CN102288975B - Capturing method based on DFT (Discrete Fourier Transformation) optimization - Google Patents

Abstract

The invention belongs to the field of communication and navigation, and discloses a capture method based on DFT optimization. Aiming at the problems of large efficiency, resources and power consumption in the existing satellite navigation capture method, the present invention realizes the optimization of DFT calculation by quantizing the coefficients of DFT, and at the same time optimizes the number of DFT points according to needs, saving A large amount of computing, storage and other resources. In navigation applications, in addition to low-bit quantization of DFT coefficients, the number of DFT points is also cut according to the search Doppler offset range, so that the calculation amount and calculation points of DFT are greatly reduced, saving storage resources, computing resources, time and power consumption etc. The method of the invention can be effectively applied to satellite navigation.

Description

A Capture Method Based on DFT Optimization

technical field

The invention belongs to the field of communication and navigation, in particular to a capturing method for satellite navigation.

Background technique

Global Positioning System (GPS, Global Position System) is a new generation of precise satellite positioning system. The processing of the received signal by the GPS receiver usually includes signal acquisition, signal carrier and code locking, extraction and calculation of navigation message and pseudo-range, and solution of positioning value. The GPS system uses spread spectrum communication technology. Before the spread spectrum receiver despreads and demodulates, the spread spectrum code recovered locally by the receiver must be synchronized with the carrier and the received signal. Only when the error between the code phase and the carrier frequency is within a certain range , the demodulator can work normally. Due to the influence of frequency source drift, radio wave transmission delay, Doppler frequency shift, multipath effect and other factors, the synchronization of code phase and carrier will have certain uncertainty, so the receiver must first capture the signal , the code phase and carrier frequency estimation error can be reduced to a certain range before it can be provided to the tracking loop for signal tracking. The capture of navigation satellite signals is the first step and the key to GPS receiver signal processing.

In current receivers, especially in military code receivers and multi-mode receivers, resources, volume and power consumption are major problems that restrict the development of receivers. Aiming at this problem, many institutions and units at home and abroad have conducted a lot of research. The acquisition of satellite signals is mostly based on the time domain and frequency domain. The traditional method is to use the serial search method to capture the spread spectrum code in the time domain. In the literature "Van Nee, Coenen, Davenport. New Fast GPS Code-Acquisition Technique Using FFT, Electronic Letters, 1991, vol.27, NO.2: 158-160" first proposed a fast acquisition method using FFT to realize the spreading code; The literature "C. Yang. Fast code acquisition with FFT and its sampling schemes, Proc. Institute of Navigation ION-GPS 96, Kansas City, MO, September 1996, 1729-173" compared and analyzed various sampling schemes of FFT ; In the document "Extended Replica Folding for DirectAcquisition of GPS P-Code and Its Performance Analysis, Proceedings of ION GPS 2000.SaltLake City, Ut: The Institute of Navigation, 2000.2070-2078" proposed XFAST to realize the fast P(Y) code The capture scheme, and in the literature "Sequential Block Search for Direct Acquisition of Long Codes under Large Uncertainty, Proceedings of the 2001 National Technical Meeting. Long Beach, CA: ION, Jan. 2001.408-414" proposed a sequence block search algorithm, and used FFT implements short-period codes, long-period codes and acquisition methods of no-period codes for classification and induction. There are also many domestic analysis methods for long-code direct capture, and many corresponding research results have been given in terms of implementation, such as the sliding correlator method of serial-parallel combination realized by large-scale parallel correlators, the extended copy overlapping mean method, and The method of PMF-FFT, etc.

Due to the relative motion between the satellite and the receiver, the Doppler frequency shift will inevitably be introduced during the use of the receiver. The Doppler frequency shift will lead to the attenuation of the spread spectrum gain and affect the capture work. Therefore, corresponding compensation must be carried out during the capture process to remove the impact of the Doppler frequency shift. In order to achieve low power consumption, low resource and miniaturized receivers, especially in future multi-mode receivers, many scholars have proposed numerous optimization methods, but the optimization problems of efficiency, resources, power consumption, etc. are still the research of capture focus.

