基于分数阶傅里叶变换的宽带Chirp信号DOA估计
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摘要
阵列信号处理是信号处理领域的主要研究方向之一，而非平稳宽带阵列信号处理不仅是目前研究的重点，也是研究的难点。对非平稳信号的宽带阵列信号处理的研究就具有非常重要的意义。本文围绕这个问题，展开了一系列的研究，并且利用分数阶傅里叶变换(Fractional Fourier Transform, FRFT)的旋转特性大大缩小了带宽，有助于宽带阵列的快速处理，为宽带阵列信号处理带来了新的思路。利用这种思路研究波达方向角估计算法，创新点包括以下几点：
1.基于WLCF算法的宽带DOA估计
提出了基于分数阶傅里叶变换的宽带Chirp信号DOA估计算法，根据线性Chirp信号与时频面的横轴呈一定角度的特点，利用分数阶傅里叶变换旋转时频面特性，让旋转得到的时频面横轴垂直于线性Chirp信号的调频斜率，使得信号的能量在新的时频面剧增。提出的算法充分利用了线性Chirp信号与时频面的关系，能让信号的能量在新的时频面集中在一点，这样可以较大程度地提高输出信噪比。通过高分辨率的空间谱搜索方法获得了波达方向角。与经典宽带DOA估计算法相比，估计精度和输出信噪比均得到了较大的提高。
2.FRFT域的宽带DOA估计
基于旋转的宽带Chirp信号DOA估计方案中，改进了相干信号子空间算法、双边相关变换算法、及投影子空间正交测试算法，利用分数阶傅里叶变换算法旋转时频面的方法，来缩小带宽，减小对宽带信号分段处理所带来的误差。与三种算法对比，仿真实验结果证明改进算法的精度有了明显提高，也说明该算法具有普遍适用性。
3.基于FRFT算法的宽带DOA估计
利用分数阶傅里叶变换旋转时频面特性，使方向矢量的时频分布可以近似地拟合成平行于新的时频面的横轴，进而达到缩小带宽的目的，使宽带阵列信号可以近似看做窄带阵列信号，解决了DOA估计中方向矢量随频率变化的问题。该算法相较于经典宽带DOA估计算法，无须对预估计角度和中心频率进行预估计，同时减少了分段之后因为“聚焦”所带来的误差，从而提高了估计精度。
4.基于分数阶累积量的宽带DOA估计
在旋转累量的宽带Chirp信号DOA估计方案中，将分数阶傅里叶变换与高阶累积量结合，提出了分数累量算法。该算法具有旋转时频面特性和对高斯过程不敏感的特性，利用这种算法进行宽带DOA估计，不仅能缩小带宽，而且能有效地抑制高斯噪声，仿真实验证实了该算法的有效性。
综上所述，通过FRFT的旋转特性对宽带DOA估计进行了系列的研究，并在缩小带宽方面得到了一定的进展。不同于以往的处理宽带DOA的一个缩小带宽的常用思路。本论文的算法中的缩小带宽的方法不但不会丢失原始数据中包含的信息，反而可以充分利用宽带信号的信息量大的特点实现DOA估计，与传统的窄带DOA估计方法相比，具有更高的精度和性能。
Array signal processing is an important field in signal processing. And non-stationarywide-band array signal processing is the emphasis and difficult to study in this field. So itis important and worthy to study the theory and method for non-stationary wide-bandsignal processing. The main work of this paper is aimed on this subject. It uses FractionalFourier Transform(FRFT) to process the wide-band signal such as chirp signal. FRFT canreduce the signal band width and transform a wide-band signal to likely narrow-bandsignal and then most traditional DOA algorithm for narrow-band signal can be used on thetransform result to estimate the arriving direction of signal source. The paper proposessome algorithm combined with FRFT and traditional algorithm, explains the algorithmsand gives simulating result of these algorithm.
(1)Wide-band DOA algorithm based on WLCF
Wide-band linear chirp FRFT method (WLCF) algorithm canestimate arrivingdirection with sensory array and chirp signal. In time-frequencyplane, chirp signal can bedescribed as a line that has a angle with time axes.Use the rotational character of FRFT,Transforming the chirp signal with FRFTwith angle that is vertical to the chirp signalin time-frequency plane, the power of signal is focused in transformresult in a narrow field.The proposed algorithm uses the relation between chirpsignal and time-frequency plane,focuses the power in a new time-frequency plane and improves the signal-noise rate(SNR). Estimate the arriving direction with traditional DOA method for narrow-bandsignal, it can improve the accuracy in some degrees.
