as follows [34]: In the context of the received signal, y(n) represents the n th received sample, ℎ(l) denotes the lth channel tap, and AWGN samples are denoted by v(n), where n is a natural number. Te equation gives the receiver's expression for the FFT of the incoming signal (3): International Transactions on Electrical Energy Systems where Y(k), H(k), X(k), and V(k) are N-point FFT of samples of y(n), ℎ(n), x(n), and v(n), respectively, and which can be represented as follows: In this case, H(k) represents the fast Fourier transform (FFT) of ℎ(l), which is achieved through zero padding of ℎ(l).

Channels with Multipath Fading
In mobile radio channels, there are two distinct types of fading: large and small. Because the structure of the received signal follows a Rayleigh or Rician probability distribution in situations with a large number of refective paths, small-scale fading is also known by these names (R-PDF).
Rayleigh fading occurs in situations with numerous diverse refective paths and the absence of a strong line-ofsight (LOS) propagation path. On the other hand, Rician fading occurs when a dominant LOS path exists alongside multipath components. Te multipath channel can be accurately represented using equation (6) [34].
In this context, a S represents the lth attenuation factor, v S denotes the lth delay factor, and F c stands for the carrier frequency.
Real and imaginary Gaussian random variables (p and q) can be represented by the following formula: a l sin j2πF c τ l .
a l e − j2πF c τ l .
As a result, the CDF can be expressed in the following manner: Te importance of the variance of channel coefcients, denoted as (σh) 2 , lies in its signifcant infuence on the probability density function, which can be mathematically represented by equation (11).
Afterward, the Rician probability density function, which accounts for the existence of a LOS path, is precisely defned by equation (12).   International Transactions on Electrical Energy Systems Here, the Bessel function is denoted by I 0 , where A is the LOS path amplitude.
In order to model the impacts of electromagnetic data transmission, fading channel models are prevalent in cellular networks and broadcast communication, as well as being employed in underwater acoustic communications to mimic the efects of water distortion. Figure 2 shows the basic block diagram of the proposed multipath fading channel model. Te input signal undergoes two separate amplifcation stages: one with a constant gain and the other with a variable gain. Te amplitude of a signal transmitted through a communication channel is assumed to undergo random variations or fading, following a Rayleigh distribution [35].
In the given context, (it) denotes the output signal, (it) represents the input signal, τ refers to the delay or phase shift, g1 stands for the constant gain, g2 represents the variable gain, and n(t) represents the impact of noise; a statistical model is employed to simulate the infuence of a radio signal's propagation environment on wireless devices. To generate noise, the following equation code was used, as indicated in equation (14) [35].
Te x-vector signal is corrupted with white Gaussian noise, congratulations to this function. Te SNR (signal-tonoise ratio) is a scalar value in decibels that represents this signal-to-noise ratio. Complex noise is introduced by the AWGN when x is a complex signal. In this syntax, the function measures the power of x before adding noise, assuming that x's power is 0. Te level of noise in a channel is typically measured using a number of diferent metrics.
(1) Signal-to-noise ratio per sample (2) Te ratio of bit energy to the noise power spectral density, denoted as E b /N0 (3) Te ratio of symbol energy to the noise power per unit bandwidth, denoted as E s /N0 Te BER represents the proportion of incorrectly received bits to the total number of transmitted bits within a defned duration. SNR or S/N represents the signal's power in relation to the noise afecting it. In simpler terms, it quantifes the strength of the desired signal (e.g., music) relative to the background noise level. A higher SNR implies that the background noise is less perceptible. Tis mathematical relationship is expressed in equation (15) [35].
After analyzing the infuence of the bit error rate (BER) on signal-to-noise ratio (SNR), the outcomes demonstrate a signifcant enhancement in BER performance at low SNR levels, whereas no signifcant improvement is observed at high SNR levels. At low SNR, the dominant factor afecting the BER is white Gaussian noise, which can be reduced by increasing SNR. However, at high SNR, the primary contributor to the BER is phase estimation error, and simply raising SNR does not lead to improvement. Consequently, fat fading channels exhibit poorer BER performance compared to frequency selective fading channels, while AWGN channels show the highest BER performance. To simulate the channel's physical processes impacting the transmitted signal, it is possible to create a physically realistic channel model. For instance, in wireless communications, channel simulation involves calculating the refections from objects present in the environment. Te "scatterplot (x)" function generates a scatter plot for the signal x. If x is a complex vector, the real and imaginary components will be displayed as phase and quadrature, respectively, in the scatter plot. However, if x is a real vector, the scatter plot displays it as such, without trying to fgure out what its phase and quadrature components are.

