Deep Neural Network-Based Channel and Carrier

Frequency Offset equalization for

OFDM systems
Dr.Ch.Tejesh Kumara ,B.Gayatrib, B.Z.Lalithc, D.Gopala krishnad and B.Krishna Tejae
Electronics and communication engineering, Raghu Institute of technology, Dakamarri, India

b,c,d,e-gayatribelihelli155@gmail.com
Abstract— An extensively utilized modulation technique in an OFDM symbol's Doppler frequency remains constant.
wireless communication systems, such as Unmanned Aerial Vehicle Orthogonal Frequency Division Multiplexing is a key technology
(UAV) networks, is orthogonal frequency division multiplexing, or in contemporary communication networks, offering high data
OFDM. Nevertheless, Carrier Frequency Offset (CFO) and
rates and resilience against frequency-selective fading. But
channel distortions might deteriorate the efficiency of OFDM
systems. A study on reducing these impacts with deep learning-
problems like dynamic channel effects and carrier frequency
based equalization methods is shown in this script. The script starts offset (CFO) still exist, especially when it comes to unmanned
by specifying the parameters of the system, such as the modulation aerial vehicle (UAV) communications. Deep Neural Networks
schemes, cyclic prefix length, and number of subcarriers. To mimic (DNNs) are one of the novel ways being investigated to address
realistic channel circumstances, it introduces CFO changes and these issues and improve the performance of OFDM systems.
creates random data symbols. Subsequently, the software applies Deep Neural Networks (DNNs) have shown remarkable
channel equalization using a deep learning neural network (DNN). efficacy across several fields, including photo identification,
After utilizing pilot symbols to train the DNN, it assesses its natural language processing, and now communication systems.
performance in a virtual setting. It also uses comparison techniques
Using DNNs' capabilities, researchers hope to develop creative
such as least squares (LS) and minimal mean square error
(MMSE). The results of the simulation show that the DNN-based improvements for channel estimation and equalization in
equalization method outperforms the conventional LS and MMSE OFDM systems. Unlike conventional approaches that rely on
approaches in mitigating channel distortions and CFO. pilot symbols or assumptions about channel circumstances,
DNN-based solutions may learn complex patterns and adapt to
Index Terms—Channel equalization, carrier frequency offset
equalization, deep learning, Deep Neural Networks, OFDM, UAV. changing conditions. The purpose of this work is to examine the
application of DNNs in OFDM systems, with an emphasis on
channel equalization and estimation when dealing with CFO
I. INTRODUCTION and dynamic channel effects. Our objective is to develop

F UTURE communication networks will need to adjust to a

dependable techniques that can efficiently estimate channel
parameters and make up for communication deficiencies in
real-time.
wide range of applications and dynamic environments due to the
need for high bandwidth and low latency. Unmanned aerial
vehicle (UAV) relay and base station integration solutions are
beginning to emerge, despite obstacles such as carrier frequency II. SYSTEM MODEL AND METHODOLOGY
offset (CFO) and dynamic channel effects. An important
Fig. 1 displays the suggested method's system model.
modulation technique is orthogonal frequency division
Together with the CFO and channel equalization networks,
multiplexing (OFDM), which provides high data rates and
which are composed of Deep Neural Networks (DNNs), it
resilience but is vulnerable to problems like CFO, particularly in
includes an OFDM transmitter and receiver. The limited effect of
UAV communications. In order to overcome these obstacles and
CFO estimated using typical methodologies under low SNR
provide dependable communication, especially in mobile
often affects the entire communication system performance,
systems, accurate CFO estimation is essential.
notably in OFDM systems. We try to replace the CFO estimation
High bandwidth and low latency demands will drive the need
module of the conventional communication system with the DL-
for future communication networks to suit a variety of needs in
based method. The network training procedure will ultimately
dynamic settings. Emerging solutions, such as the use of UAV’s
generate the carrier frequency offset estimate by independently
as base stations or relays, must overcome obstacles including
learning the relationship between the CFO and the input
carrier frequency offset (CFO) and dynamic channel effects. In
sequence.
OFDM systems, CFO breaks orthogonal, which results in inter-
carrier interference and decreased efficiency.
A. Signal Model
Furthermore, current CFO equalization techniques presume that

symbol is given by
Channel distortions, caused by multipath propagation and N −1 j 2 πkn
fading effects, introduce intersymbol interference (ISI) and
degrade the received signal quality. Moreover, CFO arises due
xm [ n]= ∑
X [ k ] e N , 0≤ n ≤ N − 1(1)
k =0
to frequency synchronization errors between the transmitter Where x [n] is the mth OFDM symbol without cyclic prefix
m
and receiver.
The Inverse Discrete Fourier Transform of the m th OFDM (CP), N is the number of sub carriers, and X[k] is the baseband
modulated data symbols to be transmitted.

