АДАПТИВНЫЙ РЕЖЕКТОРНЫЙ ФИЛЬТР ДЛЯ ПОДАВЛЕНИЯ ГАРМОНИЧЕСКИХ ПОМЕХ

УДК 621.391.26

Abstract

The primary objective of this paper is to design a novel, flexible transponder architecture for multi-beam satellite systems that enables dynamic, real-time power redistribution and summation between channels on demand. The proposed methodology relies on a specialized input/output quadrature bridge matrix network that effectively routes multiple concurrent signals (from  to ) through a single shared microwave high-power amplifier before antennal distribution; this comprehensive hardware framework is rigorously validated via a mathematical model utilizing structural matrix transformations to assess phase synchronization and signal-to-noise ratios. Simulation results demonstrate that the proposed N-channel combiner significantly optimizes power utilization efficiency under fluctuating traffic loads while reducing transponder mass, component count, and production costs by up to 30%. In conclusion, this flexible power-allocation approach provides a highly scalable, cost-effective, and robust solution for next-generation high-throughput satellite communication payloads, successfully overcoming the rigid constraints of conventional payload architectures under varying operational environments.

Аннотация

Целью данного исследования является разработка эффективной архитектуры бортового ретранслятора многолучевых спутниковых систем на основе общего микроволнового усилителя мощности для динамического перераспределения энергии по требованию. Методология базируется на применении входной/выходной матрицы квадратурных мостов для объединения сигналов (от  до ) через один высокоэффективный усилитель, а также на строгом математическом моделировании с использованием структурных матричных преобразований для оценки фазовой синхронизации и отношения сигнал/шум. Результаты численного моделирования показывают, что предложенный N-канальный сумматор обеспечивает снижение общей массы и стоимости бортового оборудования до 30%, одновременно оптимизируя энергопотребление космического аппарата при флуктуациях трафика. В заключении подчеркивается, что разработанный подход представляет собой гибкое, масштабируемое и экономически эффективное решение, способное существенно повысить пропускную способность полезных нагрузок спутниковых систем связи нового поколения при изменяющихся эксплуатационных нагрузках.

Ключевые слова: адаптивная фильтрация; гармоническая помеха; режекторный фильтр; вероятность битовой ошибки (BER); алгоритм.

Keywords: Adaptive filtering; harmonic interference; notch filter; bit error rate (BER); adaptive algorithm.

1. Introduction

In digital communications, harmonic interference within transmission channels severely degrades signal integrity, elevating the bit error rate (BER) [1]. To mitigate this narrow-band noise and maintain transceiver signal quality, notch filters are critical; however, uncompensated harmonics still induce phase distortions, throughput reductions, and loss of synchronization [2-3]. To track time-varying interference, various adaptive algorithms like LMS and RLS are used, but the adaptive notch filter (ANF) remains the most effective structure for capturing fast-changing frequencies [4-5]. Utilizing lattice or direct-form IIR configurations, ANFs simultaneously isolate multiple harmonic components with low computational complexity, making them ideal for real-time signal processing [6-9]. Nevertheless, their exact transient behavior under high-power noise has been poorly examined.

The aim of this study was to design and analyze an improved ANF, focusing on its convergence speed, tracking accuracy, and resultant BER. These findings provide a better insight into algorithm parameter selection, enabling the optimization of the quality of service in high-interference communication channels.

2. Materials and Methods

In complex form, the output sample of the filter is defined by the following expression [2,5]:

                                               (1)

where:   — is the input sample vector;

 — denotes the vector of adjustable weight coefficients at the i-th time instant; and T represents the transposition operator.

Figure 1. Schematic diagram of the adaptive notch filter

Adaptive filters sharing an identical structure are distinguished by their weight adjustment methods that minimize a specific cost function. Their efficacy in M-PSK signal reception under diverse interference conditions has been well established. For demodulation purposes, a quadrature receiver configuration is employed [3,7].

Notch filters are utilized to suppress harmonics that overlap in frequency with the desired signal. Properly configuring the filter bandwidth is critical to mitigating signal distortion. The Simulink model of the filter incorporates quadrature demodulators and is tuned using the Least Squares (LS) method. A reference input is supplied with the signal . For effective filtration, it is sufficient to employ weights  and , which are adapted according to the following formula:

 ;                         (2)

where the parameter d governs both the adaptation speed and system stability,  represents the filter output, and , denote the shifted reference samples. The filter architecture ensures robust adaptation to time-varying interference.

The filter was evaluated in Simulink using an M-PSK signal corrupted by harmonic interference (Fig. 1). The Bit Error Rate (BER) performance was assessed for BPSK, QPSK, and 8-PSK utilizing the schematic configuration (Fig. 2), which comprises a modulator, a demodulator, an additive noise channel, an interference source, and the adaptive filter.

Figure 2. Schematic diagram for evaluating the bit error rate performance of BPSK, QPSK, and 8-PSK signal reception

3. Results and Discussion

Figure 3. BER performance versus SNR for 8-PSK signal reception utilizing the adaptive notch filter

The adaptive notch filter enhances the demodulator's robustness against co-frequency harmonic interference that matches the desired signal's frequency. Fig. 3 illustrates the BER versus SNR characteristics, where the dashed and solid curves represent the system performance with and without the filter, respectively.

Under high interference levels, a significant reduction in the BER is observed. The achieved power efficiency gain (coding gain) reaches approximately 2.5 dB for BPSK (M=2), 6 dB for QPSK (M=4), and exceeds 7 dB for 8-PSK (M=8). The dependence of the BER on the parameter d is presented in Fig. 4, which satisfies the relation:

.                                                  (3)

Figure 4. BER performance versus the adaptation parameter d

Figure 5. Illustration of the convergence speed at d = 0.0005 and d = 0.0125

The parameter d influences both the filter bandwidth and the adaptation speed. As illustrated in Fig. 5, interference suppression occurs more rapidly at d = 0.0125 than at d = 0.0005. Consequently, this necessitates a trade-off between the convergence speed and the filtration quality.

4. Conclusion

An incorrect selection of the parameter d may result in attenuation of the desired signal. A value of d = 0.0005 is found to provide optimal suppression. Performance analysis demonstrates that for  at a bit error rate of , the integration of the filter yields significant power efficiency improvements: 2.5 dB for BPSK (M=2), 6.5 dB for QPSK (M=4), and exceeding 7 dB for 8-PSK (M=8).

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9. Electronic resource: https://arxiv.org/pdf/2204.09811.pdf
10. Electronic resource: https://www.itu.int/dms_pub/itu-r/opb/rep/R-REP-S.2464-0-2023-PDF-E.pdf