阅读说明：本技术 基于二次谱的AltBOC信号的伪码周期盲估计 (Secondary spectrum based pseudo code period blind estimation of AltBOC signal ) 是由 张天骐 白杨柳 冯嘉欣 张刚 张晓艳 于 2020-06-04 设计创作，主要内容包括：本发明请求保护一种基于二次谱的AltBOC伪码周期盲估计方法,属于信号处理领域。通过分析AltBOC信号模型,并分析推导出了AltBOC的功率谱函数,然后根据傅里叶变换求AltBOC信号的二次谱函数,根据二次谱函数峰值位置关系特征可以对AltBOC信号的伪码周期进行盲估计。同时通过对多段信号的二次谱函数进行累加平均,可以实现降低噪声和精确估计的目的,同时分析了在不同伪码周期条件下以及不同采样频率条件下对AltBOC信号参数估计的影响。本方法可以在低信噪比下较准确地估计AltBOC信号的伪码周期,从而对该信号的后续处理以及细微特征分析具有重要意义。(The invention requests to protect an AltBOC pseudo code period blind estimation method based on a quadratic spectrum, and belongs to the field of signal processing. The AltBOC signal model is analyzed, the power spectrum function of the AltBOC is deduced through analysis, then the quadratic spectrum function of the AltBOC signal is obtained according to Fourier transform, and the pseudo code period of the AltBOC signal can be estimated blindly according to the position relation characteristic of the peak value of the quadratic spectrum function. Meanwhile, the purposes of reducing noise and accurately estimating can be achieved by performing accumulation averaging on the quadratic spectrum functions of the multiple sections of signals, and the influence on AltBOC signal parameter estimation under different pseudo code period conditions and different sampling frequency conditions is analyzed. The method can accurately estimate the pseudo code period of the AltBOC signal under the condition of low signal-to-noise ratio, thereby having important significance on the subsequent processing and the fine feature analysis of the signal.)

1. An AltBOC pseudo code period blind estimation method based on quadratic spectrum comprises the steps of sampling frequency f_sSampling the received AltBOC signal; segmenting the sampled signals by a certain length L (generally, L at least comprises two sampling points of a pseudo code period), solving a secondary power spectrum of one section of the signals, then solving a secondary spectrum of the next section of the signals, and accumulating and averaging the secondary spectrums obtained each time; carrying out spectrum peak search on the obtained secondary spectrum accumulation average result, finding out a secondary power spectrum frequency value corresponding to the secondary spectrum accumulation average result, and solving the distance between adjacent spectrum peaks; when the accumulation is stopped after the distance between adjacent spectral peaks tends to be stable, the distance between the spectral peaks after the stability is the signal combination code period.

2. The estimation method according to claim 1, characterized in that the AltBOC signal is modeled as

Wherein

3. The method according to claim 1 and 2, wherein the AltBOC power spectrum function expression is established as follows:

wherein sa (x) sin (x)/x (·) is an impulse function; f represents a spectral frequency; t is_cRepresenting the pseudo code width.

4. A method according to claims 1, 2 and 3, characterised in that it is based onAnd solving a secondary power spectrum function of the AltBOC signal, and estimating the pseudo code period according to the peak distance of the secondary power spectrum function.

Technical Field

The invention belongs to navigation communication signal processing, and particularly relates to a pseudo code period blind estimation method of an AltBOC signal based on a quadratic spectrum.

Background

An Alternate Binary Offset Carrier (AltBOC) modulation signal is a modulation method proposed by french space research center, aiming at improving the performance of a satellite navigation system and reasonably utilizing limited frequency band resources. Compared with Binary Offset Carrier (BOC) signals, the AltBOC signals can be subjected to both single-code modulation signal processing and multi-code modulation signal processing, and signals subjected to constant envelope processing are not prone to signal distortion when passing through a radio frequency power amplifier at a receiving end. Because the signal is modulated by four-valued complex subcarriers and intermodulation products are introduced, the complexity of the signal is greatly increased, and the research and application of the signal are difficult. At present, the AltBOC signal is mainly applied to E5a and E5b frequency bands of a Galileo system, and China satellite researchers are also actively added to the research work of the signal, so that the AltBOC signal parameter effective estimation has important significance.

