CN101447969B - A Channel Estimation Method for Multi-Band Orthogonal Frequency Division Multiplexing UWB System - Google Patents

Abstract

The invention discloses a channel estimation method of a multi-band orthogonal frequency division multiplexing ultra-wideband system, which has the advantages that an m sequence with better autocorrelation property is adopted as a time domain training sequence and a cyclic prefix is added, at the receiving end, the receiving signal without the cyclic prefix and the training sequence are processed with cross-correlation operation and each training sequence is processed with self-correlation operation to obtain the impulse response estimated value of the channel, and utilizes the diagonal dominance property of the autocorrelation matrix of the m sequence, firstly, respectively makes a one-diagonal decomposition or a three-diagonal decomposition on the autocorrelation matrix of the m sequence, then, the approximation method of the first-order inverse matrix is adopted, the complex inversion operation is effectively avoided, thereby reducing the operation amount by one order of magnitude, the performance approaches to the conventional time domain channel estimation method, so that the method is a quick and effective channel estimation method of an ultra-wideband system and is easy to realize.

Description

A Channel Estimation Method for Multi-Band Orthogonal Frequency Division Multiplexing UWB System

technical field

The invention relates to a channel estimation method, in particular to a channel estimation method of a multi-band orthogonal frequency division multiplexing ultra-wideband system.

Background technique

Ultra Wideband (UWB, Ultra Wide Band) technology, as a potential high-speed, short-distance wireless personal communication technology, has attracted great attention in both academia and industry in recent years, and has become the current research and development in the field of wireless communication. hotspots. UWB technology combined with multi-band orthogonal frequency division multiplexing (MB-OFDM, Multi-Band Orthogonal Frequency Division Multiplexing) technology constitutes multi-band orthogonal frequency division multiplexing ultra-wideband (MB-OFDM UWB) technology, which can effectively combat multiple Path fading, various narrowband interferences, and flexible use of spectrum resources have become one of the mainstream implementation solutions for ultra-wideband technology. The application prospect of multi-band OFDM ultra-wideband technology is very attractive, such as in high-speed wireless personal area network, wireless Ethernet interface link, intelligent wireless local area network, outdoor peer-to-peer network and sensing, positioning and identification network, etc. Fields have a wide range of applications, especially in the field of digital home electronics products. At present, many companies choose the application of wireless home electronic products as the breakthrough of multi-band OFDM ultra-wideband technology.

In order to obtain the ideal performance of multi-band OFDM UWB system, technologies such as coherent detection, demodulation, and equalization must be used. Reliable data transmission plays a vital role in Cross-Frequency Division Multiplexing UWB communication environment. Due to the large bandwidth occupied by ultra-wideband signals, short signal duration, and high transmission rate, the channel estimation technology requires high estimation accuracy and low computational complexity. Therefore, how to perform fast and effective channel estimation in the multi-band OFDM ultra-wideband system is a major challenge faced by the current multi-band OFDM ultra-wideband technology.

然后经过内插器，利用内插的方式对在整个频域内进行内插，以便得到整个信道估计值

最后将信道估计值和接收数据送入均衡器，就可以对接收数据均衡得到原始发送数据的估计值。Most of the multi-band OFDM UWB systems adopt the channel estimation method of frequency domain pilot frequency domain, that is, insert pilot frequency in the frequency domain and perform channel estimation in the frequency domain. This type of channel estimation method includes the following steps: first, insert pilots at an appropriate position in the frequency domain at the sending end, and use the pilot data at the receiving end to obtain the channel information of the pilot position through the corresponding channel estimation criteria

Then through the interpolator, use the interpolation method to Interpolate over the entire frequency domain to obtain the entire channel estimate

Finally, the channel estimation value and the received data are sent to the equalizer, and the received data can be equalized to obtain the estimated value of the original transmitted data.

At present, the channel information for the above-mentioned pilot positions is usually obtained based on the least squares (LS, Least Squares) criterion or the minimum mean square error (MMSE, Minimum Mean Square Error) criterion. Among them, the frequency domain pilot frequency domain channel estimation method based on the least squares criterion has a simple calculation process and is easy to implement, but this method does not take into account the influence of noise, resulting in low channel estimation accuracy. The frequency-domain pilot-frequency-domain channel estimation method based on the minimum mean square error criterion can obtain good performance due to the use of the frequency-domain autocorrelation characteristics of the channel, but the estimation process of this method involves matrix inversion, which increases the The computational complexity of the method leads to poor implementability of the method. To sum up, some existing channel estimation methods in the frequency domain and pilot frequency domain have high computational complexity and are difficult to be used in practice, and because the channel characteristics of the non-pilot positions need to use interpolation, resulting in calculation accuracy No advanced question.

The current time-domain channel estimation methods mainly include estimation methods based on discrete Fourier (DFT, Discrete Fourier Transform) filtering method and maximum likelihood criterion (ML, Maximum Likelihood). These two methods can reduce the cost of channel estimation to a certain extent. The mean square error value, but the disadvantage is that the channel length (or channel finite delay extension) information needs to be accurately obtained before channel estimation, thus increasing the duration and computational complexity of the channel estimation process, making these two types of methods in practice application is limited.

与m序列s循环右移i位后的m序列sⁱ作相关运算， $\begin{array}{c}C(i,j)=(1/L_P)\underset{k=0}{\overset{L_P-1}{\mathrm{\Σ}}}\tilde{r}\left(k\right)s^i\left(k\right)\\ =\underset{j=0}{\overset{L_C-1}{\mathrm{\Σ}}}{h}_j{C}_P(i,j)+(1/L_P)\underset{k=0}{\overset{L_p-1}{\mathrm{\Σ}}}n\left(k\right)s^i\left(k\right)\end{array},$ 其中，k＝0，1，…，L_p+L_c-1，h表示由信道的各个多径的系数构成的矩阵向量， $h={[h_0,h_1,\·\·\·h_{L_{C-1}}]}^T,$ h_j为信道的第j个多径系数，h应满足条件：{h_j＝0|L≤j≤L_C-1}，L为信道的阶数，C_P(i，j)是m序列s循环右移j位后的m序列s^j和循环右移i位后的m序列sⁱ的归一化自相关系数，第二项是高斯白噪声序列n与m序列s归一化互相关系数，n为高斯白噪声，n(k)为第k时刻的高斯白噪声。噪声的幅度被压缩成原来的1/L_P倍，即 $(1/L_P)\underset{k=0}{\overset{L_p-1}{\mathrm{\Σ}}}n\left(k\right)s^i\left(k\right).$ 这样可以将 $\begin{array}{c}C(i,j)=(1/L_P)\underset{k=0}{\overset{L_P-1}{\mathrm{\Σ}}}\tilde{r}\left(k\right)s^i\left(k\right)\\ =\underset{j=0}{\overset{L_C-1}{\mathrm{\Σ}}}{h}_j{C}_P(i,j)+(1/L_P)\underset{k=0}{\overset{L_p-1}{\mathrm{\Σ}}}n\left(k\right)s^i\left(k\right)\end{array}$ 近似成C≈C_Ph，其中C_P是m序列s的自相关矩阵，插入m序列s的长度为L_P，则自相关矩阵C_P在一个周期内的归一化自相关函数满足： $\begin{array}{c}{C}_P(i,j)=(1/L_P)\underset{k=0}{\overset{L_P-1}{\mathrm{\Σ}}}{s}^j\left(k\right)s^i\left(k\right)\\ =\left\{\begin{array}{cc}1,& i=j\\ -1/L_P,& i\≠j\end{array}\right.\end{array}.$ 由此利用m序列的自相关特性得到信道的冲激响应估计值 $\tilde{h}=C_p^{-1}C.$ 该方法巧妙的利用了m序列的自相关特性获得信道冲激响应的估计值，其估计精度很高，并且还能够根据多带正交频分复用超宽带通信系统传输速率的需要灵活调整训练序列的开销，以取得估计精度和开销的折中。但从 $\tilde{h}=C_p^{-1}C$ 可知，要想得到信道冲激响应，矩阵C_P的求逆运算是必不可少的，然而自相关矩阵C_P＝[C_P(i，j)]，i＝0，1，…L_p-1，j＝0，1，…L_p-1是一个L_P阶方阵，如果需要对其进行求逆，其计算复杂度很高(计算复杂度为o(L_p ³))，高计算复杂度给这种方法的应用带来了很大的障碍。Bowei Song et al. proposed a time-domain channel estimation method based on m-sequences. The workflow of the multi-band OFDM ultra-wideband system using this method is shown in Figure 1. At the sending end, the input data signal undergoes quadrature phase shift modulation (QPSK, Quadrature Phase Shift Keying) to obtain a modulated signal, and the modulated signal undergoes serial-to-parallel conversion, inverse Fourier transform (IFFT, Inverse Fast Fourier Transform) and parallel-to-serial conversion After processing, multiple OFDM symbols are formed, and every fixed number of OFDM symbols, an m-sequence s of length L _P is inserted as a training sequence for time-domain channel estimation, and a cyclic prefix of length L _C is added according to the quality of the channel characteristics (CP, Cyclic Prefix), and assume that the multi-band OFDM ultra-wideband system is synchronous, and the training sequence obtained after adding the cyclic prefix and the input data signal are transmitted through the ultra-wideband channel after carrier modulation processing; At the receiving end, first remove the cyclic prefix in the received training sequence affected by channel fading and Gaussian white noise, and then remove the cyclic prefix from the training sequence affected by channel fading and Gaussian white noise