Channel Estimation
Communication systems frequently are using OFDM to mitigate frequency-selective fading in wireless channels. Te received signal in such channels is afected by the channel itself. To efectively retrieve the transmitted symbols, it becomes crucial to estimate and compensate for the channel efects at the receiver. Tis is typically achieved by utilizing specifc symbols known as pilots; for accurate channel estimation, the transmitter and the receiver use the timefrequency coordinates and values already in their possession. Tree diferent structures of pilot symbol arrangements are taken into consideration, which include block-type, combtype, and lattice-type, as described in [36]. In the block-type arrangement, in the beginning, the symbols of the pilot are transmitted to an OFDM block across all subcarriers. In contrast, the comb-type arrangement entails the inclusion of pilots in specifc subcarriers of a few OFDM symbols. Te lattice-type arrangement involves the insertion of pilots along both time and frequency axes, forming a diamondshaped constellation with predefned periods [37].
To infer the unknown channel response values, traditional pilot-based techniques like LS and MMSE rely on the pilot values situated within time-frequency grids. Tese methods have been fne-tuned and optimized for diverse scenarios [38]. Unlike LS estimation, which operates without any prior knowledge of the channel's statistics, MMSE estimation achieves superior performance by taking advantage International Transactions on Electrical Energy Systems of the channel's statistics and noise variance. In practical scenarios, several techniques have been suggested to implement MMSE while reducing the complexity of the scheme. Tese techniques involve using estimates of channel statistics instead of precise data. Figure 3 illustrates a common block-type pilot layout, where multiple pilot symbols are sent over multiple rt OFDM symbols simultaneously. Both LS and MMSE methods can be used to estimate the block-type pilot confguration [39]. Least square (LS) estimation is a typical technique for pilot-based channel estimation since it delivers acceptable performance with moderate complexity. Minimizing the squared diference between the transmitted and received signals is the goal of the channel least square estimator. Equation (2) demonstrates that the provided equation (6) can be utilized to compute the LS of the channel at the pilot subcarriers: For positions without pilot symbols, the channel coefcients are determined through two-dimensional interpolations. In this study, linear interpolation is employed. Te LS channel estimator ofers the advantage of low complexity and does not necessitate knowledge of the channel and noise statistics. Taking into account, block fading assumptions make the LS channel estimator even simpler. At frst, pilot symbol time-frequency grid positions are used to estimate channels with equation (3). Te channel estimating for pilot positions at diferent time instances are averaged, assuming the channel remains unchanged during the transmission of a single subframe. Afterward, one-dimensional interpolation (specifcally, linear interpolation in this case) is utilized to fnd the missing channel coefcients in the frequency domain [40][41][42].