y [ n ] =G x cℎ [ n ] + w [ n ] (5)

Where
i 2 πf ( n) n
∆ fN
G=e

x cℎ [ n ] =x [ n ] ⊗ h [n]

In this case, the transmitted OFDM frame is represented by

x[n], the received baseband OFDM signal by y[n], and the
convolution operation is shown by ⊗. The received baseband
Fig. 1. System model of the proposed DNN based CFO and channel
equalizer for OFDM systems signal, y[n] is the input of the CFO equalization network. The
output of the network is an estimate of the signal, or xch[n]
After adding the CP with length Ncp, the OFDM symbol minus the CFO impact. Considering the output of the CFO
transmitted at the transmitter is given by equalization network as G prior to the skip connection, we can
write the output xch[n] from the input following the skip

{ x m [ n+ N ] ,− Ncp≤ n ≤ −1 connection as
x m [n]= (2)
x m [ N ] , 0 ≤ n≤ N −1 ^ ∗(G x cℎ [n]+ w[n])(6)
^x cℎ [ n ] =G
The discrete-time baseband samples of the m th OFDM symbol If we disregard the impact of Additive White Gaussian Noise
received at the receiver can now be written as (AWGN), the a fore mentioned formula can be expressed as
follows:
j 2 πf ( n) n L− 1

y m [ n ] =e
∆ f ( N)
∑ ℎ [ l ] x m [ n −l − τ ] + w [ n ] ,(3) ^ ∗G x cℎ [ n ] (7)
^x cℎ [ n ] =G
l=0

0 ≤ n ≤ N s ≤ −1
The projected G ^ value needs to be near the complex
Here, ym[n] is the received samples of the mth OFDM conjugate of G in order to completely avoid the effect of CFO.
symbol, f(n) is time-varying frequency offset, τ is the symbol In order to reduce the mean-squared error cost function, the
timing offset (STO), Ns =N + Ncp is the length of OFDM network is trained.
symbol with cyclic prefix (CP), w[n] is Additive White
2
Gaussian Noise (AWGN), and h[l] is the propagation channel J CFO =( ^x cℎ [ n ] − x cℎ [ n ] ) (8)
response, Δf is the subcarrier spacing and L is Number of
multipath components or the channel taps. Here we considered The channel equalization network receives as its input the
Rician channel mode with a Line of sight(LOS) component and frequency domain CFO compensated signal, which is obtained
several nonreflective components (non-LOS components). by subtracting the CP and obtaining the FFT of the output
We also assume the perfect time synchronization between the signal from the CFO equalization network, which is
transmitter and the receiver leading to τ = 0. Many such OFDM represented by
symbols are received in serial to obtain an input sample to the
NN, given by ^
X cℎ [ k ] =FFT ( ^x cℎ [ n ] )= X [ k ] H [ k ] (9)
y [ n ] =¿] (4)
.
where H[k] represents the channel's frequency domain
B. Methodology
response. The estimated channel equalized signal Xˆ[k] is the
network's output. Considering the channel equalization
DNNs are trained in two stages. The received time domain IQ
network's output prior to the skip connection as H^ [k], we now
samples of the serial OFDM signal are first received by the CFO
obtain
equalization network, which uses them to estimate the signal
independently of the CFO effects. The signal is then converted
to a different frequency domain, and CP is removed. The ^ ^ [ k ] ∗ ( X [ k ] H [ k ] ) (10)
X [ k ]= H
channel equalization network is then trained using this CFO
equalized frequency domain signal, allowing it to predict the Consequently, by minimizing the cost function, the channel
signal without channel effects. The conveyed data is then equalization network is trained to learn the estimate Hˆ, whose
recovered by demodulating this signal. The following can be value should be near to the inverse of the real channel response
used to express the received OFDM frame. H[k].

.
 J cℎan =( ^
2 III. SIMULATION AND RESULTS
X [ k ] − X [ k ] ) (11)
A. Specifications:
C. MODEL ARCHITECTURE
The OFDM parameters for generating simulation data conform
to the LDACS standard for drone communication in the L-
In this study, we employ the Gate Recurrent Unit (GRU) Band. Important specifications include N=64 (subcarriers),
architecture to accurately estimate the Carrier Frequency Offset Ncp=16 (cyclic prefix length) and Δf = 10kHz (subcarrier
where 𝑼𝑥 is the received IQ sample preamble, represents the
(CFO) from the received preamble of 802.11n. Equation (10), spacing). Each frame consists of randomly generated data
symbols without pilots or preambles. The CFO fluctuates
estimate process. We use both the Long Training Field (LTF) within the OFDM symbol, while the channel remains
and Short Training Field (STF) fields sequentially to input the consistent within a frame but varies between frames. .
model. The model finds the complex link between the Evaluation of performance includes BPSK, QPSK, and 16-
preamble and CFO and produces the CFO value directly. Using QAM modulation schemes under a frequency-selective Rician
GRU's capacity to capture temporal correlations between past fading channel with a Line-of-Sight (LoS) component and up
and present situations, our method combines GRU with thick to 3 multipath components. Three CFO variations, representing
hidden state 𝒉 as the input for the next layer rather than its
layers. In contrast to conventional approaches, we use GRU's high speed, low speed, and acceleration/deceleration
conditions, are integrated into the datasets, as illustrated in
output. Figure 2.

