Deep Learning-Aided 5G Channel Estimation
An Le Ha, Trinh Van Chien, Tien Hoa Nguyen, Wan Choi, Van Duc Nguyen
DDeep Learning-Aided 5G Channel Estimation
An Le Ha † , ∗ , Trinh Van Chien ν,ξ , Tien Hoa Nguyen † , Wan Choi ∗ , and Van Duc Nguyen † † School of Electronics and Telecommunications, Hanoi University of Science and Technology, Hanoi, Vietnam ν School of Information and Communication Technology, Hanoi University of Science and Technology, Hanoi, Vietnam ξ Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg ∗ Department of Electrical and Computer Engineering, Seoul National University, Seoul, KoreaEmails: [email protected], [email protected], [email protected],[email protected], [email protected]
Abstract —Deep learning has demonstrated the important rolesin improving the system performance and reducing computa-tional complexity for G-and-beyond networks. In this paper,we propose a new channel estimation method with the assis-tance of deep learning in order to support the least squaresestimation, which is a low-cost method but having relatively highchannel estimation errors. This goal is achieved by utilizing aMIMO (multiple-input multiple-output) system with a multi-pathchannel profile used for simulations in the G networks underthe severity of Doppler effects. Numerical results demonstratethe superiority of the proposed deep learning-assisted channelestimation method over the other channel estimation methods inprevious works in terms of mean square errors.
Index Terms —Deep Neural Networks, Channel Estimation,Multiple-Input Multiple-Output, Frequency Selective Channels.
I. I
NTRODUCTION
The fifth-generation (5G) wireless communication has beendeveloped to adapt to the exponential increases in wirelessdata traffic and reliability communications [1]. The orthogonalfrequency division multiplexing (OFDM) technique has beendemonstrating its inevitable successes in the current networks,and has continuously adopted in 5G systems to combat thefrequency selective fading in multi-path propagation environ-ments [2]. Consequently, this technique increases the spectrumefficiency compared with single-carrier techniques. Throughthe wireless multipath channels, the transmitted signals to aparticular receiver is distorted by many detrimental effectssuch as multi-path propagation, local scattering, and mutual in-terference by sharing radio resources. Therefore, channel stateinformation and its effects must be estimated and compensatedat the receiver to recover the transmitted signals. Generally, pi-lot symbols known to both the transmitter and receiver are usedfor the channel estimation. In a G system, the structure of thepilot symbols may be varied depending on different use cases[3]. Among the conventional channel estimation methods, leastsquares (LS) estimation is a low computational complexity onesince it requires no prior information of the statistical channel
This paper was presented at the 15th International Conference on Ubiqui-tous Information Management and Communication (IMCOM 2021). ©2021IEEE. Personal use of this material is permitted. Permission from IEEE mustbe obtained for all other uses, in any current or future media, includingreprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists,or reuse of any copyrighted component of this work in other works. information. However, this estimation method yields relativelylow performance in many application scenarios. Alternatively,the minimum mean square error (MMSE) estimation methodhas been introduced, which minimizes the channel estimationerrors on average [4], [5]. The optimality of MMSE estimationis based on the assumption that the propagation channelsare modeled by a linear system and each channel responsefollows a circularly symmetric complex Gaussian distributionfor which the channel estimates can be derived in the closedform [6], [7]. Unfortunately, the MMSE estimation methodhas high computational complexity due to the requirementsof channel statistic