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Journals / Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi / 2026 / Cilt: 18

A novel optimization-based approach to the complementary error function

Tümleyen hata fonksiyonuna optimizasyon temelli yeni bir yaklaşım

Alperen Cengiz(NİĞDE ÖMER HALİSDEMİR ÜNİVERSİTESİ, MÜHENDİSLİK FAKÜLTESİ)0000-0003-1144-8815
Mehmet Bilim(NİĞDE ÖMER HALİSDEMİR ÜNİVERSİTESİ, MÜHENDİSLİK FAKÜLTESİ, ELEKTRİK-ELEKTRONİK MÜHENDİSLİĞİ BÖLÜMÜ, TELEKOMÜNİKASYON ANABİLİM DALI)0000-0003-2518-3125
Yasin Kabalcı(Niğde Ömer Halisdemir Üniversitesi, Mühendislik Fakültesi, Elektrik-Elektronik Mühendisliği Bölümü)0000-0003-1240-817X
Pages
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Publication Date
2026-09-11
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

All obtained results indicate that the analytical results derived using the proposed expression are in excellent agreement with both Monte Carlo and experimental measurement outcomes, and they can successfully approximate the exact values with a negligible error margin.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Special functions are widely and frequently employed in various fields, particularly in wireless communications, especially in theoretical analyses.
📊
Key Findings & Data:In this regard, this study proposes a tight and highly accurate five-coefficient complementary error function (erfc(.)) approximation using the standard differential evolution algorithm.
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Conclusion & Impact:All obtained results indicate that the analytical results derived using the proposed expression are in excellent agreement with both Monte Carlo and experimental measurement outcomes, and they can successfully approximate the exact values with a negligible error margin.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Tümleyen hata fonksiyonu · hata olasılığı · Nakagami-m sönümlü kanal.

Abstract

Special functions are widely and frequently employed in various fields, particularly in wireless communications, especially in theoretical analyses. Therefore, obtaining special functions in a mathematically tractable, simple, and straightforward manner is of crucial importance. In this regard, this study proposes a tight and highly accurate five-coefficient complementary error function (erfc(.)) approximation using the standard differential evolution algorithm. The coefficients of the proposed erfc(.) approximation are optimized via the standard differential evolution algorithm to achieve superior performance, and the optimal coefficient values are presented. To demonstrate the accuracy of the proposed five-term approximation, an error probability (EP) analysis is performed for a single-input single-output system operating over Nakagami‑m fading channels. The validity of the proposed approximation is verified through analytical results, Monte Carlo simulations, and experimental measurements conducted on Universal Software Radio Peripheral (USRP) platforms. All obtained results indicate that the analytical results derived using the proposed expression are in excellent agreement with both Monte Carlo and experimental measurement outcomes, and they can successfully approximate the exact values with a negligible error margin.

Özet

Özel fonksiyonlar, her alanda olduğu gibi kablosuz haberleşme alanında da özellikle kuramsal analizlerde sıklıkla yaygın bir şekilde kullanılmaktadır. Bu sebeple, özel fonksiyonların matematiksel açıdan çözüme elverişli, basit ve kolay bir şekilde elde edilmesi önemli bir husustur. Bu doğrultuda, bu çalışmada sıkı ve yüksek doğruluğa sahip beş katsayılı tümleyen hata fonksiyonu (erfc(.)) yaklaşımı, standart diferansiyel evrim algoritması kullanılarak önerilmektedir. Önerilen erfc(.) yaklaşımının katsayıları, daha iyi sonuçlar vermesi amacıyla standart diferansiyel evrim algoritması ile optimize edilmiş ve en uygun katsayı değerleri sunulmuştur. Önerilen beş terimli yaklaşımın doğruluğunu göstermek amacıyla, tek girişli tek çıkışlı bir sistemin Nakagami-m kanallarındaki hata olasılığı (error probability, EP) analizi gerçekleştirilmiştir. Önerilen yaklaşımın doğruluğu, analitik sonuçlar, Monte Carlo benzetimleri ve Evrensel Yazılım Radyo Çevre Birimi (USRP) platformlarına dayalı deneysel ölçümler aracılığıyla gösterilmiştir. Tüm sonuçlar göstermektedir ki, önerilen ifade kullanılarak elde edilen analitik sonuçlar hem Monte Carlo hem de deneysel ölçüm sonuçlarıyla mükemmel bir uyum içerisindedir ve düşük bir hata payı ile gerçek değerleri kolaylıkla yakalayabilmektedir.

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Cite This Article

Cengiz, A., Bilim, M., Kabalcı, Y. (2026). A novel optimization-based approach to the complementary error function. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, Cilt: 18. https://doi.org/10.28948/ngumuh.1981234

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