TELKOMNIKA Telecommunication Computing Electronics and Control Vol.
No.
April 2026, pp.
ISSN: 1693-6930.
DOI: 10.
12928/TELKOMNIKA.
Noise-suppression method for UAV-OFDM systems by introducing CV-VSS-NLMS algorithm and single-antenna Walid Lebbou1.
Laid Chergui1.
Saad Bouguezel2 Laboratory of Satit.
Department of Electrical Engineering.
University Abbes Laghrour Khenchela.
Khenchela.
Algeria CCNS Laboratory.
Department of Electronics.
Setif 1 University Ferhat Abbas.
Sytif.
Algeria
Article Info
ABSTRACT
Article history:
In this paper, we address the critical challenge of impulsive interference in orthogonal frequency division multiplexing (OFDM)-based unmanned aerial vehicle (UAV) communication systems, which can severely degrade data transmission reliability.
Specifically, we propose a novel complex-valued variable step-size normalized least mean square (CV-VSS-NLMS) adaptive filtering algorithm dedicated for adaptive filtering of complex-valued signals, providing real-time, lightweight, and efficient impulsive-noise suppression for UAV-OFDM signals.
In contrast, real-valued VSS-LMS filters treat the real and imaginary parts separately, resulting in poorer mean square error (MSE) convergence for complex signals.
The algorithm is developed by efficiently adapting LMS-based filtering strategies to impulsive interference scenarios and adequately integrating prior concepts of electromagnetic pulse suppression within a well-designed single-antenna UAV architecture.
This new configuration is especially suited for size, weight, and power-constrained UAV platforms, where reducing complexity is highly desirable.
In contrast to conventional blind source separation approaches, the proposed solution ensures reliable communication without excessive processing demands, since it efficiently suppresses impulsive noise and greatly reduces the number of matrix operations.
Simulation results demonstrate a significant improvement in bit error rate (BER), confirming that the proposed CV-VSS-NLMS technique provides a robust, dependable, and practical solution for modern UAV communication links.
Received Jul 13, 2025 Revised Dec 8, 2025 Accepted Jan 30, 2026 Keywords:
Least mean square algorithm Noise cancellation Orthogonal frequency division Unmanned aerial vehicle Wireless communication This is an open access article under the CC BY-SA license.
Corresponding Author:
Laid Chergui Laboratory of Satit.
Department of Electrical Engineering.
University Abbes Laghrour Khenchela Khenchela, 40004.
Algeria Email: chergui_laid@univ-khenchela.
INTRODUCTION
In recent years, unmanned aerial vehicles (UAV.
have gained considerable importance, highlighting their essential role in daily life.
They have emerged as crucial solutions in various fields, including research, medicine, industry, environmental monitoring, communication technologies and security .
Among the communication techniques used in UAVs, the orthogonal frequency division multiplexing (OFDM) is widely adopted for its high transmission speed, good spectral efficiency, and ability to mitigate inter-symbol interference (ISI) and inter-carrier interference (ICI) .
However, the OFDM in UAVs is susceptible to impulsive interference from sources like switching processes in power networks, ignition noise from passing vehicles, and other systems operating in the same frequency range .
Moreover.
OFDM systems can tolerate moderate and infrequent impulsive interference fairly well, as this Journal homepage: http://journal.
id/index.
php/TELKOMNIKA A ISSN: 1693-6930 interference is spread across multiple sub-carriers of an OFDM symbol.
However, when interference occurs frequently or has high power, it significantly impacts system performance .
, .
necessitating the use of interference mitigation techniques .
, .
In the literature, research has focused on analyzing noise in wireless communication links using single electromagnetic pulses like gaussian and square wave pulses .
The information security of UAV communication links in complex electromagnetic environments was first addressed in .
, where analytical functions have been established for typical noise, such as high-voltage sinusoidal pulses (HVSP), electrical fast transient pulses (EFTP), and surge pulses (SP).
It should be noted that .
was the first to consider the integration of UAV modulation and demodulation methods, based on the principles of OFDM, with electromagnetic pulse interference and its This approach, which is a source separation technique that incorporates a dual antenna design alongside OFDM-based noise suppression techniques, has demonstrated strong performance in mitigating electromagnetic noise in UAV communications, leading to enhanced image quality and reduced bit error rate (BER).