Contents of the invention

The invention aims to solve the problems of large efficiency, resources and power consumption in the existing satellite navigation capture method, and proposes a capture method based on DFT optimization.

Technical scheme of the present invention is: a kind of capture method based on DFT optimization, comprises the steps:

S1, correlating the N-point data of the received satellite signal with the N-point data of the local pseudo-random code;

代替原来N等分值

即N等分值

在区间 $\left[\begin{array}{cc}{e}^{-j\frac{2\mathrm{\π}}{(M-\frac{1}{2})*m}}& e^{-j\frac{2\mathrm{\π}}{(M+\frac{1}{2})*m}}\end{array}\right)$ 或 $\left(\begin{array}{cc}{e}^{-j\frac{2\mathrm{\π}}{(M-\frac{1}{2})*m}}& e^{-j\frac{2\mathrm{\π}}{(M+\frac{1}{2})*m}}\end{array}\right]$ 上的值都用M等分上的值代替，然后按照DFT计算方法计算N点DFT，得到DFT频域结果；S2, do N-point DFT to the result of each correlation operation in step S1, Among them, x(n) is the result of the correlation operation, and X(k) is the frequency domain result after DFT calculation. The specific process is as follows: N equal division points on the frequency domain complex plane are reduced to M equal division points, and N=M* After m, M is equally divided, the value on M is equally divided

Replace the original N equal value

That is, the N equivalent value

in interval $\left[\begin{array}{cc}{e}^{-j\frac{2\mathrm{\π}}{(m-\frac{1}{2})*m}}& e^{-j\frac{2\mathrm{\π}}{(m+\frac{1}{2})*m}}\end{array}\right)$ or $\left(\begin{array}{cc}{e}^{-j\frac{2\mathrm{\π}}{(m-\frac{1}{2})*m}}& e^{-j\frac{2\mathrm{\π}}{(m+\frac{1}{2})*m}}\end{array}\right]$ The values on the above are divided into equal parts by M Instead, then calculate the N-point DFT according to the DFT calculation method to obtain the DFT frequency domain result;

S3, comparing the DFT frequency domain result with the preset threshold value, if the threshold value is exceeded, the Doppler frequency shift value of the signal is obtained, if the threshold value is not exceeded, the code phase is shifted by one data, and the step S1 is continued. If there is still no result after all phase searches are completed, replace the IF or code sequence and continue searching.

Further, the following steps are also included between the step S2 and the step S3:

其中，f_s为接收到的卫星信号的采样率，Δf为多普列频率偏移最大值，然后根据计算得到的点数n_max计算DFT，即计算k的区间为[N-n_max/2N-1]和[0 n_max/2-1]的X(k)的值。Calculate the maximum value of DFT calculation points

Among them, f _s is the sampling rate of the received satellite signal, Δf is the maximum value of the Doppler frequency offset, and then calculate the DFT according to the calculated number of points n _max , that is, the interval for calculating k is [Nn _max /2N-1] and the value of X(k) of [0 n _max /2-1].

Beneficial effects of the present invention: the present invention proposes a high-efficiency and low-resource optimization algorithm by providing a DFT-based algorithm, and is effectively applied to satellite navigation. By quantizing the coefficients of the DFT, the calculation of the DFT is optimized, and the number of DFT points is optimized according to the needs, which saves a lot of storage resources and calculations. In navigation applications, in addition to low-bit quantization of DFT coefficients, the number of DFT points is also cut according to the search Doppler offset range, so that the calculation amount and calculation points of DFT are greatly reduced, saving storage resources, computing resources, time and power consumption etc.

Description of drawings

Fig. 1 is a schematic flow chart of the capture method based on DFT optimization of the present invention.

Fig. 2 is a schematic diagram of bit-quantized DFT coefficients according to an embodiment of the present invention.

