CN101789919A

CN101789919A - Channel parameter estimation method based on classical fractional Fourier transformation

Info

Publication number: CN101789919A
Application number: CN 201010132111
Authority: CN
Inventors: 沙学军; 唐珣; 吴少川; 迟永钢; 吴宣利; 白旭; 高玉龙
Original assignee: Harbin Institute of Technology Shenzhen
Current assignee: Harbin Institute of Technology Shenzhen
Priority date: 2010-03-25
Filing date: 2010-03-25
Publication date: 2010-07-28

Abstract

A channel parameter estimation method based on classical fractional Fourier transform, relating to channel parameter estimation methods in the field of wireless communication. It solves the problem that the existing channel estimation cannot well meet the estimation requirements of the rapidly changing wireless channel environment. The present invention uses the addition of two chip signals with the same center frequency and opposite modulation frequencies as the detection signal, and what the receiving end obtains is a combination of detection signals from different transmission paths, and performs a fractional Fourier transform on the received signal to detect The peak position on the magnitude spectrum in the fractional domain and the magnitude and phase values at the peak are used to estimate the magnitude, phase, time delay and Doppler shift of each path. The present invention is applicable to channel parameter estimation.

Description

A Channel Parameter Estimation Method Based on Classical Fractional Fourier Transform

技术领域technical field

本发明涉及无线通信领域中的信道参数估计方法。The invention relates to a channel parameter estimation method in the field of wireless communication.

背景技术Background technique

无线电波信号在传播过程中遇到建筑物、车辆以及其它障碍物，产生波的反射、衍射和散射，接收到的信号是来自不同路径信号的叠加，通常是一组无限多的被衰减、延迟、相移的传输信号的总和，相对于原发射信号产生了时间衰落和频率选择性衰落，极大地影响了信号的正确接收。为降低信道对信号的失真影响，通常使用均衡技术，而准确的信道估计是均衡技术有效应用的前提。已有的信道估计方法或者需要信道的先验知识或统计特性，或者需要复杂的盲计算过程，仍不能很好地满足快速变化的无线信道环境的估计要求。The radio wave signal encounters buildings, vehicles, and other obstacles during the propagation process, resulting in wave reflection, diffraction, and scattering. The received signal is the superposition of signals from different paths, usually a set of infinitely attenuated, delayed , The sum of the phase-shifted transmission signals produces time fading and frequency selective fading relative to the original transmitted signal, which greatly affects the correct reception of the signal. In order to reduce the distortion effect of the channel on the signal, an equalization technique is usually used, and accurate channel estimation is a prerequisite for the effective application of the equalization technique. Existing channel estimation methods either require prior knowledge or statistical characteristics of the channel, or require a complex blind calculation process, which still cannot well meet the estimation requirements of the rapidly changing wireless channel environment.

发明内容Contents of the invention

本发明是为了解决现有的信道估计不能很好地满足快速变化的无线信道环境的估计要求的问题，从而提出一种基于经典分数傅立叶变换的信道参数估计方法。The present invention aims to solve the problem that the existing channel estimation cannot well meet the estimation requirements of the fast-changing wireless channel environment, and thus proposes a channel parameter estimation method based on classical fractional Fourier transform.

一种基于经典分数傅立叶变换的信道参数估计方法，它由以下步骤实现：A channel parameter estimation method based on classical fractional Fourier transform, which is realized by the following steps:

步骤一、将中心频率相同、调频率互为相反数的两段切普信号相加之后作为信道探测信号，并将所述信道探测信号从发射端发射；所述信道探测信号的表达式为s(t)＝cos(2πf₀t+πkt²)+cos(2πf₀t-πkt²)；所述信道探测信号s(t)分解表示为4个复切普信号加和的形式，即：Step 1, add the two sections of chip signals with the same center frequency and the opposite number of modulation frequencies as the channel detection signal, and transmit the channel detection signal from the transmitter; the expression of the channel detection signal is s (t)=cos(2πf ₀ t+πkt ² )+cos(2πf ₀ t-πkt ² ); the channel detection signal s(t) is decomposed and expressed as the sum of 4 complex chop signals, namely:

$s the s ((t t)) = = \frac{11}{22} exp exp [[j j ((22 π π {f f}_{00} t t + + πk πk {t t}^{22}))]] + + \frac{11}{22} exp exp [[- - j j ((22 π π {f f}_{00} t t + + πk πk {t t}^{22}))]]$

$+ + \frac{11}{22} exp exp [[j j ((22 π π {f f}_{00} t t - - πk πk {t t}^{22}))]] + + \frac{11}{22} exp exp [[- - j j ((22 π π {f f}_{00} t t - - πk πk {t t}^{22}))]]$

式中-T/2≤t≤T/2，T为信道探测信号s(t)的持续时间；Where -T/2≤t≤T/2, T is the duration of the channel sounding signal s(t);

步骤二、接收端接收发射端发射的信道探测信号，记为r(t)，并对信道探测信号r(t)进行变换阶数为p＝acot(-k)/(π/2)的分数傅立叶变换，获得信道探测信号的分数域幅度谱，所述分数域幅度谱上共包括i组幅度谱曲线，每一组幅度谱曲线均对应一条路径的信道探测信号；所述每组幅度谱曲线上均包含两个峰值，所述两个峰值分别位于分数域坐标中心的两侧；Step 2, the receiving end receives the channel sounding signal transmitted by the transmitting end, denoted as r(t), and transforms the channel sounding signal r(t) into a fraction of p=acot(-k)/(π/2) Fourier transform to obtain the fractional domain amplitude spectrum of the channel sounding signal, the fractional domain amplitude spectrum includes i groups of amplitude spectrum curves, each group of amplitude spectrum curves corresponds to the channel sounding signal of a path; each group of amplitude spectrum curves Both contain two peaks, and the two peaks are respectively located on both sides of the coordinate center of the fraction domain;