System Model
Tis section describes a MIMO-OFDM system where signals are transmitted from a transmitter to a receiver. Te MIMO channel model for the 5G communication system is constructed with N T transmitter antennas and N R receiver antennas, forming an N T × N R antenna array confguration.
6.1. Transmitter. Te transmitter processes the binary data through the modulation block, where it encodes and maps it using quadrature amplitude modulation (QAM). Assuming the system transmits information in T time slots, the QAM symbols for each time slot (t � 1, . . ., T) are combined to form a data vector, denoted as x(t′) ∈ CN, following the description in [43].
where N denotes the total number of modulation symbols. After encoding, the data are divided into N T vectors, corresponding to the N T [43] transmit antennas: For each antenna, the information is converted from serial to parallel formats. Pilot signals, known to both the transmitter and the receiver, are then added to the data for each layer to facilitate channel estimation. Te IFFT block is then applied to x a (t) with a � 1, N T . Te signal vector with a pilot inserted into the corresponding data x i (t) is used to transfer the signals from the frequency domain to the time domain. Tis transformation is represented by the notation x a (t), s observed in [43].
Te CP insertion block inserts a CP of a guard interval of length N.G which is introduced to reduce intersymbol interference (ISI) after the IFFT transformation. Including the cyclic prefx enables the transmission of the signal, denoted as x ga [43,43], to be formulated in the time domain as follows: where the signal x a (t) with a length of N FFT + N G is formed by using the last NG samples of x a (t). Te last N.G samples of x a (t) are utilized as a cyclic prefx and placed at the beginning of this symbol. Te arrangement, which leads to the fnal signal format, is determined by the FFT size, NFFT.

Receiver.
Using the cyclic prefx removal module, the prefx of the cyclic could be removed from each antenna that received the signal at the receiver, providing the vector, y b (t) of length N FFT . According to [43], afterward, the signal is transformed into a parallel format and subjected to processing in the frequency domain using the FFT block. Tis process leads to the creation of a frequency-domain signal denoted as y. b (t).
Te pilot signal is extracted from the frequency-domain signal to estimate the channel. After obtaining the channel estimate, the received signal y b (t) is equalized and combined into a serial sequence using the layer demapping module. Te signal is then demodulated based on the transmitter's scheme. Te output of the MIMO-OFDM system model comprises the fnal sequence of gathered binary data. (4) Diversity and resilience: Massive MIMO exploits the spatial diversity provided by a large number of antennas. Tis diversity improves the system's resilience to fading and interference, enhancing the overall reliability and quality of service. Even in challenging environments, where certain paths may experience deep fading, the presence of multiple antennas helps maintain reliable communication by utilizing the available strong paths. (5) Energy efciency: Massive MIMO can also contribute to energy efciency in 5G systems. By focusing the transmitted energy towards the intended users through beamforming, the system can reduce the overall power consumption. In addition, the ability to serve multiple users simultaneously in a single time-frequency resource improves spectral efciency, enabling more data to be transmitted per unit of energy. (6) Overall, massive MIMO enhances the performance and spectral efciency of 5G systems by increasing capacity, improving coverage, reducing interference, providing spatial diversity, and enabling energy-effcient operations. Tese benefts make it a fundamental technology for achieving the ambitious goals of 5G networks, such as supporting massive connectivity, high data rates, low latency, and diverse application requirements.  (5) Adaptive beamforming: Massive MIMO systems continuously adapt their beamforming strategies based on channel conditions, user locations, and system requirements. Trough adaptive beamforming, the system optimizes the beamforming weights and beam directions to maximize the received signal quality, improve coverage, and minimize interference. Adaptive beamforming algorithms utilize channel state information (CSI) feedback from the user devices to adjust the beamforming parameters dynamically.

Massive MIMO
(6) By utilizing beamforming techniques, massive MIMO improves coverage and efciency in the 5G spectrum by focusing energy towards intended users, serving multiple users simultaneously, mitigating interference, and adapting to change channel conditions. Tese capabilities enhance the system's capacity, data rates, and spectral efciency, enabling better performance and user experiences in 5G networks.

