CN103346992B

CN103346992B - Doppler changing rate method of estimation in a kind of ofdm system and system

Info

Publication number: CN103346992B
Application number: CN201310258025.7A
Authority: CN
Inventors: 周一青; 侯占伟; 田霖; 姚彦斌; 苏泳涛; 石晶林
Original assignee: Institute of Computing Technology of CAS
Current assignee: Institute of Computing Technology of CAS
Priority date: 2013-06-26
Filing date: 2013-06-26
Publication date: 2016-03-30
Anticipated expiration: 2033-06-26
Also published as: CN103346992A

Abstract

The invention provides the doppler changing rate method of estimation in a kind of ofdm system and system, described method comprises: the sampling number certificate obtaining an OFDM symbol; And in span, select a value as the value of doppler changing rate, make each sampled point in described OFDM symbol Cyclic Prefix maximum at the product of the joint probability of the corresponding sampled point at described OFDM symbol end with it.Described method is applicable to doppler changing rate in multi-carrier OFDM systems and estimates, to initial Doppler frequency displacement is insensitive and precision is higher.

Description

Method and system for estimating Doppler rate of change in OFDM system

技术领域technical field

本发明涉及无线通信技术领域，具体涉及一种OFDM系统中的多普勒变化率估计方法和系统。The present invention relates to the technical field of wireless communication, in particular to a Doppler change rate estimation method and system in an OFDM system.

背景技术Background technique

在诸如高速铁路通信系统、低轨卫星通信系统和毫米波交通辅助和控制系统等的高速移动场景中，无线通信的接收信号会受到快速变化的多普勒频移的影响。因此，需要对多普勒频移和多普勒变化率进行估计和补偿以保证信号的正确接收。此外，多普勒变化率还可以为不同的通信系统提供额外的信息。例如，在高速铁路通信系统中估计出多普勒变化率，有助于预测多普勒频移变化趋势；在低轨卫星系统中，需要多普勒变化率的参数来进行轨道计算；以及在毫米波交通辅助和控制系统中，多普勒变化率可以反映出交通工具的加速度情况。可见，估计多谱勒变化率对无线通信系统来说非常重要。目前，作为主流的无线宽带通信技术，正交频分复用（OrthogonalFrequencyDivisionMultiplexing，OFDM）已在诸如LTE、WiMAX、ISDB-S等的通信标准中广泛使用。OFDM系统性能对多普勒信息非常敏感，为了能在高速移动场景下提供高质量的宽带OFDM通信，必须要设计一种OFDM系统中的多普勒变化率估计方法。In high-speed mobile scenarios such as high-speed railway communication systems, low-orbit satellite communication systems, and millimeter-wave traffic assistance and control systems, received signals for wireless communication are affected by rapidly changing Doppler shifts. Therefore, it is necessary to estimate and compensate the Doppler frequency shift and Doppler change rate to ensure the correct reception of the signal. In addition, the Doppler rate of change can provide additional information for different communication systems. For example, in the high-speed railway communication system, the Doppler change rate is estimated, which is helpful to predict the Doppler frequency shift change trend; in the low-orbit satellite system, the parameters of the Doppler change rate are needed for orbit calculation; and in In the millimeter wave traffic assistance and control system, the rate of change of Doppler can reflect the acceleration of the vehicle. It can be seen that estimating the Doppler rate of change is very important for a wireless communication system. At present, as a mainstream wireless broadband communication technology, Orthogonal Frequency Division Multiplexing (Orthogonal Frequency Division Multiplexing, OFDM) has been widely used in communication standards such as LTE, WiMAX, and ISDB-S. OFDM system performance is very sensitive to Doppler information. In order to provide high-quality broadband OFDM communication in high-speed mobile scenarios, it is necessary to design a Doppler change rate estimation method in OFDM systems.

目前，研究人员主要根据以下方法来估计多普勒变化率：首先，将观察时间长度分成N_slot个时隙，每个时隙都有一个相应的相位函数θ(j)，其中j=0,1,...,N_slot-1；接着，对该相位函数θ(j)做二阶差分操作，即通过该操作，待估计的多普勒变化率α就与对相位函数做二阶差分后的结果有关；然后，从中估计出多普勒变化率α。At present, researchers mainly estimate the Doppler rate of change according to the following method: First, the observation time length is divided into N _slot time slots, and each time slot has a corresponding phase function θ(j), where j=0, 1,...,N _slot -1; Next, do a second-order difference operation on the phase function θ(j), namely Through this operation, the Doppler rate of change α to be estimated is the result of the second-order difference of the phase function related; then, from The Doppler rate of change α is estimated from .

然而，包括上述方法的现有多普勒变化率估计方法都是针对单载波系统设计的，需要从接收信号中获取一个未调制的载波。在单载波场景下，通过一些设置是可以获取未调制的载波的。例如，在加性高斯白噪声（AdditiveWhiteGaussianNoise，AWGN）场景下，采用PSK或者QPSK的调制方式，在接收端通过将接收的导频信号与本地的导频信号做相关，可以去除调制信号的相位对载波相位的影响。在OFDM系统中，可以给定一个子载波或者一个OFDM符号来放置导频，然后使用上述方法来获得多普勒变化率。但是在现有的OFDM系统中，如LTE，WiMax，ISDB-S，由于信道估计等需求，导频是离散地放在特定的时间频率资源块上，而不是连续放满整个OFDM符号或者子载波，因此无法获得未调制的载波，从而无法使用现有方法来进行多普勒变化率的估计。此外，现有方法也没有考虑到初始多普勒频移，因此对大的多普勒频移非常敏感，随着初始多普勒频移变大，多普勒变化率的估计精度会下降。However, the existing Doppler rate-of-change estimation methods including the above methods are all designed for single-carrier systems, and need to obtain an unmodulated carrier from the received signal. In a single carrier scenario, the unmodulated carrier can be obtained through some settings. For example, in an Additive White Gaussian Noise (AWGN) scenario, using PSK or QPSK modulation, at the receiving end, by correlating the received pilot signal with the local pilot signal, the phase of the modulated signal can be removed. Effect of carrier phase. In an OFDM system, a subcarrier or an OFDM symbol can be given to place a pilot, and then the above-mentioned method can be used to obtain the Doppler change rate. However, in existing OFDM systems, such as LTE, WiMax, and ISDB-S, due to requirements such as channel estimation, pilots are discretely placed on specific time-frequency resource blocks instead of continuously filling the entire OFDM symbol or subcarrier , so the unmodulated carrier cannot be obtained, so the existing method cannot be used to estimate the Doppler rate of change. In addition, the existing methods do not take into account the initial Doppler frequency shift, so they are very sensitive to large Doppler frequency shifts. As the initial Doppler frequency shift becomes larger, the estimation accuracy of the Doppler change rate will decrease.