Correlate with the m-sequence s ⁱ after the m-sequence s is cyclically shifted to the right by i bits, $\begin{array}{c}C(i,j)=(1/L_P)\underset{k=0}{\overset{L_P-1}{\mathrm{\&Sigma;}}}\tilde{r}\left(k\right){\mathrm{the\; s}}^i\left(k\right)\\ =\underset{j=0}{\overset{L_C-1}{\mathrm{\&Sigma;}}}{h}_j{C}_P(i,j)+(1/L_P)\underset{k=0}{\overset{L_p-1}{\mathrm{\&Sigma;}}}\mathrm{no}\left(k\right){\mathrm{the\; s}}^i\left(k\right)\end{array},$ Among them, k=0, 1, ..., L _p +L _c -1, h represents a matrix vector composed of coefficients of each multipath of the channel, $h={[h_0,{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="H2008101642240E00031.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,\&Center\; Dot;\&CenterDot;\&CenterDot;h_{L_{C-1}}]}^T,$ h _j is the jth multipath coefficient of the channel, h should satisfy the condition: {h _j ＝0|L≤j≤L _C -1}, L is the order of the channel, C _P (i, j) is the sequence of m The normalized autocorrelation coefficient of the m-sequence s ^j after the cyclic right shift of j bits and the m-sequence s ⁱ after the cyclic right shift of i bits, the second item is the normalized correlation between the Gaussian white noise sequence n and the m-sequence s number, n is Gaussian white noise, and n(k) is Gaussian white noise at the kth moment. The amplitude of the noise is compressed to the original 1/L _P times, that is $(1/L_P)\underset{k=0}{\overset{L_p-1}{\mathrm{\&Sigma;}}}\mathrm{no}\left(k\right){\mathrm{the\; s}}^i\left(k\right).$ so that the $\begin{array}{c}C(i,j)=(1/L_P)\underset{k=0}{\overset{L_P-1}{\mathrm{\&Sigma;}}}\tilde{r}\left(k\right){\mathrm{the\; s}}^i\left(k\right)\\ =\underset{j=0}{\overset{L_C-1}{\mathrm{\&Sigma;}}}{h}_j{C}_P(i,j)+(1/L_P)\underset{k=0}{\overset{L_p-1}{\mathrm{\&Sigma;}}}\mathrm{no}\left(k\right){\mathrm{the\; s}}^i\left(k\right)\end{array}$ It is approximated as _C≈CP h, where C _P is the autocorrelation matrix of m sequence s, and the length of inserting m sequence s is L _P , then the normalized autocorrelation function of autocorrelation matrix C _P in one cycle satisfies: $\begin{array}{c}{C}_P(i,j)=(1/L_P)\underset{k=0}{\overset{L_P-1}{\mathrm{\&Sigma;}}}{\mathrm{the\; s}}^j\left(k\right){\mathrm{the\; s}}^i\left(k\right)\\ =\left\{\begin{array}{cc}1,& i=j\\ -1/L_P,& i\&NotEqual;j\end{array}\right.\end{array}.$ Thus, the impulse response estimate of the channel is obtained by using the autocorrelation property of the m-sequence $\tilde{h}=C_p^{-1}C.$ This method cleverly uses the autocorrelation characteristics of the m-sequence to obtain the estimated value of the channel impulse response. The overhead of the sequence to achieve a trade-off between estimation accuracy and overhead. but from $\tilde{h}=C_p^{-1}C$ It can be seen that in order to obtain the channel impulse response, the inverse operation of the matrix C _P is essential, but the autocorrelation matrix C _P =[C _P (i, j)], i=0, 1, ... L _p -1 , j=0, 1, ... L _p -1 is a square matrix of order L _P , if it needs to be inverted, its computational complexity is very high (the computational complexity is o(L _p ³ )), high computational complexity The degree of application of this method has brought great obstacles.

Contents of the invention

The technical problem to be solved by the present invention is to provide a channel estimation method suitable for multi-band OFDM ultra-wideband systems with low computational complexity for the deficiencies in the prior art.

为去循环前缀后的第k时刻的第一接收信号，h表示由信道的各个多径系数构成的矩阵向量， $h={[h_0,h_1,\&CenterDot;\&CenterDot;\&CenterDot;h_{L_{C-1}}]}^T,$ h_j为信道的第j个多径系数，h应满足条件：{h_j＝0|L≤j≤L_C-1}，L为信道的阶数，n为高斯白噪声，n(k)为第k时刻的高斯白噪声，s^j为m序列s循环右移j位后的m序列，s^j(k)为m序列s循环右移j位后的第k时刻的序列；⑦然后计算去循环前缀后的第一接收信号

与m序列s循环右移i位后的m序列sⁱ的互相关矩阵C和各个训练序列s的自相关矩阵C_P，C＝[C(i，j)]，C(i，j)为去循环前缀后的第一接收信号

与m序列s循环右移i后的m序列sⁱ的归一化互相关系数， $C(i,j)=(1/L_P)\underset{k=0}{\overset{L_P-1}{\mathrm{\&Sigma;}}}\tilde{r}\left(k\right)s^i\left(k\right),$ C_P＝[C_P(i，j)]，C_P(i，j)为m序列s循环右移j位后的m序列s^j和m序列s循环右移i位后的m序列sⁱ的归一化自相关系数， $\begin{array}{c}{C}_P(i,j)=(1/L_P)\underset{k=0}{\overset{L_p-1}{\mathrm{\&Sigma;}}}{s}^j\left(k\right)s^i\left(k\right)\\ =\left\{\begin{array}{cc}1,& i=j\\ -1/L_P,& i\&NotEqual;j\end{array}\right.\end{array}$ ，其中，i＝0，1，…，L_p，j＝0，1，…，L_p，k＝0，1，…，L_p+L_c-1，为去循环前缀后的第k时刻的第一接收信号，s^j(k)为m序列s循环右移j位后的第k时刻的序列，sⁱ(k)为m序列s循环右移i位后的第k时刻的序列。⑧再根据去循环前缀后的第一接收信号

