CN105141340A - Full-digital receiving method of direct spread MSK signal - Google Patents

Abstract

The invention provides a full-digital receiving method of a direct spread MSK signal. The full-digital receiving method comprises constructing the direct spread MSK signal into an approximate direct spread BPSK signal, acquiring the constructed approximate direct spread BPSK signal by use of a two-dimensional combined acquisition algorithm of pseudo-code phases and carrier Doppler frequency shift based on Doppler effect correction-FFT, tracking the acquired pseudo-code phases and carrier phases, and performing processing, such as de-spreading, demodulation and detection, on a synthesized signal to recover transmitted data.

Description

Translated fromChinese

直扩MSK信号的全数字接收方法All-digital receiving method of direct spread MSK signal

技术领域technical field

本发明涉及数字通信技术领域，本发明涉及一种数字通信技术，特别是一种直扩MSK信号的全数字接收方法。The present invention relates to the technical field of digital communication, and the present invention relates to a digital communication technology, in particular to an all-digital receiving method of a direct spread MSK signal.

背景技术Background technique

目前，扩频技术多基于BPSK、QPSK调制方式，在存在严重非线性失真、多普勒频移与多径衰落的应用领域，直扩BPSK/QPSK系统就无法适用了。直扩MSK信号结合了扩频系统的低截获性、多用户随机选址能力、抗干扰性等优点和最小频移键控信号的包络恒定、频谱利用率高、能量集中、旁瓣衰减快、带外辐射功率低、对非线性失真不敏感等优点，因而在战术数据链、民用航空地空数据链、导弹制导指令传输、卫星通信等领域得到了广泛应用。如美军为三军联合作战而研制的联合战术信息分发系统(JTIDS)，采用的就是“跳频+扩频+MSK调制”的工作方式，该系统被广泛应用于多种武器平台。At present, the spread spectrum technology is mostly based on BPSK and QPSK modulation methods. In the application fields with severe nonlinear distortion, Doppler frequency shift and multipath fading, the direct spread BPSK/QPSK system cannot be applied. The direct spread MSK signal combines the advantages of low interception, multi-user random site selection, and anti-interference of the spread spectrum system with the constant envelope of the minimum frequency shift keying signal, high spectrum utilization, energy concentration, and fast sidelobe attenuation , low out-of-band radiation power, and insensitivity to nonlinear distortion, etc., so it has been widely used in tactical data links, civil aviation ground-to-air data links, missile guidance command transmission, satellite communications and other fields. For example, the Joint Tactical Information Distribution System (JTIDS) developed by the U.S. military for the joint operations of the three armed forces adopts the working method of "frequency hopping + spread spectrum + MSK modulation". This system is widely used in various weapon platforms.

直扩MSK信号接收机处理的最终目标是解扩解调出发送数据，伪码相位和载波频率的捕获是解扩解调的前提条件，以往的接收机大多是对接收到的直扩MSK信号下变频处理后分别进行伪码相位捕获和载波多普勒频偏捕获。传统的伪码捕获方法有滑动相关法和匹配滤波法，在捕获速度和实现复杂度之间存在矛盾。同时在高动态环境下，接收机与发射机之间通常存在很高的径向速度，这使得接收信号存在几十KHz甚至几百KHz的多普勒频移，对扩频码的捕获和跟踪产生很大的影响。因此，必须要对载波多普勒频率进行捕获及补偿，这也叫做载波截获。于是伪码信号的捕获变成了对伪码相位和载波多普勒频偏的二维捕获，这就需要很长的捕获时间。所以，在高动态环境下，如何对直扩MSK信号准确而快速地进行捕获成为技术难点。The ultimate goal of direct spread MSK signal receiver processing is to despread and demodulate the transmitted data. The acquisition of pseudocode phase and carrier frequency is the prerequisite for despread and demodulate. After the down-conversion process, the pseudo-code phase acquisition and carrier Doppler frequency offset acquisition are respectively carried out. The traditional pseudo-code capture methods include sliding correlation method and matched filter method, and there is a contradiction between capture speed and implementation complexity. At the same time, in a high dynamic environment, there is usually a high radial velocity between the receiver and the transmitter, which makes the received signal have a Doppler frequency shift of tens of KHz or even hundreds of KHz, and the capture and tracking of the spreading code have a big impact. Therefore, it is necessary to capture and compensate the carrier Doppler frequency, which is also called carrier intercept. Therefore, the acquisition of the pseudocode signal becomes a two-dimensional acquisition of the phase of the pseudocode and the carrier Doppler frequency offset, which requires a long acquisition time. Therefore, in a highly dynamic environment, how to accurately and quickly capture direct spread MSK signals has become a technical difficulty.

G.J.R.Povey等人首先提出了基于数字部分匹配滤波器与FFT结合算法(PMF-FFT)的捕获模型，这种方法虽然在一定程度上缓解了多普勒频偏对捕获门限的影响，并且实现了伪码相位和载波频偏的二维捕获，但是这种方法主要适应于MPSK信号，并且多普勒频偏的捕获范围较小，高动态环境下仍然不适用。因而，如何在高动态环境下准确、快速地完成扩频信号的伪码相位和多普勒频偏二维捕获，成为直扩MSK信号全数字接收机的关键技术。G.J.R.Povey and others first proposed an acquisition model based on the combination of digital partial matched filter and FFT algorithm (PMF-FFT). Although this method alleviates the influence of Doppler frequency offset on the acquisition threshold to a certain extent, and realizes Two-dimensional capture of pseudo-code phase and carrier frequency offset, but this method is mainly suitable for MPSK signals, and the capture range of Doppler frequency offset is small, and it is still not applicable in high dynamic environments. Therefore, how to accurately and quickly complete the two-dimensional capture of the pseudo code phase and Doppler frequency offset of the spread spectrum signal in a high dynamic environment has become a key technology for the all-digital receiver of the direct spread MSK signal.

发明内容Contents of the invention

本发明的目的在于提供一种种直扩MSK信号的全数字接收方法，能够将接收的直扩MSK信号构造成一种近似直扩BPSK信号形式，接着在大多普勒频偏条件下，可以采用直扩BPSK信号的伪码相位和载波多普勒频偏的二维联合捕获算法，实现直扩MSK信号在高动态环境下的捕获和跟踪，避免了直接对直扩MSK信号进行捕获、跟踪的复杂处理。The purpose of the present invention is to provide a kind of all-digital receiving method of direct spread MSK signal, can construct the direct spread MSK signal that receives into a kind of approximate direct spread BPSK signal form, then under the condition of Doppler frequency deviation, can adopt direct spread The two-dimensional joint acquisition algorithm of pseudo-code phase and carrier Doppler frequency offset of BPSK signal realizes the acquisition and tracking of direct spread MSK signal in high dynamic environment, avoiding the complicated processing of directly capturing and tracking direct spread MSK signal .