However, this approach is computationally intensive, primarily due to the calculation of the covariance matrix required during the whitening phase.
This whitening process, which removes correlations between observed signals, precedes the iterative separation of the useful signal from electromagnetic noise and simplifies the extraction of independent components.
While whitening significantly improves the convergence of the algorithm, it also contributes substantially to the overall computational complexity of the Consequently, this method is not well suited for real-time applications, as it operates on data blocks rather than processing signals continuously.
There are also several source separation techniques in the literature, such as the least mean square (LMS)-based symmetric adaptive decorrelation (SAD) algorithm discussed in .
, which distinguishes between signal and noise to enable effective signal separation.
Additionally, recent advancements include the proposal of two-channel variable-step-size forward-and-backward adaptive algorithm structures for speech enhancement in scenarios involving highly correlated noisy observations .
In this paper, we propose a novel approach for mitigating impulsive interference in UAV OFDM communication systems.
The core contribution of this approach lies in the introduction of a complex-valued variable step size normalized LMS (CV-VSS-NLMS) algorithm, which is exclusively developed for realtime sample-by-sample noise cancellation and dedicated for adaptive filtering of complex-valued signals.
contrast, the existing real valued VSS-LMS algorithms must filter the real and imaginary parts separately, resulting in poorer mean square error (MSE) convergence.
The proposed approach adapts existing LMSbased adaptive filtering principles and integrates concepts from prior electromagnetic pulse suppression In order to achieve efficient, lightweight, and real-time noise suppression in UAV-OFDM communication systems, we introduce a combination of the proposed CV-VSS-NLMS algorithm and a welldesigned single-antenna architecture.
Unlike conventional blind source separation methods that rely on multiple matrix computations and block processing, the proposed combination approach significantly reduces the computational complexity while maintaining high performance.
The remainder of this paper is organized as follows: section 2 describes in detail the proposed Section 3 presents and discusses the simulation results.
Finally, section 4 concludes the paper and summarizes the main findings, as well as possible directions for future work.
METHODOLOGY
Review of electromagnetic pulse suppression method for OFDM-based UAV In this sub-section, we present a review of the dual-antenna pulse noise mitigation technique reported in .
, which corresponds to the electromagnetic pulse suppression method for OFDM-based UAV This method is illustrated in Figures 1 and 2, which show that the process involves several stages, including demeaning, combination, whitening, iterative operations, and convergence assessment.
It is seen from Figure 2 that the two signals ycu 1 = .
cu01 ,ycu11 .
A, ycuyaOe1 ]T and ycu 2 = .
cu02 ,ycu12 .
A, ycuyaOe1
]T ,
ycN where ya is the number of samples and [UI] denotes the matrix transpose operation, are captured by two separated antennas and then passed through a de-mean module.
This module subtracts the mean value of a given signal from each of its samples, resulting in the new signals ycuE 1 = .
cuE 01 ,ycuE11 .
A, ycuE yaOe1 ]T and ycuE 2 = .
cuE 02 , ycuE12 .
A, ycuE yaOe1 ] whose samples are computed as:
ycn ycuE ycuycn = ycuycuycn Oe OcyaOe1 yco=0 ycuyco , i =1, 2 and n = 0, 1, 2.
K-1 ya TELKOMNIKA Telecommun Comput El Control.
Vol.
No.
April 2026: 407-419 TELKOMNIKA Telecommun Comput El Control The purpose of the de-mean carried out in .
is to enhance the convergence of the iterative computation process.
The two signals resulted from .
are then combined in a single signal in the form of a two-row matrix as:
cuE 1 )ycN ycU = [ 2 ycN] .
cuE ) .
Figure 1.
Schematic diagram of the uplink transmission link for UAV .
Figure 2.
Schematic diagram of separation module of electromagnetic pulse noise from OFDM wireless signal .
The process of whitening of the signal ycU resulted in .
is performed as:
ycs = yu Oe2 yc ycN ycU Where yc and yu are respectively the eigenvector and eigenvalue matrixes of the covariance matrix yaycU given by:
yaycu = ( ) ycU ycN ycU where ycA corresponds to the number of the captured signals, which is considered to be equal to 2.