information, i.e., the mean and covariancematrices. In many environments, such statistical informationis either difficult to obtain or quickly variant in a short timeperiod [8], [9].Machine learning has recently drawn much attention invarious applications of wireless communications such as radioresource allocation, signal decoding, and channel estimation[10]–[13]. Regarding the channel estimation, the authors in[13] exploited the non-stationary channel conditions and thechannel fading vectors are considered as conditionally Gaus-sian random vectors with random covariance matrices. TheMMSE estimation form under those conditions may have anextremely high cost to obtain, and thus the authors used anestimation designed under a special channel condition for themachine learning aided estimation. In [14], the authors studiedchannel estimation in a wireless energy transfer system forwhich the downlink channel estimation is exploited to harvestenergy feedback information. A deep neural network model isused to predict better channel estimates than conventional es-timations as LS or linear MMSE (LMMSE). These researcheshave numerically proved the compelling potentials of machinelearning in channel estimation as long as sufficient trainingdata set is provided. However, they only focused on the quasi-static propagation models such that channels are static andfrequency flat in each coherence block.In this paper, we propose two architectures of a deepneural network (DNN) model, which are applied for thechannel estimation of a G MIMO-OFDM system underfrequency selective fading. The performance of the proposeddeep learning-aided channel estimations is then evaluated bytwo different scenarios based on the receiver velocity. The978-0-7381-0508-6/21/$31.00 ©2021 IEEE a r X i v : . [ c s . I T ] J a n hannel parameters in each scenario are generated based onthe tapped delay line type A model (TDL-A), which is reportedby GPP and of practical scenarios [15]. The performance ofthe two DNN-aided channel estimations is compared with thetraditional estimations, i.e., LS and Linear MMSE (LMMSE),in terms of mean square error (MSE) and bit error rate (BER)versus signal to noise ratio (SNR) criteria. In particular, theproposed DNN structure will exploit a fully connected neuralnetwork to learn the features of actual channels with thechannel estimates obtained by LS estimation as the input. Incomparison to LS estimation, we would like to evaluate howmuch the system performance is improved by the assistance ofa DNN. Furthermore, we would like to observe if the proposedestimation can beat the performance obtained by LMMSE.The rest of this paper is organized as follows: Section IIdescribes the 5G MIMO-OFDM system model. Section IIIpresents the problems of the conventional channel estimationmethods and proposes the DNN-aided methods to solve theseproblems. Meanwhile, Section IV shows the simulation re-sults that evaluate the performance of the proposed methodsand compare with the other benchmarks. Finally, the mainconclusions of this paper are presented in Section V.II. 5G NEW RADIO MIMO-OFDM SYSTEMIn this paper, we consider a MIMO-OFDM system compris-ing a transmitter sending signals to a receiver as illustrated inFig. 1. Both the transmitter and receiver are equipped withtwo antennas and therefore creating a × MIMO channelmodel as in Fig. 2.
A. Transmitter