步骤三、检测步骤二所述的i组幅度谱曲线的两个峰值，获得每组幅度谱曲线的两个峰值的位置坐标

幅度值和相位值

所述每组幅度谱曲线的两个峰值分别对应两个复切普信号exp[j(2πf₀t+πkt²)]和exp[-j(2πf₀t-πkt²)]；Step 3, detect the two peaks of the i group of amplitude spectrum curves described in step 2, and obtain the position coordinates of the two peaks of each group of amplitude spectrum curves

amplitude value and phase value

The two peaks of each group of amplitude spectrum curves correspond to two complex chop signals exp[j(2πf ₀ t+πkt ² )] and exp[-j(2πf ₀ t-πkt ² )] respectively;

步骤四、根据步骤三获得的第i组幅度谱曲线的两个峰值的位置坐标

幅度值

和相位值

估计接收到的第i条路径上的两个复切普信号exp[j(2πf₀t+πkt²)]和exp[-j(2πf₀t-πkt²)]的中心频率

幅度

和相位 Step 4, according to the position coordinates of the two peaks of the i-th group of amplitude spectrum curves obtained in step 3

amplitude value

and phase value

Estimate the center frequencies of the received two complex chip signals exp[j(2πf ₀ t+πkt ² )] and exp[-j(2πf ₀ t-πkt ² )] on the i-th path

amplitude

and phase

步骤五、根据步骤四获得的第i条路径上的两个复切普信号exp[j(2πf₀t+πkt²)]和exp[-j(2πf₀t-πkt²)]的中心频率

幅度

和相位获得第i条路径的时延

的估计值、多普勒频移

的估计值、相位的估计值和幅度

的估计值；Step 5. According to the center frequency of the two complex chop signals exp[j(2πf ₀ t+πkt ² )] and exp[-j(2πf ₀ t-πkt ² )] on the i-th path obtained in step 4

amplitude

and phase Get the delay of the i-th path

Estimated value of Doppler frequency shift

Estimated value, phase The estimated value and magnitude of

estimated value of

所述f₀为信道探测信号中心频率；k为切普信号的调频率，α为分数傅立叶变换角；i为整数。The f ₀ is the center frequency of the channel detection signal; k is the modulation frequency of the chip signal, and α is the fractional Fourier transform angle; i is an integer.

步骤四中所述的根据步骤三获得的第i组幅度谱曲线的两个峰值的位置坐标幅度值

和相位值估计接收到的第i条路径上的两个复切普信号exp[j(2πf₀t+πkt²)]和exp[-j(2πf₀t-πkt²)]的中心频率

是根据公式：The position coordinates of the two peaks of the i-th group of amplitude spectrum curves obtained according to step 3 described in step 4 amplitude value

and phase value Estimate the center frequencies of the received two complex chip signals exp[j(2πf ₀ t+πkt ² )] and exp[-j(2πf ₀ t-πkt ² )] on the i-th path

is according to the formula:

${\overset{^^}{f f}}_{00} = = {\overset{^^}{u u}}_{p p} csc csc α α$

实现的。Achieved.

步骤四中所述的根据步骤三获得的第i组幅度谱曲线的两个峰值的位置坐标

幅度值和相位值

估计接收到的第i条路径上的两个复切普信号exp[j(2πf₀t+πkt²)]和exp[-j(2πf₀t-πkt²)]的幅度

是根据公式：The position coordinates of the two peaks of the i-th group of amplitude spectrum curves obtained according to step 3 described in step 4

amplitude value and phase value

Estimate the received amplitudes of the two complex chop signals exp[j(2πf ₀ t+πkt ² )] and exp[-j(2πf ₀ t-πkt ² )] on the i-th path

is according to the formula:

$\overset{^^}{a a} = = \frac{| | {f f}_{p p} (({\overset{^^}{u u}}_{p p})) | |}{T T / / \sqrt{| | sin sin α α | |}}$

实现的。Achieved.

幅度值

和相位值

估计接收到的第i条路径上的两个复切普信号exp[j(2πf₀t+πkt²)]和exp[-j(2πf₀t-πkt²)]的相位

amplitude value

and phase value

Estimate the phases of the received two complex chip signals exp[j(2πf ₀ t+πkt ² )] and exp[-j(2πf ₀ t-πkt ² )] on the i-th path

is according to the formula:

$\overset{^^}{φ φ} = = arg arg [[\frac{{f f}_{p p} (({\overset{^^}{u u}}_{p p}))}{{e e}^{j j ((\frac{α α}{22} + + \frac{π π}{44} + + π π {\overset{^^}{u u}}_{p p}^{22} cot cot α α))}}]]$

实现的。Achieved.

步骤五中所述根据步骤四获得的第i条路径上的两个复切普信号exp[j(2πf₀t+πkt²)]和exp[-j(2πf₀t-πkt²)]的中心频率

幅度

和相位获得第i条路径的时延

的估计值是通过公式：The center of the two complex chop signals exp[j(2πf ₀ t+πkt ² )] and exp[-j(2πf ₀ t-πkt ² )] on the i-th path obtained in step 5 according to step 4 frequency

amplitude

and phase Get the delay of the i-th path

The estimated value of is given by the formula:

${\overset{^^}{τ τ}}_{i i} = = \frac{{\overset{^^}{f f}}_{00 ((i i,, 11))} + + {\overset{^^}{f f}}_{00 ((i i,, 22))}}{- - 22 k k}$

实现的。Achieved.

幅度

和相位

获得第i条路径的多普勒频移

amplitude

and phase

Get the Doppler shift of the i-th path

The estimated value of is given by the formula:

$Δ Δ {\overset{^^}{f f}}_{i i} = = \frac{{\overset{^^}{f f}}_{00 ((i i,, 11))} - - {\overset{^^}{f f}}_{00 ((i i,, 22))}}{22} - - {f f}_{00}$

实现的。Achieved.

