OFDM系统非参数信道估计算法研究
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摘要
在以IMT2000标准为核心的第三代移动通信业务已经在全球全面铺开的同时，人们已经对新一代无线宽带多媒体通信系统做了大量的研究工作。新一代无线通信系统又称为超3代移动通信系统，简称B3G或4G系统。该系统的目标是在高速移动环境中支持最高约100Mbps的速率，因此新一代无线通信系统在传输速率和频谱利用率上需要有新的突破。
正交频分复用(OFDM)是一种多载波数字通信调制技术，它具有频谱利用率高、可对抗多径时延扩展以及实现简单等特点，已经被确定为B3G移动通信系统中的核心技术之一。要在OFDM系统中进行高速率的数据传输，同时要保持较高的频谱利用率，OFDM系统需要使用密度更高的星座点进行符号映射并采用相干检测技术。在这种情况下，接收端必须知道精确的信道状态信息。同时，现代传输技术包括自适应调制、MIMO系统、波束成形、空时编码以及跨层自适应技术等都需要精确的信道状态信息。因此信道估计在OFDM系统中是不可或缺的。
本论文在研究深入传统LS估计器，LMMSE估计器和基于DFT的变换域估计器的优缺点后，提出几种基于非参数函数估计的信道估计方法。这些方法不需要信道和传输数据的先验知识，在仅增加线性计算复杂度的前提下，大大提高了LS估计器的性能。
论文首先讨论了衰落无线信道的特性，对信道的时域与频域特性作了简单的分析，详细介绍了常用的确定性衰落信道模型，并深入分析了它们的可微性、Lipschitz性及可逼近性等数学特性；并在简要介绍非参数函数估计方法的原理的基础上分析了将非参数方法用于衰落信道估计的可行性，为全文奠定了理论基础。
接着我们提出一种基于局部线性回归的OFDM系统的信道估计方法，该方法明确提出将信道估计的插值过程和噪声消除过程进行分离：首先对估计出的导频处的信道估计值进行插值，然后对插值后的信道估计值进行局部线性回归以消除信道噪声和插值引入的误差。该方法不仅能够有效的抵抗线性插值所带来的误差，而且能有效的回避变换域方法受到附加矩形窗的影响，从而明显改善信道估计的性能。该方法不需要知道信道和数据的先验知识，因此具有很高的鲁棒性。算法的计算复杂度仅为O(N)。
为了在不增加计算复杂度的前提下进一步提高估计精度，我们又提出了基于Saviztky-Golay平滑的OFDM频域信道估计算法，该算法实际上是一种局部多项式回归平滑算法，可以转化为卷积运算进行计算。利用通常Saviztky-Golay滤波器的抽头数远大于回归多项式阶数这一特点可以大大降低估计的计算复杂度，使得计算复杂度仅为O(N)。该方法具有局部线性回归估计算法的所有优点，且由于采用了局部多项式回归，估计精度比局部线性回归要高，同样不需要知道信道和数据的先验知识。
对于块衰落信道，我们提出了基于二维核回归估计的OFDM系统信道估计方法。在核回归方法中，我们可以利用核函数来刻画信道复增益在时域频域上的相关性，因此估计性能比简单的局部回归要好。由于WSUSS信道的相关性可以进行时频分解，该算法可以分解为两个级联的一维核回归算法，复杂度大大降低。通过优化时域和频域核函数的支撑区间的长度，该算法的性能在低信噪比时甚至超过一维MMSE估计算法，而复杂度远低于一维MMSE估计算法，但比前两种算法的计算复杂度稍高一些，每点数据的算法复杂度与两个核函数长度和成正比。
最后论文讨论了基于小波阈值估计的基本原理并提出了基于块阈值估计的小波阈值信道估计算法，该算法的性能优于基于传统的小波去噪信道估计算法，且在信道多径扩展大于CP长度时仍然具有较好的估计性能，且不存在模型失配问题，而计算复杂度仅为O(N)。
通过全文的研究我们可以发现，非参数估计方法可以很好地在OFDM信道估计领域进行应用，并且可以在较低的计算复杂度下取得较好的估计性能。对基于非参数估计的信道估计方法，下一步的研究可以包括如何以较低的计算复杂度将这些算法推广到MIMO-OFDM系统中、算法的性能界的分析、估计窗长的选择、核函数的选择以及进一步降低二维核回归算法的计算量等方面。
Along with the extensive deployment of 3G wireless mobile communication systems, which are based on IMT2000 standard, the innovative B3G or 4G broadband multimedia communication techniques are widely investigated. To adapt to the need for multimedia services, the aim of the B3G/4G systems is achieving a transmission rate of 100Mbps in high-mobility environment and 1Gbps in low-mobility environment. So there must be some major progress in frequency efficiency and transmission rate in these systems.