一种直扩MSK信号的全数字接收方法，包括：将直扩MSK信号构造成近似直扩BPSK信号，采用基于多普勒补偿-FFT的伪码相位和载波多普勒频偏的二维联合捕获算法对构造后的近似直扩BPSK信号进行捕获，对捕获后的伪码相位和载波相位进行跟踪，及对同步后的信号通过解扩、解调、检测等处理恢复出发送数据。所述近似直扩BPSK信号是将经过中频采样、数字下变频和低通滤波后的直扩MSK信号与波形函数相乘后进行抽取并交替取样构造而成的。所述基于多普勒补偿-FFT的伪码相位和载波多普勒频偏的二维联合捕获算法包括：基于FFT的多普勒滤波；基于相位补偿因子和循环移动本地伪码的多普勒补偿；基于分段FFT的伪码相位并行捕获。An all-digital receiving method of a direct spread MSK signal, comprising: constructing a direct spread MSK signal into an approximate direct spread BPSK signal, using a two-dimensional combination of pseudo code phase and carrier Doppler frequency offset based on Doppler compensation-FFT The capture algorithm captures the constructed approximate direct spread BPSK signal, tracks the captured pseudo-code phase and carrier phase, and restores the transmitted data through despreading, demodulation, and detection of the synchronized signal. The approximate direct-spread BPSK signal is constructed by multiplying the direct-spread MSK signal after intermediate frequency sampling, digital down-conversion and low-pass filtering with a waveform function, and then extracting and alternately sampling. The two-dimensional joint acquisition algorithm of pseudo code phase and carrier Doppler frequency offset based on Doppler compensation-FFT includes: Doppler filtering based on FFT; Doppler based on phase compensation factor and circular mobile local pseudo code Compensation; Pseudo-code phase parallel acquisition based on segmented FFT.

采用上述直扩MSK信号的全数字接收方法，所述近似直扩BPSK信号的构造具体包括：Adopt the all-digital receiving method of above-mentioned direct spread MSK signal, the structure of described approximate direct spread BPSK signal specifically comprises:

低通滤波后得到的I、Q两路正交基带信号分别与波形函数相乘得到四路输出信号，其中T_c为扩频码的码片宽度；The I and Q quadrature baseband signals obtained after low-pass filtering are respectively compared with the waveform function Multiply to obtain four output signals, where T is the chip_width of the spreading code;

对四路输出信号进行P倍(P为过采样倍数)抽取得到四路信号，分别为y_I1(k’)、y_Q1(k’)、y_I2(k’)、y_Q2(k’)；其中y_I1(k’)和y_Q1(k’)分别为I路基带信号、Q路基带信号与波形函数相乘后抽取得到的信号，y_I2(k’)和y_Q2(k’)分别为Q路基带信号、I路基带信号与波形函数相乘后抽取得到的信号；其中k’≥0,且为整数，当k’为奇数时y_I1(k’)和y_Q1(k’)为0，当k’为偶数时y_I2(k’)、y_Q2(k’)为0；Extract the four output signals by P times (P is the oversampling multiple) to obtain four signals, namely y_I1 (k'), y_Q1 (k'), y_I2 (k'), y_Q2 (k') ; where y_I1 (k') and y_Q1 (k') are the I subgrade band signal, the Q subgrade band signal and the waveform function respectively The signals extracted after multiplication, y_I2 (k') and y_Q2 (k') are the Q subgrade band signal, the I subgrade band signal and the waveform function The signal obtained after multiplication; where k'≥0, and is an integer, when k' is odd, y_I1 (k') and y_Q1 (k') are 0, when k' is even, y_I2 (k '), y_Q2 (k') are 0;

对y_I1(k’)和-y_I2(k’)交替取样作为I路，对y_Q1(k’)和y_Q2(k’)交替取样作为Q路，将I、Q两路信号组合而成的复信号I+jQ即为近似直扩BPSK信号。Alternately sample y_I1 (k') and -y_I2 (k') as the I channel, alternately sample y_Q1 (k') and y_Q2 (k') as the Q channel, and combine the I and Q signals to form The resulting complex signal I+jQ is an approximate direct spread BPSK signal.

采用上述直扩MSK信号的全数字接收方法，在对近似直扩BPSK信号进行捕获前，进行以下处理：对构造后的近似直扩BPSK信号，采集K个伪码周期的扩频信号，伪码周期为N；对K*N个样点进行重排序，得到N段长为K的新序列。Adopt the all-digital receiving method of above-mentioned direct spread MSK signal, before the approximate direct spread BPSK signal is captured, carry out following processing: to the approximate direct spread BPSK signal after the construction, collect the spread spectrum signal of K pseudocode period, pseudocode The period is N; K*N sample points are reordered to obtain N new sequences with a length of K.

采用上述直扩MSK信号的全数字接收方法，通过对每一段长为K的序列做K点FFT，进行多普勒滤波。Using the above-mentioned all-digital receiving method of direct-spread MSK signals, Doppler filtering is performed by performing K-point FFT on each sequence with a length of K.

采用上述直扩MSK信号的全数字接收方法，多普勒频偏补偿包括：将多普勒频偏表示为f_c为扩频码速率，Δf为剩余频偏，其中每一个具体的f_d仅对应一组(k,m)，其中k和m为整数，k≤K-1，m≥0；通过对多普勒滤波后的N段FFT结果乘以相应的相位补偿因子补偿其中i＝0,1,...N-1，j为虚部单位；通过在时域上将本地伪码乘以一个的频率分量补偿部分，等价于在频域上将本地伪码的FFT序列循环右移m位；通过适当地设置K的取值，使剩余频偏Δf不大于f_c/2KN，从而不影响后面的伪码相位估计。Using the above-mentioned all-digital receiving method of the direct spread MSK signal, the Doppler frequency offset compensation includes: expressing the Doppler frequency offset as f_c is the spreading code rate, Δf is the remaining frequency offset, and each specific f_d corresponds to only one group (k, m), where k and m are integers, k≤K-1, m≥0; The N-segment FFT result after Doppler filtering is multiplied by the corresponding phase compensation factor compensate Where i=0,1,...N-1, j is the imaginary unit; by multiplying the local pseudocode by a frequency component compensation part, which is equivalent to cyclically shifting the FFT sequence of the local pseudo-code by m bits in the frequency domain; by setting the value of K appropriately, the remaining frequency offset Δf is not greater than f_c /2KN, thus not affecting the following pseudo-code phase estimation.

采用上述直扩MSK信号的全数字接收方法，采用分段FFT进行伪码相位并行捕获，包括Using the above-mentioned all-digital receiving method of the direct spread MSK signal, the pseudo-code phase parallel acquisition is carried out by using segmented FFT, including

对经过多普勒滤波、相位补偿及伪码FFT序列的移位处理后的输出信号进行二次重排序恢复为原来的顺序，即重排为K段长为N的序列，并对每段长为N的序列进行基于FFT的伪码相位并行捕获，得到伪码的相关输出结果；After Doppler filtering, phase compensation and pseudo-code FFT sequence shift processing, the output signal is reordered twice and restored to the original order, that is, it is rearranged into a sequence of K segments with a length of N, and each segment has a length of N Perform FFT-based pseudo-code phase parallel capture for the sequence of N, and obtain the relevant output results of the pseudo-code;

基于恒虚警准则设置判决门限；Set the judgment threshold based on the constant false alarm criterion;

采用包络检测法，对相关输出结果求模，并将峰值与判决门限进行比较：Using the envelope detection method, the relevant output results are modulo, and the peak value is compared with the decision threshold:

(1)若峰值超过判决门限，则伪码相位捕获成功；(1) If the peak value exceeds the decision threshold, the phase capture of the pseudo code is successful;

(2)若峰值未超过判决门限，将K段数据中的第一段数据丢弃，其余K-1段数据依次向前移动，后面将继续接收N点数据，重排后，得到新的N段长为K点的序列，继续对伪码相位捕获，直到峰值超过判决门限为止。(2) If the peak value does not exceed the judgment threshold, the first segment of data in the K segment data is discarded, and the remaining K-1 segment data moves forward sequentially, and the N point data will continue to be received later. After rearrangement, a new N segment is obtained For a sequence of K points long, continue to capture the phase of the pseudo code until the peak value exceeds the decision threshold.