At the transmitter side, the binary data are mapped to theconstellation points by utilizing the modulation block thatexploits a modulation scheme such as quadrature amplitudemodulation (QAM). We suppose that the system needs T timeslots to transmit the data and the QAM symbols at time slot t , t = 1 , · · · , T, are combined to a data vector x ( t ) ∈ C N as x ( t ) = [ x ( t ) , x ( t ) , · · · , x N ( t )] , (1)where N is the total number of the modulation symbols. Then,the layer mapping block will separate vector x ( t ) into the twovectors x odd ( t ) and x even ( t ) corresponding to the two transmitantennas as follows: x ( t ) = x odd ( t ) = [ x ( t ) , x ( t ) , · · · , x N − ( t )] , (2) x ( t ) = x even ( t ) = [ x ( t ) , x ( t ) , · · · , x N ( t )] . (3)The signals for each antenna are then converted from the serialto parallel one. At the pilot insertion block, the pilot symbolsknown by both the transmitter and receiver are inserted alongwith data subcarriers in every layer for the channel estimationpurposes. Let us denote x a ( t ) with a = 1 , , the signal vectorsobtained after the pilot insertion block, then the IFFT (inverse This paper uses LMMSE estimation as a benchmark for comparisonbecause the channel estimates by MMSE estimation are nontrivial to obtainfor the considered channel profile. fast Fourier transform) block is applied to x a ( t ) such that thesignals are transformed from the frequency domain into timedomain (denoted by ˜ x a ( t ) ) as ˜ x a ( t ) = IFFT { x a ( t ) } . (4)To avoid inter-symbol interference, a cyclic prefix of thelength N G is inserted in each OFDM symbol by utilizing theCP (cyclic prefix) insertion block. So the transmitted signalincluding cyclic prefix, denoted by ˜ x ga ( t ) , is represented intime domain as follows: [˜ x ga ( t )] n = (cid:40) [˜ x a ( t )] n + N FFT n = − N G , − N G + 1 , . . . , − x a ( t )] n n = 0 , , . . . , N FFT − , (5)where N FFT denotes the FFT size. In more detail, the last N G samples of ˜ x a ( t ) are used as cyclic prefix and inserted to thebeginning of this symbol, resulting in the signal ˜ x ga ( t ) withlength of N FFT + N G . B. 5G Channel Model
The 5G MIMO channel model is depicted in Fig. 2 with thetwo transmit antennas and two receive antennas. This paperexploits the multipath fading channel model, which is time-variant and frequency selective. We denote the time-variantchannel impulse response from the a -th transmit antenna to b -th receive antenna ( b = 1 , ) is h a,b ( τ i , t ) , where τ i is thetransmission delay at the i -th path. As reported in [16], thetime-variant channel impulse response is modulated using theMonte-Carlo method as h a,b ( τ i , t ) = 1 √ M L (cid:88) i =1 ρ ( i ) M (cid:88) l =1 e j ((2 πf a,b,l,i t + θ a,b,l,i δ ( τ − τ i ) , (6)where M is the number of harmonic functions. L is the totalnumber of paths for which i = 1 , . . . , L . The discrete Dopplerfrequency and Doppler phase are respectively defined as f a,b,l,i = f d, max sin(2 πu a,b,l,i ) , (7) θ a,b,l,i = 2 πu a,b,l,i , (8)where f d, max is the maximum Doppler frequency. The channelimpulse response are simulated based on uniformly indepen-dent random variables u a,b,l,i in the range [0 , . In (6), ρ ( i ) is the linear delay power at the i -th path. In particular, theTDL-A model defined by 3GPP standard [15] for 5G channelmodel are exploited as reference power delay profile (PDP).Consequently, the transmitted signal after passing through the5G multi-path channel is formulated as ˜ y gb ( t ) = (cid:88) a ∈{ , } ˜h a,b ( τ, t ) ⊗ ˜ x ga ( t ) + ˜w b ( t ) , (9)where h a,b ( τ, t ) = [ h a,b ( τ , t ) , . . . , h a,b ( τ L , t )] ; ˜w b ( t ) isadditive noise vector, whose elements are independent andidentically distributed random variables following a circularlysymmetric complex Gaussian distribution with zero-mean andvariance σ w . ⊗ is the convolutional operator. odulation Layer
Mapping S/P
PilotInsertion
IFFT
Cyclic Prefix Insertion . . . . . . . . .
P/SBits
Cyclic Prefic
Removal S/P FFT Equalization P/S . . . . . . . . . . . . LS DNN Layer
Demapping Demodulation
Transmitter
S/P
Pilot
Insertion IFFT
Cyclic Prefix
Insertion . . . . . . . . .
P/S
Cyclic Prefic
Removal S/P FFT Equalization P/S . . . . . . . . . . . . LS DNN Bits
Receiver
Fig. 1. The considered MIMO-OFDM system model with the transmitter and receiver. The proposed DNN-aided module is in blue color. Notations: CP isCyclic Prefix; S/P is Serial to Parallel; P/S is Parallel to Serial; IFFT is Inverse Fast Fourier Transform; FFT is Fast Fourier Transform.