与m序列s循环右移i位后的m序列sⁱ的互相关矩阵C和各个训练序列s的自相关矩阵C_P，计算信道的冲激响应估计值

$\tilde{h}=C_p^{-1}C,$ 其中，C_p ^-1为自相关矩阵C_P的逆矩阵；根据所述的自相关矩阵C_P的对角占优性，将所述的自相关矩阵C_P分解为第一矩阵和第二矩阵之和，将所述的第一矩阵记为D，将所述的第二矩阵记为E，C_P＝D+E，在所述的第一矩阵D和所述的第二矩阵E满足||D^-1E||＜1时，计算所述的自相关矩阵C_P的逆矩阵C_P ^-1， $C_p^{-1}=(I-D^{-1}E+{\left(D^{-1}E\right)}^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(-1)}^m{\left(D^{-1}E\right)}^m+\&CenterDot;\&CenterDot;\&CenterDot;)D^{-1},$ 其中，符号“||||”为范数符号，I为单位矩阵，D^-1为第一矩阵D的逆矩阵，m＝1，2，…，∞；再根据 $C_p^{-1}=(I-D^{-1}E+{\left(D^{-1}E\right)}^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(-1)}^m{\left(D^{-1}E\right)}^m+\&CenterDot;\&CenterDot;\&CenterDot;)D^{-1}$ 计算C_p ^-1的一阶近似值， $C_p^{-1}\&ap;(I-D^{-1}E)D^{-1}\&ap;D^{-1}-D^{-1}{\mathrm{ED}}^{-1}.$ The technical solution adopted by the present invention to solve the above-mentioned technical problems is: a channel estimation method for a multi-band OFDM ultra-wideband system, which includes the following steps: ① At the sending end, firstly perform quadrature phase estimation on the input data signal The modulated signal is obtained through shift modulation processing; ②then serial-to-parallel conversion, inverse Fourier transform, and parallel-to-serial conversion are performed on the modulated signal in sequence to form multiple OFDM symbols; ③in the multiple formed OFDM symbols, set A number of OFDM symbols are inserted into an m-sequence s of length _LP , and the m-sequence s is used as a training sequence, and a cyclic prefix of length _LC is added before the training sequence according to the channel characteristics, and the training sequence after the cyclic prefix is obtained , denoted by x, x=[x(0), x(1),...x(L _P +L _C -1)]; ④Finally, the training sequence x after adding the cyclic prefix and the formed OFDM symbol are carried by the carrier After modulation processing, it is transmitted to the receiving end through an ultra-wideband channel. During the transmission process, the training sequence x and OFDM symbols after adding the cyclic prefix are affected by channel fading and Gaussian white noise; ⑤ At the receiving end, define the channel received by the receiving end The training sequence x of the additional cyclic prefix affected by fading and Gaussian white noise is the first received signal, and the OFDM symbol received by the receiving end after channel fading and Gaussian white noise is defined as the second received signal, and the first received signal The tapped delay line model is expressed as $r\left(k\right)=\underset{t=0}{\overset{L_C-1}{\mathrm{\&Sigma;}}}{h}_{t}x(k-t)+\mathrm{no}\left(k\right),$ Wherein, k=0, 1,..., _Lp + _Lc -1, r(k) is the first received signal at the kth moment, h represents a matrix vector composed of coefficients of each multipath of the channel, $h={[h_0,{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="H2008101642240E00031.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,\&CenterDot;\&CenterDot;\&CenterDot;h_{L_{C-1}}]}^T,$ h _t is the tth multipath coefficient of the channel, h should satisfy the condition: {h _t = 0|L≤t≤L _C -1}, L is the order of the channel, x is the training sequence after adding the cyclic prefix, x(kt) is the training sequence after the additional cyclic prefix at the kt moment, n is Gaussian white noise, and n(k) is the Gaussian white noise at the kth moment; ⑥ First, the first received signal r(k) is decarrier modulation, and de-cyclic prefix processing is performed on the first received signal after de-carrier modulation processing to obtain $\tilde{r}\left(k\right)=\underset{j=0}{\overset{L_C-1}{\mathrm{\&Sigma;}}}{h}_j{\mathrm{the\; s}}^j\left(k\right)+\mathrm{no}\left(k\right),$ Among them, k=0, 1, ..., L _p +L _c -1,

is the first received signal at the kth moment after the cyclic prefix is removed, and h represents a matrix vector composed of each multipath coefficient of the channel, $h={[h_0,{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="H2008101642240E00031.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;h_{L_{C-1}}]}^T,$ h _j is the jth multipath coefficient of the channel, h should satisfy the condition: {h _j ＝0|L≤j≤L _C -1}, L is the order of the channel, n is Gaussian white noise, n(k) is the Gaussian white noise at the k-th moment, s ^j is the m-sequence after the m-sequence s is cyclically shifted to the right by j bits, s ^j (k) is the sequence at the k-th moment after the m-sequence s is cyclically shifted to the right by j bits; ⑦ Then calculate The first received signal after removing the cyclic prefix

The cross-correlation matrix C of the m-sequence s ⁱ and the autocorrelation matrix C _P of each training sequence s after cyclically shifting right by i bits with the m-sequence s, C=[C(i, j)], C(i, j) is The first received signal after removing the cyclic prefix

The normalized cross-correlation coefficient of the m-sequence s ⁱ after the m-sequence s is cyclically shifted right by i, $C(i,j)=(1/L_P)\underset{k=0}{\overset{L_P-1}{\mathrm{\&Sigma;}}}\tilde{r}\left(k\right){\mathrm{the\; s}}^i\left(k\right),$ C _P = [C _P (i, j)], C _P (i, j) is the m-sequence s j after m-sequence s is cyclically shifted to the right by ^j bits and the m-sequence s i after m-sequence s is cyclically shifted to the right by ⁱ The normalized autocorrelation coefficient of , $\begin{array}{c}{C}_P(i,j)=(1/L_P)\underset{k=0}{\overset{L_p-1}{\mathrm{\&Sigma;}}}{\mathrm{the\; s}}^j\left(k\right){\mathrm{the\; s}}^i\left(k\right)\\ =\left\{\begin{array}{cc}1,& i=j\\ -1/L_P,& i\&NotEqual;j\end{array}\right.\end{array}$ , where, i=0, 1, ..., L _p , j = 0, 1, ..., L _p , k = 0, 1, ..., L _p +L _c -1, is the first received signal at the k-th moment after removing the cyclic prefix, s ^j (k) is the sequence at the k-th moment after the m-sequence s is cyclically shifted right by j bits, and s ⁱ (k) is the m-sequence s cyclically shifted right by i The sequence of the kth moment after the bit. ⑧ Then according to the first received signal after removing the cyclic prefix

The cross-correlation matrix C of m-sequence s ⁱ and the autocorrelation matrix C _P of each training sequence s after cyclically shifting right by i bits with m-sequence s calculate the estimated value of the impulse response of the channel