本发明的直扩MSK信号二维联合捕获方法具有以下优点：(1)由于直扩MSK信号形式的特殊性，与直扩BPSK信号有很多成熟的捕获算法相比，直扩MSK信号的捕获方法相对较少。将直扩MSK信号转换成一种近似直扩BPSK信号形式以后，对直扩BPSK的成熟算法进行修改后就可用到直扩MSK信号中来，降低了直扩MSK全数字接收机的开发难度和代价。(2)本发明中的捕获方法通过循环移动本地伪码的FFT序列来对大多普勒频偏进行补偿，可以方便地扩大多普勒频率搜索范围，而不降低二维捕获的性能，因而非常适合高动态环境下的各种应用。(3)对伪码相位和载波频偏同时进行搜索，减少了捕获时间，可满足高数据速率扩频通信的应用需求。The direct spread MSK signal two-dimensional joint capture method of the present invention has the following advantages: (1) due to the particularity of the direct spread MSK signal form, there are many mature capture algorithms compared with the direct spread BPSK signal, and the capture method of the direct spread MSK signal Relatively small. After the direct spread MSK signal is converted into an approximate direct spread BPSK signal form, the mature algorithm of the direct spread BPSK can be used in the direct spread MSK signal after modification, which reduces the development difficulty and cost of the direct spread MSK all-digital receiver . (2) the acquisition method in the present invention compensates the Doppler frequency offset by cyclically moving the FFT sequence of the local pseudocode, which can easily expand the Doppler frequency search range without reducing the performance of two-dimensional capture, so it is very Suitable for a variety of applications in highly dynamic environments. (3) Simultaneously search the pseudocode phase and carrier frequency offset, which reduces the acquisition time and can meet the application requirements of high data rate spread spectrum communication.

下面结合说明书附图对本发明做进一步描述。The present invention will be further described below in conjunction with the accompanying drawings.

附图说明Description of drawings

图1是本发明方法流程图。Fig. 1 is a flow chart of the method of the present invention.

图2是本发明实施例的捕获模块相关输出的三维图形。Fig. 2 is a three-dimensional graph of the relevant output of the capture module of the embodiment of the present invention.

图3是本发明实施例的检测概率和虚警概率随输入信噪比的变化曲线。Fig. 3 is a variation curve of detection probability and false alarm probability with input signal-to-noise ratio according to an embodiment of the present invention.

图4是本发明实施例的全数字接收机系统组成图。Fig. 4 is a system composition diagram of an all-digital receiver according to an embodiment of the present invention.

具体实施方式Detailed ways

本发明输入的中频信号可以表示为The input intermediate frequency signal of the present invention can be expressed as

其中，γ_i为发送的第i个扩频后的数据符号，有γ_i＝±1，d_i为发送的数据序列，c_i为伪码序列，中的|i|_N为|i|模N运算，表示当前的chip序号，N为扩频码周期，T_c＝T/M为扩频码的码片宽度，M为扩频因子，T为扩频前数据符号宽度，f_c＝1/T_c为扩频码速率，f_I为中频频率，ε为接收的伪码信号与本地伪码相差的码片数，εT_c为接收的伪码信号与本地伪码的相位差，θ为信号接收时刻波形函数的初相，θ与ε满足一定的对应关系，即为信号接收时刻载波函数的初相，f_d为输入信号与本地参考信号的频率之差，主要由多普勒效应产生，因此称为多普勒频率。接收机捕获的目的就是得到ε、f_d的估计值。Wherein, γ_i is the transmitted i-th spread data symbol, and γ_i =±1, d_i is the data sequence sent,_ci is the pseudocode sequence, where |i|_N is |i| modulo N operation, which means the current chip serial number, N is the spreading code period, T_c =T/M is the chip width of the spreading code, M is the spreading factor, and T is Data symbol width before spreading, f_c =1/T_c is the spreading code rate, f_I is the intermediate frequency frequency, ε is the number of chips that the pseudo-code signal received differs from the local pseudo-code, and εT_c is the pseudo-code received The phase difference between the signal and the local pseudo-code, θ is the initial phase of the waveform function at the moment of signal reception, and θ and ε satisfy a certain corresponding relationship, namely It is the initial phase of the carrier function at the time of signal reception, and f_d is the frequency difference between the input signal and the local reference signal, which is mainly produced by the Doppler effect, so it is called the Doppler frequency. The purpose of receiver acquisition is to obtain the estimated values of ε and f_d .

对输入的中频信号以采样频率f_s＝P/T_c(P为过采样倍数)进行中频采样、数字下变频处理后，得到I、Q两路基带信号为After the input intermediate frequency signal is sampled at the sampling frequency f_s =P/T_c (P is the oversampling multiple), after intermediate frequency sampling and digital down-conversion processing, the two baseband signals of I and Q are obtained as

结合图1，一种直扩MSK信号的全数字接收方法，包括以下步骤：In conjunction with Fig. 1, a kind of all-digital receiving method of direct spread MSK signal, comprises the following steps:

步骤S101，将直扩MSK信号构造成近似直扩BPSK信号；Step S101, constructing the direct spread MSK signal into an approximate direct spread BPSK signal;

步骤S102，采用基于多普勒补偿-FFT的伪码相位和载波多普勒频偏的二维联合捕获算法对构造后的近似直扩BPSK信号进行捕获；Step S102, using a two-dimensional joint acquisition algorithm based on Doppler compensation-FFT pseudo-code phase and carrier Doppler frequency offset to capture the constructed approximate direct spread BPSK signal;

步骤S103，对捕获后的伪码相位和载波相位进行跟踪；Step S103, tracking the captured pseudo-code phase and carrier phase;

步骤S104，对同步后的信号通过解扩、解调、检测等处理恢复出发送数据。In step S104, the synchronized signal is processed to recover the transmitted data through despreading, demodulation, detection and other processing.

在步骤S101中，为了消除调制波形函数的影响，将这两路基带信号分别与波形函数进行相乘，得到四路信号，接下来对四路信号进行P倍抽取，得到以T_c为采样间隔的四路信号。四路基带信号可表示为：In step S101, in order to eliminate the influence of the modulation waveform function, the two baseband signals are respectively combined with the waveform function Multiplication is performed to obtain four-channel signals, and then P-fold extraction is performed on the four-channel signals to obtain four-channel signals with T_c as the sampling interval. The four baseband signals can be expressed as:

γ_I、γ_Q分别是γ_i进行串并变换后内插两倍得到的偶数序列和奇数序列，并且γ_Q比γ_I延迟一位。对四路输出信号进行P倍(P为过采样倍数)抽取得到四路信号，本发明采用12倍，分别为y_I1(k’)、y_Q1(k’)、y_I2(k’)、y_Q2(k’)；其中y_I1(k’)和y_Q1(k’)分别为I路基带信号、Q路基带信号与波形函数相乘后抽取得到的信号，y_I2(k’)和y_Q2(k’)分别为Q路基带信号、I路基带信号与波形函数相乘后抽取得到的信号。γ_I and γ_Q are respectively the even sequence and the odd sequence obtained by interpolating twice the serial-to-parallel transformation of γ_i , and γ_Q is delayed by one bit from γ_I. Carry out P times (P is oversampling multiple) to four-way output signal and obtain four-way signal, the present invention adopts 12 times, respectively y_I1 (k'), y_Q1 (k'), y_I2 (k'), y_Q2 (k'); where y_I1 (k') and y_Q1 (k') are I subgrade band signal, Q subgrade band signal and waveform function respectively The signals extracted after multiplication, y_I2 (k') and y_Q2 (k') are the Q subgrade band signal, the I subgrade band signal and the waveform function The signal obtained after multiplication.