The matrix ycs whitened in .
, which can be expressed as ycs = .
c1 yc.
, is subsequently utilized in the iterative computation process performed for each weight vector as:
yc1ycn = ya.
c ycn O ycycaycuEa.
cO ycN y yc.
} Oe ya.
Oe .
cycaycuEa.
cO ycN y yc.
2 )} O yc ycn , i = 1, 2 ycn where yc ycn =.
c0ycn , yc1ycn .
A, ycycAOe1 ]T , i = 1, 2, are two weight vectors used during the iterative process, which are combined in a two-row matrix as ycO = .
c 1 yc 2 ], the operators y and * denote, respectively, the dot and Hadamard products, and E{O.
is the expectation operation.
The two vectors yc1ycn = .
c1ycn0 , yc11ycn .
A, yc1ycnycAOe1 ]T, ycn = 1, 2, resulted from .
are also arranged in a two-row matrix as ycO1 = .
c11 yc12 ].
By adapting the vector ycO1, a new vector ycO2is obtained as:
ycO2 = ycO1 Oe OcycAOe1 ycn=1 .
cO1 y yc ] O yc Noise-suppression method for UAV-OFDM systems by introducing CV-VSS-NLMS A (Walid Lebbo.
A ISSN: 1693-6930 which can be expressed as ycO2 = .
c21 weight vectors are normalized as:
ycn ycn ycn yc22 ], where yc2ycn =.
c20 , yc21 .
A, yc2ycAOe1 ]T, i=1, 2.
These two E ycn = yc2ycn /Anyc2ycn An, ycn = 1, 2 E = .
c and then combined in a two-row matrix as ycO yc E 2 ] , where AnOoAn denotes the norm operation defined as:
ycn Anyc2ycn An = ocycAOe1 yco=0 .
c2yco ) , i= 1, 2.
and M = 2 In the iterative process, ycO1 and ycO2 are intermediate variables matrixes derived from ycO.
The E represents the update of ycO after each iteration.
matrix ycO After each iteration, the condition given by:
E ycO| < yc .
cO .
must be verified, where q is the convergence value used to judge the convergence of ycO E is updated and used If condition .
is satisfied, ycO is considered to have converged.
Otherwise, ycO as the new ycO according to:
E =ycO ycO Finally, the output demixing matrix is then obtained as:
E ycNycs ycI=ycO .
E , contains both noise and the original signal.
This process ensures that The matrix ycI, derived using ycO the hybrid matrix ycs achieves maximum non-Gaussianity, allowing for effective component separation and facilitating the extraction of the signal of interest from ycI.
Proposed approach In this sub-section, we present a novel noise mitigation system for the UAV communication link by using three adaptive noise cancellers (ANC.
units and introducing a new CV-VSS-NLMS algorithm.
These three cancellers operate in parallel, each using one of the three types of noise as a reference input signal to give an estimation ycuCyco of the unknown complex valued noise ycuyco present in the captured signal given as:
yccyco = ycyco ycuyco The complex valued reference signals are specifically defined as follows: ycuyco .
= ycuyco .
, ycuyco .
= ycuyco and ycuyco .
= ycuyco .
The estimated noises are then subtracted from yccyco to de-noise the desired signal of interest ycyco .
At the output of the proposed system, we designed a module using a cost function to identify which of the three ANCAos provides the best de-noised version ycCyco of the desired signal ycyco .
Each of the three CVVSS-NLMS ANCs is defined by:
ycyco 1 .
= ycyco yuNyco .
ycCyco cuyco ) .
, ycn = 1, 2, 3 cuyco ) ycuyco yuA where(UI)O and(UI)ya denote the complex conjugate and the Hermitian transpose operations, respectively.
= .
ycN .
, ycyco .
, .
, ycyco .
cA Oe .
] is the filter weight vector of length N, i =1, 2,3 and the term .
cuyco ) ycuyco .
corresponds to the power estimate of ycuyco , which enables its power normalization, the parameter yuA is a regularization term that takes small values to prevent overflow, and yuNyco .
is the variable step-size parameter .
used to control the convergence behavior of the adaptive algorithm.