Detailed ways

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

进行计算，即每个频域分量都得计算N个输入信号与频域复平面上N个等分点的乘积。因此在接收机捕获过程中，基于传统的DFT的捕获方法，会带来效率、资源和功耗较大的问题。The traditional method of calculating DFT is based on the formula

Perform calculations, that is, each frequency domain component has to calculate the product of N input signals and N equal division points on the frequency domain complex plane. Therefore, in the acquisition process of the receiver, the acquisition method based on the traditional DFT will bring problems of efficiency, resource and power consumption.

The capture method based on DFT optimization of the present invention, concrete process as shown in Figure 1, comprises the following steps:

S1, correlating the N-point data of the received satellite signal with the N-point data of the local pseudo-random code;

其中x(n)为相关运算的结果，X(k)为计算DFT后的频域结果，具体过程如下：把频域复平面上N个等分点缩小为M等分，设N=M*m，M等分后，把M等分上的值

代替原来N等分值

即N等分值

在区间 $\left[\begin{array}{cc}{e}^{-j\frac{2\mathrm{\π}}{(M-\frac{1}{2})*m}}& e^{-j\frac{2\mathrm{\π}}{(M+\frac{1}{2})*m}}\end{array}\right)$ 或 $\left(\begin{array}{cc}{e}^{-j\frac{2\mathrm{\π}}{(M-\frac{1}{2})*m}}& e^{-j\frac{2\mathrm{\π}}{(M+\frac{1}{2})*m}}\end{array}\right]$ 上的值都用M等分上的值

代替，然后按照DFT计算方法进行计算N点DFT，得到DFT频域结果；这里的m可以为整数，也可以为小数。S2, do N-point DFT to the result of each correlation operation in step S1,

Among them, x(n) is the result of the correlation operation, and X(k) is the frequency domain result after DFT calculation. The specific process is as follows: N equal division points on the frequency domain complex plane are reduced to M equal division points, and N=M* After m, M is equally divided, the value on M is equally divided

Replace the original N equal value

That is, the N equivalent value

in interval $\left[\begin{array}{cc}{e}^{-j\frac{2\mathrm{\π}}{(m-\frac{1}{2})*m}}& e^{-j\frac{2\mathrm{\π}}{(m+\frac{1}{2})*m}}\end{array}\right)$ or $\left(\begin{array}{cc}{e}^{-j\frac{2\mathrm{\π}}{(m-\frac{1}{2})*m}}& e^{-j\frac{2\mathrm{\π}}{(m+\frac{1}{2})*m}}\end{array}\right]$ The values on the above are divided into equal parts by M

Instead, calculate the N-point DFT according to the DFT calculation method to obtain the DFT frequency domain result; m here can be an integer or a decimal.

S3, comparing the DFT frequency domain result with the preset threshold value, if the threshold value is exceeded, the Doppler frequency shift value of the signal is obtained, if the threshold value is not exceeded, the code phase is shifted by one data, and the step S1 is continued. If there is still no result after all phase searches are completed, replace the IF or code sequence and continue searching.

其中，f_s为接收到的卫星信号的采样率，Δf为多普列频率偏移最大值，然后根据计算得到的点数n_max计算DFT，即计算k的区间为[N-n_max/2 N-1]和[0 n_max/2-1]的X(k)的值。在这里，DFT变换频域表示范围为0到f_s，搜索多普列频移范围为-1*Δf～Δf。In order to further reduce the calculation amount, the following steps are also included between step S2 and step S3: calculating the maximum value of DFT calculation points

Among them, f _s is the sampling rate of the received satellite signal, Δf is the maximum value of the Doppler frequency offset, and then calculate the DFT according to the calculated number of points n _max , that is, the interval for calculating k is [Nn _max /2 N-1 ] and the value of X(k) of [0 n _max /2-1]. Here, the DFT transform frequency domain representation ranges from 0 to f _s , and the search Doppler frequency shift ranges from -1*Δf to Δf.