幅度

和相位

获得第i条路径的相位

amplitude

and phase

Get the phase of the i-th path

The estimated value of is given by the formula:

${\overset{^^}{φ φ}}_{i i} = = (({\overset{^^}{φ φ}}_{((i i,, 11))} - - {\overset{^^}{φ φ}}_{((i i,, 22))} + + 44 π π {f f}_{00} {\overset{^^}{τ τ}}_{i i})) / / 22$

实现的。Achieved.

步骤五中所述根据步骤四获得的第i条路径上的两个复切普信号exp[j(2πf₀t+πkt²)]和exp[-j(2πf₀t-πkt²)]的中心频率幅度

和相位

获得第i条路径的幅度

的估计值是通过公式：The center of the two complex chop signals exp[j(2πf ₀ t+πkt ² )] and exp[-j(2πf ₀ t-πkt ² )] on the i-th path obtained in step 5 according to step 4 frequency amplitude

and phase

Get the magnitude of the i-th path

The estimated value of is given by the formula:

${\overset{^^}{a a}}_{i i} = = (({\overset{^^}{a a}}_{((i i,, 11))} + + {\overset{^^}{a a}}_{((i i,, 22))})) / / 22$

实现的。Achieved.

本发明使用中心频率相同、调频率互为相反数的两个切普信号加和作为探测信号，接收端得到的是来自不同传输路径的探测信号的组合，对接收信号进行一次分数傅立叶变换，检测分数域幅度谱上的峰值位置及峰值处的幅度值和相位值估计各路径的幅度、相位、时延和多普勒频移，无需信道的先验知识、计算过程简单，很好地满足快速变化的无线信道环境的估计要求。The present invention uses the sum of two chip signals with the same center frequency and opposite modulation frequencies as the detection signal, and what the receiving end obtains is a combination of detection signals from different transmission paths, and performs a fractional Fourier transform on the received signal to detect Estimate the amplitude, phase, delay and Doppler frequency shift of each path based on the peak position on the amplitude spectrum in the fractional domain and the amplitude and phase values at the peak, without prior knowledge of the channel, and the calculation process is simple, which satisfies the fast Estimation requirements for changing wireless channel environments.

附图说明Description of drawings

图1是本发明的信道探测信号经两径信道作用后在分数域上的幅度谱。Fig. 1 is the amplitude spectrum in the fractional domain of the channel detection signal of the present invention after being acted on by a two-path channel.

具体实施方式Detailed ways

具体实施方式一、一种基于经典分数傅立叶变换的信道参数估计方法，它由以下步骤实现：The specific embodiment one, a kind of channel parameter estimation method based on classical fractional Fourier transform, it is realized by the following steps:

步骤三、检测步骤二所述的i组幅度谱曲线的两个峰值，获得每组幅度谱曲线的两个峰值的位置坐标幅度值

和相位值

所述每组幅度谱曲线的两个峰值分别对应两个复切普信号exp[j(2πf₀t+πkt²)]和exp[-j(2πf₀t-πkt²)]；Step 3, detect the two peaks of the i group of amplitude spectrum curves described in step 2, and obtain the position coordinates of the two peaks of each group of amplitude spectrum curves amplitude value

and phase value

步骤四、根据步骤三获得的第i组幅度谱曲线的两个峰值的位置坐标幅度值

幅度

和相位

Step 4, according to the position coordinates of the two peaks of the i-th group of amplitude spectrum curves obtained in step 3 amplitude value

amplitude

and phase

幅度和相位获得第i条路径的时延的估计值、多普勒频移

的估计值、相位

的估计值和幅度

amplitude and phase Get the delay of the i-th path Estimated value of Doppler frequency shift

Estimated value, phase

The estimated value and magnitude of

estimated value of

幅度值

和相位值

估计接收到的第i条路径上的两个复切普信号exp[j(2πf₀t+πkt²)]和exp[-j(2πf₀t-πkt²)]的中心频率是根据公式：The position coordinates of the two peaks of the i-th group of amplitude spectrum curves obtained according to step 3 described in step 4

amplitude value

and phase value

Estimate the center frequencies of the received two complex chip signals exp[j(2πf ₀ t+πkt ² )] and exp[-j(2πf ₀ t-πkt ² )] on the i-th path is according to the formula:

${\overset{^^}{f f}}_{00} = = {\overset{^^}{u u}}_{p p} csc csc α α$

实现的。Achieved.

幅度值

和相位值估计接收到的第i条路径上的两个复切普信号exp[j(2πf₀t+πkt²)]和exp[-j(2πf₀t-πkt²)]的幅度

amplitude value

and phase value Estimate the received amplitudes of the two complex chop signals exp[j(2πf ₀ t+πkt ² )] and exp[-j(2πf ₀ t-πkt ² )] on the i-th path

is according to the formula:

实现的。Achieved.

幅度值和相位值

估计接收到的第i条路径上的两个复切普信号exp[j(2πf₀t+πkt²)]和exp[-j(2πf₀t-πkt²)]的相位是根据公式：The position coordinates of the two peaks of the i-th group of amplitude spectrum curves obtained according to step 3 described in step 4

amplitude value and phase value

Estimate the phases of the received two complex chip signals exp[j(2πf ₀ t+πkt ² )] and exp[-j(2πf ₀ t-πkt ² )] on the i-th path is according to the formula:

实现的。Achieved.

幅度

和相位

获得第i条路径的时延

amplitude

and phase

Get the delay of the i-th path

The estimated value of is given by the formula:

实现的。Achieved.

幅度

和相位获得第i条路径的多普勒频移

amplitude

and phase Get the Doppler shift of the i-th path

The estimated value of is given by the formula:

实现的。Achieved.