Tx1
Tx2 Rx1Rx2
Fig. 2. The MIMO × channel model where Tx and Tx are the transmitantenna indices, while Rx and Rx are the receive antenna indices. C. Receiver
At the receiver, the cyclic prefix is first removed out fromthe received signal ˜ y gb ( t ) on each antenna by the cyclicprefix removal module to obtain the vector ˜ y b ( t ) of the length N FFT . The signals are then split into parallel subcarriers andtransformed into frequency-domain by the FFT block, whichgives the frequency-domain signal y b ( t ) as y b ( t ) = FFT { ˜ y b ( t ) } . (10)The received pilot signal is exacted from frequency-domainsignal for channel estimation purposes. Then, the processedsignal y b ( t ) is equalized and congregated into a serial se-quence from all the receive antennas by the layer demappingblock. The signal is further demodulated by the demodulationscheme that corresponds to what the transmitter has used. Atthis point, the output of the MIMO-OFDM system model isobtained as the final binary data sequence.III. P ROPOSED
DNN-A
IDED C HANNEL E STIMATION
The coherent detection used in wireless communicationsneeds knowledge of the propagation channels between thetransmitter and the receiver, which are able to traditionallyobtain by utilizing a channel estimation technique. This sectionpresents the two widely-used channel estimation techniques,which motivates us to exploit a DNN architecture to mitigatethe channel estimation errors.
A. Motivation
As long as there is no inter-carrier interference occurs, eachsubcarrier can be expressed as an independent channel, andtherefore preserving the orthogonality among the subcarriers.The orthogonality allows each subcarrier component of thesignal in (10) to be expressed as the Hadamard product ofthe transmitted signal and channel frequency response at thesubcarrier [17] as y b ( t ) = (cid:88) a ∈{ , } h a,b ( t ) (cid:12) x a ( t ) + w a ( t ) , (11)where (cid:12) is the Hadamard product. w b ( t ) , h a,b ( t ) , and x a ( t ) are the Fourier transforms of noise, channel, and signal re-spectively (or we are working in frequency domain). In aconventional estimation, the pilot symbols are supposed toknow to both the transmitter and receiver are inserted alongwith data in frequency and time domain. In this paper, weapply the pilot structure of the 5G system defined in GPPstandard [18], which is shown in Fig. 3. The pilot symbolsare uniformly spaced in the time domain, denoted by D t andin the frequency domain, denoted by D f . The values of D t and D f depend on the different use cases of a 5G system,which are defined explicitly in, for example [3].Among all conventional channel estimation techniques, LSestimation is one of the most common. We denote ˆ h LS by thechannel estimate from the transmit antennas by this estimationtechnique. LS estimation gives the closed-form expression ofthe channel estimate as [4]: ˆ h LS ( t ) = ( x ( t ) H x ( t )) − x H ( t ) y b ( t ) , (12)where ( · ) H denotes the Hermitian transpose, and x ( t ) = (cid:2) diag( x ( t )) , diag( x ( t )) (cid:3) T (13)is the N P × (2 N P ) matrix denoting transmitted signal from thetwo transmit antennas; N P is the number of the pilot signalsin an OFDM symbol; and ( · ) T is the regular transpose. Thechannel estimate from each transmit antenna can be formulatedas ˆ h LSi ( t ) = (cid:104)(cid:2) ˆ h LS ( t ) (cid:3) ( i − N P , . . . , (cid:2) ˆ h LS ( t ) (cid:3) iN P − (cid:105) T ,i = 1 , . (14)Then, the channel responses from all sub-carriers can beobtained by applying a linear interpolation method. Let us ig. 3. The pilot structure applied for the considered MIMO-OFDM system. denote as ˆ h LS ( t ) . It should be noticed that LS estimation is awidely-used estimation because of its simplicity. However, thistechnique does not exploit the side information from noise andstatistical channel properties in the estimation, and thereforehigh channel estimation errors might be obtained when apply-ing LS estimation for complex propagation environments.To overcome the drawbacks, one can utilize LMMSE es-timation, which