$\tilde{h}=C_p^{-1}C,$ Wherein, C _p ^-1 is the inverse matrix of the autocorrelation matrix C _P ; according to the diagonal dominance of the autocorrelation matrix C _P , the autocorrelation matrix C _P is decomposed into a first matrix and a second matrix sum, the first matrix is marked as D, the second matrix is marked as E, C _P =D+E, and the first matrix D and the second matrix E satisfy | When |D ^-1 E||<1, calculate the inverse matrix C _P ^-1 of the autocorrelation matrix C _P , $C_p^{-1}=(I-{\mathrm{D.}}^{-1}\mathrm{E.}+{\left({\mathrm{D.}}^{-1}\mathrm{E.}\right)}^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(-1)}^m{\left({\mathrm{D.}}^{-1}\mathrm{E.}\right)}^m+\&CenterDot;\&CenterDot;\&CenterDot;){\mathrm{D.}}^{-1},$ Wherein, the symbol "||||" is a norm symbol, I is an identity matrix, D ^-1 is the inverse matrix of the first matrix D, m=1, 2, ..., ∞; then according to $C_p^{-1}=(I-{\mathrm{D.}}^{-1}\mathrm{E.}+{\left({\mathrm{D.}}^{-1}\mathrm{E.}\right)}^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(-1)}^m{\left({\mathrm{D.}}^{-1}\mathrm{E.}\right)}^m+\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;){\mathrm{D.}}^{-1}$ Compute a first-order approximation of _Cp ^-1 , $C_p^{-1}\&ap;(I-{\mathrm{D.}}^{-1}\mathrm{E.}){\mathrm{D.}}^{-1}\&ap;{\mathrm{D.}}^{-1}-{\mathrm{D.}}^{-1}{\mathrm{ED}}^{-1}.$

The first matrix D is a diagonal matrix composed of the diagonal elements of the autocorrelation matrix C _P , and the second matrix E is a diagonal matrix composed of the off-diagonal elements of the autocorrelation matrix C _P An off-diagonal matrix composed of elements, the diagonal matrix is denoted as D ₁ , and the off-diagonal matrix is denoted as E ₁ , to obtain $C_p^{-1}\&ap;{\mathrm{D.}}_1^{-1}-{\mathrm{D.}}_1^{-1}{\mathrm{E.}}_1{\mathrm{D.}}_1^{-1};$ The coefficient of described autocorrelation matrix _CP is carried out normalization process, described diagonal matrix D ₁ after normalization process is a identity matrix I; According to $C_p^{-1}\&ap;{\mathrm{D.}}_1^{-1}-{\mathrm{D.}}_1^{-1}{\mathrm{E.}}_1{\mathrm{D.}}_1^{-1}$ get $C_p^{-1}=I-{\mathrm{E.}}_1.$

The first matrix D is a tridiagonal matrix composed of tridiagonal elements of the autocorrelation matrix C _P , and the second matrix E is divided by three pairs of the autocorrelation matrix C _P A non-tridiagonal matrix composed of elements other than corner elements, the tridiagonal matrix is denoted as D ₃ , and the non-tridiagonal matrix is denoted as E ₃ , to obtain $C_p^{-1}\&ap;{\mathrm{D.}}_3^{-1}-{\mathrm{D.}}_3^{-1}{\mathrm{E.}}_3{\mathrm{D.}}_3^{-1};$ The tridiagonal matrix D ₃ is decomposed into a diagonal matrix consisting of the diagonal elements of the autocorrelation matrix C _P and a diagonal matrix consisting of 0 diagonal elements of the autocorrelation matrix C _P The sum of the di-diagonal matrix composed of diagonal elements, the diagonal matrix is recorded as D ₁ , the di-diagonal matrix is recorded as D ₂ , and the inverse matrix of the tri-diagonal matrix D ₃ is calculated D ₃ ^-1 , ${\mathrm{D.}}_3^{-1}=(I-{\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2+{\left({\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2\right)}^2+\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;+{(-1)}^m{\left({\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2\right)}^m+\&Center\; Dot;\&Center\; Dot;\&CenterDot;){\mathrm{D.}}_1^{-1}$ , where I is the identity matrix, D ₁ ^-1 is the inverse matrix of the diagonal matrix D ₁ , m=1, 2,..., ∞; then according to ${\mathrm{D.}}_3^{-1}=(I-{\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2+{\left({\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2\right)}^2+\&CenterDot;\&Center\; Dot;\&CenterDot;+{(-1)}^m{\left({\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2\right)}^m+\&Center\; Dot;\&CenterDot;\&CenterDot;){\mathrm{D.}}_1^{-1}$ Compute a first-order approximation ^of _D3-1 , ${\mathrm{D.}}_3^{-1}\&ap;(I-{\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2){\mathrm{D.}}_1^{-1};$ The coefficient of described autocorrelation matrix _CP is carried out normalization processing, and after normalization processing, diagonal matrix D ₁ is identity matrix I, according to ${\mathrm{D.}}_3^{-1}\&ap;(I-{\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2){\mathrm{D.}}_1^{-1}$ get ${\mathrm{D.}}_3^{-1}=I-{\mathrm{D.}}_2;$ Then according to $C_p^{-1}\&ap;{\mathrm{D.}}_3^{-1}-{\mathrm{D.}}_3^{-1}{\mathrm{E.}}_3{\mathrm{D.}}_3^{-1}$ and ${\mathrm{D.}}_3^{-1}=I-{\mathrm{D.}}_2,$ get $C_p^{-1}\&ap;(I-{\mathrm{D.}}_2)-(I-{\mathrm{D.}}_2){\mathrm{E.}}_3(I-{\mathrm{D.}}_2).$

Compared with the prior art, the advantage of the present invention is that the m-sequence with better autocorrelation characteristics is used as the time-domain training sequence, and at the receiving end, the cross-correlation operation is performed on the first received signal with the cyclic prefix removed and the training sequence and each The training sequence is used for autocorrelation operation to obtain the estimated value of the impulse response of the channel, and the autocorrelation matrix of the m-sequence is used to have a diagonal dominant characteristic. Decomposition, and then using the approximation method of the first-order inverse matrix, effectively avoiding the complex inversion operation, reducing the amount of calculation by an order of magnitude, and the performance is close to the conventional time-domain channel estimation method, which is a fast and effective method for ultra-wideband systems. The channel estimation method is easy to implement.

Description of drawings

Fig. 1 is a schematic diagram of the workflow of a multi-band OFDM ultra-wideband system;

Fig. 2 is the graph that the bit error rate of the conventional time-domain channel estimation method and the LS algorithm corresponding to different length m-sequences change with the signal-to-noise ratio;

Fig. 3 is the performance comparison figure of LS algorithm, conventional time-domain estimation method, a pair of angle decomposition method of the present invention and tri-diagonal decomposition method when _LP =31;

Fig. 4 is a performance comparison chart of the conventional time domain estimation method, the diagonal decomposition method and the tridiagonal decomposition method of the present invention when L _P = 15.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

A channel estimation method for a multi-band OFDM ultra-wideband system, comprising the following steps:

① At the sending end, the existing quadrature phase shift modulation (QPSK) technology is first used to process the input data signal with quadrature phase shift modulation to obtain the modulated signal.

② Then serial-to-parallel conversion, inverse Fourier transform (IFFT) and parallel-to-serial conversion are performed on the modulated signal in sequence to form multiple OFDM symbols. In this embodiment, each OFDM symbol uses 128 subcarriers, the frequency interval between adjacent subcarriers is 4.1254MHz, and the duration of each OFDM symbol is T ₀ =242.4ns.

③In the formed multiple OFDM symbols, insert an m-sequence s with a length of L _P at intervals of a set number of OFDM symbols, and use the m-sequence s as a training sequence. Add a cyclic prefix (CP) with a length of L _C to obtain the training sequence after the additional cyclic prefix, the training sequence after the additional cyclic prefix is represented by x, x=[x(0), x(1),...x( L _P +L _C -1)], where L _P is the length of the m-sequence s, which is the training sequence, and L _C is the length of the cyclic prefix. In this embodiment, the set number selected is 4, that is, an m-sequence s of length L _P is inserted every 4 OFDM symbols.