幅度

和相位

获得第i条路径的相位的估计值是通过公式：The center of the two complex chop signals exp[j(2πf ₀ t+πkt ² )] and exp[-j(2πf ₀ t-πkt ² )] on the i-th path obtained in step 5 according to step 4 frequency

amplitude

and phase

Get the phase of the i-th path The estimated value of is given by the formula:

实现的。Achieved.

幅度和相位

获得第i条路径的幅度

amplitude and phase

Get the magnitude of the i-th path

The estimated value of is given by the formula:

实现的。Achieved.

步骤三中每条路径上的两个峰值中的复切普信号exp[j(2πf₀t+πkt²)]和复切普信号exp[-j(2πf₀t-πkt²)]受信道影响，这两个复切普信号的参数均已发生变化，但是其中心频率仍为一正一负。The complex chip signal exp[j(2πf ₀ t+πkt ² )] and the complex chip signal exp[-j(2πf ₀ t-πkt ² )] in the two peaks on each path in step 3 are affected by the channel , the parameters of the two complex chop signals have changed, but their center frequencies are still one positive and one negative.

分数傅立叶变换是一种广义的傅立叶变换，信号在分数阶傅立叶域上的表示，同时包含了信号在时域和频域的信息。经典分数傅立叶变换的积分形式定义为：Fractional Fourier transform is a generalized Fourier transform, which represents the signal in the fractional Fourier domain, and contains the information of the signal in the time domain and frequency domain. The integral form of the classical fractional Fourier transform is defined as:

${f f}_{p p} ((u u)) = = \{\begin{matrix} \sqrt{\frac{11 - - j j cot cot α α}{22 π π}} {&Integral; &Integral;}_{- - \infty \infty}^{+ + \infty \infty} {{f f ((t t)) \cdot &Center Dot; \\ exp exp [[j j ((\frac{{u u}^{22} + + {t t}^{22}}{22} cot cot α α - - ut out csc csc α α))]]}} dt dt,, α α &NotEqual; &NotEqual; qπ qπ \\ \begin{matrix} f f ((t t)),, & α α = = 22 qπ qπ \\ f f ((- - t t)),, & α α = = ((22 q q &PlusMinus; &PlusMinus; 11)) π π \end{matrix} \end{matrix}$

其中f(t)为信号的时域表达形式，f(t)的p阶分数傅立叶变换为f_p(u)，u为分数域坐标，α＝pπ/2为分数傅立叶变换角，p为变换阶数，q为任意整数。当α＝π/2时f_p(u)为普通的傅立叶变换。由于分数傅立叶变换是信号在一组正交的切普(chirp)基上的展开，因此分数傅立叶变换在某个分数阶傅立叶域中对给定的切普信号具有最好的能量聚集特性，即一个切普信号在适当的分数阶傅立叶变换域中将表现为一个冲击函数。复切普信号的表达式为：Where f(t) is the time-domain expression of the signal, the p-order fractional Fourier transform of f(t) is f _p (u), u is the coordinate in the fractional domain, α=pπ/2 is the fractional Fourier transform angle, and p is the transformation Order, q is any integer. When α=π/2, f _p (u) is an ordinary Fourier transform. Since the fractional Fourier transform is the expansion of the signal on a set of orthogonal chirp bases, the fractional Fourier transform has the best energy aggregation characteristics for a given chirp signal in a certain fractional Fourier domain, namely A chip signal will appear as an impulse function in the appropriate fractional Fourier transform domain. The expression of the complex chip signal is:

(-T/2≤t≤T/2)

参数

f₀、k、A分别表示切普信号的相位，中心频率，频率变化率和幅度。k与带宽B的关系为B＝kT，其中T为切普信号时域宽度。复切普信号的分数傅立叶变换表达式为parameter

f ₀ , k, and A represent the phase, center frequency, frequency change rate, and amplitude of the Chip signal, respectively. The relationship between k and the bandwidth B is B=kT, where T is the time domain width of the Chip signal. The fractional Fourier transform expression of the complex Chepp signal is

${f f}_{p p} ((u u)) = = A A {((11 - - j j cot cot α α))}^{\frac{11}{22}} {&Integral; &Integral;}_{- - T T / / 22}^{T T / / 22} exp exp [[jπ jπ (({t t}^{22} cot cot α α - - 22 ut out csc csc α α))]] exp exp ((jπu jπu {t t}^{22})) dt dt$

$= = \frac{A A}{{((sin sin α α))}^{\frac{11}{22}}} exp exp [[j j ((\frac{α α}{22} + + \frac{π π}{44} + + π π {u u}^{22} cot cot α α))]] {&Integral; &Integral;}_{- - T T / / 22}^{T T / / 22} exp exp [[jπ jπ {t t}^{22} ((cot cot α α + + k k))]] exp exp [[j j 22 πt πt (({f f}_{00} - - u u csc csc α α))]] dt dt$

可知，当k＝-cotα，f₀＝ucscα时，分数域出现峰值。It can be seen that when k=-cotα, f ₀ =ucscα, the peak appears in the fraction domain.

本发明使用中心频率相同、调频率互为相反数的两个切普信号加和作为探测信号，接收端得到的是来自不同传输路径的探测信号的组合，对接收信号进行一次分数傅立叶变换，检测分数域幅度谱上的峰值位置及峰值处的幅度值和相位值即可计算出各路径的幅度、相位、时延和多普勒频移。相对于传统信道参数估计方法，既不需要信道的先验知识和统计特性，也没有复杂的计算过程，且分数傅立叶算法可用快速傅立叶变换实现，系统复杂度低。The present invention uses the sum of two chip signals with the same center frequency and opposite modulation frequencies as the detection signal, and what the receiving end obtains is a combination of detection signals from different transmission paths, and performs a fractional Fourier transform on the received signal to detect The amplitude, phase, delay and Doppler frequency shift of each path can be calculated from the peak position on the amplitude spectrum in the fractional domain and the amplitude and phase values at the peak. Compared with the traditional channel parameter estimation method, neither prior knowledge and statistical characteristics of the channel are required, nor a complicated calculation process, and the fractional Fourier algorithm can be realized by fast Fourier transform, and the system complexity is low.