Assuming that the result of the correlation operation is x(n), according to the DFT transformation, the DFT of the sequence x(n) is:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\mathrm{<span\; class="notranslate">\; k\; n</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j\&omega;</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; .</span>$

是单位圆上的N等分点上的数据。如果把圆分成M<N，通常N为M的整数倍，那么DFT的系数只有M个，但是输入数据点数不变，通过把原来圆N等分的数据在M等分附近的数据划入M等分的数据之中。选择合适的M，可以极大节约DFT的存储资源、计算量和计算资源。Since e ^jθ =cosθ-jsinθ, the DFT coefficient

is the data on the N equally divided points on the unit circle. If the circle is divided into M<N, usually N is an integer multiple of M, then there are only M coefficients of DFT, but the number of input data points remains unchanged, by dividing the data of the original circle N equal parts into M among the equally divided data. Choosing an appropriate M can greatly save the storage resources, calculation amount and computing resources of DFT.

When M is equal to 8, a better effect can be obtained. The following uses M=8 as an example for illustration.

可知量化后所有的系数都位于复平面的单位圆上。如图2所示，把一个复平面圆周分成了8等份，对DFT系数进行2比特量化即可把八等分上的点全部表示完毕，并对系数进行适当的放大以后的量化系数为[1.5,1+i,1.5i,-1+i,-1.5,-1-i,-1.5i,1-i]。根据DFT的量化系数，DFT运算乘法资源可以由原来的乘法器变成了直连信号（系数为±1）或者几个寄存器和加法器（系数为±1.5），这将大大缩减了DFT的运算量。假设现在要做256点DFT，因为M取8进行等分，所以原来256等分中的240～256和1～16等分点用M=8等分点中的第一个等分点对应的DFT系数为(1.5,0)代替，17～48等分点用八等分点的第二个等分点的DFT系数变为(1,i)代替，49～80等分点用八等分点的第三个等分点DFT系数变为(15i)代替，剩余的系数及其它点数的DFT以此类推。The present invention calculates when taking 8 equal divisions by M, according to the DFT

It can be seen that all the coefficients after quantization are located on the unit circle of the complex plane. As shown in Figure 2, a complex plane circle is divided into 8 equal parts, and the 2-bit quantization of the DFT coefficients can express all the points on the eight equal parts, and the quantized coefficients after proper amplification of the coefficients are [ 1.5,1+i,1.5i,-1+i,-1.5,-1-i,-1.5i,1-i]. According to the quantization coefficient of DFT, the multiplication resource of DFT operation can be changed from the original multiplier to a direct signal (with a coefficient of ±1) or several registers and adders (with a coefficient of ±1.5), which will greatly reduce the operation of DFT quantity. Suppose now to do 256-point DFT, because M takes 8 for equal division, so the 240-256 and 1-16 equal-division points in the original 256 equal-division points correspond to the first equal-division point among M=8 equal-division points The DFT coefficient is replaced by (1.5,0), and the DFT coefficient of the second equal point of the 17th to 48th equal point is replaced by (1,i), and the 49th to 80th equal point is replaced by the eighth equal point The DFT coefficient of the third bisection point of the point becomes (15i) instead, and the DFT of the remaining coefficients and other points can be deduced by analogy.

就可以计算出最大的计算点数为n_max，然后根据这个点数就可以计算需要的DFT。假设采用4ms数据做256点DFT，因此频谱分辨率为对应

在计算离散DFT时候，为了搜索±10KHz信号，需要计算的点数为因此只需要216点到255点、0点到39点的X(k)即可。因而不需要计算全部的256点DFT。同样如果只搜索±5KHz，只需要计算236到255点、0点到19点的DFT即可，其它频率计算原理一样。如果需要全频域搜索，或者搜索范围很大，导致计算步骤数超过FFT的方式的话，可以把这种量化方式应用到FFT上去。In order to search only the Doppler frequency band, the DFT coefficients can be adjusted, and the coefficients are concentrated in the required frequency band range for transformation, while the parameters of other frequency bands are not calculated, which can also save a lot of calculation. If the sampling rate is f _s , then the DFT transform frequency domain representation ranges from 0 to f _s . If the range of the search Doppler column is ±10KHZ, then the calculation range is as long as