④Finally, the training sequence x after the cyclic prefix is added and the formed OFDM symbols are processed by the carrier modulation and then transmitted to the receiving end through the ultra-wideband channel. During the transmission process, the training sequence x and the OFDM symbols after the cyclic prefix will be subject to channel fading and Gaussian white noise.

⑤ At the receiving end, define the training sequence x of the additional cyclic prefix received by the receiving end after being affected by channel fading and Gaussian white noise as the first received signal, and define the training sequence x received by the receiving end after being affected by channel fading and Gaussian white noise The OFDM symbol is the second received signal, and the first received signal is represented by a tapped delay line model as $r\left(k\right)=\underset{t=0}{\overset{L_C-1}{\mathrm{\&Sigma;}}}{h}_{t}x(k-t)+\mathrm{no}\left(k\right),$ Wherein, k=0, 1,..., _Lp + _Lc -1, r(k) is the first received signal at the kth moment, h represents a matrix vector composed of each multipath coefficient of the channel, $h={[h_0,{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="H2008101642240E00031.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,\&CenterDot;\&Center\; Dot;\&Center\; Dot;h_{L_{C-1}}]}^T,$ h _t is the tth multipath coefficient of the channel, h should satisfy the condition: {h _t = 0|L≤t≤L _C -1}, L is the order of the channel, x is the training sequence after adding the cyclic prefix, x(kt) is the training sequence after the additional cyclic prefix at the kt moment, n is Gaussian white noise, and n(k) is the Gaussian white noise at the kth moment.

为去循环前缀后的第k时刻的第一接收信号，h表示由信道的各个多径系数构成的矩阵向量， $h={[h_0,h_1,\&CenterDot;\&CenterDot;\&CenterDot;h_{L_{C-1}}]}^T,$ h_j为信道的第j个多径系数，h应满足条件：{h_j＝0|L≤j≤L_C-1}，L为信道的阶数，n为高斯白噪声，n(k)为第k时刻的高斯白噪声，s^j为m序列s循环右移j位后的m序列，s^j(k)为m序列s循环右移j位后的第k时刻的序列。⑥ First, carry out carrier-removal modulation on the first received signal r(k), and perform de-cyclic prefix processing on the first received signal after carrier-removal modulation processing to obtain $\tilde{r}\left(k\right)=\underset{j=0}{\overset{L_C-1}{\mathrm{\&Sigma;}}}{h}_j{\mathrm{the\; s}}^j\left(k\right)+\mathrm{no}\left(k\right),$ Among them, k=0, 1, ..., L _p +L _c -1,

is the first received signal at the kth moment after the cyclic prefix is removed, and h represents a matrix vector composed of each multipath coefficient of the channel, $h={[h_0,{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="H2008101642240E00031.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,\&CenterDot;\&CenterDot;\&CenterDot;h_{L_{C-1}}]}^T,$ h _j is the jth multipath coefficient of the channel, h should satisfy the condition: {h _j ＝0|L≤j≤L _C -1}, L is the order of the channel, n is Gaussian white noise, n(k) is the Gaussian white noise at the k-th moment, s ^j is the m-sequence after the m-sequence s is cyclically shifted to the right by j bits, and s ^j (k) is the sequence at the k-th moment after the m-sequence s is cyclically shifted to the right by j bits.

与m序列s循环右移i位后的m序列sⁱ的互相关矩阵C和各个训练序列s的自相关矩阵C_P，C＝[C(i，j)]，C(i，j)为去循环前缀后的第一接收信号

与m序列s循环右移i后的m序列sⁱ的归一化互相关系数， $C(i,j)=(1/L_P)\underset{k=0}{\overset{L_P-1}{\mathrm{\&Sigma;}}}\tilde{r}\left(k\right)s^i\left(k\right),$ C_P＝[C_P(i，j)]，C_P(i，j)为m序列s循环右移j位后的m序列s^j和m序列s循环右移i位后的m序列sⁱ的归一化自相关系数， $\begin{array}{c}{C}_P(i,j)=(1/L_P)\underset{k=0}{\overset{L_P-1}{\mathrm{\&Sigma;}}}{s}^j\left(k\right)s^i\left(k\right)\\ =\left\{\begin{array}{cc}1,& i=j\\ -1/L_P,& i\&NotEqual;j\end{array}\right.\end{array},$ 其中，i＝0，1，…，L_p，j＝0，1，…，L_p，k＝0，1，…，L_p+L_c-1，

为去循环前缀后的第k时刻的第一接收信号，s^j(k)为m序列s循环右移j位后的第k时刻的序列，sⁱ(k)为m序列s循环右移i位后的第k时刻的序列。⑦ Then calculate the first received signal after removing the cyclic prefix

The cross-correlation matrix C of the m-sequence s ⁱ and the autocorrelation matrix C _P of each training sequence s after cyclically shifting right by i bits with the m-sequence s, C=[C(i, j)], C(i, j) is The first received signal after removing the cyclic prefix

The normalized cross-correlation coefficient of the m-sequence s ⁱ after the m-sequence s is cyclically shifted right by i, $C(i,j)=(1/L_P)\underset{k=0}{\overset{L_P-1}{\mathrm{\&Sigma;}}}\tilde{r}\left(k\right){\mathrm{the\; s}}^i\left(k\right),$ C _P = [C _P (i, j)], C _P (i, j) is the m-sequence s j after m-sequence s is cyclically shifted to the right by ^j bits and the m-sequence s i after m-sequence s is cyclically shifted to the right by ⁱ The normalized autocorrelation coefficient of , $\begin{array}{c}{C}_P(i,j)=(1/L_P)\underset{k=0}{\overset{L_P-1}{\mathrm{\&Sigma;}}}{\mathrm{the\; s}}^j\left(k\right){\mathrm{the\; s}}^i\left(k\right)\\ =\left\{\begin{array}{cc}1,& i=j\\ -1/L_P,& i\&NotEqual;j\end{array}\right.\end{array},$ Wherein, i=0, 1, ..., L _p , j = 0, 1, ..., L _p , k = 0, 1, ..., L _p +L _c -1,

is the first received signal at the kth moment after removing the cyclic prefix, s ^j (k) is the sequence at the kth moment after the m-sequence s is cyclically shifted right by j bits, s ⁱ (k) is the m-sequence s cyclically shifted right by i The sequence of the kth moment after the bit.

与m序列s循环右移i位后的m序列sⁱ的互相关矩阵C和各个训练序列s的自相关矩阵C_P，计算信道的冲激响应估计值

$\tilde{h}=C_p^{-1}C,$ C_p ^-1表示各个训练序列s的自相关矩阵C_P的逆矩阵。在该步骤中，在计算信道的冲激响应估计值

之前先根据自相关矩阵C_P的对角占优性，将自相关矩阵C_P分解为第一矩阵和第二矩阵之和，将第一矩阵记为D，将第二矩阵记为E，则有C_P＝D+E，，在第一矩阵D和第二矩阵E满足||D^-1E||＜1时，计算自相关矩阵C_P的逆矩阵C_p ^-1， $C_p^{-1}=(I-D^{-1}E+{\left(D^{-1}E\right)}^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(-1)}^m{\left(D^{-1}E\right)}^m+\&CenterDot;\&CenterDot;\&CenterDot;)D^{-1},$ 其中，符号“||||”为范数符号，I为单位矩阵，D^-1为第一矩阵D的逆矩阵，m＝1，2，…，∞；若仅考虑C_p ^-1的一阶近似值，则根据 $C_p^{-1}=(I-D^{-1}E+{\left(D^{-1}E\right)}^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(-1)}^m{\left(D^{-1}E\right)}^m+\&CenterDot;\&CenterDot;\&CenterDot;)D^{-1}$ 计算C_p ^-1的一阶近似值， $C_p^{-1}\&ap;(I-D^{-1}E)D^{-1}\&ap;D^{-1}-D^{-1}E{D}^{-1},$ 最后利用 $C_p^{-1}\&ap;D^{-1}-D^{-1}E{D}^{-1}$ 计算信道的冲激响应估计值