时变信道的冲击响应可以使用参数模型进行描述，如式(1)：The impulse response of a time-varying channel can be described using a parametric model, such as formula (1):

$h h ((t t,, τ τ)) = = {Σ Σ}_{i i = = 11}^{N N} {a a}_{i i} \cdot &Center Dot; {e e}^{j j {φ φ}_{i i}} \cdot &Center Dot; {e e}^{j j 22 πΔ πΔ {f f}_{i i} t t} \cdot &Center Dot; δ δ ((t t - - {τ τ}_{i i})) - - - - - - ((11))$

其中i是多径序号，N是多径总数，a_i，φ_i，Δf_i和τ_i分别是各路径的幅度、相位、多普勒频移和时延。假设发射信号为x(t)，则接收信号r(t)可表示为(2)：Where i is the multipath number, N is the total number of multipaths, a _i , φ _i , Δf _i and τ _i are the amplitude, phase, Doppler frequency shift and time delay of each path, respectively. Assuming that the transmitted signal is x(t), the received signal r(t) can be expressed as (2):

$r r ((t t)) = = {&Integral; &Integral;}_{- - \infty \infty}^{\infty \infty} h h ((t t,, τ τ)) x x ((t t - - τ τ)) dτ dτ + + n no ((t t))$

$= = {Σ Σ}_{i i = = 11}^{N N} {a a}_{i i} \cdot &Center Dot; {e e}^{j j {φ φ}_{i i}} \cdot &Center Dot; {e e}^{j j 22 πΔ πΔ {f f}_{i i} t t} \cdot &Center Dot; x x ((t t - - {τ τ}_{i i})) + + n no ((t t)) - - - - - - ((22))$

其中n(t)是加性高斯白噪声。本发明使用的信道探测信号为中心频率相同、调频率互为相反数的两个切普信号加和，表达式如(3)：where n(t) is additive white Gaussian noise. The channel sounding signal used by the present invention is the sum of two cutting signals whose central frequency is the same and the modulation frequency is the opposite number to each other, and the expression is as (3):

s(t)＝cos(2πf₀t+πkt²)+cos(2πf₀t-πkt²)(-T/2≤t≤T/2) (3)s(t)＝cos(2πf ₀ t+πkt ² )+cos(2πf ₀ t-πkt ² )(-T/2≤t≤T/2) (3)

s(t)可以分解表示为4个复切普信号加和(4)s(t) can be decomposed and expressed as the sum of 4 complex chip signals (4)

$+ + \frac{11}{22} exp exp [[j j ((22 π π {f f}_{00} t t - - πk πk {t t}^{22}))]] + + \frac{11}{22} exp exp [[- - j j ((22 π π {f f}_{00} t t - - πk πk {t t}^{22}))]],, ((- - T T / / 22 \leq \leq t t \leq \leq T T / / 22)) - - - - - - ((44))$

其中具有+k调频率的复切普信号有两项，分别为exp[j(2πf₀t+πkt²)]和exp[-j(2πf₀t-πkt²)]；具有-k调频率的复切普信号有两项，分别为exp[-j(2πf₀t+πkt²)]和exp[j(2πf₀t-πkt²)]。根据分数傅立叶变换特性，当变换阶数p＝acot(-k)/(π/2)时，具有+k调频率的复切普信号将在分数域上产生能量聚集，即exp[j(2πf₀t+πkt²)]和exp[-j(2πf₀t-πkt²)]将产生峰值，且由于这两个复切普信号的中心频率不同，分别为±f₀，所以两个峰值在分数域分别位于中心两侧；此时具有-k调频率的复切普信号不会产生能量聚集，在分数域上表现为相对平坦的部分。由于本发明是基于切普信号在相应分数域上的能量聚集特性，所以以下分析将关注exp[j(2πf₀t+πkt²)]和exp[-j(2πf₀t-πkt²)]两项，其余两项视为干扰项，则s(t)可以表示为(5)：Among them, there are two items of the complex chop signal with +k modulation frequency, respectively exp[j(2πf ₀ t+πkt ² )] and exp[-j(2πf ₀ t-πkt ² )]; There are two items in the complex chip signal, which are exp[-j(2πf ₀ t+πkt ² )] and exp[j(2πf ₀ t-πkt ² )]. According to the characteristics of fractional Fourier transform, when the transformation order p=acot(-k)/(π/2), the complex chop signal with +k modulation frequency will generate energy accumulation in the fractional domain, that is, exp[j(2πf ₀ t+πkt ² )] and exp[-j(2πf ₀ t-πkt ² )] will generate peaks, and since the center frequencies of the two complex chop signals are different, respectively ±f ₀ , the two peaks are at The fractional domain is located on both sides of the center; at this time, the complex chop signal with -k modulation frequency will not produce energy accumulation, and it appears as a relatively flat part in the fractional domain. Since ^the present invention is based on ^the energy aggregation characteristics of _the Chip signal in the corresponding fractional domain, _the following analysis will focus on the two item, and the other two items are regarded as interference items, then s(t) can be expressed as (5):

$s the s ((t t)) = = \frac{11}{22} q q ((t t)) + + I I ((t t)) - - - - - - ((55))$

其中，in,

q(t)＝exp[j(2πf₀t+πkt²)]+exp[j(-2πf₀t+πkt²)] (6)q(t)=exp[j(2πf ₀ t+πkt ² )]+exp[j(-2πf ₀ t+πkt ² )] (6)