a) Deep Neural Network architecture The CFO variations across different modulation schemes
The proposed Deep Neural Network (DNN) targets a (BPSK, QPSK, and 16QAM) over a sequence of OFDM
particular subcarrier inside the OFDM frame and is intended symbols within a frame are analyzed as shown in Fig 2.
for channel equalization in orthogonal frequency division 1.The CFO-1 variation, involves an initial increase for the
multiplexing systems. There are various layers in this initial 16 symbols followed by a decrease for the
architecture that include follows: subsequent 16 symbols, mimicking acceleration and
deceleration.
Input layer: 2.The CFO-2 variation commences with a positive
A sequence input layer makes up the DNN's input Doppler shift and swiftly shifts to negative Doppler
layer. A series of features is used to represent the input data, values, indicating high speeds following the formula as
with each feature representing the real and imaginary below,
portions of the received symbols on the chosen subcarrier.

( )
The number of OFDM symbols ({NumOFDMsym}) 2 πn
multiplied by the number of subcarriers ({NumSC}) and f ( n )=500 ∗ cos (12)
doubled to accommodate for real and imaginary parts yields 2 N f ( N + N cp )
the input size.
3.The CFO-3 likewise exhibits a transition from positive
LSTM layer: to negative Doppler shift, albeit at a significantly slower
The signal that is received sequences are exposed to rate, indicating lower speeds following the formula as
temporal dependencies and dynamics that are stored by the below,
Long Short-Term Memory (LSTM) layer. Because LSTM
networks perform well in sequence modeling applications,
they can handle time-series data, including OFDM symbols.
The size of the hidden state is determined by the
( √ N n∆ f )(13)
f ( n )=50 − 103 −

{NumHiddenUnits} units of the LSTM layer.

B. Graphs and Results
Fully connected layer:
A completely connected layer receives the LSTM Figure 3's SNRvs BER plot shows the symbol error
layer's output. The LSTM output and the output classes are rates (BER) attained by the DL, LS, and MMSE
mapped by this layer. This layer has the same number of techniques at various SNR values. For all approaches, BER
neurons as there are output classes ({NumClass}). lowers with increasing SNR, suggesting improving signal
quality. Particularly at lower SNR values, DL consistently
Softmax layer: outperforms LS and MMSE, indicating the trained neural
network's efficacy in symbol detection even under noisy
. The fully connected layer's raw output scores are circumstances. The performance of the LS and MMSE
transformed into probabilities by the soft max layer. In this algorithms is comparable, with MMSE marginally
layer, the probability of belonging to a particular class is outperforming LS, especially at lower SNR values. This is
represented by each output neuron. in line with what was anticipated.

Classification layer:
The input sequence is assigned to one of the
predetermined classes by the classification layer, which is
the last layer. During training, this layer computes the loss
 Fig 3.BER vs SNR under DL, LS and MMSE

amid noisy environments. LS and MMSE techniques exhibited

comparable results, with MMSE demonstrating a slight edge,
. particularly at lower SNR values, due to its capacity to account
for noise variance during channel estimation. Looking ahead,
there are numerous avenues for future exploration and
enhancement. Firstly, refining the neural network architecture
and training procedures could potentially amplify DL's
performance, leveraging advanced methodologies such as

transfer learning or ensemble techniques. Moreover, exploring

adaptive algorithms for LS and MMSE estimation could
enhance their resilience and adaptability to fluctuating channel
conditions. Additionally, delving into alternative signal
processing approaches, such as deep reinforcement learning or
Fig 4.DNN Training progress unsupervised learning methods, may offer innovative insights
and solutions for symbol detection within communication
systems. Overall, sustained research and development in these
The DNN is trained using the provided training data domains hold promise for further bolstering the reliability and
(`XTrain` and `YTrain`) with the specified layers and options. efficacy of symbol detection methodologies, thus advancing the
The trained network, along with the mini-batch size, is saved capabilities of communication systems in practical settings.
into a file named `TrainedNet.mat`. Subsequently, the trained
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