因此，需要一种能够估计高速运动场景下OFDM系统中的多普勒变化率的方法，该方法对初始多普勒频移不敏感，且估计精度高。Therefore, there is a need for a method capable of estimating the Doppler rate of change in an OFDM system in a high-speed motion scene, which is insensitive to the initial Doppler frequency shift and has high estimation accuracy.

发明内容Contents of the invention

根据本发明的一个实施例，提供一种OFDM系统中的多普勒变化率估计方法，包括：According to one embodiment of the present invention, a method for estimating Doppler rate of change in an OFDM system is provided, comprising:

步骤1）、获得一个OFDM符号的采样点数据；Step 1), obtaining sampling point data of an OFDM symbol;

步骤2）、在取值范围内选择一个值作为多普勒变化率的值，使得所述OFDM符号循环前缀中的每个采样点与其在所述OFDM符号末尾的对应的采样点的联合概率的乘积最大。Step 2), select a value in the value range as the value of the Doppler rate of change, so that the joint probability of each sampling point in the OFDM symbol cyclic prefix and its corresponding sampling point at the end of the OFDM symbol is The product is the largest.

在一个实施例中，步骤2）包括：In one embodiment, step 2) includes:

步骤21）、根据下式在归一化搜索范围内选择一个值作为归一化多普勒变化率的值：Step 21), according to the following formula, select a value within the normalized search range as the value of the normalized Doppler rate of change:

$\overset{^^}{α α} = = \underset{α α}{arg arg max max} {{| | {Σ Σ}_{k k = = L L - - ηL ηL}^{L L - - 11} exp exp {{jπα jπα ((22 k k + + N N + + 11))}} {r r}_{k k + + N N}^{* *} {r r}_{k k} | |}},,$

其中，L是OFDM符号循环前缀的采样点数，N是有效OFDM符号的采样点数，j是虚数符号，k是采样点序号，r_k是第k个接收信号，是第k+N个接收信号的共轭，0≤η≤1；Among them, L is the number of sampling points of the cyclic prefix of the OFDM symbol, N is the number of sampling points of the effective OFDM symbol, j is the imaginary number symbol, k is the serial number of the sampling point, r _k is the kth received signal, is the conjugate of the k+Nth received signal, 0≤η≤1;

步骤22）、根据下式计算多普勒变化率的值：Step 22), calculate the value of the Doppler rate of change according to the following formula:

${Δf Δ f}_{Doppler Doppler} = = \frac{{Δf Δ f}_{subcarrier subcarrier}}{{T T}_{s the s}} α α,,$

其中，Δf_subcarrier是所述OFDM系统的子载波间隔，T_s是采样间隔，α是归一化多普勒变化率的值。Wherein, Δf _subcarrier is the subcarrier spacing of the OFDM system, T _s is the sampling interval, and α is the value of the normalized Doppler rate of change.

在一个实施例中，In one embodiment,

${r r}_{k k} = = {s the s}_{k k} exp exp [[j j ((\frac{22 π π}{N N} {Σ Σ}_{p p = = 11}^{k k} (({ϵ ϵ}_{00} + + αp αp)) + + {θ θ}_{00}))]] + + {n no}_{k k},,$

其中，j是虚数符号，k是采样点序号，s_k和n_k分别表示第k个发送信号和第k个噪声信号，ε₀表示初始多普勒频移，θ₀是未知的初始相位。Among them, j is an imaginary number symbol, k is the sampling point number, s _k and _nk represent the kth transmitted signal and the kth noise signal respectively, ε ₀ represents the initial Doppler frequency shift, and θ ₀ is the unknown initial phase.

在一个实施例中，步骤1）之前还包括：In one embodiment, step 1) also includes:

步骤0）、将得到的连续信号经过A/D转换获得基带数字信号。Step 0), A/D conversion is performed on the obtained continuous signal to obtain a baseband digital signal.

在一个实施例中，步骤21）之前还包括：确定归一化搜索范围。In one embodiment, before step 21) further includes: determining a normalized search range.

根据本发明的一个实施例，还提供一种OFDM系统中的多普勒变化率估计系统，包括：According to an embodiment of the present invention, a Doppler rate of change estimation system in an OFDM system is also provided, including:

用于获得一个OFDM符号的采样点数据的装置；以及means for obtaining sample point data of an OFDM symbol; and

用于在取值范围内选择一个值作为多普勒变化率的值，使得所述OFDM符号循环前缀中的每个采样点与其在所述OFDM符号末尾的对应的采样点的联合概率的乘积最大的装置。It is used to select a value in the value range as the value of the Doppler rate of change, so that the product of the joint probability of each sampling point in the cyclic prefix of the OFDM symbol and its corresponding sampling point at the end of the OFDM symbol is the largest installation.

与现有方法相比，采用本发明可以达到如下的有益效果：Compared with existing methods, the present invention can achieve the following beneficial effects:

1）、针对现有方法仅适用于可以获得未调制载波的场景，本发明提供的方法适用于多载波OFDM系统中的多普勒变化率估计。1) As the existing methods are only applicable to the scene where the unmodulated carrier can be obtained, the method provided by the present invention is applicable to the Doppler change rate estimation in the multi-carrier OFDM system.