(2) FRFT-based algorithm for wideband DOA estimation
Use the time-frequency plane characteristic of fractional Fourier transform rotation,the time-frequency distribution of the direction vector can be approximated by fittingparallel to the horizontal axis at the new time-frequency plane, and thus achieve a narrowbandwidth, so this can achieve a narrow bandwidth, see the wideband array signal as thenarrow-band array signal to solve the problem of direction vector varies with frequency inDOA estimated,which is the advantage of this algorithm. Compared with the classicwideband DOA estimation algorithm methods, this algorithm method have no need of thepre-estimate of the angle and center frequency, reduce the error caused by the“Focus”after the segment,so this algorithm has higher estimation accuracy.
(3) FRFT-based algorithm for wideband DOA estimation
Using the time-frequency plane characteristic of fractional Fourier transform rotation,the time-frequency distribution of the direction vector can be approximated by fittingparallel to the horizontal axis at the new time-frequency plane, and thus achieve a narrowbandwidth, so this can achieve a narrow bandwidth, see the wideband array signal as thenarrow-band array signal to solve the problem of direction vector varies with frequency inDOA estimated,which is the advantage of this algorithm. Compared with the classicwideband DOA estimation algorithm methods, this algorithm method have no need of thepre-estimate of the angle and center frequency, reduce the error caused by the“Focus”after the segment,so this algorithm has higher estimation accuracy.
(4) Wideband DOA estimation based on Fractional-Cumulant
In the scheme of wideband DOA rotational Cumulant estimation based on fractionalFourier transform for Chirp signal, this method is combined fractional cumulant algorithmwith high order cumulant. The algorithm has rotation characteristics in time frequencyplane and is not sensitive to the Gauss process, and is used in wideband DOA estimation.We can see that this algorithm is not only to reduce the bandwidth, but also can effectivelyrestrain Gauss noise, and the simulation verified the effectiveness of our algorithm.
In summary, the wideband DOA estimation is studied by rotational characteristics ofFRFT, and got some progress. The proposed algorithm, which is based on shorting thebandwidth, is different form the common idea of processing the wideband DOAestimation. This is outstanding point of our work. Moreover, the advantage of thisalgorithm can prevent from losing the message and reduce the estimation accuracy.Compared with the narrowband DOA estimation, these algorithms perform better andhave higher accuracy.
1.基于WLCF算法的宽带DOA估计
提出了基于分数阶傅里叶变换的宽带Chirp信号DOA估计算法，根据线性Chirp信号与时频面的横轴呈一定角度的特点，利用分数阶傅里叶变换旋转时频面特性，让旋转得到的时频面横轴垂直于线性Chirp信号的调频斜率，使得信号的能量在新的时频面剧增。提出的算法充分利用了线性Chirp信号与时频面的关系，能让信号的能量在新的时频面集中在一点，这样可以较大程度地提高输出信噪比。通过高分辨率的空间谱搜索方法获得了波达方向角。与经典宽带DOA估计算法相比，估计精度和输出信噪比均得到了较大的提高。
2.FRFT域的宽带DOA估计
基于旋转的宽带Chirp信号DOA估计方案中，改进了相干信号子空间算法、双边相关变换算法、及投影子空间正交测试算法，利用分数阶傅里叶变换算法旋转时频面的方法，来缩小带宽，减小对宽带信号分段处理所带来的误差。与三种算法对比，仿真实验结果证明改进算法的精度有了明显提高，也说明该算法具有普遍适用性。
3.基于FRFT算法的宽带DOA估计
利用分数阶傅里叶变换旋转时频面特性，使方向矢量的时频分布可以近似地拟合成平行于新的时频面的横轴，进而达到缩小带宽的目的，使宽带阵列信号可以近似看做窄带阵列信号，解决了DOA估计中方向矢量随频率变化的问题。该算法相较于经典宽带DOA估计算法，无须对预估计角度和中心频率进行预估计，同时减少了分段之后因为“聚焦”所带来的误差，从而提高了估计精度。
4.基于分数阶累积量的宽带DOA估计
在旋转累量的宽带Chirp信号DOA估计方案中，将分数阶傅里叶变换与高阶累积量结合，提出了分数累量算法。该算法具有旋转时频面特性和对高斯过程不敏感的特性，利用这种算法进行宽带DOA估计，不仅能缩小带宽，而且能有效地抑制高斯噪声，仿真实验证实了该算法的有效性。
综上所述，通过FRFT的旋转特性对宽带DOA估计进行了系列的研究，并在缩小带宽方面得到了一定的进展。不同于以往的处理宽带DOA的一个缩小带宽的常用思路。本论文的算法中的缩小带宽的方法不但不会丢失原始数据中包含的信息，反而可以充分利用宽带信号的信息量大的特点实现DOA估计，与传统的窄带DOA估计方法相比，具有更高的精度和性能。