The input signals ycuyco , ycn = 1, 2, 3, of the adaptive filters correspond to the three considered noise types.
Specifically, the noise types are ycuyco .
: HVSP, ycuyco .
: EFTP, andycuyco .
: SP.
TELKOMNIKA Telecommun Comput El Control.
Vol.
No.
April 2026: 407-419 TELKOMNIKA Telecommun Comput El Control The estimated signal at the output of each of the three ANCs is then computed as:
ycN .
ycCyco = yccyco Oe .
cyco ) ycuyco where (UI)ycN denote the transpose operation, whereas the variable step size yuNyco .
is defined as:
2 yuNyco .
= yuyuNycoOe1 .
yuAnycyCyco An .
ycyCyco .
= yuycyCycoOe1 .
Oe y.
ycCyco .
O .
eoyco ) .
eoyco ) yeoyco yuA the parameters yu and yuare positive scalars used for controlling the variable step size yuNyco .
, and yu is the smoothing factor with values taken in the range .
, .
It should be noted that the proposed CV-VSS-NLMS algorithm formulated in .
is derived from the variable step size pre-whitening transform-domain LMS introduced in .
for an ANC system operating in the transform domain.
However, in the present work, the proposed CV-VSS-NLMS-based ANC algorithm operates in the time domain.
In contrast to the system in .
, the proposed system requires only a single antenna as shown in Figure 3, and the interfering noise ycuyco in .
, affecting the UAV communication link, can be one of the three considered types of noise.
To identify which of the outputs ycCyco , ycn = 1, 2, 3, corresponds to the best de-noised recovered signal, we have designed an identification system based on the calculation of a cost function.
This system relies on .
the estimation of the average energy of the signalycCyco , recovered at the output of each ANC, in order to determine the type of noise that contaminated the received signal.
The average energy is computed, at each instant k, after the convergence of the CV-VSS-NLMS algorithms, as .
= OcyaOe1 cCycoOeycu .
) ycu=0 ycC ycoOeycu ya ycoOuycu where ya is the length of the smoothing window.
Subsequently, we look for the lowest average energy among yayco .
, yayco .
, and consequently, the corresponding estimated signal is considered to be the one at the output of the system.
The proposed system replaces the existing separation module in the OFDM-Based UAV receiver with a module that uses only a single antenna as the signal source.
Figure 3.
Proposed system Noise-suppression method for UAV-OFDM systems by introducing CV-VSS-NLMS A (Walid Lebbo.
A ISSN: 1693-6930
RESULTS AND DISCUSSIONS
Simulations In this section, we simulate the proposed system under the same conditions considered in .
use the three considered noises, namely: HVSP, the EFTP and the SP.
The field analytic functions of the noises are defined respectively by .
= yca ycycnycu( 2yuUyceya yc yu.
where yca = 500 V/m, yceya = 4 kHz and yuc = 0 rad.
This noise is a strong electromagnetic pulse generated near high-voltage transmission lines, which significantly impacts drone communication link .
yc y 109 , 0 O yc O 4.
4 UI 10Oe9 yaya 2 .
= { 4yce Oe0.
cOe4.
4y10 )y10 , 4.
4 UI 10Oe9 O yc O 1000 y 10Oe9 48y10 yyc Oe 1 , 0 O yc O 1.
2 y 10Oe6 yaya .
= { Oeyc Oe 1.
2 y 10Oe6 y 104 1,1.
2 y 10Oe6 O yc O 130 y 10Oe6 yc Oe 1.
2 y 10Oe6 y 104 Oe 0.
570,130 y 106 O yc O 158 y 10Oe6 These pulse noises continuously disrupt wireless communication with their instantaneous energy being sufficient to directly cause drone communication failures .
, .
, .
The single pulse waveforms of the three noises are presented in Figures 4.
The baud rate for a fixed-wing UAV is typically assumed to be 4000, while the carrier frequency yceyca is set to 4 kHz.
These parameters commonly adopted as standard simulation conditions to comprehensively analyze the impact of various electromagnetic pulses on the communication link, ensuring the results remain broadly applicable, see Table 1.