2）、对初始多普勒频移不敏感，精度较高。2) It is not sensitive to the initial Doppler frequency shift and has high precision.

3）、利用了OFDM符号已有的信号结构循环前缀，不需要额外的导频作为辅助，提高了系统的频谱效率。3) The cyclic prefix of the existing signal structure of the OFDM symbol is used, and no additional pilot frequency is used as an auxiliary, which improves the spectral efficiency of the system.

附图说明Description of drawings

图1是OFDM符号的结构示意图；FIG. 1 is a schematic structural diagram of an OFDM symbol;

图2是根据本发明一个实施例的OFDM系统中的多普勒变化率估计方法的流程图；Fig. 2 is a flow chart of a method for estimating Doppler rate of change in an OFDM system according to an embodiment of the present invention;

图3是根据本发明一个实施例的用于搜索归一化多普勒变化率的方法的流程图；FIG. 3 is a flowchart of a method for searching for a normalized Doppler rate of change according to an embodiment of the present invention;

图4是根据本发明一个实施例的OFDM符号采样点示意图；Fig. 4 is a schematic diagram of OFDM symbol sampling points according to one embodiment of the present invention;

图5是采用本发明提供的方法与现有方法估计OFDM系统中的多普勒变化率的精度示意图；Fig. 5 is a schematic diagram of the accuracy of Doppler rate of change estimation in the OFDM system using the method provided by the present invention and the existing method;

图6是采用本发明提供的OFDM系统中的多普勒变化率估计方法对初始多普勒频移的敏感性示意图；以及Fig. 6 is a schematic diagram of the sensitivity of the Doppler rate of change estimation method to the initial Doppler frequency shift in the OFDM system provided by the present invention; and

图7是采用本发明提供的方法及其改进方法在衰落信道下估计OFDM系统中的多普勒变化率的精度示意图。Fig. 7 is a schematic diagram of the accuracy of Doppler change rate estimation in an OFDM system under a fading channel by using the method provided by the present invention and its improved method.

具体实施方式detailed description

下面结合附图和具体实施方式对本发明加以说明。The present invention will be described below in conjunction with the accompanying drawings and specific embodiments.

根据本发明的一个实施例，提供一种OFDM系统中的多普勒变化率估计方法。该方法根据一个OFDM符号内的采样点数据，通过构建的最大似然函数来估计多普勒变化率。According to an embodiment of the present invention, a method for estimating Doppler rate of change in an OFDM system is provided. This method estimates the Doppler rate of change by constructing a maximum likelihood function based on the sampling point data in an OFDM symbol.

在构建极大似然函数之前，首先确定接收信号的表示方法。考虑AWGN信道下在一个OFDM符号内时变的多普勒频移，可将接收信号表示为：Before constructing the maximum likelihood function, first determine the representation method of the received signal. Considering the time-varying Doppler shift within one OFDM symbol under the AWGN channel, the received signal can be expressed as:

${r r}_{t t} = = {s the s}_{t t} exp exp [[j j ((22 π π {&Integral; &Integral;}_{00}^{t t} {f f}_{Doppler Doppler} ((τ τ)) dτ dτ + + {θ θ}_{00}))]] + + {n no}_{t t},, - - - - - - ((11))$

其中，r_t、s_t和n_t分别表示在t时刻的接收信号、发送信号和噪声信号，f_Doppler(τ)表示τ时刻的多普勒频移，j是虚数符号，θ₀是未知的初始相位。Among them, r _t , st _t and n _t represent the received signal, transmitted signal and noise signal at time t respectively, f _Doppler (τ) represents the Doppler frequency shift at time τ, j is the imaginary symbol, and θ ₀ is the unknown initial phase.

将接收的连续信号经过A/D转换之后，得到的离散信号可以用下式表示：After the received continuous signal undergoes A/D conversion, the obtained discrete signal can be expressed by the following formula:

${r r}_{k k} = = {s the s}_{k k} exp exp [[j j ((22 π π {Σ Σ}_{p p = = 11}^{k k} {f f}_{Doppler Doppler} ((p p)) \cdot \cdot {T T}_{s the s} + + {θ θ}_{00}))]] + + {n no}_{k k},, - - - - - - ((22))$

其中，时长t=kT_s，T_s是采样间隔。k=0,1,…,N+L-1，表示采样点序号（采样点数为N+L个），L为CP（CyclicPrefix，循环前缀）长度，N是有效OFDM符号的长度，r_k是第k个接收信号（或称第k个采样点/采样点k的接收信号）。图1示出了OFDM符号的固有信号循环前缀，CP是将OFDM符号末尾的一部分采样点复制到OFDM头部，以对抗多径时延造成的符号间干扰问题。在一个实施例中，N可以是有效OFDM符号的采样点数，L是循环前缀的采样点数。Wherein, the duration t=kT _s , and T _s is the sampling interval. k=0,1,...,N+L-1, indicating the number of sampling points (the number of sampling points is N+L), L is the length of CP (CyclicPrefix, cyclic prefix), N is the length of an effective OFDM symbol, r _k is The kth received signal (or called the received signal of the kth sample point/sample point k). Figure 1 shows the inherent signal cyclic prefix of the OFDM symbol. The CP is to copy a part of the sampling points at the end of the OFDM symbol to the head of the OFDM symbol to combat the intersymbol interference problem caused by multipath delay. In an embodiment, N may be the number of sampling points of an effective OFDM symbol, and L is the number of sampling points of a cyclic prefix.