根据γ_I、γ_Q分别是γ_i进行串并变换后内插两倍得到的偶数序列和奇数序列，并且γ_Q比γ_I延迟一位的规律，对y_I1、-y_I2交替取样作为I路，对y_Q1、y_Q2交替取样作为Q路，将I、Q两路信号组合而成复信号I+jQ，可得到输出信号为According to the rule that γ_I and γ_Q are the even sequence and odd sequence obtained by interpolating twice after γ_i is serial-parallel transformed, and γ_Q is delayed by one bit from γ_I , y_I1 and -y_I2 are alternately sampled as I y_Q1 and y_Q2 are alternately sampled as the Q channel, and the I and Q signals are combined to form a complex signal I+jQ, and the output signal can be obtained as

式(8)即为将直扩MSK信号转换成的近似直扩BPSK信号。Equation (8) is the approximate direct-spread BPSK signal converted from the direct-spread MSK signal.

在步骤S102中，由Gold序列的自相关特性知，将r(k)与伪随机序列进行匹配时，上式中的前后两项互不影响，令s_k＝γ(k-εT_c)·cosθ+j·γ(k-εT_c-T_c)·sinθ来分析接收机如何在大多普勒频偏下进行伪码相位和载波多普勒频偏的二维捕获。In step S102, based on the autocorrelation characteristics of the Gold sequence, when r(k) is matched with the pseudo-random sequence, the two terms in the above formula do not affect each other, let s_k =γ(k-εT_c )· cosθ+j·γ(k-εT_c -T_c )·sinθ to analyze how the receiver performs two-dimensional capture of pseudocode phase and carrier Doppler frequency offset under large frequency offset.

接收K个数据符号，每个数据符号里面包含一个周期为N的伪码序列，即接收一个长度为K×N的序列，样点可表示为r_0,0,r_1,0,…r_K-1,0,r_0,1,r_1,1,…r_K-1,1,……,r_0,N-1,r_1,N-1,…,r_K-1,N-1，对该序列以N为间隔进行抽取后重排序，得到N段长为K的新序列，新序列的排列顺序为r_0,0,r_0,1,…r_0,K-1,r_1,0,r_1,1,…r_1,K-1,……,r_N-1,0,r_N-1,1,…,r_N-1,K-1，为了能够更直观地进行观察，把这个数据序列用矩阵A的形式表示为Receive K data symbols, and each data symbol contains a pseudocode sequence with a period of N, that is, a sequence with a length of K×N is received, and the sample points can be expressed as r_0,0 , r_1,0 ,…r_{K -1,0} ,r_0,1 ,r_1,1 ,…r_K-1,1 ,…,r_0,N-1 ,r_1,N-1 ,…,r_K-1,N-1 , the sequence is extracted at intervals of N and reordered to obtain N new sequences of length K. The order of arrangement of the new sequences is r_0,0 ,r_0,1 ,…r_0,K-1 ,r_{1 ,0} ,r_1,1 ,…r_1,K-1 ,……,r_N-1,0 ,r_N-1,1 ,…,r_N-1,K-1 , in order to be more intuitive Observe, express this data sequence in the form of matrix A as

$\mathrm{<span><span>A</span>A</span>}<span><span>=</span>=</span>\left[\begin{array}{cccc}{\mathrm{<span><span>r</span>r</span>}}_{\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span>\mathrm{<span><span>0</span>0</span>}}& {\mathrm{<span><span>r</span>r</span>}}_{\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>0</span>0</span>}}& <span><span>...</span>...</span>& {\mathrm{<span><span>r</span>r</span>}}_{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>0</span>0</span>}}\\ {\mathrm{<span><span>r</span>r</span>}}_{\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}& {\mathrm{<span><span>r</span>r</span>}}_{\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}& <span><span>...</span>...</span>& {\mathrm{<span><span>r</span>r</span>}}_{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}\\ \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}& \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}& \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}& \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}\\ {\mathrm{<span><span>r</span>r</span>}}_{\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}& {\mathrm{<span><span>r</span>r</span>}}_{\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}& <span><span>...</span>...</span>& {\mathrm{<span><span>r</span>r</span>}}_{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}\end{array}\right]<span><span>=</span>=</span>\left[\begin{array}{cccc}{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>0</span>0</span>}}& {\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>e</span>e</span>}}^{{\mathrm{<span><span>j\&omega;</span>j\&omega;</span>}}_{\mathrm{<span><span>d</span>d</span>}}\frac{\mathrm{<span><span>1</span>1</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}& <span><span>...</span>...</span>& {\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>e</span>e</span>}}^{{\mathrm{<span><span>j\&omega;</span>j\&omega;</span>}}_{\mathrm{<span><span>d</span>d</span>}}\frac{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}\\ {\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\mathrm{<span><span>e</span>e</span>}}^{{\mathrm{<span><span>j\&omega;</span>j\&omega;</span>}}_{\mathrm{<span><span>d</span>d</span>}}\frac{\mathrm{<span><span>N</span>N</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}& {\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>e</span>e</span>}}^{{\mathrm{<span><span>j\&omega;</span>j\&omega;</span>}}_{\mathrm{<span><span>d</span>d</span>}}\frac{\mathrm{<span><span>N</span>N</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}& <span><span>...</span>...</span>& {\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>e</span>e</span>}}^{{\mathrm{<span><span>j\&omega;</span>j\&omega;</span>}}_{\mathrm{<span><span>d</span>d</span>}}\frac{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}\\ \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}& \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}& \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}& \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}\\ {\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\mathrm{<span><span>e</span>e</span>}}^{{\mathrm{<span><span>j\&omega;</span>j\&omega;</span>}}_{\mathrm{<span><span>d</span>d</span>}}\frac{<span><span>(</span>(</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>\mathrm{<span><span>N</span>N</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}& {\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>e</span>e</span>}}^{{\mathrm{<span><span>j\&omega;</span>j\&omega;</span>}}_{\mathrm{<span><span>d</span>d</span>}}\frac{<span><span>(</span>(</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>\mathrm{<span><span>N</span>N</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}& <span><span>...</span>...</span>& {\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>e</span>e</span>}}^{{\mathrm{<span><span>j\&omega;</span>j\&omega;</span>}}_{\mathrm{<span><span>d</span>d</span>}}\frac{\mathrm{<span><span>K</span>K</span>}\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}\end{array}\right]<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>9</span>9</span>}<span><span>)</span>)</span>$