In recent years, the research on the AltBOC signal is mainly focused on acquisition and tracking, most of documents simplify the research into two QPSK forms, and relatively few documents are available for parameter estimation of the AltBOC signal. Since the double-code AltBOC signal can be converted into a sine or cosine subcarrier BOC modulation signal under certain conditions, the AltBOC signal can be researched by referring to a parameter estimation method for the BOC or direct sequence spread spectrum signal. In the literature [ "zhangtianqi, liu luo hua, yuansai, etc. ] combining the pseudo code period of a binary offset carrier signal and the combined code sequence to blindly estimate [ J ]. the mathematical report of electronics and information, 2019,41(04): 917) 924" ] providing a method for estimating the pseudo code period of a direct-spread signal by calculating the power spectrum of the signal twice and taking a modulus average, wherein the method has good anti-noise performance and lower complexity; the literature [ Wu is good, Zhao Zhijin, Shang Jun Na, etc. ] proposes a direct-spread signal detection and multi-parameter estimation method [ J ] computer simulation, 2008,25(2): 153-; the estimation effect of the pseudo code period of the direct-spread signal is achieved by solving the signal correlation entropy in the literature [ "gold bright, sun eagle, Ji Hongshen.

Through the analysis and comprehensive consideration of the complexity of the AltBOC signal and the subcarrier four-value property of the AltBOC signal, blind estimation of the AltBOC signal by a secondary power spectrum method is proposed. Firstly, an autocorrelation function of the AltBOC signal is obtained according to an AltBOC signal model, then a power spectrum of the AltBOC signal is obtained according to the relationship that the autocorrelation and the power spectrum are Fourier transform pairs, a secondary spectrum function of the signal is further obtained, the secondary spectrum of the signal can generate spike pulses at a pseudo code period and integral multiple frequencies of the pseudo code period, and the pseudo code period of the signal can be obtained by detecting the distance between the spectrum peaks.

Disclosure of Invention

The invention aims to solve the technical problem that AltBOC signal parameters are difficult to estimate under the current low signal-to-noise ratio environment, provides a quadratic spectrum function algorithm and solves the problem that AltBOC signal pseudo code sequence period parameters are difficult to estimate. In order to estimate the pseudo code period more accurately, one-dimensional search is carried out by utilizing a secondary spectrum frequency domain and accumulated and averaged, compared with cyclic spectrum two-dimensional search, the calculation amount is greatly reduced, and the purpose of reducing noise can be achieved by accumulation and averaging.

The technical scheme for solving the technical problems is as follows: an AltBOC signal pseudo code period estimation method based on a quadratic spectrum. The method comprises the following specific steps: at a sampling frequency f_sSampling the received AltBOC signal; segmenting the sampled signals by a certain length L (generally, L at least comprises two sampling points of a pseudo code period), solving a secondary power spectrum of one section of the signals, then solving a secondary spectrum of the next section of the signals, and accumulating and averaging the secondary spectrums obtained each time; carrying out spectrum peak search on the obtained secondary spectrum accumulation average result, finding out a secondary power spectrum frequency value corresponding to the secondary spectrum accumulation average result, and solving the distance between adjacent spectrum peaks; when the accumulation is stopped after the distance between adjacent spectral peaks tends to be stable, the distance between the spectral peaks after the stabilization is the signal pseudo code period.

Without loss of generality, assume that the AltBOC signal is represented as

WhereinExpressing the intermodulation signal, the expression is:

in the formula e_E5a-I(t)、e_E5b-I(t) spreading codes obtained by pseudo code modulation of data channel signals respectively representing E5a signals and E5b signals, E_E5a-Q(t)、e_E5b-Q(t) is the pilot channel signal of the E5a signal and the E5b signal, and only the pseudo code sequence is transmitted. sc (sc)_E5-s(t)、sc_E5-p(t) is a four-level subcarrier, which can be expressed as:

its corresponding time-varying autocorrelation function can be expressed as:

wherein τ represents the time delay, (.)^*And representing a conjugate function of the signals in the bracket, and according to the relation that the signal autocorrelation function and the power spectral density are a Fourier transform pair, the power spectral function of the AltBOC signal can be obtained by Fourier transform of the signal autocorrelation function:

the quadratic spectrum of the AltBOC (15,10) signal can be obtained by solving the Fourier transform of the equation (6) and solving the square of the absolute value of the Fourier transform function, and can be represented as follows:

in the formula, FT [. cndot. ] represents Fourier transform.