OFDM is a multi-carrier modulation or transmission technique. It has the advantages of high frequency, resistant to multipath delay spread and realization simplisity etc., therefore is chosen as one of the core techniques of B3G/4G communication system. To transmission in OFDM system with high data rates while reserving high frequency efficiency, big constelation mapping and coherent detection must be employed. In this situation, the receiver must know the channel state information. Otherwise, many transmission schemes such as adaptive modulation and coding, space time transmission, MIMO, beamforming and crosslayer processing, all have to know the CSI. So channel estimation is a essential part of OFDM systems.
Our focus is on the nonparametric estimation based OFDM channel estimation algorithm. In the dissertation, the radio fading channel property and nonparametric estimation theory were firstly discussed, then some channel estimation algorithm based on nonparametric function estimation were proposed and analysed after the briefly intruducing of conventional LS estimator, LMMSE estimator and DFT base transform domain estimator. These algorithm do not neen the a priori information of the channel and transmitted data, and can highly improve estimation performance only at a cost of computation complexity O(N).
In the first part, the properties of the radio fading channel were firstly discusseded, then the channel mode and its mathmatical characters were carefully analysed and the nonparametric estimation theory was introduced. Finally the conclusion was drawn that the radio fading channel can be estimated by nonparametric function estimation. Therefore a solid theorical basis is laid for the rest part of the dissertation.
In the second part, a nonparametric frequecy domain channel estimation algorithm based on local linear regression was proposed. In this method, the interpolation processing and noise cancellatiod processing were seperated, the LS estimated channel gain at pilot tones were firstly interpolated by piece-wise constant or piece-wise linear interpolation and then smoothed by local linear regression. This method can efficiently suppress the channel and interpolation error as well as avoid the windowing effect of the DFT based algorithm, so the performance was improved greatly.
To enhence the accuracy of the estimation while reserving the computational complexity, a nonparametric frequecy domain channel estimation algorithm based on Savitzky-Golay smoothing filter was proposed in the third part. Savitzky-Golay smoothing filter can be considered as a local polynomial estimator, and can be calculated by convolution. Because the filter length is always far more longer then the order of the regression polynomial, the computional complexty can be reduced greatly and only be O(N). It outperform the local linear regression algorithm and don't need a priori information either.
For block fading channel a nonparametric frequecy domain channel estimation algorithm based on 2D kernel smoothing was proposed. According to that the frequency and time domain correlation can be seperated in WSSUS fading channel, a simplified 2D kernel smoothing filter using two cascaded 1D kernel smoothing filters in time domain and frequency domain respectely was adopted to reduce the computaion complexity. Because it can utilize the correlation of the channel gain in time and frequency domain, the estimation performance is better than the above two. If the adaptive kernel window size was employed, the performance can be improved further, and outperforms 1D LMMSE estimator in the low SNR area and the computational complexity is much mo lower.
The last part introdused a wavelet block-thresholding channel estimation method. It outperforms the soft threshold wavelet estimator and hard thresholding wavelet estimator because it utilize the correlation of the wavelet detail coefficients. The proposed estimator maintains better performance even when the CP is shorter then the multipath delay spread and with no model mismatch. The computational complexity is only O(N).