矩阵中的N列对应重排序后的N段序列，对这N段数据进行多普勒滤波，即对矩阵A的每一列分别进行K点FFT变换，得到的结果用矩阵B的形式表示为The N columns in the matrix correspond to the reordered N segments of the sequence, and Doppler filtering is performed on the N segments of data, that is, K-point FFT transformation is performed on each column of the matrix A, and the obtained result is expressed in the form of the matrix B as

$\mathrm{<span><span>B</span>B</span>}<span><span>=</span>=</span>\left[\begin{array}{cccc}\mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>& \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>& <span><span>...</span>...</span>& \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>\\ \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>& \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>& <span><span>...</span>...</span>& \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>\\ \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}& \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}& \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}& \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}\\ \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>& \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>& <span><span>...</span>...</span>& \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>\end{array}\right]<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>10</span>10</span>}<span><span>)</span>)</span>$

式(10)矩阵B的每一个元素可表示为Each element of matrix B in formula (10) can be expressed as

$\mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>n</span>no</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>e</span>e</span>}}^{{\mathrm{<span><span>j\&omega;</span>j\&omega;</span>}}_{\mathrm{<span><span>d</span>d</span>}}\frac{\mathrm{<span><span>n</span>no</span>}\mathrm{<span><span>N</span>N</span>}<span><span>+</span>+</span>\mathrm{<span><span>i</span>i</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>j</span>j</span>}\frac{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}}{\mathrm{<span><span>K</span>K</span>}}\mathrm{<span><span>n</span>no</span>}\mathrm{<span><span>k</span>k</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>e</span>e</span>}}^{{\mathrm{<span><span>j\&omega;</span>j\&omega;</span>}}_{\mathrm{<span><span>d</span>d</span>}}\frac{\mathrm{<span><span>i</span>i</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}\underset{\mathrm{<span><span>n</span>no</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}{\mathrm{<span><span>e</span>e</span>}}^{{\mathrm{<span><span>j\&omega;</span>j\&omega;</span>}}_{\mathrm{<span><span>d</span>d</span>}}\frac{\mathrm{<span><span>n</span>no</span>}\mathrm{<span><span>N</span>N</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}<span><span>-</span>-</span>\mathrm{<span><span>j</span>j</span>}\frac{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}}{\mathrm{<span><span>K</span>K</span>}}\mathrm{<span><span>n</span>no</span>}\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span><span><span>...</span>...</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span><span><span>...</span>...</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>11</span>11</span>}<span><span>)</span>)</span>$

其中，ω_d＝2πf_d是接收信号的多普勒角频率，每一个具体的ω_d仅对应一组(k,m)其中k和m为整数，k≤K-1，m≥0，使得成立，将ω_d代入到式(11)得到当接收信号多普勒频率在FFT频点上时，有Δω＝0，Among them, ω_d = 2πf_d is the Doppler angular frequency of the received signal, each specific ω_d only corresponds to a group (k, m) where k and m are integers, k≤K-1, m≥0, so that established, substituting ω_d into formula (11) to get When the Doppler frequency of the received signal is at the FFT frequency point, Δω=0,

将矩阵B的第k行看作是一个中心频率为的多普勒滤波通道，当接收信号频率在附近时，经过多普勒滤波，信号频谱的大部分在第k个滤波通道输出，只有很小一部分会泄漏到其他通道。可见，对接收信号的多普勒滤波使得有用信号的绝大部分能量都集中在了相应的多普勒通道上，又由于高斯白噪声的功率谱在整个频带上都是均匀分布的，它的能量会均匀分布在各个通道中，因此多普勒滤波还具有一定的去噪功能。但是滤波后的输出仍然包含多普勒频偏，本发明采用相位补偿的方法对每个通道进行处理，具体的做法是将多普勒滤波器输出乘以相应的相位补偿因子。相位补偿因子矩阵C可表示为Think of row k of matrix B as a center frequency of Doppler filter channel, when the received signal frequency is in When it is near, after Doppler filtering, most of the signal spectrum is output in the kth filtering channel, and only a small part will leak to other channels. It can be seen that the Doppler filtering of the received signal makes most of the energy of the useful signal concentrated on the corresponding Doppler channel, and because the power spectrum of Gaussian white noise is evenly distributed on the entire frequency band, its The energy will be evenly distributed in each channel, so the Doppler filter also has a certain denoising function. However, the filtered output still contains Doppler frequency offset. The present invention uses a phase compensation method to process each channel. The specific method is to multiply the Doppler filter output by a corresponding phase compensation factor. The phase compensation factor matrix C can be expressed as

$\mathrm{<span><span>C</span>C</span>}<span><span>=</span>=</span>\left[\begin{array}{cccc}\mathrm{<span><span>1</span>1</span>}& \mathrm{<span><span>1</span>1</span>}& <span><span>...</span>...</span>& \mathrm{<span><span>1</span>1</span>}\\ \mathrm{<span><span>1</span>1</span>}& {\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>j</span>j</span>}\frac{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}}{\mathrm{<span><span>K</span>K</span>}\mathrm{<span><span>N</span>N</span>}}}& <span><span>...</span>...</span>& {\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}}{\mathrm{<span><span>K</span>K</span>}\mathrm{<span><span>N</span>N</span>}}<span><span>(</span>(</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>}\\ \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}& \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}& \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}& \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}\\ \mathrm{<span><span>1</span>1</span>}& {\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>j</span>j</span>}\frac{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>K</span>K</span>}\mathrm{<span><span>N</span>N</span>}}}& <span><span>...</span>...</span>& {\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>j</span>j</span>}\frac{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>K</span>K</span>}\mathrm{<span><span>N</span>N</span>}}<span><span>(</span>(</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>}\end{array}\right]<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>12</span>12</span>}<span><span>)</span>)</span>$

相位补偿后的输出矩阵D＝B*C为The output matrix D=B*C after phase compensation is

$\mathrm{<span><span>D</span>D.</span>}<span><span>=</span>=</span>\left[\begin{array}{cccc}\mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>& \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>& <span><span>...</span>...</span>& \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>\\ \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>& \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>j</span>j</span>}\frac{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}}{\mathrm{<span><span>K</span>K</span>}\mathrm{<span><span>N</span>N</span>}}}& <span><span>...</span>...</span>& \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>j</span>j</span>}\frac{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}}{\mathrm{<span><span>K</span>K</span>}\mathrm{<span><span>N</span>N</span>}}<span><span>(</span>(</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>}\\ \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}& \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}& \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}& \begin{array}{c}<span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\end{array}\\ \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>& \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>j</span>j</span>}\frac{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>K</span>K</span>}\mathrm{<span><span>N</span>N</span>}}}& <span><span>...</span>...</span>& \mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>j</span>j</span>}\frac{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>K</span>K</span>}\mathrm{<span><span>N</span>N</span>}}<span><span>(</span>(</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>}\end{array}\right]<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>13</span>13</span>}<span><span>)</span>)</span>$

