基于二分法改进的Chirp信号参数估计算法

刘国峰; 廖烨; 李康; 周文峰

doi:doi:10.13756/j.gtxyj.2020.02.013

光通信研究, 2020 (2): 61, 网络出版: 2020-11-11

基于二分法改进的Chirp信号参数估计算法

Chirp Signal Parameter Estimation Algorithm based on Dichotomy

论文大纲

刘国峰 ^*廖烨李康周文峰

作者单位

重庆邮电大学通信与信息工程学院, 重庆 400065

啁啾信号二分法修正的幅度插值短时傅里叶变换 Chirp signal dichotomy M-Rife STFT

摘要

针对啁啾(Chirp)信号参数估计的高复杂度和在低信噪比(SNR)下保持高精度等问题, 文章提出了一种改进的Chirp信号参数估计算法。该算法根据当信号能量和周期长度一定时Chirp信号频谱幅度的平方与调频率成反比的特性, 不断地产生已知Chirp信号的共轭与未知Chirp信号相乘, 找到使相乘后频谱幅度平方最大的已知Chirp信号的调频率。为了做到参数估计的高精度, 用修正的幅度插值(M-Rife)算法估计中心频率和修正相乘后信号频谱的幅值。将该算法与短时傅里叶变换(STFT)结合, 首先用STFT估计出调频率的大致范围和信号周期, 然后用二分法代替等步长使改进的Chirp信号参数估计算法在这个大致范围内搜索, 极大地降低了计算复杂度。实验结果表明, 在SNR≥-10 dB时, 该算法估计调频率归一化均方误差(NMSE)要优于分数阶傅里叶变换(FRFT)约1~2 dB, 接近克拉美罗下界(CRLB)。

Abstract

The Chirp signal parameter estimation has the problems of high computational complexity and low precision under low Signal-to-Noise Ratio (SNR). In order to solve these issues, an improved Chirp parameter estimation algorithm is proposed. According to the Chirp signal energy and the signal period, the square of the signal spectrum amplitude is inversely proportional to the frequency modulation slope. The Chirp signal is multiplied by the unknown Chirp signal to find the known Chirp signal with the largest square of the spectral amplitude. In order to achieve the parameter estimation with high accuracy, the Modified Rife (M-Rife) is used to estimate the center frequency and correct the amplitude of the multiplied signal. The algorithm is combined with the Short-Time Fourier Transform (STFT). First, STFT is used to estimate the approximate range and signal period of Chirp. The dichotomy is used instead of the equal step size to allow the improved Chirp signal parameter estimation algorithm to search within this approximate range, resulting in significant complexity reduction. The experimental results show that when the SNR is not less than -10 dB, the Normalized Mean Square Error (NMSE) of modulation frequency estimated by our proposed algorithm is better than Fractional Fourier Transform (FRFT) by 1~2 dB. When the signal-to-noise ratio is not less than -10 dB, the NMSE of center frequency estimated by our proposed algorithm is significantly better than FRFT and close to the Cramer-Rao Low Bound (CRLB) line.

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刘国峰, 廖烨, 李康, 周文峰. 基于二分法改进的Chirp信号参数估计算法[J]. 光通信研究, 2020, 46(2): 61. LIU Guo-feng, LIAO Ye, LI Kang, ZHOU Wen-feng. Chirp Signal Parameter Estimation Algorithm based on Dichotomy[J]. Study On Optical Communications, 2020, 46(2): 61.

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