The maximum number of calculation points can be calculated as n _max , and then the required DFT can be calculated according to this number of points. Assume that 4ms data is used to do 256-point DFT, so the spectral resolution is corresponding to

When calculating the discrete DFT, in order to search for ±10KHz signals, the number of points to be calculated is Therefore, only X(k) from 216 to 255 and from 0 to 39 is needed. Thus there is no need to compute the full 256-point DFT. Similarly, if you only search for ±5KHz, you only need to calculate the DFT from 236 to 255 points, and from 0 to 19 points, and the calculation principles for other frequencies are the same. If you need to search in the full frequency domain, or the search range is so large that the number of calculation steps exceeds the FFT method, you can apply this quantization method to the FFT.

It can be seen that the present invention can simplify DFT calculation by quantizing DFT coefficients, and at the same time optimize the number of DFT points after quantization according to needs, which can save a lot of storage resources and calculation amount. In navigation applications, in addition to quantizing DFT coefficients, the number of DFT points is also tailored according to the search Doppler offset range, which reduces the number of DFT calculation points and the amount of calculation, saving storage resources, computing resources, time and power consumption etc., this method can be effectively applied to satellite navigation.

Those skilled in the art will appreciate that the embodiments described here are to help readers understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical revelations disclosed in the present invention without departing from the essence of the present invention, and these modifications and combinations are still within the protection scope of the present invention.

Claims (4)

1. A method for capturing based on DFT optimization, comprising the steps of: S1, correlating the N-point data of the received satellite signal with the N-point data of the local pseudo-random code; S2, do N-point DFT to the result of each correlation operation in step S1,

Among them, x(n) is the result of the correlation operation, and X(k) is the frequency domain result after DFT calculation. The specific process is as follows: N equal division points on the frequency domain complex plane are reduced to M equal division points, and N=M* After m, M is equally divided, the value on M is equally divided

Replace the original N equal value N equivalent value in interval $\left[\begin{array}{cc}{e}^{-j\frac{2\mathrm{\&pi;}}{(m-\frac{1}{2})*m}}& e^{-j\frac{2\mathrm{\&pi;}}{(m+\frac{1}{2})*m}}\end{array}\right)$ or $\left(\begin{array}{cc}{e}^{-j\frac{2\mathrm{\&pi;}}{(m-\frac{1}{2})*m}}& e^{-j\frac{2\mathrm{\&pi;}}{(m+\frac{1}{2})*m}}\end{array}\right]$ The values on the above are divided into equal parts by M

Instead, then calculate N-point DFT according to the DFT calculation method to obtain the DFT frequency domain result; S3, comparing the DFT frequency domain result with the preset threshold value, if the threshold value is exceeded, the Doppler frequency shift value of the signal is obtained, if the threshold value is not exceeded, the code phase is shifted by one data, and the step S1 is continued. If there is still no result after all phase searches are completed, replace the IF or code sequence and continue searching. 2. The acquisition method based on DFT optimization according to claim 1, characterized in that, between the step S2 and the step S3, the following steps are also included: Calculate the maximum value of DFT calculation points

Among them, f _s is the sampling rate of the received satellite signal, Δf is the maximum value of the Doppler frequency offset, and then calculate the DFT according to the calculated number of points n _max , that is, the interval for calculating k is [Nn _max /2N-1] and the value of X(k) of [0 n _max /2-1]. 3. The acquisition method based on DFT optimization according to claim 1 or 2, wherein said N is an integer multiple of M. 4. The acquisition method based on DFT optimization according to claim 1 or 2, characterized in that, said M is 8.

Images