多普勒滤波处理中FFT变换的频率分辨率为Δf＝f_c/KN，无模糊带宽为[0,f_c/N]，当多普勒频偏落在无模糊带宽范围内时，通过多普勒滤波和相位补偿，若在第k个通道上出现相关峰输出，根据前文所述k与ω_d的一一对应关系，便能够得到接收信号的多普勒频率。然而在高动态环境下，多普勒频偏一般可以达到几十甚至几百kHz，超出了无模糊带宽，高动态下的多普勒频偏可以表示为$f_d=\frac{k}{KN}{f}_c+\frac{m}{N}{f}_c+\mathrm{\&Delta;}f,m\&NotEqual;0,$为多普勒滤波和相位补偿后固定的剩余频偏，它的存在会降低伪码相位估计的相关峰值导致无法捕获到正确的伪码相位，在时域上将本地伪码乘以一个的频率分量可以消除这个固定的剩余频偏，等价于在频域上将本地伪码的FFT序列循环右移m位，这样处理后总会有一个通道中的输出只剩下不大于f_c/2KN的频差Δf，这样就可以通过适当地设置K的取值使这个剩余频差Δf不会影响后面的伪码相位估计。可见，搜索范围和本地伪码FFT变换结果的移位情况有关，如果向左最大移动n_L位，向右最大移动n_R位，那么频率的有效搜索范围变为假设系统要求的多普勒频偏搜索范围为[-f_d,f_d]，那么可以取其中为向上取整，表示向下取整。The frequency resolution of FFT transformation in Doppler filtering processing is Δf=f_c /KN, and the unambiguous bandwidth is [0, f_c /N]. When the Doppler frequency offset falls within the range of unambiguous bandwidth, multiple For Doppler filtering and phase compensation, if there is a correlation peak output on the kth channel, according to the one-to-one correspondence between k and_ωd mentioned above, the Doppler frequency of the received signal can be obtained. However, in a high dynamic environment, the Doppler frequency deviation can generally reach tens or even hundreds of kHz, exceeding the unambiguous bandwidth. The Doppler frequency deviation under high dynamics can be expressed as$f_d=\frac{k}{KN}{f}_c+\frac{m}{N}{f}_c+\mathrm{\&Delta;}f,m\&NotEqual;0,$ It is the fixed residual frequency offset after Doppler filtering and phase compensation. Its existence will reduce the correlation peak of the pseudo-code phase estimation and make it impossible to capture the correct pseudo-code phase. In the time domain, the local pseudo-code is multiplied by a The frequency component of can eliminate this fixed residual frequency offset, which is equivalent to cyclically shifting the FFT sequence of the local pseudocode to the right by m bits in the frequency domain, so that after processing, there will always be an output in a channel that is not greater than f_c /2KN frequency difference Δf, so that the remaining frequency difference Δf can not affect the following pseudo-code phase estimation by properly setting the value of K. It can be seen that the search range is related to the shift of the local pseudocode FFT transformation result. If the maximum shift is n_L bits to the left and n_R bits to the right, the effective search range of the frequency becomes Assuming that the Doppler frequency offset search range required by the system is [-f_d ,f_d ], then we can take in For rounding up, Indicates rounding down.

构造后的近似直扩BPSK信号存在数据符号跳变，一个伪码周期中有一部分伪随机码的极性发生变化破坏了它的自相关特性，从而对伪码相位捕获产生影响。为了消除符号跳变的影响，将构造后的信号进行延迟相乘。延迟相乘后的信号多普勒频率变为原来的两倍，所以在设置参数时多普勒频率的动态范围也要变为原来的两倍，且估计出多普勒频率之后要除2才是真正的多普勒频率。The constructed approximate DS BPSK signal has data symbol hopping, and the polarity of a part of the pseudo-random code changes in a pseudo-code cycle, which destroys its autocorrelation characteristics, thereby affecting the phase acquisition of the pseudo-code. In order to eliminate the influence of symbol hopping, the constructed signal is delayed and multiplied. The Doppler frequency of the signal after delay multiplication is doubled, so the dynamic range of the Doppler frequency is also doubled when setting parameters, and the Doppler frequency must be divided by 2 after the estimated Doppler frequency. is the true Doppler frequency.

经过多普勒滤波、相位补偿及伪码FFT序列的移位处理后，与信号多普勒频率对应的第k个通道输出信号为After Doppler filtering, phase compensation and pseudo-code FFT sequence shift processing, the kth channel output signal corresponding to the signal Doppler frequency is

$\mathrm{<span><span>D</span>D.</span>}<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>e</span>e</span>}}^{\mathrm{<span><span>j</span>j</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>2</span>2</span>}{\mathrm{<span><span>\&pi;mf</span>\&pi;mf</span>}}_{\mathrm{<span><span>c</span>c</span>}}}{\mathrm{<span><span>N</span>N</span>}}<span><span>+</span>+</span>\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>)</span>)</span>\frac{\mathrm{<span><span>i</span>i</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}\underset{\mathrm{<span><span>n</span>no</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}{\mathrm{<span><span>e</span>e</span>}}^{\mathrm{<span><span>j</span>j</span>}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}\mathrm{<span><span>\&omega;</span>\&omega;</span>}\frac{\mathrm{<span><span>n</span>no</span>}\mathrm{<span><span>N</span>N</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span><span><span>...</span>...</span><span><span>,</span>,</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>14</span>14</span>}<span><span>)</span>)</span>$

接下来，对处理后的输出信号进行二次重排序恢复为原来的顺序，即重排为K段长为N的序列，并对每段长为N的序列进行基于FFT的伪码相位并行捕获，即对整个序列做基于分段FFT的伪码相位并行捕获得到伪码的相关输出结果。Next, reorder the processed output signal twice to restore it to the original order, that is, rearrange it into K segments of N-length sequences, and perform FFT-based pseudo-code phase parallel capture on each N-length sequence , that is, the pseudo-code phase parallel capture based on segmented FFT is performed on the entire sequence to obtain the correlation output result of the pseudo-code.

基于FFT的伪码相位并行捕获采用两次FFT加一次IFFT来代替匹配滤波，本地伪码序列{c_i}FFT向右循环移动位的结果可以看成是序列进行FFT的结果。最终基于多普勒补偿-FFT的二维捕获输出结果即为：FFT-based pseudo-code phase parallel capture uses two FFTs plus one IFFT to replace matched filtering, and the local pseudo-code sequence {c_i }FFT moves circularly to the right The result of bits can be viewed as a sequence The result of performing an FFT. The final two-dimensional capture output based on Doppler compensation-FFT is:

$\begin{array}{c}\mathrm{<span><span>z</span>z</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&epsiv;</span>\&epsiv;</span>}<span><span>,</span>,</span>\mathrm{<span><span>k</span>k</span>}<span><span>,</span>,</span>\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>m</span>m</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>I</span>I</span>}\mathrm{<span><span>F</span>f</span>}\mathrm{<span><span>F</span>f</span>}\mathrm{<span><span>T</span>T</span>}<span><span>\{</span>\{</span>\mathrm{<span><span>F</span>f</span>}\mathrm{<span><span>F</span>f</span>}\mathrm{<span><span>T</span>T</span>}<span><span>\{</span>\{</span>\mathrm{<span><span>B</span>B</span>}<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>,</span>,</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>j</span>j</span>}\frac{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>K</span>K</span>}\mathrm{<span><span>N</span>N</span>}}<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>}<span><span>\}</span>\}</span><span><span>\&CenterDot;</span>\&CenterDot;</span>{\mathrm{<span><span>FFT</span>FFT</span>}}^{<span><span>*</span>*</span>}<span><span>\{</span>\{</span>{\mathrm{<span><span>c</span>c</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>e</span>e</span>}}^{\mathrm{<span><span>j</span>j</span>}\frac{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>m</span>m</span>}}{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}{\mathrm{<span><span>N</span>N</span>}}<span><span>\&CenterDot;</span>\&Center\; Dot;</span>\frac{\mathrm{<span><span>i</span>i</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}<span><span>\}</span>\}</span><span><span>\}</span>\}</span>\\ <span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&epsiv;</span>\&epsiv;</span>}}{\mathrm{<span><span>e</span>e</span>}}^{\mathrm{<span><span>j</span>j</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>2</span>2</span>}{\mathrm{<span><span>\&pi;mf</span>\&pi;mf</span>}}_{\mathrm{<span><span>c</span>c</span>}}}{\mathrm{<span><span>N</span>N</span>}}<span><span>+</span>+</span>\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>)</span>)</span>\frac{\mathrm{<span><span>i</span>i</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}{\mathrm{<span><span>c</span>c</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>j</span>j</span>}\frac{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>m</span>m</span>}}{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}{\mathrm{<span><span>N</span>N</span>}}<span><span>\&CenterDot;</span>\&Center\; Dot;</span>\frac{\mathrm{<span><span>i</span>i</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}\underset{\mathrm{<span><span>n</span>no</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}{\mathrm{<span><span>e</span>e</span>}}^{\mathrm{<span><span>j</span>j</span>}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}\mathrm{<span><span>\&omega;</span>\&omega;</span>}\frac{\mathrm{<span><span>n</span>no</span>}\mathrm{<span><span>N</span>N</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}\end{array}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>15</span>15</span>}<span><span>)</span>)</span>$

当时，有when when there is

$\mathrm{<span><span>z</span>z</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&tau;</span>\&tau;</span>}<span><span>,</span>,</span>\mathrm{<span><span>k</span>k</span>}<span><span>,</span>,</span>\mathrm{<span><span>m</span>m</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&epsiv;</span>\&epsiv;</span>}}{\mathrm{<span><span>c</span>c</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>e</span>e</span>}}^{\mathrm{<span><span>j</span>j</span>}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}\mathrm{<span><span>\&omega;</span>\&omega;</span>}\frac{\mathrm{<span><span>i</span>i</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}\underset{\mathrm{<span><span>n</span>no</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}{\mathrm{<span><span>e</span>e</span>}}^{\mathrm{<span><span>j</span>j</span>}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}\mathrm{<span><span>\&omega;</span>\&omega;</span>}\frac{\mathrm{<span><span>n</span>no</span>}\mathrm{<span><span>N</span>N</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>n</span>no</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>K</span>K</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&epsiv;</span>\&epsiv;</span>}}{\mathrm{<span><span>c</span>c</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>e</span>e</span>}}^{\mathrm{<span><span>j</span>j</span>}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}\mathrm{<span><span>\&omega;</span>\&omega;</span>}\frac{\mathrm{<span><span>i</span>i</span>}<span><span>+</span>+</span>\mathrm{<span><span>n</span>no</span>}\mathrm{<span><span>N</span>N</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}<span><span>=</span>=</span>\underset{{\mathrm{<span><span>i</span>i</span>}}^{<span><span>\&prime;</span>\&prime;</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>K</span>K</span>}\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}}{\mathrm{<span><span>s</span>the\; s</span>}}_{{\mathrm{<span><span>i</span>i</span>}}^{<span><span>\&prime;</span>\&prime;</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&epsiv;</span>\&epsiv;</span>}}{\mathrm{<span><span>c</span>c</span>}}_{{\mathrm{<span><span>i</span>i</span>}}^{<span><span>\&prime;</span>\&prime;</span>}}{\mathrm{<span><span>e</span>e</span>}}^{\mathrm{<span><span>j</span>j</span>}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}\mathrm{<span><span>\&omega;</span>\&omega;</span>}\frac{{\mathrm{<span><span>i</span>i</span>}}^{<span><span>\&prime;</span>\&prime;</span>}}{{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>c</span>c</span>}}}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>16</span>16</span>}<span><span>)</span>)</span>$

本系统中的伪码捕获采用包络检测和恒虚警门限设置的方法。对IFFT的输出结果求模，并将相关峰值与判决门限进行比较，如果相关峰值大于判决门限，则表示伪码相位捕获成功，峰值所处的频点就是多普勒频率的估计值，所处的相位就是伪码相位的估计值；如果相关峰值没有超过判决门限，则表示没有捕获成功，将K段数据中的第一段数据丢弃，其余K-1段数据依次向前移动，后面将继续接收N点数据重排后，得到新的N段长为K点的序列继续进行快速捕获处理，直到相关峰值大于判决门限为止，完成伪码相位捕获。The pseudo-code capture in this system adopts the methods of envelope detection and constant false alarm threshold setting. Calculate the modulus of the output result of IFFT, and compare the correlation peak value with the decision threshold. If the correlation peak value is greater than the decision threshold, it means that the pseudocode phase capture is successful. The frequency point where the peak value is located is the estimated value of the Doppler frequency. The phase of is the estimated value of the phase of the pseudo code; if the correlation peak value does not exceed the judgment threshold, it means that the capture is not successful, and the first segment of data in the K segment data is discarded, and the remaining K-1 segments of data move forward sequentially, and the following will continue After receiving N-point data rearrangement, a new sequence of N segments with a length of K points is obtained to continue the fast acquisition process until the correlation peak is greater than the decision threshold, and the pseudo-code phase acquisition is completed.

步骤S103和步骤S104中，上述快速捕获处理模块对伪码相位和多普勒频偏进行了粗估计，要想从接收信号中解扩、解调出发送数据，还要进行精同步，即对伪码相位和载波相位进行跟踪，本发明采用超前-滞后延迟锁相环、科斯塔斯环分别实现伪码相位和载波相位的跟踪。完成了伪码相位和载波频率同步后，进入到解扩、解调和检测模块，最终恢复出发送数据符号。In step S103 and step S104, the above-mentioned fast acquisition processing module has roughly estimated the phase of the pseudo code and the Doppler frequency offset. If the transmitted data is to be despread and demodulated from the received signal, fine synchronization must be carried out, that is, the Pseudo-code phase and carrier phase are tracked, and the present invention uses a lead-lag delay phase-locked loop and a Costas loop to respectively realize the tracking of the pseudo-code phase and carrier phase. After completing the pseudo-code phase and carrier frequency synchronization, it enters the despreading, demodulation and detection modules, and finally recovers the transmitted data symbols.

本发明采用图4所示的系统对直扩MSK信号进行接收，系统采样频率f_s＝245.52MHz，中频频率为76.725MHz，过采样倍数P＝12，扩频码速率为20.46Mchip/s，数据速率为20kbps，扩频码采用Gold序列，码长N＝1023，二维搜索的码周期数，即K值为32，多普勒频率范围为[-200KHz,200KHz]，因此n_L＝20，n_R＝20，频率搜索步进为625Hz，伪码搜索步进为一个码片。The present invention adopts the system shown in Figure 4 to receive the direct spread MSK signal, the system sampling frequency f_s =245.52MHz, the intermediate frequency frequency is 76.725MHz, the oversampling multiple P=12, the spreading code rate is 20.46Mchip/s, the data The rate is 20kbps, the spreading code adopts the Gold sequence, the code length N=1023, the number of code periods of the two-dimensional search, that is, the K value is 32, and the Doppler frequency range is [-200KHz, 200KHz], so n_L =20, n_R =20, the frequency search step is 625Hz, and the pseudo code search step is one chip.