Array signal processing is an important field in signal processing. And non-stationarywide-band array signal processing is the emphasis and difficult to study in this field. So itis important and worthy to study the theory and method for non-stationary wide-bandsignal processing. The main work of this paper is aimed on this subject. It uses FractionalFourier Transform(FRFT) to process the wide-band signal such as chirp signal. FRFT canreduce the signal band width and transform a wide-band signal to likely narrow-bandsignal and then most traditional DOA algorithm for narrow-band signal can be used on thetransform result to estimate the arriving direction of signal source. The paper proposessome algorithm combined with FRFT and traditional algorithm, explains the algorithmsand gives simulating result of these algorithm.
(1)Wide-band DOA algorithm based on WLCF
Wide-band linear chirp FRFT method (WLCF) algorithm canestimate arrivingdirection with sensory array and chirp signal. In time-frequencyplane, chirp signal can bedescribed as a line that has a angle with time axes.Use the rotational character of FRFT,Transforming the chirp signal with FRFTwith angle that is vertical to the chirp signalin time-frequency plane, the power of signal is focused in transformresult in a narrow field.The proposed algorithm uses the relation between chirpsignal and time-frequency plane,focuses the power in a new time-frequency plane and improves the signal-noise rate(SNR). Estimate the arriving direction with traditional DOA method for narrow-bandsignal, it can improve the accuracy in some degrees.
(2) FRFT-based algorithm for wideband DOA estimation
Use the time-frequency plane characteristic of fractional Fourier transform rotation,the time-frequency distribution of the direction vector can be approximated by fittingparallel to the horizontal axis at the new time-frequency plane, and thus achieve a narrowbandwidth, so this can achieve a narrow bandwidth, see the wideband array signal as thenarrow-band array signal to solve the problem of direction vector varies with frequency inDOA estimated,which is the advantage of this algorithm. Compared with the classicwideband DOA estimation algorithm methods, this algorithm method have no need of thepre-estimate of the angle and center frequency, reduce the error caused by the“Focus”after the segment,so this algorithm has higher estimation accuracy.
(3) FRFT-based algorithm for wideband DOA estimation
Using the time-frequency plane characteristic of fractional Fourier transform rotation,the time-frequency distribution of the direction vector can be approximated by fittingparallel to the horizontal axis at the new time-frequency plane, and thus achieve a narrowbandwidth, so this can achieve a narrow bandwidth, see the wideband array signal as thenarrow-band array signal to solve the problem of direction vector varies with frequency inDOA estimated,which is the advantage of this algorithm. Compared with the classicwideband DOA estimation algorithm methods, this algorithm method have no need of thepre-estimate of the angle and center frequency, reduce the error caused by the“Focus”after the segment,so this algorithm has higher estimation accuracy.
(4) Wideband DOA estimation based on Fractional-Cumulant
In the scheme of wideband DOA rotational Cumulant estimation based on fractionalFourier transform for Chirp signal, this method is combined fractional cumulant algorithmwith high order cumulant. The algorithm has rotation characteristics in time frequencyplane and is not sensitive to the Gauss process, and is used in wideband DOA estimation.We can see that this algorithm is not only to reduce the bandwidth, but also can effectivelyrestrain Gauss noise, and the simulation verified the effectiveness of our algorithm.
In summary, the wideband DOA estimation is studied by rotational characteristics ofFRFT, and got some progress. The proposed algorithm, which is based on shorting thebandwidth, is different form the common idea of processing the wideband DOAestimation. This is outstanding point of our work. Moreover, the advantage of thisalgorithm can prevent from losing the message and reduce the estimation accuracy.Compared with the narrowband DOA estimation, these algorithms perform better andhave higher accuracy.
引文
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