可根据下式归一化公式（2）中的时变多普勒频移：The time-varying Doppler shift in equation (2) can be normalized according to:

${ϵ ϵ}_{p p} = = \frac{{f f}_{Doppler Doppler} ((p p))}{{Δf Δ f}_{subcarrier subcarrier}},, - - - - - - ((33))$

其中，表示OFDM系统的子载波间隔。因此，公式（2）可表示为：in, Indicates the subcarrier spacing of the OFDM system. Therefore, formula (2) can be expressed as:

${r r}_{k k} = = {s the s}_{k k} exp exp [[j j ((\frac{22 π π}{N N} {Σ Σ}_{p p = = 11}^{k k} {ϵ ϵ}_{p p} + + {θ θ}_{00}))]] + + {n no}_{k k},, - - - - - - ((44))$

在一个OFDM符号内考虑线性多普勒频移变化，即一个OFDM符号内的多普勒变化率固定，则归一化的多普勒频移可表示为：Considering the linear Doppler shift change within one OFDM symbol, that is, the Doppler change rate within one OFDM symbol is fixed, then the normalized Doppler shift can be expressed as:

ε_p=ε₀+αp（5）εp ₌ ε0 + αp ( ₅ )

其中，表示在一个OFDM符号内固定的归一化多普勒变化率，Δf_Doppler是以Hz/s为单位的多普勒变化率，ε₀表示初始多普勒频移。则公式（4）可进一步表示为：in, Indicates the fixed normalized Doppler change rate within one OFDM symbol, Δf _Doppler is the Doppler change rate in Hz/s, and ε ₀ represents the initial Doppler frequency shift. Then formula (4) can be further expressed as:

${r r}_{k k} = = {s the s}_{k k} exp exp [[j j ((\frac{22 π π}{N N} {Σ Σ}_{p p = = 11}^{k k} (({ϵ ϵ}_{00} + + αp αp)) + + {θ θ}_{00}))]] + + {n no}_{k k},, - - - - - - ((66))$

基于上文的接收信号表示，在完成定时同步后，根据接收到的一个完整的OFDM符号，可以构建最大似然函数：Based on the above received signal representation, after the timing synchronization is completed, the maximum likelihood function can be constructed according to a complete OFDM symbol received:

$Λ Λ (({ϵ ϵ}_{00},, α α)) = = log log f f ((r r | | {ϵ ϵ}_{00},, α α))$

$= = log log ((\underset{k k &Element; &Element; {M m}_{CP CP}}{Π Π} f f (({r r}_{k k},, {r r}_{k k + + N N})) \underset{k k &NotElement; &NotElement; {M m}_{CP CP} \cup \cup {M m}_{CP CP}^{' '}}{Π Π} f f (({r r}_{k k}))))$

$= = log log ((\underset{k k &Element; &Element; I I}{Π Π} \frac{f f (({r r}_{k k},, {r r}_{k k + + N N}))}{f f (({r r}_{k k})) f f (({r r}_{k k + + N N}))} \underset{k k}{Π Π} f f (({r r}_{k k})))) - - - - - - ((77))$

其中M_CP表示OFDM符号的循环前缀的L个采样点集合，M'_CP表示OFDM符号中从后往前数L个采样点集合，I表示M_CP集合，f(r_k,r_k+N)表示r_k、r_k+N的联合概率密度。Where M _CP represents the L sampling point set of the cyclic prefix of the OFDM symbol, M' _CP represents the L sampling point set counting from the back to the front in the OFDM symbol, I represents the M _CP set, f(r _k , r _k+N ) represents the joint probability density of r _k and r _k+N .

由于与多普勒频移ε₀和多普勒变化率α均无关，所以公式（7）可以简化为：because It has nothing to do with the Doppler frequency shift ε ₀ and the Doppler change rate α, so formula (7) can be simplified as:

$Λ Λ (({ϵ ϵ}_{00},, α α)) = = log log ((\underset{k k &Element; &Element; I I}{Π Π} \frac{f f (({r r}_{k k},, {r r}_{k k + + N N}))}{f f (({r r}_{k k})) f f (({r r}_{k k + + N N}))})),, - - - - - - ((88))$

其中log{·}表示自然对数，f(r_k,r_k+N)服从二维高斯分布，即 $[\begin{matrix} r_{k} \\ r_{k + N} \end{matrix}] ~ CN [\begin{matrix} 0 & σ_{s}^{2} + σ_{n}^{2} \\ 0 & σ_{s}^{2} + σ_{n}^{2} \end{matrix}],$ 可以得到其联合概率密度：Where log{·} represents the natural logarithm, f(r _k ,r _k+N ) obeys a two-dimensional Gaussian distribution, namely $[\begin{matrix} r_{k} \\ r_{k + N} \end{matrix}] ~ CN [\begin{matrix} 0 & σ_{the s}^{2} + σ_{no}^{2} \\ 0 & σ_{the s}^{2} + σ_{no}^{2} \end{matrix}],$ Its joint probability density can be obtained:

$f f (({r r}_{k k},, {r r}_{k k + + N N})) = = \frac{exp exp ((\frac{11}{((11 - - {| | ρ ρ | |}^{22})) (({σ σ}_{s the s}^{22} + + {σ σ}_{n no}^{22}))} [[{| | {r r}_{k k} | |}^{22} - - 22 Re Re (({ρ ρ}^{* *} {r r}_{k k + + N N}^{* *} {r r}_{k k})) {| | {r r}_{k k + + N N} | |}^{22}]]))}{{π π}^{22} ((11 - - {| | ρ ρ | |}^{22})) (({σ σ}_{s the s}^{22} + + {σ σ}_{n no}^{22}))} - - - - - - ((99))$

其中in

$ρ ρ = = \frac{E E. {{{r r}_{k k} {r r}_{k k + + N N}^{* *}}}}{\sqrt{{| | {r r}_{k k} | |}^{22} {| | {r r}_{k k + + N N} | |}^{22}}} - - - - - - ((1010))$ $= = \frac{{σ σ}_{s the s}^{22}}{{σ σ}_{s the s}^{22} + + {σ σ}_{n no}^{22}} exp exp {{- - j j 22 π π [[{ϵ ϵ}_{00} + + \frac{11}{22} α α ((22 k k + + N N + + 11))]]}}$

其中，E{.}表示期望，表示r_k+N的共轭。值得注意的是，|ρ|（即）与多普勒频移ε₀和多普勒变化率α均无关。Among them, E{.} represents expectation, Indicates the conjugate of rk _+N . It is worth noting that |ρ| (ie ) has nothing to do with the Doppler frequency shift ε ₀ and the Doppler rate of change α.