Different peak values will appear in the secondary spectrogram of the AltBOC signal obtained according to the formula (7), and the corresponding pseudo code period can be estimated according to the position relation between the peak values.

The invention analyzes and deduces the quadratic spectrum function of the AltBOC signal by using the quadratic spectrum function method to carry out blind estimation on the AltBOC signal pseudo-code period under low signal-to-noise ratio, more accurately realizes the estimation of the pseudo-code period, overcomes the problems that intermodulation component is introduced into the AltBOC signal and the signal modulation mode is extremely complicated by adopting four-valued complex subcarrier modulation and the like, and simultaneously utilizes the frequency domain of the accumulation average to increase the anti-noise performance. The method can accurately estimate the pseudo code period of the AltBOC signal.

Drawings

FIG. 1 is a flow chart of pseudo code period estimation of AltBOC signal according to the present invention

FIG. 2 is an AltBOC signal power spectrum of the present invention.

FIG. 3 is a diagram of the AltBOC signal secondary spectrum of the present invention.

FIG. 4 is a graph of the estimated performance of the present invention for a pseudo-code period at different pseudo-code period lengths.

FIG. 5 is a graph of the performance of the present invention in estimating the period of the pseudo code at different sampling frequencies.

FIG. 6 is a comparison graph of the performance of the AltBOC signal pseudo code period estimation method and the time domain autocorrelation method

Detailed Description

The invention is further described in the following with reference to the figures and the specific examples

The invention adopts a correlation diagram method to calculate the power spectrum function of the signal, namely, firstly, the autocorrelation function of the signal is calculated, then, the power spectrum is calculated through Fourier transform, and further, the power spectrum of the signal is subjected to Fourier transform again. Find x_E5(t) the autocorrelation function of all sub-signals must be considered, and since any two pseudo-code sequences are independent of each other, the autocorrelation function of the signal with constant envelope AltBOC (15,10) can be expressed as:

in formula (8):

in the formula []^*Represents taking a conjugate, wherein:

similarly, the autocorrelation functions of other functions can be obtained, and since different spreading codes are independent from each other and occur with equal probability, the power spectral density of the AltBOC signal can be obtained according to the autocorrelation functions of the AltBOC signal. Can be expressed as:

in the formula G_d(f) Representing a spreading sequence d_kThe power spectral densities of SC _ a1(f), SC _ a2(f), SC _ p1(f), and SC _ p2(f) represent the power spectral densities of SC _ a1, SC _ a2, SC _ p1, and SC _ p2, respectively.

Information code sequence b₁(t) and the pseudo code sequence may be expressed as:

G_b(f)＝NT_csa²(πfNT_c) (14)

according to

Can be combined with G_d(f) Expressed as:

the power spectral densities SC _ a1(f), SC _ a2(f), SC _ p1(f), SC _ p2(f) of the subcarriers of the AltBOC (15,10) signal may be expressed as:

the power spectral density of the AltBOC (15,10) signal can be obtained according to the formula (16) and the formula (17) as follows:

the quadratic spectrum of the AltBOC (15,10) signal is obtained by taking the Fourier transform of equation (18) and squaring the absolute value of the Fourier transform function, and can be expressed as:

in the formula, FT [. cndot. ] represents Fourier transform.

After the AltBOC (15,10) signal is processed by the quadratic spectrum, the energy is concentrated at the integral multiple of the combined code period, so that the pseudo code period of the signal can be estimated by detecting the distance between the quadratic spectrum peaks. Because the AltBOC (15,10) signal is sensitive to noise influence due to the four-value subcarrier property, the quadratic spectrum function of the signal adopts an accumulative average method to reduce the influence of noise,

fig. 1 is a flowchart of a pseudo code period estimation method of the present invention, which comprises the following specific steps: at a sampling frequency f_sSampling the received AltBOC signal; segmenting the sampled signals by a certain length L (generally, L at least comprises two sampling points of a pseudo code period) and respectively calculating the power spectrum function of each segment of signals; work on all segmentsAnd the rate spectrum function calculates a secondary spectrum function according to Fourier transform, performs accumulative averaging, and observes the distance relationship between spectrum peaks of the secondary spectrum after the accumulative averaging, thereby estimating the AltBOC signal pseudo code period.