minimizes the mean square error and havingthe channel estimation as [17]: ˆ h LMMSEi ( t ) = R h ˆ h LSi (cid:18) R hh + σ w σ x I N P (cid:19) − ˆ h LSi ( t ) ,i = 1 , , (15)where ˆ h LMMSEi ( t ) is the LMMSE estimated channel from the i − th transmit antenna, R hh = E { hh H } is the autocorrelationmatrix of channel response in frequency-domain with thesize of N P × N P with E {·} being the expectation operator; R h ˆ h LSi = E { h ˆ h H LSi } is the cross-correlation between theactual channel and the channel estimate obtained by LS esti-mation with the size of N FFT × N P ; σ x is the variance of thetransmitted signals, respectively; I N P is the identity matrix ofsize N P × N P . Since the impact of noise is taken into accountby LMMSE estimation, which is able to improve the channelestimation accuracy. However, LMMSE estimation requiresthe prior knowledge of channel statistical properties, thusthe computational complexity is higher than LS estimation.Additionally, it may be difficult to obtain the exact distributionof channel impulse responses in general [19], the performanceof LMMSE estimation can not always be guaranteed. B. DNN-Aided Channel Estimation
To overcome the aforementioned drawbacks of LS andLMMSE estimations, we propose a DNN-aided estimation thatminimizes the MSE between the channel estimate obtained
Fig. 4. The DNN structure used for channel estimation. by LS estimation and the actual channel. The structure ofthe proposed DNN-aided estimation is depicted in Fig. 4.As shown in this figure, the proposed DNN structure isorganized as layers including the input layer, hidden layersand output layer. Notice that a DNN may have many hiddenlayers. However, for the considered MIMO-OFDM system,the proposed DNN structure is designed with hidden layerswhich include multiple neurons. In particular, a neuron is acomputational unit which performs the following calculation: o = f ( z ) = f (cid:32) M (cid:88) i =1 w i x i + b (cid:33) , (16)where M is the number of inputs to this neuron for which x i is the i -th input ( i = 1 , . . . , M ); w i is the i -th weightcorresponding to the i -th input; b is a bias and o is theoutput of this neuron. In (16), f ( . ) is well-known as aactivation function which is used to characterize the non-linearity of the data. In our proposed framework, we use thetanh function as the activation function, which is expressed as: f ( z ) = e z − e − z e z + e − z . (17)To minimize the MSE, the DNN-aided estimation will learnthe actual channel information given the channel estimatesobtained by LS estimation as the input. In detail, we define arealization of the input for the training process as M nt = (cid:110) Re (cid:110)(cid:2) ˆ h n LS ( t ) (cid:3) (cid:111) , Im (cid:110)(cid:2) ˆ h n LS ( t ) (cid:3) (cid:111) , . . . , Re (cid:110)(cid:2) ˆ h n LS ( t ) (cid:3) (cid:111) , Im (cid:110)(cid:2) ˆ h n LS ( t ) (cid:3) (cid:111)(cid:111) , (18)where the superscript n denotes the n -th realization; Re {·} and Im {·} give the real and imaginary part of a complex number,respectively. The output of the neural network is O nt = (cid:110) Re (cid:110)(cid:2) ˆ h n ( t ) (cid:3) (cid:111) , Im (cid:110)(cid:2) ˆ h n ( t ) (cid:3) (cid:111) , . . . , Re (cid:110)(cid:2) ˆ h n ( t ) (cid:3) (cid:111) , Im (cid:110)(cid:2) ˆ h n ( t ) (cid:3) (cid:111)(cid:111) , (19) According to the universal approximation theorem, there are other deepneural networks that give the similar or better performance than a fully-connected neural network with a limited data volume. However, the maintheme of this paper is to point out the assistance of deep learning to channelestimation for 5G wireless communications. Therefore, the fully-connectedDNN is selected due to its simplicity and low computational complexity. Anoptimized DNN structure is left for the future work.ABLE IA
RCHITECTURE OF
DNN
MODELS FOR CHANNEL ESTIMATION
Layer DNN-1 DNN-2Nodes f ( . ) Nodes f ( . ) Input layer 8 - 8 -Hidden layer
16 tanh 32 tanhHidden layer
16 tanh 32 tanhHidden layer