f(r_k)和f(r_k+N)分别服从一维高斯分布，即f(r _k ) and f(r _k+N ) respectively obey the one-dimensional Gaussian distribution, namely

$f f (({r r}_{k k})) = = \frac{11}{π π (({σ σ}_{s the s}^{22} + + {σ σ}_{n no}^{22}))} exp exp ((- - \frac{{| | {r r}_{k k} | |}^{22}}{{σ σ}_{s the s}^{22} + + {σ σ}_{n no}^{22}})) - - - - - - ((1111))$

和and

$f f (({r r}_{k k + + N N})) = = \frac{11}{π π (({σ σ}_{s the s}^{22} + + {σ σ}_{n no}^{22}))} exp exp ((- - \frac{{| | {r r}_{k k + + N N} | |}^{22}}{{σ σ}_{s the s}^{22} + + {σ σ}_{n no}^{22}})) - - - - - - ((1212))$

将公式（9）、（11）和（12）分别代入公式（8）所示的最大似然函数中可得：Substituting formulas (9), (11) and (12) into the maximum likelihood function shown in formula (8) can be obtained as follows:

$Λ Λ ((ϵ ϵ,, α α)) = = - - {Σ Σ}_{k k = = 00}^{L L - - 11} log log ((11 - - {| | ρ ρ | |}^{22}))$

$+ + \frac{22}{((11 - - {| | ρ ρ | |}^{22})) (({σ σ}_{s the s}^{22} + + {σ σ}_{n no}^{22}))} [[{Σ Σ}_{k k = = 00}^{L L - - 11} Re Re (({ρ ρ}^{* *} {r r}_{k k + + N N}^{* *} {r r}_{k k})) - - {| | ρ ρ | |}^{22} \frac{11}{22} {Σ Σ}_{k k = = 00}^{L L - - 11} (({| | {r r}_{k k} | |}^{22} + + {| | {r r}_{k k + + N N} | |}^{22}))]],, - - - - - - ((1313))$

其中，Re(·)表示取复数的实部，L为循环前缀中的采样点数。并且，由于|ρ|、 $- Σ_{k = 0}^{L - 1} \log (1 - {| ρ |}^{2}),$ $\frac{2}{(1 - {| ρ |}^{2}) (σ_{s}^{2} + σ_{n}^{2})}$ 和 ${| ρ |}^{2} \frac{1}{2} Σ_{k = 0}^{L - 1} ({| r_{k} |}^{2} + {| r_{k + N} |}^{2})$ 均与初始多普勒频移ε₀和多普勒变化率α均无关，公式（13）可以简化为：Among them, Re(·) means taking the real part of a complex number, and L is the number of sampling points in the cyclic prefix. And, due to |ρ|, $- Σ_{k = 0}^{L - 1} \log (1 - {| ρ |}^{2}),$ $\frac{2}{(1 - {| ρ |}^{2}) (σ_{the s}^{2} + σ_{no}^{2})}$ and ${| ρ |}^{2} \frac{1}{2} Σ_{k = 0}^{L - 1} ({| r_{k} |}^{2} + {| r_{k + N} |}^{2})$ are independent of the initial Doppler frequency shift ε ₀ and the Doppler change rate α, formula (13) can be simplified as:

${Λ Λ}^{' '} (({ϵ ϵ}_{00},, α α)) = = {Σ Σ}_{k k = = 00}^{L L - - 11} Re Re (({ρ ρ}^{* *} {r r}_{k k + + N N}^{* *} {r r}_{k k})) = = Re Re (({Σ Σ}_{k k = = 00}^{L L - - 11} {ρ ρ}^{* *} {r r}_{k k + + N N}^{* *} {r r}_{k k})) - - - - - - ((1414))$

将公式（10）中ρ的定义代入式（14）可得到最大似然函数：Substituting the definition of ρ in formula (10) into formula (14) can obtain the maximum likelihood function:

${Λ Λ}^{' '} (({ϵ ϵ}_{00},, α α)) = = | | ρ ρ | | | | {Σ Σ}_{k k = = 00}^{L L - - 11} exp exp {{jπα jπα ((22 k k + + N N + + 11))}} {r r}_{k k + + N N}^{* *} {r r}_{k k} | |$

$\cdot &Center Dot; cos cos (({22 πϵ πϵ}_{00} + + arg arg {{{Σ Σ}_{k k = = 00}^{L L - - 11} exp exp {{jπα jπα ((22 k k + + N N + + 11))}} {r r}_{k k + + N N}^{* *} {r r}_{k k}}})) - - - - - - ((1515))$

为了最大化Λ′(ε₀,α)，余弦部分应该最大化以取到局部极大值，因此余弦部分应取2πm，m为正整数（以Z表示）；且绝对值部分应该最大化，即：In order to maximize Λ′(ε ₀ ,α), the cosine part should be maximized to obtain a local maximum value, so the cosine part should be 2πm, m is a positive integer (expressed in Z); and the absolute value part should be maximized, which is:

$\overset{^^}{α α} = = \underset{α α}{arg arg max max} {{| | {Σ Σ}_{k k = = 00}^{L L - - 11} exp exp {{jπα jπα ((22 k k + + N N + + 11))}} {r r}_{k k + + N N}^{* *} {r r}_{k k} | |}} - - - - - - ((1616))$

和and

${\overset{^^}{ϵ ϵ}}_{00} = = - - \frac{11}{22 π π} arg arg {{{Σ Σ}_{k k = = 00}^{L L - - 11} exp exp {{jπα jπα ((22 k k + + N N + + 11))}} {r r}_{k k + + N N}^{* *} {r r}_{k k}}} + + m m,, m m &Element; &Element; Z Z - - - - - - ((1717))$

公式（16）和式（17）即构成一个最大似然估计方法。Formula (16) and formula (17) constitute a maximum likelihood estimation method.