The OFDM transceiver employs a quadrature phase shift keyin (QPSK) modulation scheme with an fast fourier transform (FFT) size of 32 and a cyclic prefix length of 8.
The parameters of the CV-VSS-NLMS adaptive filters used for all ANCs are listed in Table 2.
To assess the systemAos capability to identify the type of noise affecting the UAV communication link, i.
, the interference impacting the signal of interest in .
, and to evaluate its denoising performance, several key criteria are considered.
These include the residual noise energy in the denoised signal, the convergence behavior of the MSE for the CV-VSS-NLMS algorithms, and the BER of the received signal.
To simulate realistic flight conditions, a Rayleigh fading channel with Doppler effects is adopted.
The channel model consists of 10 coefficients, corresponding to a UAV velocity of 20 m/s, a carrier frequency of 5 GHz, and a resulting Doppler frequency of 333.
33 Hz.
The channel bandwidth is set to 10 MHz.
The OFDM system parameters in this case include a 64-point FFT and a cyclic prefix length of 12 .
At the receiver side, the resulting signal yccyco in .
yccyco = ycyco O Ea ycuyco where (O)denotes the convolution operation, and Ea denotes the impulse response of the Rayleigh fading channel with Doppler effects.
The key performance criterion considered in this study is the convergence behavior of the MSE.
To achieve this, we conducted three distinct experiments, each focusing on a specific type of noise:
, nk.
and nk.
as defined in .
, respectively.
Table I.
Simulation parameters .
Parameters Baud rate .
or a fixed-wing UAV) Sampling frequency yceyc of the receiving end LowAapass filter cutAaoff frequency yceyc Electric field strength generated by the communication link Electric field strength generated by the pulse signal Carrier Frequency yceyca Values 64 kHz 6 kHz 5 V/m 500 V/m 4 kHz TELKOMNIKA Telecommun Comput El Control.
Vol.
No.
April 2026: 407-419 TELKOMNIKA Telecommun Comput El Control Table 2.
CV-VSS-NLMS algorithm parameters Parameters Filter length N Initial yuNyco .
Initial yuNyco .
Initial yuNyco .
yu yu yu yuA Values .
Figure 4.
Representative waveforms of the three considered high-voltage interference noises: .
highAavoltage sinusoidal pulse waveform, .
single high voltage EFTP pulse waveform, and .
single high voltage surge pulse waveform These experiments were carried out to rigorously evaluate the performance of the system across diverse conditions and to confirm its robustness in handling different types of noise.
In each experiment, the average energies yayco .
, as defined in .
, are computed.
Figures 5.
depict the convergence behavior of the MSE for the three ANCs in the proposed system, evaluated under communication links individually affected by three distinct types of noise: HVSP.
EFTP, and SP, respectively.
The results obtained for both channel conditions, namely, the flat fading channel and the UAV Rayleigh Doppler channel, clearly indicate that each adaptive filter, when driven by a specific noise source, performs effectively when the communication link is subject to the same type of disturbance.
This effectiveness is more pronounced under the flat fading channel, where the filters exhibit superior MSE convergence performance, characterized by a faster convergence rate and a lower steady-state level.
This behavior reflects the efficiency of the adaptation mechanism, demonstrating the capability of the CV-VSSNLMS filters to selectively suppress the noise type for which they were originally designed.
In contrast, under the UAV Rayleigh Doppler scenario, a degradation in the steady-state MSE is observed.
This degradation is attributed to the Doppler-induced time variations of the channel, which alter the statistical properties of the received signal and consequently deteriorate the convergence performance .
Noise-suppression method for UAV-OFDM systems by introducing CV-VSS-NLMS A (Walid Lebbo.
A ISSN: 1693-6930 .
Figure 5.
Convergence behavior of the MSE for various CV-VSS-NLMS algorithms in the proposed ANC system under two channel conditions.
a flat fading channel and UAV Rayleigh Doppler channel:
communication link affected by HVSP noise, .
communication link affected by EFTP noise, and .
communication link affected by SP noise, and .
communication links affected by simultaneous noise Figure 5.
illustrates the sensitivity analysis of the proposed CV-VSS-NLMS adaptive filter under the EFTP noise environment for different step-size values, particularly for yuN = 0.