16 tanh 32 tanhOutput layer 8 - 8 - where ˆ h n ( t ) is the output of the neural network at the n -threalization. In (18) and (19), we separate the channel estimateinto into the real and imaginary parts to tackle the complexnumbers for the neural network. The learning process handlesthe one-by-one mapping: (cid:16) Re (cid:110)(cid:2) ˆ h n LS ( t ) (cid:3) s (cid:111) , Im (cid:110)(cid:2) ˆ h n LS ( t ) (cid:3) s (cid:111)(cid:17) → (cid:16) Re (cid:110)(cid:2) ˆ h n ( t ) (cid:3) s (cid:111) , Im (cid:110)(cid:2) ˆ h n ( t ) (cid:3) s (cid:111)(cid:17) , s = 0 , . . . , , (20)As desired, the output of the neural network should beidentical to the actual channels. Alternatively, the purpose ofthe DNN-aided estimation is to minimize the MSE betweenthe prediction and actual channels on average, thus the lossfunction utilized for the training phase is defined as L ( W , B ) = 1 N T N (cid:88) n =1 T (cid:88) t =1 (cid:13)(cid:13) ˆ h n ( t ) − h n ( t ) (cid:13)(cid:13) , (21)where N is the number of realizations used for training,and h n ( t ) is the actual channel corresponding to ˆ h n ( t ) . W and B include all the weights and biases, respectively. Froma set of initial values, the weights and biases are updatedby minimizing the loss function (21) with the forward andbackward propagation [12]. Remark 1:
The loss function (21) formulates a supervisedlearning. It is based on the fact that the actual channels areavailable in the training phase, which is obtained if the pilotpower or coherence interval is sufficiently large. Consequently,the proposed learning-based approach possibly outperformsLS estimation. For future works, we can investigate the sys-tem performance under an unsupervised learning frameworktogether with imperfect channel state information.In order to train and test the proposed neural network, a setof data with realizations are gathered. We use data for training, as the validation set, and data fortesting. In this paper, the two DNN models, labeled DNN-1and DNN-2, are proposed for channel estimation with 5 layerscomprising the input layer, hidden layers, and output layer.As illustrated in Table. I, the number of neurons of each layerare , , , , for DNN- , respectively. Meanwhile, thoseare , , , , for DNN- . Notice that the number neuronsin input and output layers corresponds to the total number ofreal and image parts for 4 path channel, which is 8. TABLE IIP
ARAMETERS FOR
MIMO-OFDM
SYSTEM
Parameters ValuesMIMO 2x2FFT size 512Cyclic prefix 64Type of modulation QPSKChannel PDP TDL-AMaximum Doppler frequency 36 Hz, 200 HzNoise model Gaussian NoiseTABLE IIIP
ARAMETERS FOR D EEP NEURAL NETWORK MODELS
Parameters ValuesTraining function Levenberg-MarquardtMaximum number of epoches
Mini-bath size Training error − Gradient descent accuracy − Learning rate . Maximum validation failures IV. SIMULATION RESULTSTo evaluate the performance of the DNN-aided estima-tion, the simulation has been carried out and the results arecompared with the conventional LS estimation and LMMSEestimation by utilizing the bit error rate (BER) and meansquare error (MSE) versus signal to noise ratio (SNR). Thesetup parameters of the considered MIMO-OFDM systemare shown in Table II, while those parameters used for theDNN model are in Table III. In the simulations, we use thefading multi-path model channel with the TDL-A Power DelayProfile as aforementioned in Section II. For comparison, LSand LMMSE estimations are also included as benchmarks.To investigate the performance of all the considered channelestimations exploiting in the MIMO-OFDM system throughthe 5G channel model, the two different scenarios corre-sponding to the velocity of mobiles are exploited: In the firstscenario, the receiver moves with a low speed such that themaximum Doppler frequency is Hz. The pilot symbols areinserted along with data in both frequency and time domain.Because the channel is slowly changed over time, the pilotspacing in the time domain is D t = 4 and in the frequencydomain is D f = 2 ; In the second scenario, the system serveshigh-speed mobility, which results in the maximum Dopplerfrequency of Hz. In this scenario, the setup D t = D f = 2 is to cope with a rapid change of the channels over time.Fig. 5 and 6 show the MSE of different channel estimationsutilizing the first and second scenarios, respectively. TheQPSK (quadrature phase-shift keying modulation) is deployedto modulate the transmitted data in the simulation. As shown inFig. 