结合图2，输入信噪比SNR＝-15dB、伪码相位ε＝478.4chip、多普勒频率f_d＝169.85KHz时，进行伪码相位和载波多普勒频偏的二维搜索，得到归一化相关输出的三维图形。从图中可以看出伪码相位的估计值与实际值相差0.4chip，在半个码片范围内；载波频偏的估计值与实际值相差162.5Hz，在最大剩余频差的范围内。可见本发明设计的全数字接收方法能够在高动态环境下对直扩MSK信号的伪码相位和载波频偏进行快速而准确的捕获。Combined with Figure 2, when the input signal-to-noise ratio SNR=-15dB, pseudo-code phase ε=478.4chip, and Doppler frequency f_d =169.85KHz, perform a two-dimensional search of pseudo-code phase and carrier Doppler frequency offset, and obtain the normalized A 3D plot of the correlation output. It can be seen from the figure that the difference between the estimated value of the pseudo-code phase and the actual value is 0.4chip, which is within half a chip; the difference between the estimated value and the actual value of the carrier frequency offset is 162.5Hz, which is within the range of the maximum remaining frequency difference. It can be seen that the all-digital receiving method designed in the present invention can quickly and accurately capture the pseudo code phase and carrier frequency offset of the direct spread MSK signal in a high dynamic environment.

结合图3，输入信噪比为SNR＝[-30dB,-5dB]、f_d＝40KHz、虚警概率P_f＝0.01时，进行5000次捕获，得到检测概率和虚警概率随信噪比的变化曲线。结果发现当信噪比达到-17dB后，检测概率趋近于1，由于采用了恒虚警门限设置准则，虚警概率几乎不受信噪比的影响。Combined with Figure 3, when the input signal-to-noise ratio is SNR=[-30dB,-5dB], f_d =40KHz, and the false alarm probability P_f =0.01, 5000 captures are carried out, and the detection probability and false alarm probability vary with the signal-to-noise ratio. Curve. The results show that when the signal-to-noise ratio reaches -17dB, the detection probability approaches 1. Because of the constant false alarm threshold setting criterion, the false alarm probability is hardly affected by the signal-to-noise ratio.

Claims (8)

1. a digital method of reseptance for DS msk signal, is characterized in that, comprise

DS msk signal is configured to approximate DS-BPSK signal signal,

Adopt and based on the pseudo-code phase of Doppler effect correction-FFT and the two-dimentional joint acquisition algorithm of carrier doppler frequency deviation, posttectonic approximate DS-BPSK signal signal caught,

Pseudo-code phase and carrier phase are followed the tracks of,

By process such as despreading, demodulation, detections, transmission data are recovered to the signal after synchronous.

Described approximate DS-BPSK signal signal constructs carrying out extracting also alternate samples after if sampling, the Digital Down Convert DS msk signal after low-pass filtering is multiplied with wave function;

The two-dimentional joint acquisition algorithm of the described pseudo-code phase based on Doppler effect correction-FFT and carrier doppler frequency deviation comprises:

Based on the doppler filtering of FFT;

Based on the Doppler effect correction of the local pseudo-code of phase compensating factor and loopy moving;

Based on the pseudo-code phase parallel capture of section FFT.

2. the digital method of reseptance of DS msk signal according to claim 1, is characterized in that, the structure of described approximate DS-BPSK signal signal specifically comprises:

I, Q two-way digital orthogonal baseband signal obtained after low-pass filtering respectively with wave functionbe multiplied and obtain four tunnel output signals, wherein T_cfor the chip width of spreading code;

Carry out P to four tunnels output signals doubly to extract (P is over-sampling multiple) and obtain four road signals, be respectively y_i1(k '), y_q1(k '), y_i2(k '), y_q2(k '); Wherein y_i1(k ') and y_q1(k ') be respectively I roadbed band signal, Q roadbed band signal and wave functionthe signal obtained is extracted, y after being multiplied_i2(k ') and y_q2(k ') be respectively Q roadbed band signal, I roadbed band signal and wave functionthe signal obtained is extracted after being multiplied; Wherein k '>=0, and be integer, when k ' is y during odd number_i1(k ') and y_q1(k ') be 0, when k ' is y during even number_i2(k '), y_q2(k ') be 0;

To y_i1(k ') and-y_i2(k ') alternate samples as I road, to y_q1(k ') and y_q2the complex signal I+jQ that I, Q two paths of signals combines, as Q road, is approximate DS-BPSK signal signal by (k ') alternate samples.

3. the digital method of reseptance of DS msk signal according to claim 2, is characterized in that, before pairing approximation DS-BPSK signal signal is caught, carries out following process:

To posttectonic approximate bpsk signal, gather the spread-spectrum signal of K PN-code capture, PN-code capture is N;

K*N sampling point is reordered, obtains the new sequence that N segment length is K.

4. the digital method of reseptance of DS msk signal according to claim 3, is characterized in that, is K point FFT, carries out doppler filtering by the sequence being K to each segment length.

5. the digital method of reseptance of DS msk signal according to claim 3, it is characterized in that, Doppler effect correction comprises:

Doppler shift is expressed asf_cfor spread-spectrum code rate, Δ f is inherent spurious frequency deviation,wherein each concrete f_donly corresponding one group (k, m), wherein k and m is integer, k≤K-1, m>=0;

By being multiplied by corresponding phase compensating factor to the N section FFT result after doppler filteringcompensatewherein i=0,1 ... N-1, j are imaginary part unit;

By local pseudo-code being multiplied by one in time domainfrequency compensationbe equivalent to the m position that to be moved to right by the FFT sequence loops of local pseudo-code on frequency domain;

By suitably arranging the value of K, inherent spurious frequency deviation Δ f is made to be not more than f_c/ 2KN, thus do not affect pseudorandom codes phase estimation below.

6. the digital method of reseptance of DS msk signal according to claim 3, is characterized in that, adopts section FFT to carry out pseudo-code phase parallel capture, comprising:

Carry out secondary to the output signal after the shifting processing of doppler filtering, phase compensation and pseudo-code FFT sequence to reorder and revert to original order, namely the sequence that K segment length is N is rearranged to, and the pseudo-code phase parallel capture based on FFT is carried out to the sequence that every segment length is N, obtain the correlation output result of pseudo-code;

Based on CFAR criterion, decision threshold is set;

Adopt envelope detected method, mould asked to correlation output result, and peak value and decision threshold are compared:

(1) if peak value exceedes decision threshold, then pseudo-code phase acquisition success;

(2) if peak value does not exceed decision threshold, first paragraph data in K segment data are abandoned, all the other K-1 segment datas move forward successively, continuation is received N point data below, after rearrangement, obtain the sequence of new N segment length for K point, continue to catch pseudo-code phase, until peak value exceedes decision threshold.

7. the digital method of reseptance of DS msk signal according to claim 1, is characterized in that, adopts advanced-hysteresis delay locking ring, tracking that Costas loop realizes pseudo-code phase and carrier phase respectively.

8. the digital method of reseptance of DS msk signal according to claim 1, is characterized in that, employing coherent demodulation, feedback judgement detection method are carried out process to the msk signal after despreading and recovered transmission data.