FIG. 2 and FIG. 3 show the primary power spectrum and the secondary power spectrum of AltBOC (15,10) signal, respectively, for setting the spreading pseudo-code rate R of the signal_c10.23MHz, subcarrier rate R_sSetting the period of the signal pseudo code to 1023 bits when 15.345MHz is obtained; sampling frequency f_s122.76 MHz; under the condition that the signal-to-noise ratio is-5 dB, the information code number M is 100, the information code number M is divided into 20 groups, a primary power spectrum and a secondary power spectrum of a signal are respectively obtained, and a simulation result is shown in fig. 2 and fig. 3. fig. 2 shows that the power spectrum of an AltBOC (15,10) signal does not have periodicity and only has spectrum splitting characteristics, while fig. 3 shows that a higher peak value appears at integral multiples of a signal combination code period, which is consistent with theoretical analysis of the invention, and the combination code period can be obtained by analyzing the secondary spectrum of the AltBOC (15,10) signal.

FIG. 4 is a graph showing the effect of different pseudo code periods on the performance of the present invention. The influence of the length of the pseudo code period on the estimation performance is verified by comparing the accumulated times required by estimating the AltBOC (15,10) signal pseudo code period under different pseudo code period lengths, the value range of the signal to noise ratio is set to be-17-0 dB, 127 bits, 255 bits, 511 bits and 1023 bits are respectively taken in the pseudo code period, the sampling frequency is 122.76MHz, and 200 Monte Carlo simulations are carried out. It can be seen from fig. 4 that the pseudo code period of the AltBOC (15,10) signal can be effectively estimated by the quadratic spectrum algorithm, and the accumulation times required for correctly estimating the pseudo code period all decrease with the increase of the signal-to-noise ratio, in the three sets of pseudo code periods under the same signal-to-noise ratio, 1023 bits can correctly estimate the pseudo code period of the signal only with less accumulation times, and as the length of the pseudo code period decreases, the more accumulation times required for correct estimation increases, which indicates that the larger the pseudo code period is, the better the estimation performance of the algorithm is.

Fig. 5 shows that the influence of the sampling frequency on the estimation performance is verified by comparing the number of accumulation times required for estimating the pseudocode period of the AltBOC (15,10) signal under different sampling frequencies, the range of the signal-to-noise ratio is set to-17-0 dB, the sampling frequencies are set to 30.69MHz,61.38MHz and 122.76MHz, and monte carlo simulation experiments are performed 200 times. As can be seen from fig. 5, under different sampling frequencies, the average accumulation times required for correctly estimating the period length of the pseudo code of the signal gradually decreases with the increase of the signal-to-noise ratio and tends to be stable at a certain value. Under the condition of a fixed signal-to-noise ratio, the larger the sampling frequency, the smaller the average accumulation times adopted, because the larger the sampling frequency, the more useful information is obtained, the probability of estimation error is relatively reduced, and the number of required signal groups is reduced. According to the characteristic, the probability of correctly estimating the pseudo code period of the signal can be improved by increasing the sampling frequency in reality.

Fig. 6 shows a comparison of the estimation performance of the AltBOC (15,10) signal pseudo code period by different algorithms, where a signal-to-noise ratio (SNR) value range is set to-15-0 dB, a pseudo code period is 127 bits, a sampling frequency is 122.76MHz, 200 Monte Carlo experiments are performed, and the number of accumulations required by correctly estimating the signal pseudo code period by using the secondary power spectrum and the time domain autocorrelation method is calculated, as can be seen from fig. 6, under the condition of taking the same pseudo code period and signal-to-noise ratio, the number of accumulations required by correctly estimating the pseudo code period by using the secondary power spectrum is less than that of the time domain autocorrelation algorithm on average, which indicates that the estimation performance of the secondary power spectrum algorithm on the signal pseudo code period is better.