A Successive Convex Approximation Optimization based Prototype Filter Design Method for Universal Filtered Multi-Carrier Systems

HUA Jingyu; YANG Le; WEN Jiangang; ZHOU Yuanping; SHENG Bin

doi:10.11999/JEIT250278

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HUA Jingyu, YANG Le, WEN Jiangang, ZHOU Yuanping, SHENG Bin. A Successive Convex Approximation Optimization based Prototype Filter Design Method for Universal Filtered Multi-Carrier Systems[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250278

Citation:

HUA Jingyu, YANG Le, WEN Jiangang, ZHOU Yuanping, SHENG Bin. A Successive Convex Approximation Optimization based Prototype Filter Design Method for Universal Filtered Multi-Carrier Systems[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250278

Citation:

HUA Jingyu, YANG Le, WEN Jiangang, ZHOU Yuanping, SHENG Bin. A Successive Convex Approximation Optimization based Prototype Filter Design Method for Universal Filtered Multi-Carrier Systems[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250278

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A Successive Convex Approximation Optimization based Prototype Filter Design Method for Universal Filtered Multi-Carrier Systems

doi: 10.11999/JEIT250278 cstr: 32379.14.JEIT250278

1.
School of Information & Electronic Engineering, Zhejiang Gongshang University, Hangzhou Zhejiang 310018, China
2.
National Mobile Communications Research Laboratory, Southeast University, Nanjing Jiangsu 211111, China

Funds: The National Natural Science Foundation of China (62271445)

Received Date: 2025-04-15
Rev Recd Date: 2025-09-01

Available Online: 2025-09-09

Abstract

Abstract

Objective In response to the extensive demands of sixth-generation (6G) communications, new waveform designs are expected to play a critical role. Conventional Orthogonal Frequency Division Multiplexing (OFDM) relies on strict orthogonality among subcarriers; however, this orthogonality is highly vulnerable to synchronization errors, which lead to severe Inter-Carrier Interference (ICI). To address this issue, filtered multicarrier modulation techniques apply high-performance filters to each subcarrier, thereby confining spectral leakage and mitigating ICI caused by non-ideal frequency synchronization. Among these techniques, Universal Filtered Multi-Carrier (UFMC) has shown particular promise, offering enhanced spectral flexibility and reduced out-of-band emissions compared with traditional OFDM. Despite these advantages, most existing studies recommend Dolph–Chebyshev (DC) filters as UFMC prototype filters. Nevertheless, DC filters suffer from limited controllability over design parameters and insufficient robustness against interference. Recent research has sought to improve system performance by applying constrained optimization techniques in filter design, typically optimizing metrics such as Signal-to-Interference Ratio (SIR) and Signal-to-Interference-plus-Noise Ratio (SINR). Nevertheless, the Symbol Error Rate (SER) has not achieved an optimal level, indicating room for further improvement. To bridge this gap, this paper proposes a novel prototype filter design method that directly targets the average SER in interference-limited UFMC systems. This approach improves the anti-interference capability of UFMC systems and contributes to the development of robust waveform solutions for 6G communications. Methods This study first derives the SINR of the UFMC system under non-zero Carrier Frequency Offset (CFO) and formulates the SER expression under interference-limited conditions. A mathematical model is then established for prototype filter optimization, with SER defined as the objective function. Because the nonlinear coupling between SINR and the filter coefficients introduces strong non-convexity, the Successive Convex Approximation (SCA) framework is employed to locally linearize the non-convex components. Furthermore, a quadratic upper-bound technique is applied to guarantee both convexity and convergence of the approximated problem. Finally, an iterative algorithm is developed to solve the optimization model and determine the optimal prototype filter.. Results and Discussions The interference suppression capability of the proposed SCA filter is comprehensively evaluated, as shown in Figs. 2 and 3. The simulation results in Fig. 2 reveal several important findings. (1) The deviation between the theoretical SINR and Monte Carlo simulation results is less than 0.1 dB (Fig. 2a), confirming the accuracy of the derived closed-form expressions. (2) CFO is shown to have a strong association with system interference. As the residual CFO increases from 0 to 0.05, the SINR with conventional DC filters decreases by 3.6 dB, whereas the SCA filter achieves an SINR gain of approximately 1 dB compared with the DC filter. (3) Under a CFO of 0.025, the UFMC waveform demonstrates clear superiority over the ideal OFDM system. At a Signal-to-Noise Ratio (SNR) of 18 dB, the UFMC system with the SCA filter attains an SINR of 18.4 dB, outperforming OFDM by 0.3 dB. Fig. 3 further highlights the robustness of the SCA filter in dynamic interference environments. Although the SER increases with both larger CFO and higher modulation orders, the SCA filter consistently yields the lowest SER across all interference scenarios. Under severe interference conditions (CFO = 0.05, 16QAM modulation, SNR = 17 dB), the SCA filter achieves an SER of 7.4×10^-³, markedly outperforming the DC filter, which exhibits an SER of 2.9×10^-². These results demonstrate that the proposed SCA filter substantially enhances the anti-interference capability of UFMC systems. Conclusions This study first derives analytical expressions for the SINR and SER of the UFMC system under CFO. On this basis, an optimization model is established to design the prototype filter with the objective of minimizing the average SER. To address the non-convexity arising from the nonlinear coupling between SINR and filter coefficients, the SCA method is employed to reformulate the problem into a series of convex subproblems. An iterative algorithm is then proposed to obtain the optimal prototype filter. Simulation results demonstrate that, compared with conventional filters, the proposed SCA-based optimization algorithm provides flexible control over key filter parameters, achieving a narrower transition band and higher stopband attenuation under the same filter length. This improvement translates into significantly enhanced anti-interference performance under various system conditions. In summary, the main contributions of this work are: (1) Proposing a novel SCA-based optimization method for UFMC prototype filter design, which overcomes the parameter control limitations of traditional DC filters; (2) Systematically analyzing the performance advantages of the SCA filter under different modulation schemes and CFO conditions, and quantitatively demonstrating its contributions to SINR and SER improvements.
- Universal Filtered Multi-Carrier (UFMC),
- Carrier Frequency Offset (CFO),
- Filter design,
- Successive Convex Approximation (SCA),
- Symbol Error Rate (SER)

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References(26)

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