$\begin{array}{c}\tilde{h}=C_p^{-1}C\\ =(D^{-1}-D^{-1}E{D}^{-1})C\end{array}.$ ⑧ Then according to the first received signal after removing the cyclic prefix

The cross-correlation matrix C of m-sequence s ⁱ and the autocorrelation matrix C _P of each training sequence s after cyclically shifting right by i bits with m-sequence s calculate the estimated value of the impulse response of the channel

$\tilde{h}=C_p^{-1}C,$ C _p ⁻¹ represents the inverse matrix of the autocorrelation matrix C _P of each training sequence s. In this step, when calculating the impulse response estimate of the channel

According to the diagonal dominance of the autocorrelation matrix C _P , the autocorrelation matrix C _P is decomposed into the sum of the first matrix and the second matrix, the first matrix is recorded as D, and the second matrix is recorded as E, then There is C _P =D+E, when the first matrix D and the second matrix E satisfy ||D ^-1 E||<1, the inverse matrix C _p ^-1 of the autocorrelation matrix C _P is calculated, $C_p^{-1}=(I-{\mathrm{D.}}^{-1}\mathrm{E.}+{\left({\mathrm{D.}}^{-1}\mathrm{E.}\right)}^2+\&Center\; Dot;\&CenterDot;\&Center\; Dot;+{(-1)}^m{\left({\mathrm{D.}}^{-1}\mathrm{E.}\right)}^m+\&CenterDot;\&CenterDot;\&CenterDot;){\mathrm{D.}}^{-1},$ Among them, the symbol "||||" is the norm symbol, I is the identity matrix, D ^-1 is the inverse matrix of the first matrix D, m=1, 2, ..., ∞; if only one of C _p ^-1 is considered Order approximation, then according to $C_p^{-1}=(I-{\mathrm{D.}}^{-1}\mathrm{E.}+{\left({\mathrm{D.}}^{-1}\mathrm{E.}\right)}^2+\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;+{(-1)}^m{\left({\mathrm{D.}}^{-1}\mathrm{E.}\right)}^m+\&Center\; Dot;\&CenterDot;\&CenterDot;){\mathrm{D.}}^{-1}$ Compute a first-order approximation of _Cp ^-1 , $C_p^{-1}\&ap;(I-{\mathrm{D.}}^{-1}\mathrm{E.}){\mathrm{D.}}^{-1}\&ap;{\mathrm{D.}}^{-1}-{\mathrm{D.}}^{-1}\mathrm{E.}{\mathrm{D.}}^{-1},$ last use $C_p^{-1}\&ap;{\mathrm{D.}}^{-1}-{\mathrm{D.}}^{-1}\mathrm{E.}{\mathrm{D.}}^{-1}$ Calculate the impulse response estimate for the channel

$\begin{array}{c}\tilde{h}=C_p^{-1}C\\ =({\mathrm{D.}}^{-1}-{\mathrm{D.}}^{-1}\mathrm{E.}{\mathrm{D.}}^{-1})C\end{array}.$

In order to reduce the computational complexity, the present invention proposes two fast approximation methods for solving the C _P inverse matrix: a diagonal decomposition method and a tridiagonal decomposition method.

L_P为在发送端插入的训练序列的长度；由于自相关矩阵C_P的对角占优性， $\left|\right|D_1^{-1}{E}_1\left|\right|<1,$ 因此C_P ^-1有下列展开式： $C_p^{-1}=(I-D_1^{-1}{E}_1+{\left(D_1^{-1}{E}_1\right)}^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(-1)}^m{\left(D_1^{-1}{E}_1\right)}^m+\&CenterDot;\&CenterDot;\&CenterDot;)D_1^{-1},$ 其中，||||为范数符号，(D₁ ^-1E₁)^m为D₁ ^-1E₁的m次方，I为单位矩阵，D₁ ^-1为对角矩阵D₁的逆矩阵，m＝1，2，…，∞；根据C_P ^-1的展开式得到C_P ^-1的一阶近似值为 $C_p^{-1}\&ap;D_1^{-1}-D_1^{-1}{E}_1{D}_1^{-1},$ 从 $C_p^{-1}\&ap;D_1^{-1}-D_1^{-1}{E}_1{D}_1^{-1}$ 可以看出，采用一对角分解方法，仅涉及对角矩阵的求逆，对自相关矩阵C_P的系数进行归一化处理，归一化处理后对角矩阵D₁为一单位矩阵I，因此C_P ^-1的一阶近似值为 $C_p^{-1}=I-E_1,$ 从 $C_p^{-1}=I-E_1$ 可以得出计算C_P ^-1不需要求逆的过程，计算复杂度大大降低，而该方法性能的好坏完全依赖于自相关矩阵C_P的对角占优性。Diagonal decomposition method: Decompose the autocorrelation matrix C _P into a diagonal matrix composed of diagonal elements of the autocorrelation matrix C _P and an off-diagonal matrix composed of off-diagonal elements of the autocorrelation matrix C _P and, record the diagonal matrix as D ₁ , and the non-diagonal matrix as E ₁ , then C _P =D ₁ +E ₁ , where,

L _P is the length of the training sequence inserted at the sending end; due to the diagonal dominance of the autocorrelation matrix C _P , $\left|\right|{\mathrm{D.}}_1^{-1}{\mathrm{E.}}_1\left|\right|<1,$ So C _P ^-1 has the following expansion: $C_p^{-1}=(I-{\mathrm{D.}}_1^{-1}{\mathrm{E.}}_1+{\left({\mathrm{D.}}_1^{-1}{\mathrm{E.}}_1\right)}^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(-1)}^m{\left({\mathrm{D.}}_1^{-1}{\mathrm{E.}}_1\right)}^m+\&Center\; Dot;\&CenterDot;\&CenterDot;){\mathrm{D.}}_1^{-1},$ Among them, |||| is the norm symbol, (D ₁ ^-1 E ₁ ) ^m is the m power of D ₁ ^-1 E ₁ , I is the identity matrix, and D ₁ ^-1 is the inverse matrix of the diagonal matrix D ₁ , m=1, 2,..., ∞; according to the expansion of C _P ^-1 , the first-order approximation of C _P ^-1 is $C_p^{-1}\&ap;{\mathrm{D.}}_1^{-1}-{\mathrm{D.}}_1^{-1}{\mathrm{E.}}_1{\mathrm{D.}}_1^{-1},$ from $C_p^{-1}\&ap;{\mathrm{D.}}_1^{-1}-{\mathrm{D.}}_1^{-1}{\mathrm{E.}}_1{\mathrm{D.}}_1^{-1}$ It can be seen that the use of a pair of diagonal decomposition method only involves the inversion of the diagonal matrix, and the coefficients of the autocorrelation matrix C _P are normalized. After normalization, the diagonal matrix D ₁ is an identity matrix I, So a first order approximation of C _P ^-1 is $C_p^{-1}=I-{\mathrm{E.}}_1,$ from $C_p^{-1}=I-{\mathrm{E.}}_1$ It can be concluded that the calculation of C _P ^-1 does not require an inversion process, and the computational complexity is greatly reduced, and the performance of this method depends entirely on the diagonal dominance of the autocorrelation matrix C _P.