Through the dissertation we can make a conclution that nonparametric estimation can be well adapted to channel estimation, the derived channel estimation algorithm has better performance while reserving low computational complexity. But there are still many problems, such as the estimation bounds of the estimators, the selection of the windows size of the estimators whitch more adapted to OFDM channel estimation, the smoothing kernel selection of the estimator and the generalization of the nonparametric channel estimation algorithm, to be solved.
正交频分复用(OFDM)是一种多载波数字通信调制技术，它具有频谱利用率高、可对抗多径时延扩展以及实现简单等特点，已经被确定为B3G移动通信系统中的核心技术之一。要在OFDM系统中进行高速率的数据传输，同时要保持较高的频谱利用率，OFDM系统需要使用密度更高的星座点进行符号映射并采用相干检测技术。在这种情况下，接收端必须知道精确的信道状态信息。同时，现代传输技术包括自适应调制、MIMO系统、波束成形、空时编码以及跨层自适应技术等都需要精确的信道状态信息。因此信道估计在OFDM系统中是不可或缺的。
本论文在研究深入传统LS估计器，LMMSE估计器和基于DFT的变换域估计器的优缺点后，提出几种基于非参数函数估计的信道估计方法。这些方法不需要信道和传输数据的先验知识，在仅增加线性计算复杂度的前提下，大大提高了LS估计器的性能。
论文首先讨论了衰落无线信道的特性，对信道的时域与频域特性作了简单的分析，详细介绍了常用的确定性衰落信道模型，并深入分析了它们的可微性、Lipschitz性及可逼近性等数学特性；并在简要介绍非参数函数估计方法的原理的基础上分析了将非参数方法用于衰落信道估计的可行性，为全文奠定了理论基础。
接着我们提出一种基于局部线性回归的OFDM系统的信道估计方法，该方法明确提出将信道估计的插值过程和噪声消除过程进行分离：首先对估计出的导频处的信道估计值进行插值，然后对插值后的信道估计值进行局部线性回归以消除信道噪声和插值引入的误差。该方法不仅能够有效的抵抗线性插值所带来的误差，而且能有效的回避变换域方法受到附加矩形窗的影响，从而明显改善信道估计的性能。该方法不需要知道信道和数据的先验知识，因此具有很高的鲁棒性。算法的计算复杂度仅为O(N)。
为了在不增加计算复杂度的前提下进一步提高估计精度，我们又提出了基于Saviztky-Golay平滑的OFDM频域信道估计算法，该算法实际上是一种局部多项式回归平滑算法，可以转化为卷积运算进行计算。利用通常Saviztky-Golay滤波器的抽头数远大于回归多项式阶数这一特点可以大大降低估计的计算复杂度，使得计算复杂度仅为O(N)。该方法具有局部线性回归估计算法的所有优点，且由于采用了局部多项式回归，估计精度比局部线性回归要高，同样不需要知道信道和数据的先验知识。
对于块衰落信道，我们提出了基于二维核回归估计的OFDM系统信道估计方法。在核回归方法中，我们可以利用核函数来刻画信道复增益在时域频域上的相关性，因此估计性能比简单的局部回归要好。由于WSUSS信道的相关性可以进行时频分解，该算法可以分解为两个级联的一维核回归算法，复杂度大大降低。通过优化时域和频域核函数的支撑区间的长度，该算法的性能在低信噪比时甚至超过一维MMSE估计算法，而复杂度远低于一维MMSE估计算法，但比前两种算法的计算复杂度稍高一些，每点数据的算法复杂度与两个核函数长度和成正比。
最后论文讨论了基于小波阈值估计的基本原理并提出了基于块阈值估计的小波阈值信道估计算法，该算法的性能优于基于传统的小波去噪信道估计算法，且在信道多径扩展大于CP长度时仍然具有较好的估计性能，且不存在模型失配问题，而计算复杂度仅为O(N)。
通过全文的研究我们可以发现，非参数估计方法可以很好地在OFDM信道估计领域进行应用，并且可以在较低的计算复杂度下取得较好的估计性能。对基于非参数估计的信道估计方法，下一步的研究可以包括如何以较低的计算复杂度将这些算法推广到MIMO-OFDM系统中、算法的性能界的分析、估计窗长的选择、核函数的选择以及进一步降低二维核回归算法的计算量等方面。
Along with the extensive deployment of 3G wireless mobile communication systems, which are based on IMT2000 standard, the innovative B3G or 4G broadband multimedia communication techniques are widely investigated. To adapt to the need for multimedia services, the aim of the B3G/4G systems is achieving a transmission rate of 100Mbps in high-mobility environment and 1Gbps in low-mobility environment. So there must be some major progress in frequency efficiency and transmission rate in these systems.