Channel Model
In order to determine the channel, the signal of that pilot is separated from the signal in the frequency domain. Once the channel estimate has been obtained, the received signal y. b (t) is equalized and merged using the layer demapping module, which includes all receiving antennas. Te signal is then demodulated using the same method as the transmitter. Te output of the MIMO-OFDM system model is the fnal sequence of binary data [45][46][47].
Tere are two main types of channels based on the mobility between the transmitter and the receiver: timeinvariant channels and time-varying channels. A channel is considered time-invariant when both the transmitter and the receiver remain stationary in one location. Tere are two primary kinds of channels: time-invariant and time-varying channels, depending on the mobility between the transmitter and receiver. A channel is regarded to be time-invariant when both the transmitter and the receiver stay fxed at a single place. For example, a simple cable connection between a transmitter and a receiver or a fxed WiMAX system in which the base station and subscriber's premises equipment are immovable and are examples of time-invariant channels [48].
Communication design engineers use the basic to validate the development of transmitters and receivers; channel models like AWGN, Rayleigh, and Rician are employed. For complex communication systems, the establishment of channel models is crucial to verify the performance of the transmitter and the receiver. When building channel models, a variety of elements, various factors, such as the number of pathways, delays at each path, terrain type, Doppler frequency, and speed, are taken into consideration [49,50].
(1) AWGN: Additive white Gaussian noise, commonly observed in semifex or coaxial cables connecting transmit and receive paths, as well as in space communication, is primarily associated with thermal noise in the channel. Tis noise may arise from electrical equipment at both the transmitter and the receiver ends [35].
In this context, T denotes the transmitted vector, while R represents the received vector, including noise, based on the signal-to-noise ratio (SNR) measured in decibels (dB).  Table 1 shows a comparison of three fast-fading channel models with other reference works. It is crucial to recognize that there is no universal channel model that is ideal for every scenario. Te best model to use will depend on the fading environments and noise channel; the communication channel can be categorized into three types such as additive white Gaussian noise (AWGN), Rayleigh fading, and Rician fading channels. In this paper, the performance of MIM-O-OFDM has been analyzed with respect to these three types of channels.

AWGN Channel.
Te AWGN channel is commonly employed in communication systems because of its nonfading nature and straightforward implementation. When signals traverse the AWGN channel, it adds white Gaussian noise to the signal [9][10][11]. Te probability density function of the noise always follows a Gaussian distribution, which is mathematically expressed as [58] Te received signal in the AWGN channel is represented as follows, with x being a random variable, µ denoting the mean value, and σ representing the standard deviation [58]: where x(t) � transmitted signal and n(t) � additive white Gaussian noise.

Rayleigh Fading Channel.
In a Rayleigh fading channel, the signal passing through the channel undergoes distortion caused by the Rayleigh distribution. Multipath reception is the root cause of Rayleigh fading. Te antennas receive a large number of refected and scattered waves. Te antennas receive numerous refected and scattered waves, leading to constructive and destructive interference due to the efects of multipath. Rayleigh fading is more suitable in scenarios where there is no direct line-of-sight communication between the transmitter and the receiver [59]; the probability density function (pdf ) of the Rayleigh random variable is provided by [58]: where σ is the received signal's time-average power.

Rician Fading Channel.
In a Rician fading channel, the amplitude gain follows the Rician distribution. In this type of channel, there is a line-of-sight signal path between the transmitter and the receiver. Te Rician fading occurs when one of the received signals is stronger (typically line of sight component is stronger than the other) [60,61]. Te Rician distribution is represented by the following equation [58]: where A represents the peak amplitude of the dominant signal. l 0 [.] is the modifed Bessel function.
Here are some additional information about the diferent fast-fading channel models: (1) Rayleigh fading: Tis is the most common fast-fading channel model. It is a good model for channels that are subject to a large number of uncorrelated multipath refections. Te choice of channel model will afect the design of the MIMO-OFDM system. For example, a system that uses a Rayleigh fading model will need to be more robust to signal loss than a system that uses a Rician fading model. Similarly, a system that uses an AWGN model will not need to be as robust to signal loss as a system that uses a Rayleigh fading model [22].