图2示出了OFDM系统中的多普勒变化率估计方法的一个实施例，图2示出了该方法的具体步骤，包括：Figure 2 shows an embodiment of the Doppler rate of change estimation method in the OFDM system, and Figure 2 shows the specific steps of the method, including:

第一步、获得一个OFDM符号的采样点数据The first step is to obtain the sampling point data of an OFDM symbol

首先将射频端得到的连续信号经过A/D转换获得基带数字信号，缓存一个OFDM符号的采样点数据。First, the continuous signal obtained at the radio frequency end is converted through A/D to obtain a baseband digital signal, and the sampling point data of one OFDM symbol is buffered.

第二步：确定搜索范围(0,l)Step 2: Determine the search range (0,l)

该搜索范围是指多普勒变化率的取值范围，其包括实际中可能的最大多普勒变化率。在一个实施例中，可以通过在设备调试阶段的离线统计得到可能的最大多普勒变化率（简称统计最大值）。例如，当在设备调试阶段离线统计得到的实际最大多普勒变化率为0.1，则搜索范围的最大值可以确定为该统计最大值的1.5倍，即可以将搜索范围确定为（0，0.15）。应理解，搜索范围的最大值可以是统计最大值的其他倍数，但该范围应该包括统计最大值。The search range refers to a value range of the Doppler change rate, which includes a practically possible maximum Doppler change rate. In one embodiment, the possible maximum Doppler change rate (statistical maximum value for short) can be obtained through offline statistics during the equipment debugging stage. For example, when the actual maximum Doppler change rate obtained from offline statistics in the equipment debugging stage is 0.1, the maximum value of the search range can be determined to be 1.5 times the statistical maximum value, that is, the search range can be determined as (0, 0.15) . It should be understood that the maximum value of the search range may be other multiples of the statistical maximum value, but the range should include the statistical maximum value.

第三步：确定搜索步长λStep 3: Determine the search step size λ

搜索步长λ可由需求精度以及允许的硬件复杂度和时延来决定。搜索步长越小，可以获得的精度越大，但是允许的硬件复杂度和时延也越大。在一个实施例中，步长λ可以取0.01。The search step size λ can be determined by the required accuracy and the allowable hardware complexity and time delay. The smaller the search step size, the greater the precision that can be obtained, but the greater the allowable hardware complexity and delay. In an embodiment, the step size λ may be 0.01.

第四步：根据公式（16）在搜索范围中搜索归一化多普勒变化率的最大似然估计值Step 4: Search for the maximum likelihood estimate of the normalized Doppler rate of change in the search range according to formula (16)

在一个实施例中，可按照搜索步长遍历搜索范围来得到归一化多普勒变化率。例如，可通过线搜索的方法找最大值。图3示出了线搜索方法的步骤，该方法包括：In one embodiment, the normalized Doppler change rate can be obtained by traversing the search range according to the search step size. For example, the maximum value can be found by the method of line search. Figure 3 shows the steps of the line search method, which includes:

从0开始，按照步长λ遍历搜索范围内的所有归一化多普勒变化率估计值，根据公式（16），选择当 $P_{try} = | Σ_{k = 0}^{L - 1} \exp {jπα (2 k + N + 1)} r_{k + N}^{*} r_{k} |$ 最大时，所对应的多普勒变化率估计值。Starting from 0, traverse all normalized Doppler change rate estimates within the search range according to the step size λ, according to formula (16), select when $P_{try} = | Σ_{k = 0}^{L - 1} \exp {jπα (2 k + N + 1)} r_{k + N}^{*} r_{k} |$ At the maximum, the corresponding Doppler rate of change estimate.

在进一步的实施例中， $P_{try} = | Σ_{k = 0}^{L - 1} \exp {jπα (2 k + N + 1)} r_{k + N}^{*} r_{k} |$ 的指数计算可以通过查表的方式实现，三部分的相乘可以通过并行的复数乘法的方式实现。In a further embodiment, $P_{try} = | Σ_{k = 0}^{L - 1} \exp {jπα (2 k + N + 1)} r_{k + N}^{*} r_{k} |$ The index calculation of can be realized by looking up the table, The multiplication of the three parts can be realized by means of parallel complex multiplication.

第五步：根据公式来计算实际多普勒变化率Step 5: According to the formula to calculate the actual Doppler rate of change

在实际实现的过程中，可以提前计算出来，存成表格，通过使用查表的方式来降低复杂度。In the actual implementation process, It can be calculated in advance and stored as a table, and the complexity can be reduced by using the table lookup method.

上文描述了在AWGN信道下的OFDM系统中的多普勒变化率估计方法，然而在衰落信道下，直接使用上文描述的多普勒变化率估计方法，相比在AWGN信道下，其性能会有所下降。根据本发明的一个实施例，还提供一种在衰落信道下的改进方法。The above describes the Doppler change rate estimation method in the OFDM system under the AWGN channel. However, under the fading channel, the Doppler change rate estimation method described above is directly used. Compared with the AWGN channel, its performance will decline. According to an embodiment of the present invention, an improved method under fading channels is also provided.

基于衰落信道的多径时延扩展会造成OFDM符号之间的符号间干扰，使得CP中接近前一个符号的若干个采样点会受到前一个OFDM符号的影响，不适合用来估计多普勒变化率。因此，针对在衰落信道下的情况，仅使用CP尾部的部分采样点来进行估计。如图4所示，可采用CP尾部与OFDM符号末尾部分相关的ηL个采样点，其中η为所使用的采样点占CP所有采样点的百分比，0≤η≤1。The multipath delay spread based on the fading channel will cause intersymbol interference between OFDM symbols, so that several sampling points in the CP close to the previous symbol will be affected by the previous OFDM symbol, which is not suitable for estimating the Doppler change Rate. Therefore, for the case of a fading channel, only some sampling points at the tail of the CP are used for estimation. As shown in Figure 4, ηL sampling points related to the tail of the CP and the end of the OFDM symbol can be used, where η is the percentage of the sampling points used in all sampling points of the CP, 0≤η≤1.