9, 0.
1 and 0.
Based on the fact that the proposed algorithm employs a variable step-size adaptation mechanism, these values were selected to evaluate its performance under different adaptation rates.
The obtained results show that the convergence behavior of the algorithm varies with changes in the step-size parameter, confirming the sensitivity of the proposed filter to this parameter.
As illustrated in Figure 5.
, the convergence of the MSE is analyzed for adaptive filters operating over communication links affected by simultaneous noise sources.
Three noise combinations are considered:
HVSP EFTP.
HVSP SP, and EFTP SP.
It is evident from the Figure 5 that the adaptive filter achieves effective convergence only in the case where the filter is driven by the EFTP signal and the communication link is simultaneously affected by HVSP and EFTP noise sources.
In this configuration, the filter exhibits the best MSE convergence performance, characterized by a faster convergence rate and a lower steady state MSE compared to the other cases.
Figures 6.
present the cost function profiles at the output of the CV-VSS-NLMS algorithm under a communication link affected by HVSP noise, using adaptive filters driven by different noise types.
HVSP.
EFTP and SP, respectively.
It should be clarified that the results presented in Figures 6 and 7 correspond to the flat fading channel scenario.
According to the obtained results, it is evident that the cost function associated with the CV-VSS-NLMS filter driven by the noise corresponding to the one affecting the TELKOMNIKA Telecommun Comput El Control.
Vol.
No.
April 2026: 407-419 TELKOMNIKA Telecommun Comput El Control communication link, particularly in the case of HVSP noise, exhibits the lowest energy compared to the This criterion thus makes it possible to identify and select the most suitable filter among the three, in order to provide the filtered signal with the best noise cancellation performance.
Furthermore, as shown in Figures 7.
, the residual noise in the signal filtered by the appropriate CV-VSS-NLMS filter presents the lowest level, confirming the effectiveness of the filter selection strategy.
Figure 6.
Cost function profile at the output of the CV-VSS-NLMS algorithm with the adaptive filter:
driven by HVSP noise and communication link affected by HVSP noise, .
driven by EFTP noise and communication link affected by HVSP noise, and .
driven by SP noise and communication link affected by HVSP noise .
Figure 7.
Residual interference in the communication link affected by HVSP noise and processed by the CVVSS-NLMS algorithm: .
driven by HVSP noise, .
driven by EFTP noise, and .
driven by SP noise.
Figures 8.
respectively present the original communication signal, the communication signal corrupted by HVSP noise, and the de-noised signal at the output of the proposed system.
It is clear that the de-noised signal closely matches the original signal, confirming the effectiveness of the proposed system.
Figure 8.
Communication link scenarios: .
clean communication link, .
noisy communication link, and .
denoised communication link Noise-suppression method for UAV-OFDM systems by introducing CV-VSS-NLMS A (Walid Lebbo.
A ISSN: 1693-6930 Table 3 presents a comparison of the BER performance between the proposed noise suppression method and the existing method reported in .
within the UAV-OFDM system, under three types of considered noises: HVSP.
SP, and EFTP, all subjected to the same field strength amplitude of 500 V/m.
The BER values for both the proposed and the existing methods were obtained using the image depicted in Figure 9.
Table 3.
BER of the proposed noise suppression method Corrupting noise HVSP noise SP noise EFTP noise BER before denoising (%) BER after de-noising by the existing system .
(%) BER after de-noising by the proposed system (%) Figure 9.
Original image As shown in Table 3, the BER achieved using the proposed noise suppression method is significantly lower across all considered noise types.
HVSP.
SP, and EFTP, compared to the existing method proposed in .
, under a uniform field strength amplitude of 500 V/m.
These results confirm the effectiveness of the proposed method in mitigating noise in the UAV-OFDM system.
After applying the proposed noise suppression method, the BER is significantly reduced, approaching zero in all cases.
Notably, the lowest BER is observed under HVSP noise conditions, indicating the most effective suppression performance among the three.
Computational complexity This sub-section analyzes the computational complexity of the proposed algorithm and compares it with that of the conventional independent component analysis (ICA) method .
The evaluation is based on the number of arithmetic operations required, providing an objective measure of processing cost.