Simulation Results and Analysis
Tis study conducts a link-level simulation to analyze the BER for various channel models in the MIMO-OFDM system, both with and without channel estimation using LS estimators, and applying various modulation methods. Based on the 5G system's air interface standard, the simulated environment uses time-frequency resource slots with a total of 72 subcarriers (6 resource blocks (RBs) of 12 subcarriers each) and 14 OFDM symbols. Te 2.1 GHz frequency, 1.6 MHz bandwidth, 1730 ns delay spread, and 50 km/h UE speed used in the experiment are all specifcs of the PedA channel model under investigation. Te experimental channel environment is built using the channel simulator produced at the University of Vienna [21]. Te PedA channel model is subjected to noise levels ranging from 0 to 35 dB to make sure that the performance of the proposed scenario is evaluated in diferent signal-to-noise ratio circumstances. Figures 4 and 5 compare the bit error rate (BER) and throughput for three distinct channel models Rician fading, Rayleigh fading, and AWGN, utilizing 64-QAM modulation and no channel estimation. Table 2 includes specifc BER and the throughput for diferent values of SNR ranging from 0 to 35 dB. Te fndings reveal that the channel with no fading (AWGN) has the greatest bit error rate, while the uplink Rayleigh channel model has a lower BER and higher throughput than the Rician channel model. Tis is attributed International Transactions on Electrical Energy Systems to the Rayleigh channel's presence of multiple non-line-ofsight paths, whereas the Rician channel model includes both a direct line-of-sight (LOS) signal and multiple paths. In contrast, for the nonfading downlink AWGN channels, the bit error rate is the lowest, resulting in the highest throughput. Te Rayleigh channel model still exhibits a higher BER than the Rician channel model, which demonstrates a relatively lower BER. Table 3 shows the bit error rate and throughput for LS estimator values for various SNR values in 64-QAM. Te BER for 64-QAM in Table 3 shows that the AWGN-LS channel gives lower BER, lower MSE, and higher throughput for uplink than Rayleigh and Rician fading channels. For the downlink, Rayleigh gives the best performance in terms of BER, MSE, and throughput as compared with AWGN and Rician. If we look at each value of SNR, we can notice that the bit error rate is decreased since the value of SNR increases especially when that value reaches its maximum, and of course that will be afected by the throughput value for both uplink and downlink, then that will be diferent when we compare those values with Table 4, where the channel is 256-QAM and we can notice that the value of SNR reaches its Table 1: Comparison of the three fast-fading channel models with other recently referenced works.

Channel model Reference Description
Rayleigh fading [51] An investigation into the performance of MIMO-OFDM systems in Rayleigh fading channels, considering varying numbers of transmit and receive antennas, as well as diferent modulation schemes Rician fading [52] An examination of the performance of MIMO-OFDM systems in Rician fading channels, involving various Rician factor values and diferent antenna confgurations AWGN fading [53] An investigation into the performance of MIMO-OFDM systems in AWGN channels, considering diferent noise power levels. Te fndings indicate that as the noise power decreases, the performance of MIMO-OFDM systems in AWGN channels improves Block fading [54] An examination of the performance of MIMO-OFDM systems in block fading channels, exploring various block lengths and employing diferent channel estimation techniques Nakagami fading [55] An investigation into the performance of MIMO-OFDM systems in Nakagami fading channels, considering varying Nakagami parameter values and utilizing diferent precoding techniques Log-normal fading [56] An examination of the performance of MIMO-OFDM systems in log-normal fading channels, with varying log-normal shadowing factor values, and employing diferent power allocation schemes Weibull fading [57] A study of performance of MIMO-OFDM systems in Weibull fading channels, considering diverse Weibull shape parameter values and utilizing diferent diversity techniques    International Transactions on Electrical Energy Systems Table  4: Te bit error rate (BER) and throughput (both uplink and downlink) for 64-QAM employing LS estimators in AWGN, Rayleigh, and Rician channels.     maximum value which is 27 and the lowest value of BER 0.0003 for uplink and around 0.0119 for downlink and the throughput reach its maximum value in this case and the same happen for Rayleigh-LS as well as for Rician-LS. Ten, the performance of the scenario will be diferent for those channels. Figure 6 shows a comparison for BER estimator performance for uplink and downlink where M � 64-QAM across AWGN, Rayleigh, and Rician channels. In contrast, Figure 7 shows the comparison of the LS estimator according to throughput in 64-QAM, Rayleigh, and Rician channels for both uplink and downlink.