从而公式（16）可进一步表示为：Thus formula (16) can be further expressed as:

$\overset{^^}{α α} = = \underset{α α}{arg arg max max} {{| | {Σ Σ}_{k k = = L L - - ηL ηL}^{L L - - 11} exp exp {{jπα jπα ((22 k k + + N N + + 11))}} {r r}_{k k + + N N}^{* *} {r r}_{k k} | |}} - - - - - - ((1818))$

公式（16）是公式（18）中η=1时的情况。Formula (16) is the case when η=1 in formula (18).

在一个实施例中，可以根据以下方法来确定η：In one embodiment, η can be determined according to the following method:

如果可以估计出信道的多径时延扩展t_spread，则可以根据估计出的多径时延扩展t_spread来确定采样点百分比η，如下式所示：If the multipath time delay spread t _spread of the channel can be estimated, the sampling point percentage η can be determined according to the estimated multipath time delay spread t _spread , as shown in the following formula:

其中，表示大于x的最小整数，n₀为考虑到系统多径时延扩展t_spread估计误差留出的余量，例如，可以取n₀=5。in, Indicates the smallest integer greater than x, and n ₀ is a margin for considering the system multipath delay spread t _spread estimation error, for example, n ₀ =5 may be taken.

上述方法可以尽可能多的利用采样点。在另一个实施例中，可以不考虑实时的信道多径时延扩展，而是采用某个经验值作为参考，即采用一个固定的百分比η=η₀。该方法的好处是可以避免估计实时的信道多径时延扩展带来的额外复杂度。The above method can utilize as many sampling points as possible. In another embodiment, instead of considering the real-time channel multipath delay extension, a certain empirical value is used as a reference, that is, a fixed percentage η=η ₀ is used. The advantage of this method is that it can avoid the extra complexity of estimating real-time channel multipath delay spread.

根据本发明的一个实施例，还提供一种OFDM系统中的多普勒变化率估计系统，该系统包括：用于获得一个OFDM符号的采样点数据的装置；以及，用于在取值范围内选择一个值作为多普勒变化率的值，使得OFDM符号循环前缀中的每个采样点与其在OFDM符号末尾的对应的采样点的联合概率的乘积最大的装置。According to an embodiment of the present invention, a system for estimating Doppler rate of change in an OFDM system is also provided, the system includes: a device for obtaining sampling point data of an OFDM symbol; A device that selects a value as the value of the Doppler change rate such that the product of the joint probability of each sampling point in the OFDM symbol cyclic prefix and its corresponding sampling point at the end of the OFDM symbol is maximum.

为了验证本发明提供的多普勒变化率估计方法的有效性，发明人进行了多次仿真实验，表1示出了仿真中采用的OFDM系统配置：In order to verify the effectiveness of the Doppler rate of change estimation method provided by the present invention, the inventor has carried out multiple simulation experiments, and Table 1 shows the OFDM system configuration adopted in the simulation:

表1Table 1

仿真实验一、验证本发明提供的多普勒变化率估计方法的精度Simulation experiment 1. Verify the accuracy of the Doppler rate-of-change estimation method provided by the present invention

将OFDM系统中的归一化多普勒变化率设置为0.1，分别采用本发明提供的估计方法（简称为ML方法）与现有技术中的单载波估计方法对多普勒变化率进行估计，图5给出了实验结果。从图5可见，传统的单载波多普勒变化率估计方法在OFDM场景下会失效，即在图中没有显示其精度。而本发明提供的多普勒变化率估计方法在OFDM场景下可以获得较高的精度，MSE在10^-3到10^-6之间。The normalized Doppler change rate in the OFDM system is set to 0.1, and the Doppler change rate is estimated by using the estimation method provided by the present invention (abbreviated as the ML method) and the single carrier estimation method in the prior art respectively, Figure 5 shows the experimental results. It can be seen from Fig. 5 that the traditional single-carrier Doppler rate of change estimation method will fail in the OFDM scenario, that is, its accuracy is not shown in the figure. However, the method for estimating the rate of change of Doppler provided by the present invention can obtain higher precision in the OFDM scene, and the MSE is between 10 ^-3 and 10 ^-6 .

仿真实验二、验证本发明提供的多普勒变化率估计方法对多普勒频移的敏感性Simulation experiment 2. Verify the sensitivity of the Doppler rate-of-change estimation method provided by the present invention to Doppler frequency shift

将信噪比设定为15dB，目标归一化多普勒变化率设置为0.1，在初始多普勒频移为0-1的情况下采用本发明提供的多普勒变化率估计方法对多普勒变化率的进行估计。图6给出了在不同初始多普勒频移的情况下的估计结果，该结果表明，随着初始多普勒频移的变化MSE几乎没有波动，表明本发明提供的估计方法对多普勒频移不敏感。Signal-to-noise ratio is set as 15dB, target normalized Doppler rate of change is set to 0.1, adopts the Doppler rate of change estimation method that the present invention provides under the situation that initial Doppler frequency shift is 0-1 to multiple Estimates of the Puller rate of change. Fig. 6 has provided the estimation result under the situation of different initial Doppler frequency shifts, and this result shows, along with the change MSE of initial Doppler frequency shifts has no fluctuation almost, shows that the estimation method provided by the present invention has great influence on Doppler Insensitive to frequency shifts.

仿真实验三、验证本发明提供的多普勒变化率估计方法及其改进方法在衰落场景下的精度Simulation experiment 3. Verify the accuracy of the Doppler rate of change estimation method and its improved method provided by the present invention in fading scenarios

将目标归一化多普勒变化率设置为0.1，衰落信道配置如表2所示：Set the target normalized Doppler rate of change to 0.1, and the fading channel configuration is shown in Table 2:

表2Table 2

图7给出了分别采用本发明提供的多普勒变化率估计方法（ML方法）及其改进方法（即使用CP尾部的部分采样点的方法）进行多普勒变化率估计的精度，从图7可见，使用改进的方法，MSE均小于原始ML方法，因而改进的方法与原始的ML方法相比可以提高在衰落信道下的估计精度。Figure 7 shows the accuracy of Doppler rate of change estimation using the Doppler rate of change estimation method provided by the present invention (ML method) and its improved method (that is, the method of using some sampling points at the CP tail), respectively, from Fig. 7 It can be seen that the MSE of the improved method is smaller than that of the original ML method, so compared with the original ML method, the improved method can improve the estimation accuracy in fading channels.