$I I ((t t)) = = \frac{11}{22} exp exp [[- - j j ((22 π π {f f}_{00} t t + + πk πk {t t}^{22}))]] + + \frac{11}{22} exp exp [[j j ((22 π π {f f}_{00} t t - - πk πk {t t}^{22}))]] - - - - - - ((77))$

将式(5)代入式(2)中，同时考虑接收信号实数形式和复数形式的一致性，我们得到接收信号r(t)的表达式为：Substituting Equation (5) into Equation (2), and considering the consistency of the real and complex forms of the received signal, we get the expression of the received signal r(t) as:

$r r ((t t)) = = \frac{11}{22} (({Σ Σ}_{i i = = 11}^{N N} {a a}_{i i} \cdot \cdot exp exp [[j j ((πk πk {t t}^{22} + + 22 π π (({f f}_{00} + + Δf Δ f - - k k {τ τ}_{i i})) t t + + ((πk πk {τ τ}_{i i}^{22} - - 22 π π {f f}_{00} {τ τ}_{i i} + + {φ φ}_{i i}))))]]$

$+ + {Σ Σ}_{i i = = 11}^{N N} {a a}_{i i} \cdot &Center Dot; exp exp [[j j ((πk πk {t t}^{22} + + 22 π π ((- - {f f}_{00} - - Δf Δf - - k k {τ τ}_{i i})) t t + + ((πk πk {τ τ}_{i i}^{22} + + 22 π π {f f}_{00} {τ τ}_{i i} - - {φ φ}_{i i}))))]])) + + I I ((t t)) * * h h ((t t,, τ τ)) + + n no ((t t)) - - - - - - ((88))$

从(8)中可以看出，接收信号可以看做由两组能够产生能量聚集的切普信号，与干扰项和噪声组成，同时由于受信道影响，接收信号中的复切普信号的幅度、相位、中心频率相对于原探测信号都发生了改变，其中具有正的中心频率的一组切普信号的幅度、相位、中心频率分别为：It can be seen from (8) that the received signal can be regarded as composed of two groups of chip signals that can generate energy aggregation, interference items and noise. At the same time, due to the influence of the channel, the amplitude of the complex chip signal in the received signal Compared with the original detection signal, the phase and center frequency have changed, and the amplitude, phase and center frequency of a group of chip signals with positive center frequency are respectively:

a_(i，1)＝a_i (9)a _{(i, 1)} = a _i (9)

φ_(i，1)＝(πkτ_i ²-2πf₀τ_i+φ_i) (10)φ _{(i, 1)} ＝(πkτ _i ² -2πf ₀ τ _i +φ _i ) (10)

f_0(i，1)＝(f₀+Δf-kτ_i) (11)f _{0(i, 1)} = (f ₀ +Δf-kτ _i ) (11)

具有负的中心频率的一组切普信号的幅度、相位、中心频率分别为：The amplitude, phase, and center frequency of a group of chip signals with a negative center frequency are:

a_(i，2)＝a_i (12)a _{(i, 2)} = a _i (12)

φ_(i，2)＝(πkτ_i ²+2πf₀τ_i-φ_i) (13)φ _{(i, 2)} = (πkτ _i ² +2πf ₀ τ _i -φ _i ) (13)

f_0(i，2)＝(-f₀-Δf-kτ_i) (14)f _{0(i, 2)} ＝(-f ₀ -Δf-kτ _i ) (14)

可以看到，新的复切普信号的幅度、相位、中心频率表达式包含着信道参数，若能够估计出新的复切普信号的参数，即可计算出信道参数。It can be seen that the expressions of the amplitude, phase, and center frequency of the new complex chip signal contain channel parameters. If the parameters of the new complex chip signal can be estimated, the channel parameters can be calculated.

对接收信号进行p＝acot(-k)/(π/2)阶分数傅立叶变换，对于每一条路径i由于两复切普信号中心频率的正负号不同，在分数域中心两侧将分别产生两个峰值。根据已有研究结论，利用峰值点的位置坐标

幅度值

和相位值

对切普信号的中心频率、幅度、相位的估计公式为Perform p=acot(-k)/(π/2) order fractional Fourier transform on the received signal. For each path i, due to the different signs of the center frequencies of the two complex chop signals, the two sides of the center of the fractional domain will generate two peaks. According to the existing research conclusions, using the position coordinates of the peak point

amplitude value

and phase value

The estimation formulas for the center frequency, amplitude and phase of the chip signal are

${\overset{^^}{f f}}_{00} = = {\overset{^^}{u u}}_{p p} csc csc α α - - - - - - ((1515))$

$\overset{^^}{a a} = = \frac{| | {f f}_{p p} (({\overset{^^}{u u}}_{p p})) | |}{T T / / \sqrt{| | sin sin α α | |}} - - - - - - ((1616))$

$\overset{^^}{φ φ} = = arg arg [[\frac{{f f}_{p p} (({\overset{^^}{u u}}_{p p}))}{{e e}^{j j ((\frac{α α}{22} + + \frac{π π}{44} + + π π {\overset{^^}{u u}}_{p p}^{22} cot cot α α))}}]] - - - - - - ((1717))$

则对接收信号进行分数傅立叶变换后，检测并记录每一个峰值的位置坐标，幅度值和相位值，代入公式(15)-(17)，即可以计算出每一个峰值所代表的复切普信号的中心频率、幅度和相位。又由于每条路径对应两个峰值，令代表第i条路径的两复切普信号的中心频率估计值分别记为