AWGN-LS
In Figure 8, the performance of the estimator comes with a comparison for all of the AWGN, Rayleigh, and Rician channels. According to mean squared error (MSE) for M � 64-QAM, we can notice that the value Rayleigh channel is the best performance compared to the other channels (AWGN and Rician).
Te bit error rate against SNR with the value of M � 256 for both uplink and downlink, Figure 9 shows a comparison for performance in diferent channel types AWGN, Rayleigh, and Rician. Te result shows that the Rayleigh channel is better for downlink scenario due to the lower BER, while the AWGN channel is best for uplink scenario.
In Figure 10, the comparison comes for throughput against SNR (dB) in both uplink and downlink where M � 256 QAM for AWGN, Rayleigh, and Rician channels.
We can notice from the curve that the value of throughput in downlink is the best for the Rayleigh channel and that is diferent for uplink where the AWGN channel overtakes the other channels. In Figure 11, the comparison come for MSE against SNR and it shows the performance for LS estimator in AWGN, Rayleigh, and Rician channels.
If we look forward at Figures 12-14, we can notice that the Rayleigh channel can give a worse performance in terms of BER, MSE, and throughput for all cases for M � 1024-QAM, and we compare this value with the same parameters according to AWGN and Rician in 1024-QAM for uplink. For downlink with M � 1024-QAM, as we can see, the Rayleigh show lower BER and MSE, and higher throughput than the AWG and Rician; as a result of all of these, Table 5 can show all the diferences according to each value of BER and MSE which has been mentioned in all fgures below and that will come out with diferent performances for LS estimators. Table 6 shows a comparison between diferent values of SNR based on the channels' type: AWGN, Rayleigh, and Rician; we notice that the values of BER varied from 0.3392 to 0.0001 for uplink of AWGN and from 0 to 4098000 as a throughput; the comparison is diferent from one channel to others. Based on the simulation result, the best throughput we obtain is from the Rayleigh-LS channel.     Figure 15 shows that the BER performance before the channel was estimated and shows the performance foe LS estimator in AWGN, Rayleigh, and Rician channels, where M � 64 QAM and the proposed AWGN is the best performance for both (a) BER/perfect and (b) BER/LS.

Conclusions
Tis study thoroughly investigates multipath AWGN, Rayleigh, and Rician channel models. Utilizing 64-QAM modulation, the research evaluates the performance of an OFDM-MIMO system without channel estimation under these three channel conditions. In the uplink, simulation results reveal that the nonfading AWGN channel performs better than the Rayleigh and Rician fading channels, exhibiting a lower bit error rate. However, in the case of the Rician fading channel, the presence of a strong signal received through a direct line of sight enables it to achieve a better BER performance than the Rayleigh channel. We analyze how the LS estimator performs in Rayleigh, Rician, and AWGN nonfading channels with diferent modulation schemes, including 64-QAM, 256-QAM, and 1024-QAM. Te investigation focuses on evaluating the bit error rate (BER), mean squared error (MSE), and throughput. As the signal-to-noise ratio increases, both the BER and MSE of the LS estimator decrease for both uplink and downlink scenarios across all modulation schemes. In future research, we plan to explore the capabilities of deep learning techniques, such as the super-resolution conventional neural network (SRCNN) and the denoising algorithm (DnCNN), in massive MIMO systems with RIS. Te objective is to address channel estimation challenges in cascaded channels and enhance BER and MSE performance.

Data Availability
Te data used to support the fndings of this study are available from the corresponding authors upon request.

Conflicts of Interest
Te authors declare that they have no conficts of interest. their support and assistance. Also, the authors are grateful to the University Putra Malaysia Faculty of Computer and Communication Engineering and Iraq University College.