应该注意到并理解，在不脱离后附的权利要求所要求的本发明的精神和范围的情况下，能够对上述详细描述的本发明做出各种修改和改进。因此，要求保护的技术方案的范围不受所给出的任何特定示范教导的限制。It should be noted and understood that various modifications and improvements can be made to the invention described in detail above without departing from the spirit and scope of the invention as claimed in the appended claims. Accordingly, the scope of the claimed technical solution is not limited by any particular exemplary teaching given.

Claims

1. A Doppler rate-of-change estimation method in an OFDM system, comprising:

Step 1), obtaining sampling point data of an OFDM symbol;

Step 2), select a value in the range of values as the value of the normalized Doppler rate of change, so that each sampling point in the OFDM symbol cyclic prefix and its corresponding sampling point at the end of the OFDM symbol The product of the joint probabilities is the largest, and the value of the Doppler rate of change is calculated from the value of the normalized Doppler rate of change, including:

Step 21), select the value α in the normalized search range, a value α that will make the value of the following formula the largest as the value of the normalized Doppler rate of change

| | {Σ Σ}_{k k = = L L - - η η L L}^{L L - - 11} exp exp {{j j π π α α ((22 k k + + N N + + 11))}} {r r}_{k k + + N N}^{* *} {r r}_{k k} | |,,

Among them, L is the number of sampling points of the cyclic prefix of the OFDM symbol, N is the number of sampling points of the effective OFDM symbol, j is the imaginary number symbol, k is the serial number of the sampling point, r _k is the kth received signal, is the conjugate of the k+Nth received signal, 0≤η≤1;

Step 22), calculate the value of Doppler rate of change according to the following formula:

{Δf Δ f}_{D D. o o p p p p l l e e r r} = = \frac{{Δf Δ f}_{s the s u u b b c c a a r r r r i i e e r r}}{{T T}_{s the s}} \overset{^^}{α α},,

Wherein, Δf _subcarrier is the subcarrier spacing of the OFDM system, T _s is the sampling interval, is the value of the normalized Doppler rate of change.

2. The method of claim 1, wherein,

{r r}_{k k} = = {s the s}_{k k} exp exp [[j j ((\frac{22 π π}{N N} {Σ Σ}_{p p = = 11}^{k k} (({ϵ ϵ}_{00} + + α α p p)) + + {θ θ}_{00}))]] + + {n no}_{k k},,

j is an imaginary number symbol, k is the sampling point number, s _k and _nk represent the kth transmitted signal and the kth noise signal respectively, ε ₀ represents the initial Doppler frequency shift, and θ ₀ is the unknown initial phase.

3. The method according to claim 1 or 2, wherein n is determined according to the following formula:

Among them, L is the number of sampling points of the OFDM symbol cyclic prefix, t _spread is the multipath delay spread, T _s is the sampling interval, Indicates the smallest integer greater than x, and n ₀ is the margin left in consideration of the multipath delay spread t _spread estimation error.

4. The method according to claim 1 or 2, wherein,

η is a constant.

5. The method of claim 4, wherein,

n=1.

6. The method according to claim 1 or 2, wherein, step 1) also includes before:

Step 0), A/D conversion is performed on the obtained continuous signal to obtain a baseband digital signal.

7. The method according to claim 1 or 2, wherein, step 21) also includes before:

Determine the normalized search scope.

8. The method of claim 7, wherein the normalized search range is determined from offline statistics of the commissioning phase.

9. The method according to claim 1 or 2, wherein step 21) comprises:

Step 211), starting from the minimum value of the normalized search range, traverse the value α _test in the normalized search range with the search step size λ and calculate the following formula according to this value:

{P P}_{t t r r y the y} = = | | {Σ Σ}_{k k = = L L - - η η L L}^{L L - - 11} exp exp {{{jπα jπα}_{t t e e s the s t t} ((22 k k + + N N + + 11))}} {r r}_{k k + + N N}^{* *} {r r}_{k k} | |,,

Among them, L is the number of sampling points of the cyclic prefix of the OFDM symbol, N is the number of sampling points of the effective OFDM symbol, j is the imaginary number symbol, k is the serial number of the sampling point, r _k is the kth sampling point, is the conjugate of the k+N sampling point, 0≤η≤1;

Step 212), selecting α _test corresponding to P _try with the largest value as the value of the normalized Doppler rate of change.

10. The method according to claim 9, wherein, before step 211) also includes:

Determine the search step size λ.

11. A Doppler rate of change estimation system in an OFDM system, comprising:

means for obtaining sample point data of an OFDM symbol; and

Used to select a value in the value range as the value of the normalized Doppler rate of change, so that the joint probability of each sampling point in the OFDM symbol cyclic prefix and its corresponding sampling point at the end of the OFDM symbol The product of is the largest, and a device that calculates the value of the Doppler rate of change based on the value of the normalized Doppler rate of change, wherein, selecting the value α within the normalized search range will maximize the value of the following formula α as the value of the normalized Doppler rate of change

| | {Σ Σ}_{k k = = L L - - η η L L}^{L L - - 11} exp exp {{j j π π α α ((22 k k + + N N + + 11))}} {r r}_{k k + + N N}^{* *} {r r}_{k k} | |,,

Among them, L is the number of sampling points of the cyclic prefix of the OFDM symbol, N is the number of sampling points of the effective OFDM symbol, j is the imaginary number symbol, k is the serial number of the sampling point, r _k is the kth received signal, is the conjugate of the k+Nth received signal, 0≤η≤1; and

Calculate the value of the Doppler rate of change according to the following formula:

{Δf Δf}_{D D. o o p p p p l l e e r r} = = \frac{{Δf Δf}_{s the s u u b b c c a a r r r r i i e e r r}}{{T T}_{s the s}} \overset{^^}{α α},,