幅度估计值分别为

相位估计值分别为

根据切普信号参数值与信道参数之间的关系，如式(9)-(14)所示，各路径信道参数估计值可写为Then, after fractional Fourier transform of the received signal, detect and record the position coordinates, amplitude value and phase value of each peak value, and substitute them into formulas (15)-(17), the complex chip signal represented by each peak value can be calculated center frequency, amplitude and phase. And because each path corresponds to two peaks, let the center frequency estimates of the two complex chip signals representing the i-th path be recorded as

The amplitude estimates are

The phase estimates are

According to the relationship between chip signal parameter values and channel parameters, as shown in equations (9)-(14), the estimated channel parameter values of each path can be written as

${\overset{^^}{τ τ}}_{i i} = = \frac{{\overset{^^}{f f}}_{00 ((i i,, 11))} + + {\overset{^^}{f f}}_{00 ((i i,, 22))}}{- - 22 k k} - - - - - - ((1818))$

$Δ Δ {\overset{^^}{f f}}_{i i} = = \frac{{\overset{^^}{f f}}_{00 ((i i,, 11))} - - {\overset{^^}{f f}}_{00 ((i i,, 22))}}{22} - - {f f}_{00} - - - - - - ((1919))$

${\overset{^^}{φ φ}}_{i i} = = (({\overset{^^}{φ φ}}_{((i i,, 11))} - - {\overset{^^}{φ φ}}_{((i i,, 22))} + + 44 π π {f f}_{00 i i} {\overset{^^}{τ τ}}_{i i})) / / 22 - - - - - - ((2020))$

${\overset{^^}{a a}}_{i i} = = (({\overset{^^}{a a}}_{((i i,, 11))} + + {\overset{^^}{a a}}_{((i i,, 22))})) / / 22 - - - - - - ((21 twenty one))$

以下通过仿真说明方法的有效性The effectiveness of the method is illustrated by simulation

仿真参数设定：探测信号中心频率f₀＝247.5kHz，采样频率f_s＝1MHz，调频率分别为k＝±400MHz/s，带宽B＝400KHz，持续时间T＝1ms，幅度为1，初相位为0，则探测信号s(t)的表达式为s(t)＝cos(2π·247500t+π·4×10⁸t²)+cos(2π·247500t-π·4×10⁸t²)。假设信道有两条多径，路径A幅度为1，相位为π，时延17μs，多普勒频移120Hz，路径B幅度为1，相位为π，时延35μs，多普勒频移-90Hz，信噪比10dB。Simulation parameter setting: detection signal center frequency f ₀ =247.5kHz, sampling frequency f _s =1MHz, modulation frequency k=±400MHz/s, bandwidth B=400KHz, duration T=1ms, amplitude 1, initial phase is 0, the expression of detection signal s(t) is s(t)=cos(2π·247500t+π·4×10 ⁸ t ² )+cos(2π·247500t-π·4×10 ⁸ t ² ) . Assume that the channel has two multipaths, path A has an amplitude of 1, a phase of π, a delay of 17 μs, and a Doppler frequency shift of 120 Hz, path B has an amplitude of 1, a phase of π, a delay of 35 μs, and a Doppler frequency shift of -90 Hz , SNR 10dB.

对接收到的探测信号进行如步骤二所述的分数傅立叶变换，得到的分数域幅度谱如图1，可以看到对应于每一条路径，在分数域上都出现了两个峰值，两条路径共有4个峰值。路径A在分数域前半段的峰值记为PA1，路径A在分数域后半段的峰值记为PA2，路径B在分数域前半段的峰值记为PB1，路径B在分数域后半段的峰值记为PB2。各峰值的幅度、相位、位置坐标如表1：Perform the fractional Fourier transform as described in step 2 on the received detection signal, and the obtained fractional domain amplitude spectrum is shown in Figure 1. It can be seen that corresponding to each path, two peaks appear in the fractional domain, and the two paths There are 4 peaks in total. The peak value of path A in the first half of the fractional domain is marked as PA1, the peak value of path A in the second half of the fractional domain is marked as PA2, the peak value of path B in the first half of the fractional domain is marked as PB1, and the peak value of path B in the second half of the fractional domain Denote it as PB2. The amplitude, phase and position coordinates of each peak are shown in Table 1:

表1Table 1

PA1PA1 PA2PA2 PB 1PB 1 PB2PB2 幅度Amplitude 10.2510.25 10.1510.15 10.3310.33 10.1510.15 相位Phase 2.3722.372 -0.8609-0.8609 0.10550.1055 0.0530.053 位置坐标 Position coordinates 44174417 56175617 44344434 56355635

按步骤三所述，将表1的结果代入公式(15-17)估计接收信号中产生能量聚集的两复切普信号的中心频率、幅度、相位，然后将此结果代入到公式(18-21)，得到信道中各多径的时延、多普勒频移、相位、幅度估计值，计算结果如表2，从表2中可以看到本发明提出的信道参数估计方法具有很高的准确度。As described in step 3, substitute the results in Table 1 into formula (15-17) to estimate the center frequency, amplitude, and phase of the two complex chip signals that generate energy aggregation in the received signal, and then substitute this result into formula (18-21 ), obtain the time delay, Doppler frequency shift, phase, amplitude estimation value of each multipath in the channel, calculation result is as table 2, can see from table 2 that the channel parameter estimation method that the present invention proposes has very high accuracy Spend.