L_P为在发送端插入的训练序列的长度；类似一对角分解方法，由于自相关矩阵C_P的对角占优性， $\left|\right|D_3^{-1}{E}_3\left|\right|<1,$ 因此C_p ^-1有下列展开式： $C_p^{-1}=(I-D_3^{-1}{E}_3+{\left(D_3^{-1}{E}_3\right)}^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(-1)}^m{\left(D_3^{-1}{E}_3\right)}^m+\&CenterDot;\&CenterDot;\&CenterDot;)D_3^{-1},$ 其中，||||为范数符号，(D₃ ^-1E₃)^m为D₃ ^-1E₃的m次方，I为单位矩阵，D₃ ^-1为三对角矩阵D₃的逆矩阵，m＝1，2，…，∞；根据C_P ^-1的展开式得到C_p ^-1的一阶近似值可以表示 $C_p^{-1}\&ap;D_3^{-1}-D_3^{-1}{E}_3{D}_3^{-1};$ 将三对角矩阵D₃分解为由自相关矩阵C_P的对角线元素组成的对角矩阵和由自相关矩阵C_P的对角线元素为0的二对角元素组成的二对角矩阵之和，将对角矩阵记为D₁，将二对角矩阵记为D₂，则有D₃＝D₁+D₂，其中，

计算三对角矩阵D₃的逆矩阵D₃ ^-1， $D_3^{-1}=(I-D_1^{-1}{D}_2+{\left(D_1^{-1}{D}_2\right)}^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(-1)}^m{\left(D_1^{-1}{D}_2\right)}^m+\&CenterDot;\&CenterDot;\&CenterDot;)D_1^{-1}$ ，其中，I为单位矩阵，D₁ ^-1为对角矩阵D₁的逆矩阵，m＝1，2，…，∞；然后根据 $D_3^{-1}=(I-D_1^{-1}{D}_2+{\left(D_1^{-1}{D}_2\right)}^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(-1)}^m{\left(D_1^{-1}{D}_2\right)}^m+\&CenterDot;\&CenterDot;\&CenterDot;)D_1^{-1}$ 计算D₃ ^-1的一阶近似值， $D_3^{-1}\&ap;(I-D_1^{-1}{D}_2)D_1^{-1};$ 对自相关矩阵C_P的系数进行归一化处理，归一化处理后对角矩阵D₁为单位矩阵I，根据 $D_3^{-1}\&ap;(I-D_1^{-1}{D}_2)D_1^{-1}$ 得到 $D_3^{-1}=I-D_2;$ 再根据 $C_p^{-1}\&ap;D_3^{-1}-D_3^{-1}{E}_3{D}_3^{-1}$ 和 $D_3^{-1}=I-D_2,$ 得到 $C_p^{-1}\&ap;(I-D_2)-(I-D_2)E_3(I-D_2),$ 可知三对角分解方法计算C_P ^-1同样也可以不需要求逆的过程，计算复杂度大大降低。Tridiagonal decomposition method: Decompose _the autocorrelation matrix C _P into a tridiagonal matrix composed of the tridiagonal elements of the autocorrelation matrix C _P and a non- The sum of tridiagonal matrices, the tridiagonal matrix is recorded as D ₃ , and the non-tridiagonal matrix is recorded as E ₃ , then C _P =D ₃ +E ₃ , where,

L _P is the length of the training sequence inserted at the sending end; similar to the diagonal decomposition method, due to the diagonal dominance of the autocorrelation matrix C _P , $\left|\right|{\mathrm{D.}}_3^{-1}{\mathrm{E.}}_3\left|\right|<1,$ Therefore C _p ^-1 has the following expansion: $C_p^{-1}=(I-{\mathrm{D.}}_3^{-1}{\mathrm{E.}}_3+{\left({\mathrm{D.}}_3^{-1}{\mathrm{E.}}_3\right)}^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(-1)}^m{\left({\mathrm{D.}}_3^{-1}{\mathrm{E.}}_3\right)}^m+\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;){\mathrm{D.}}_3^{-1},$ Among them, |||| is the norm symbol, (D ₃ ^-1 E ₃ ) ^m is the m power of D ₃ ^-1 E ₃ , I is the identity matrix, and D ₃ ^-1 is the inverse of the tridiagonal matrix D ₃ Matrix, m=1, 2, ..., ∞; according to the expansion of C _P ^-1 , the first-order approximation of C _p ^-1 can be expressed $C_p^{-1}\&ap;{\mathrm{D.}}_3^{-1}-{\mathrm{D.}}_3^{-1}{\mathrm{E.}}_3{\mathrm{D.}}_3^{-1};$ Decompose the tridiagonal matrix _D3 into a diagonal matrix consisting of the diagonal elements of the autocorrelation matrix C _P and a didiagonal matrix consisting of the didiagonal elements of the autocorrelation matrix C _P whose diagonal elements are 0 sum, the diagonal matrix is recorded as D ₁ , and the di-diagonal matrix is recorded as D ₂ , then there is D ₃ =D ₁ +D ₂ , where,

Compute the inverse matrix D ₃ ^-1 of the tridiagonal matrix D ₃ , ${\mathrm{D.}}_3^{-1}=(I-{\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2+{\left({\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2\right)}^2+\&Center\; Dot;\&Center\; Dot;\&CenterDot;+{(-1)}^m{\left({\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2\right)}^m+\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;){\mathrm{D.}}_1^{-1}$ , where I is the identity matrix, D ₁ ^-1 is the inverse matrix of the diagonal matrix D ₁ , m=1, 2,..., ∞; then according to ${\mathrm{D.}}_3^{-1}=(I-{\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2+{\left({\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2\right)}^2+\&Center\; Dot;\&CenterDot;\&CenterDot;+{(-1)}^m{\left({\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2\right)}^m+\&CenterDot;\&CenterDot;\&CenterDot;){\mathrm{D.}}_1^{-1}$ Compute a first-order approximation ^of _D3-1 , ${\mathrm{D.}}_3^{-1}\&ap;(I-{\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2){\mathrm{D.}}_1^{-1};$ The coefficients of the autocorrelation matrix C _P are normalized, and after normalization, the diagonal matrix D ₁ is the identity matrix I, according to ${\mathrm{D.}}_3^{-1}\&ap;(I-{\mathrm{D.}}_1^{-1}{\mathrm{D.}}_2){\mathrm{D.}}_1^{-1}$ get ${\mathrm{D.}}_3^{-1}=I-{\mathrm{D.}}_2;$ Then according to $C_p^{-1}\&ap;{\mathrm{D.}}_3^{-1}-{\mathrm{D.}}_3^{-1}{\mathrm{E.}}_3{\mathrm{D.}}_3^{-1}$ and ${\mathrm{D.}}_3^{-1}=I-{\mathrm{D.}}_2,$ get $C_p^{-1}\&ap;(I-{\mathrm{D.}}_2)-(I-{\mathrm{D.}}_2){\mathrm{E.}}_3(I-{\mathrm{D.}}_2),$ It can be seen that the calculation of C _P ^-1 by the tridiagonal decomposition method also does not require the process of inversion, and the calculation complexity is greatly reduced.

Table 1 has listed the size of computational complexity of the existing m-sequence-based time-domain channel estimation method (referred to as the direct inversion method in Table 1), the diagonal decomposition method of the present invention and the tri-diagonal decomposition method .

Table 1 Computational complexity comparison table

Direct inversion method Diagonal Decomposition Method Tridiagonal Decomposition Method o(L _p ³ ) o(L _p ² ) o(L _p ² )

It can be seen from Table 1 that the processing method of the present invention using the pair-diagonal decomposition and the tri-diagonal decomposition can greatly reduce the computational complexity of the existing direct inversion method.