In the proposed algorithm, defined by .
, the total computational cost per filter is approximately 18ycA 2ya 5 multiplications and 14ycA 2ya additions.
For the complete system, the overall complexity becomes 54ycA 6ya 15 multiplications and 42ycA 6ya additions, where ycA is the filter length and ya is the smoothing window length.
In contrast, the ICA algorithm, described in .
, involves several computationally demanding steps, including de-meaning in .
, covariance estimation in .
, whitening in .
, iterative update in .
, weight adaptation in .
, normalization in .
, convergence testing in .
, and demixing in .
The total complexity per iteration can be approximated as 2ycA3 3ycA2 ya 3ycAya additions and ycA3 3ycA2 ya 3ycAya Since the ICA algorithm must be executed separately two times for the real and imaginary parts of the complex OFDM signal.
So, the total computational cost doubles, yielding approximately 4ycA3 6ycA2 ya 6ycAya additions and 2ycA3 6ycA2 ya 6ycAya multiplications, where ycA is the number of source signals and ya the total number of samples.
For the purpose of comparison, we consider for instance the total number of samples used in .
, which is 3003136.
By letting the parameters ya = 5 and ycA = 8 in the above expressions, the proposed algorithm requires approximately 1.
43y10 9 multiplications and 1.
10y109 additions.
Also, by letting the parameters ycA = 2 and the total number of iterations ya = 36, the ICA algorithm requires approximately 89y109 multiplications and 3.
89y109 additions.
These numerical illustrations clearly demonstrate that the proposed algorithm achieves a significantly lower computational cost, being nearly three times more efficient than the conventional ICA method.
TELKOMNIKA Telecommun Comput El Control.
Vol.
No.
April 2026: 407-419
TELKOMNIKA Telecommun Comput El Control
CONCLUSION
In this paper, we propose a novel approach for mitigating impulsive interference in OFDM-based UAV communication systems by developing an efficient CV-VSS-NLMS adaptive filtering algorithm.
This approach extends existing LMS-based filtering principles to handle impulsive interference in UAV scenarios and integrates them within a well-designed single-antenna architecture.
In contrast, real-valued VSS-LMS filters treat the real and imaginary parts separately, resulting in poorer MSE convergence for complex Compared to conventional blind source separation techniques, the proposed method achieves better noise suppression.
It exhibits fast MSE convergence, reaching steady states between -60 dB and -80 dB across the considered noise types, while maintaining a low residual noise level in the denoised signal.
Moreover, it significantly reduces computational complexity and requires only 1.
43y10A multiplications and 10y10A additions, compared to 3.
89y10A multiplications and 3.
89y10A additions required by the ICA This reduction in the complexity corresponds to a gain of nearly a factor of three.
This substantially lower computational complexity makes the proposed algorithm more practical for deployment in real-time constrained UAV applications.
The superiority of the proposed approach is further confirmed by performance evaluations, which demonstrate notable efficiency in BER, specifically about 90% improvements under HVSP noise, 29% under SP noise, and 66% under EFTP noise.
Furthermore, the proposed CV-VSS-NLMS algorithm provides a lightweight, efficient, and real-time solution for interference mitigation in UAV OFDM networks.
As a future direction, the algorithm could be implemented on embedded hardware and tested through hardware-in-the-loop simulations or real UAV experiments.
FUNDING INFORMATION
Authors state no funding involved.
AUTHOR CONTRIBUTIONS STATEMENT
This journal uses the Contributor Roles Taxonomy (CRediT) to recognize individual author contributions, reduce authorship disputes, and facilitate collaboration.
Name of Author Walid Lebbou Laid Chergui Saad Bouguezel C : Conceptualization M : Methodology So : Software Va : Validation Fo : Formal analysis ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue I : Investigation R : Resources D : Data Curation O : Writing - Original Draft E : Writing - Review & Editing ue ue ue ue ue ue ue ue ue ue ue Vi : Visualization Su : Supervision P : Project administration Fu : Funding acquisition CONFLICT OF INTEREST STATEMENT Authors state no conflict of interest.
DATA AVAILABILITY
Authors state that data availability is not applicable to this paper as no new data were created or analyzed in this study.
REFERENCES