表2Table 2

幅度Amplitude 相位Phase 时延Latency 多普勒频移Doppler shift 路径A真实值True value of path A 1 1 3.14163.1416 17μs17μs -90Hz-90Hz

幅度Amplitude 相位Phase 时延Latency 多普勒频移Doppler shift 路径A估计值Estimated value of path A 1.00491.0049 3.17013.1701 16.993μs16.993μs -90.2Hz-90.2Hz 相对误差 Relative error 0.49％0.49% 0.91％0.91% 0.04％0.04% 0.2％0.2% 路径B真实值True value of path B 1 1 3.14163.1416 3.5000e-0053.5000e-005 120Hz120Hz 路径B估计值Path B estimate 1.01161.0116 3.23073.2307 3.5015e-0053.5015e-005 120.2Hz120.2Hz 相对误差 Relative error 1.16％1.16% 2.84％2.84% 0.04％0.04% 0.17％0.17%

Claims

1. A channel parameter estimation method based on classical fractional Fourier transform is characterized in that: the method is realized by the following steps:

adding two sections of chirp signals with the same center frequency and opposite frequency modulation rates to serve as a channel detection signal, and transmitting the channel detection signal from a transmitting end; the expression of the channel detection signal is s (t) cos (2 pi f)₀t+πkt²)+cos(2πf₀t-πkt²) (ii) a The channel detection signal s (t) is decomposed into a form of 4 complex chirp signals added, that is:

wherein T is more than or equal to T/2 and less than or equal to T/2, and T is the duration of the channel detection signal s (T);

step two, the receiving end receives the channel detection signal transmitted by the transmitting end, and the channel detection signal is recorded as r (t), and fractional Fourier transform with the transformation order p ═ acot (-k)/(pi/2) is carried out on the channel detection signal r (t), so as to obtain a fractional domain amplitude spectrum of the channel detection signal, wherein the fractional domain amplitude spectrum comprises i groups of amplitude spectrum curves, and each group of amplitude spectrum curves corresponds to the channel detection signal of one path; each group of amplitude spectrum curves comprises two peak values, and the two peak values are respectively positioned on two sides of the coordinate center of the fractional domain;

step three, detecting the i groups of amplitude spectra curves in the step twoTwo peaks of the line, the position coordinates of the two peaks of each set of amplitude spectrum curves being obtained

Magnitude value

Sum phase value

Two peak values of each group of amplitude spectrum curves respectively correspond to two complex chirp signals exp [ j (2 pi f)₀t+πkt²)]And exp [ -j (2 π f)₀t-πkt²)]；

Step four, according to the position coordinates of two peak values of the ith group of amplitude spectrum curves obtained in the step three

Magnitude value

Sum phase value

Estimating two received complex chirp signals exp [ j (2 pi f) on ith path₀t+πkt²)]And exp [ -j (2 π f)₀t-πkt²)]Center frequency ofAmplitude of

And phase

Step five, obtaining two complex chirp signals exp [ j (2 pi f) on the ith path according to the step four₀t+πkt²)]And exp [ -j (2 π f)₀t-πkt²)]Center frequency ofAmplitude of

And phase

Obtaining the delay of the ith path

Estimated value of (1), Doppler shiftEstimated value of (1), phase

Estimate and amplitude of

An estimated value of (d);

f is₀Detecting a signal center frequency for the channel; k is the frequency modulation rate of the chirp signal, and alpha is the fractional Fourier transform angle; i is an integer.

2. The method of claim 1, wherein the position coordinates of two peaks of the ith set of amplitude spectrum curves obtained according to the step three are obtained in the step four

Magnitude value

Sum phase value

Estimating two received complex chirp signals exp [ j (2 pi f) on ith path₀t+πkt²)]And exp [ -j (2 π f)₀t-πkt²)]Center frequency ofAccording to the formula:

and (4) realizing.

3. The method of claim 1, wherein the position coordinates of two peaks of the ith set of amplitude spectrum curves obtained according to the step three are obtained in the step four

Magnitude value

Sum phase value

Estimating two received complex chirp signals exp [ j (2 pi f) on ith path₀t+πkt²)]And exp [ -j (2 π f)₀t-πkt²)]Amplitude of (2)

According to the formula:

and (4) realizing.

4. The method of claim 1, wherein the position coordinates of two peaks of the ith set of amplitude spectrum curves obtained according to the step three are obtained in the step four

Magnitude value

Sum phase value

Estimating two received complex chirp signals exp [ j (2 pi f) on ith path₀t+πkt²)]And exp [ -j (2 π f)₀t-πkt²)]Phase of

According to the formula:

and (4) realizing.

5. The method as claimed in claim 1, wherein the step five of estimating channel parameters based on classical fractional fourier transform is implemented by obtaining two complex chirp signals exp [ j (2 π f) on ith path according to the step four₀t+πkt²)]And exp [ -j (2 π f)₀t-πkt²)]Center frequency of

Amplitude ofAnd phase

Obtaining the delay of the ith path

Is estimated by the formula:

and (4) realizing.

6. The method as claimed in claim 1, wherein the step five of estimating channel parameters based on classical fractional fourier transform is implemented by obtaining two complex chirp signals exp [ j (2 π f) on ith path according to the step four₀t+πkt²)]And exp [ -j (2)πf₀t-πkt²)]Center frequency ofAmplitude ofAnd phase

Obtaining Doppler shift of ith path

Is estimated by the formula:

and (4) realizing.

7. The method as claimed in claim 1, wherein the step five of estimating channel parameters based on classical fractional fourier transform is implemented by obtaining two complex chirp signals exp [ j (2 π f) on ith path according to the step four₀t+πkt²)]And exp [ -j (2 π f)₀t-πkt²)]Center frequency of

Amplitude of

And phase

Obtaining the phase of the ith pathIs estimated by the formula:

and (4) realizing.

8. The method as claimed in claim 1, wherein the step five of estimating channel parameters based on classical fractional fourier transform is implemented by obtaining two complex chirp signals exp [ j (2 π f) on ith path according to the step four₀t+πkt²)]And exp [ -j (2 π f)₀t-πkt²)]Center frequency of

Amplitude of

And phase

Obtaining the amplitude of the ith path

Is estimated by the formula:

{\hat{a}}_{i} = ({\hat{a}}_{(i, 1)} + {\hat{a}}_{(i, 2)}) / 2

and (4) realizing.