5 and 6, all the channel estimation methods provide MSEdeclining gradually as the SNR grows. In both the scenarios,LS estimation yields the worst MSE performance since it doesnot take the statistical channel information into account whenperforming the channel estimation. On the contrary, LMMSE ig. 5. The MSE of the channel estimate versus the SNR level for the firstscenario f D = 36 Hz.Fig. 6. The MSE of the channel estimate versus the SNR level for the secondscenario f D = 200 Hz. estimation exploits the mean and covariance matrices, whichresults in the better MSE performance than the LS counterpart.Our proposed deep learning methods yield the best MSEperformance, especially at the low and mediate SNR levels.When the SNR increases above dB, the deep learning-based approaches give worse MSE than the performance ofLMMSE estimation. This may be because the structure of theDNN models is still not optimal at high SNR levels and thehyper-parameters should be tuned more carefully. Althoughthe DNN- model has more neurons in each hidden layer thanthe DNN- model, the results are only slightly different. Thismeans that a complex DNN structure is not always along withbetter accuracy. Although the pilot symbols are inserted moredensely in time domain in the second scenario with the highspeed of the receiver, the MSE of all four channel estimationmethods is worse than those of the first scenario due to the Fig. 7. The BER of the channel estimate versus the SNR level for the firstscenario f D = 36 Hz.Fig. 8. The BER of the channel estimate versus the SNR level for the firstscenario f D = 200 Hz. severity of Doppler effects.We provide the BER performance of the considered sce-narios in Fig. 7 and 8 with the different channel estimationmethods, respectively. The discrepancies across the channel es-timation methods are not seen clearly in the BER performance.However, we still observe that LS estimation provides theworst performance among the four methods in both scenarios,while the BER performance of the remaining ones are almostthe same to each other. Even though LS estimation performsworse than the others, the performance gap is relatively small.This can be explained by the fact that the loss function hasbeen defined to minimize the channel estimation errors insteadof the BER metric. Besides, Fig. 7 and 8 also show thesignificant improvements of the BER when increasing the SNRlevel with combating the Doppler effects more effectively. Forinstance, at f D = 36 Hz, the BER gets × better if the SNRevel increases from dB to dB.V. CONCLUSIONSIn this paper, the deep neural network with the two typicalinstances called DNN-1 and DNN-2 has been proposed to as-sist the channel estimation in a MIMO-OFDM system with thetwo different scenarios of fading multi-path channel modelsbased on the TDL-A model defined in the 5G networks. Theproposed DNN-based channel estimation methods are trainedwith the channel estimate from least squares estimation and thecorresponding perfect channels. By utilizing the QPSK modu-lation scheme, the performance of the proposed estimations iscompared with the conventional LS and LMMSE estimationsin terms of channel estimation errors and bit error ratio asa function of the SNR levels. Due to learning the channelproperties effectively, we observed the superior improvementsof the proposed DNN-aided estimation in reducing channelestimation errors. The future work should focus on a designto reduce the bit error ratio as well.ACKNOWLEDGEMENTThis work was funded by the Vietnam’s Ministry of Edu-cation and Training (MOET) Project B2019-BKA-10.R EFERENCES[1] T. Van Chien and E. Bj¨ornson, “Massive MIMO communications,” in
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