通用滤波多载波系统原型滤波器的连续凸近似优化设计方法

华惊宇; 杨乐; 闻建刚; 邹园萍; 盛斌

doi:10.11999/JEIT250278

通用滤波多载波系统原型滤波器的连续凸近似优化设计方法

doi: 10.11999/JEIT250278 cstr: 32379.14.JEIT250278

1.
浙江工商大学信息与电子工程学院杭州 310018
2.
东南大学移动通信全国重点实验室南京 211111

基金项目: 国家自然科学基金(62271445)

详细信息

作者简介:
华惊宇：男，教授，博士，研究方向为无线通信、无线定位、信号处理、数字滤波器等

杨乐：男，硕士生，研究方向为多载波传输中的滤波器设计

闻建刚：男，讲师，博士，研究方向为多载波传输、信号处理、数字滤波器等

邹园萍：女，副教授，博士，研究方向为宽带通信、移动通信、信号处理等

盛斌：男，教授，博士，研究方向为通信与信息系统、未来移动通信系统、无线传输技术研究等

通讯作者:
华惊宇　eehjy@163.com

中图分类号: TN929.5
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出版历程
- 收稿日期: 2025-04-15
- 修回日期: 2025-09-01
- 网络出版日期: 2025-09-09

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

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)

摘要

摘要: 通用滤波多载波(UFMC)通过在正交频分复用(OFDM)技术中引入原型滤波器实现更优的载波间干扰(ICI)抑制能力，成为未来无线通信的重要波形。研究聚焦于UFMC系统在载波频率偏移(CFO)影响下进一步强化ICI抑制能力。该文首先研究了存在CFO时，UFMC系统的信号与干扰噪声比(SINR)表达式，其次构建了一个以最小化平均误码率(SER)为目标的滤波器优化设计模型。通过采用连续凸近似(SCA)处理，对原始非凸非线性问题进行了转换，并提出了一种原型滤波器最优设计方法。仿真结果表明，该文设计的最优原型滤波器在SER性能上优于过去推荐的切比雪夫(DC)滤波器，具有较强的抗干扰能力。对于UFMC在ICI严重场景中应用具有重要价值。
- 通用滤波多载波 /
- 载波频率偏移 /
- 滤波器设计 /
- 连续凸近似 /
- 误码率
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)

HTML全文

图 1 UFMC系统框图

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图 2 SINR性能的验证与对比

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图 3 不同CFO和滤波器下的SINR比较

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图 4 不同 CFO、滤波器和调制方式下的 SER 性能比较

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1 基于SCA的原型滤波器设计算法

(1) 根据式(42)－式(49)计算目标函数的梯度$\nabla g({x^t})$，
(2) 将步骤(1)得到的目标函数的梯度$\nabla g({x^t})$代入式(41)，对目标　函数进行凸近似得到近似函数$ \tilde g({{\boldsymbol{f}}^0},{{\boldsymbol{f}}^t}) $，
(3) 在步骤(2)得到近似函数$ \tilde g({{\boldsymbol{f}}^0},{{\boldsymbol{f}}^t}) $的基础上，根据式(51)、　式(52)计算下降方向$ {{\boldsymbol{d}}^t} $，
(4) 将$ {{\boldsymbol{f}}^t} + \gamma {{\boldsymbol{d}}^t} $代入式(53)得到精确线搜索步长，
(5) 确定下降方向$ {{\boldsymbol{d}}^t} $和搜索步长${\gamma ^t}$后，根据式(58)更新迭代，
(6) 若不满足终止条件，返回步骤(3)，否则进入步骤(7)，
(7) 记录最优原型滤波器系数和此时的系统性能。

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表 1 仿真参数

系统参数	设定
FFT大小	128
子载波数、子带数	96, 6
滤波器	DC, SCA
滤波器长度	33
调制方式	QPSK, 16 QAM, 64 QAM
信噪比	1:1:20 dB
载波频率偏移	0:0.025:0.05

下载: 导出CSV

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