OFDM is a multi-carrier modulation or transmission technique. It has the advantages of high frequency, resistant to multipath delay spread and realization simplisity etc., therefore is chosen as one of the core techniques of B3G/4G communication system. To transmission in OFDM system with high data rates while reserving high frequency efficiency, big constelation mapping and coherent detection must be employed. In this situation, the receiver must know the channel state information. Otherwise, many transmission schemes such as adaptive modulation and coding, space time transmission, MIMO, beamforming and crosslayer processing, all have to know the CSI. So channel estimation is a essential part of OFDM systems.
Our focus is on the nonparametric estimation based OFDM channel estimation algorithm. In the dissertation, the radio fading channel property and nonparametric estimation theory were firstly discussed, then some channel estimation algorithm based on nonparametric function estimation were proposed and analysed after the briefly intruducing of conventional LS estimator, LMMSE estimator and DFT base transform domain estimator. These algorithm do not neen the a priori information of the channel and transmitted data, and can highly improve estimation performance only at a cost of computation complexity O(N).
In the first part, the properties of the radio fading channel were firstly discusseded, then the channel mode and its mathmatical characters were carefully analysed and the nonparametric estimation theory was introduced. Finally the conclusion was drawn that the radio fading channel can be estimated by nonparametric function estimation. Therefore a solid theorical basis is laid for the rest part of the dissertation.
In the second part, a nonparametric frequecy domain channel estimation algorithm based on local linear regression was proposed. In this method, the interpolation processing and noise cancellatiod processing were seperated, the LS estimated channel gain at pilot tones were firstly interpolated by piece-wise constant or piece-wise linear interpolation and then smoothed by local linear regression. This method can efficiently suppress the channel and interpolation error as well as avoid the windowing effect of the DFT based algorithm, so the performance was improved greatly.
To enhence the accuracy of the estimation while reserving the computational complexity, a nonparametric frequecy domain channel estimation algorithm based on Savitzky-Golay smoothing filter was proposed in the third part. Savitzky-Golay smoothing filter can be considered as a local polynomial estimator, and can be calculated by convolution. Because the filter length is always far more longer then the order of the regression polynomial, the computional complexty can be reduced greatly and only be O(N). It outperform the local linear regression algorithm and don't need a priori information either.
For block fading channel a nonparametric frequecy domain channel estimation algorithm based on 2D kernel smoothing was proposed. According to that the frequency and time domain correlation can be seperated in WSSUS fading channel, a simplified 2D kernel smoothing filter using two cascaded 1D kernel smoothing filters in time domain and frequency domain respectely was adopted to reduce the computaion complexity. Because it can utilize the correlation of the channel gain in time and frequency domain, the estimation performance is better than the above two. If the adaptive kernel window size was employed, the performance can be improved further, and outperforms 1D LMMSE estimator in the low SNR area and the computational complexity is much mo lower.
The last part introdused a wavelet block-thresholding channel estimation method. It outperforms the soft threshold wavelet estimator and hard thresholding wavelet estimator because it utilize the correlation of the wavelet detail coefficients. The proposed estimator maintains better performance even when the CP is shorter then the multipath delay spread and with no model mismatch. The computational complexity is only O(N).
Through the dissertation we can make a conclution that nonparametric estimation can be well adapted to channel estimation, the derived channel estimation algorithm has better performance while reserving low computational complexity. But there are still many problems, such as the estimation bounds of the estimators, the selection of the windows size of the estimators whitch more adapted to OFDM channel estimation, the smoothing kernel selection of the estimator and the generalization of the nonparametric channel estimation algorithm, to be solved.
引文
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