The present invention utilizes the diagonal dominance characteristic of the autocorrelation matrix of the special training sequence, that is, the m-sequence. Firstly, the autocorrelation matrix of the m-sequence is decomposed into a pair of angles and tri-diagonals, and then the approximation of the first-order inverse matrix is adopted. method, compared with the traditional time-domain channel estimation method, the calculation amount of the diagonal decomposition method and the tri-diagonal decomposition method proposed by the present invention is reduced by an order of magnitude, but the performance is close to the traditional time-domain channel estimation value. The computer simulation results verify the effectiveness of the present invention.

A training sequence is inserted every 4 OFDM symbols, and m-sequences of four different lengths L _P =15, 31, 63, and 127 are respectively inserted. Figure 2 compares the curves of bit error rate versus signal-to-noise ratio between the conventional time-domain channel estimation method (ie, the direct inversion method) and the frequency-domain LS channel estimation method corresponding to different lengths of m-sequences. It is easy to know from Figure 2 that under the same SNR condition, the shorter the length of the m-sequence, the higher the bit error rate and the worse the performance of the conventional time-domain channel estimation method, and the longer the length of the m-sequence, the lower the bit error rate , the better the performance. The purpose of the simulation in Fig. 2 is to select the appropriate length of the training sequence. However, considering the amount of computation and system performance, the pilot length should not be too long in practice. Since the performance of the m-sequence lengths L _P = 31 and L _P = 64 are similar, it should be considered that the m-sequence with the length L _P = 31 is more appropriate in practice.

Fig. 3 compares the change curves of bit error rate and signal-to-noise ratio of conventional time-domain estimation method, pair-diagonal decomposition method, tri-diagonal decomposition method, and frequency-domain LS channel estimation method when m-sequence length L _P =31. It can be seen from Fig. 3 that the performance of the pair-diagonal decomposition and tri-diagonal decomposition methods is very similar to the conventional time-domain estimation method, but the computational complexity of the first two methods is reduced by an order of magnitude.

In order to further compare the performance of the pair-diagonal decomposition and tri-diagonal decomposition methods, as well as the performance difference with the conventional time-domain estimation method, Figure 4 shows the three methods in the case of poor m-sequence autocorrelation characteristics ( Performance simulation of m sequence length L _P =15). It can be seen from FIG. 4 that the performances of the diagonal decomposition methods proposed by the present invention are slightly lowered, but the performance of the three-diagonal decomposition method is obviously better than that of the pair-diagonal decomposition method.

Claims (1)

1. A channel estimation method of multi-band OFDM ultra-wideband system, comprising the following steps: 1. at the transmitting end, first carry out quadrature phase shift modulation processing to the input data signal to obtain the modulated signal; 2. then modulate The signal undergoes serial-to-parallel conversion, inverse Fourier transform, and parallel-to-serial conversion in sequence to form a plurality of OFDM symbols; (3) insert a length L _P into the formed plurality of OFDM symbols every set number of OFDM symbols m-sequence s, use m-sequence s as a training sequence, and add a cyclic prefix of length L _C before the training sequence according to the channel characteristics, and obtain the training sequence after adding the cyclic prefix, denoted by x, x=[x(0 ), x(1),...x(L _P +L _C -1)]; ④Finally, the training sequence x after adding the cyclic prefix and the formed OFDM symbols are processed by carrier modulation and then transmitted to the receiving end through the ultra-wideband channel , the training sequence x and OFDM symbols after the additional cyclic prefix are affected by channel fading and Gaussian white noise during transmission; ⑤ At the receiving end, define the additional cyclic prefix received by the receiving end after being affected by channel fading and Gaussian white noise The training sequence x of is the first received signal, define the OFDM symbols received by the receiving end after being affected by channel fading and Gaussian white noise as the second received signal, and express the first received signal with a tapped delay line model as

Wherein, k=0, 1,..., _Lp + _Lc -1, r(k) is the first received signal at the kth moment, h represents a matrix vector composed of coefficients of each multipath of the channel,

h _t is the tth multipath coefficient of the channel, h should satisfy the condition: {h _t = 0|L≤t≤L _C -1}, L is the order of the channel, x is the training sequence after adding the cyclic prefix, x(kt) is the training sequence after the additional cyclic prefix at the kt moment, n is Gaussian white noise, and n(k) is the Gaussian white noise at the kth moment; ⑥ First, the first received signal r(k) is decarrier modulation, and perform decyclic prefix processing on the first received signal after decarrier modulation processing to obtain

Among them, k=0, 1, ..., L _p +L _c -1,

is the first received signal at the kth moment after the cyclic prefix is removed, and h represents a matrix vector composed of each multipath coefficient of the channel,

h _j is the jth multipath coefficient of the channel, h should satisfy the condition: {h _j ＝0|L≤j≤L _C -1}, L is the order of the channel, n is Gaussian white noise, n(k) is the Gaussian white noise at the k-th moment, s ^j is the m-sequence after the m-sequence s is cyclically shifted to the right by j bits, s ^j (k) is the sequence at the k-th moment after the m-sequence s is cyclically shifted to the right by j bits; ⑦ Then calculate The first received signal after removing the cyclic prefix

The cross-correlation matrix C of the m-sequence s ⁱ and the autocorrelation matrix C _P of each training sequence s after cyclically shifting right by i bits with the m-sequence s, C=[C(i, j)], C(i, j) is The first received signal after removing the cyclic prefix

The normalized cross-correlation coefficient of the m-sequence s ⁱ after the m-sequence s is cyclically shifted right by i, C _P = [C _P (i, j)], C _P (i, j) is the m-sequence s j after m-sequence s is cyclically shifted to the right by ^j bits and the m-sequence s i after m-sequence s is cyclically shifted to the right by ⁱ The normalized autocorrelation coefficient of ,

Wherein, i=0, 1, ..., L _p , j = 0, 1, ..., L _p , k = 0, 1, ..., L _p +L _c -1,

is the first received signal at the kth moment after removing the cyclic prefix, s ^j (k) is the sequence at the kth moment after the m-sequence s is cyclically shifted right by j bits, s ⁱ (k) is the m-sequence s cyclically shifted right by i The sequence at the kth moment after the bit; ⑧ according to the first received signal after the cyclic prefix

The cross-correlation matrix C of m-sequence s ⁱ and the autocorrelation matrix C _P of each training sequence s after cyclically shifting right by i bits with m-sequence s calculate the estimated value of the impulse response of the channel

in,

Be the inverse matrix of autocorrelation matrix C _P ; It is characterized in that according to the diagonal dominance of described autocorrelation matrix C _P , described autocorrelation matrix C _P is decomposed into the sum of the first matrix and the second matrix, The first matrix is marked as D, the second matrix is marked as E, C _P =D+E, and the first matrix D and the second matrix E satisfy ||D ^{- 1} When E||<1, calculate the inverse matrix of the autocorrelation matrix C _P

Wherein, the symbol "|| ||" is a norm symbol, I is an identity matrix, D ^-1 is the inverse matrix of the first matrix D, m=1, 2, ..., ∞; then according to

calculate

A first-order approximation of , $C_p^{-1}\&ap;(I-{\mathrm{D.}}^{-1}\mathrm{E.}){\mathrm{D.}}^{-1}\&ap;{\mathrm{D.}}^{-1}-{\mathrm{D.}}^{-1}{\mathrm{ED}}^{-1};$ The first matrix D is a diagonal matrix composed of the diagonal elements of the autocorrelation matrix C _P , and the second matrix E is a diagonal matrix composed of the off-diagonal elements of the autocorrelation matrix C _P An off-diagonal matrix composed of elements, the diagonal matrix is denoted as D ₁ , and the off-diagonal matrix is denoted as E ₁ , to obtain

The coefficient of described autocorrelation matrix _CP is carried out normalization process, described diagonal matrix D ₁ after normalization process is a identity matrix I; According to

get

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