CN111953380A - Non-periodic long code direct sequence spread spectrum signal time delay estimation method and system based on norm fitting - Google Patents
Non-periodic long code direct sequence spread spectrum signal time delay estimation method and system based on norm fitting Download PDFInfo
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Abstract
The invention belongs to the technical field of signal processing, and particularly relates to a method and a system for estimating time delay of a non-periodic long code direct spread spectrum signal based on norm fitting, wherein the method comprises the steps of carrying out carrier synchronization and timing synchronization on a received signal to obtain a non-periodic long code direct spread spectrum CDMA baseband waveform; modeling a long code direct sequence spread spectrum signal into a short code direct sequence spread spectrum signal containing missing observation, rearranging a baseband waveform into a missing data matrix according to the code element width of an information code, and acquiring an F norm curve of the missing data matrix; setting an equivalent period, representing a missing data matrix as a cyclic repetitive representation of a cellular matrix, and acquiring a square template of a user signal F norm curve according to the cellular matrix and a screening matrix; and modeling the multi-user signal F norm curve as the cyclic convolution of the template curve, and solving the model by using least square to obtain the time parameter of the desynchronizing of each user. The invention can realize the time delay estimation of a large-capacity asynchronous NPLC-DSSS-CDMA system under the non-cooperative receiving condition, and effectively reduces the operation complexity of the system while ensuring good estimation precision.
Description
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a non-periodic long code direct sequence spread spectrum signal time delay estimation method and system based on norm fitting.
Background
Direct Sequence Spread Spectrum (DSSS) signals are widely used in a variety of important communication applications, such as mass commercial communications, due to their significant security. Meanwhile, the system also has excellent anti-interference and multi-access capabilities, and particularly has better channel fading resistance, so that the application scene is continuously expanded, and the system is gradually applied to strong interference systems such as mobile communication, underwater communication and the like in recent years. The DSSS transmitter modulates the transmission sequence by adopting a pseudo-random sequence, reduces the transmission power while spreading the spectrum, and enables the received signal to show the characteristic of similar Gaussian white noise, so that the traditional analysis method is difficult to directly apply. Therefore, detection and analysis of such signals under non-cooperative reception conditions has been a research hotspot and difficulty. In general, DSSS signals can be classified into three categories according to the multiple relationship between the pseudo code period and the information code period: when the pseudo code period is equal to the information code period, the signal is called a short code direct sequence spread spectrum signal (SC-DSSS); when the period of the pseudo code is integral multiple of the period of the information code, the pseudo code is called a periodic long code direct sequence spread spectrum signal (PLC-DSSS); when the pseudo code period is larger than the information code period and there is no integral multiple relationship between the two, it is called non-periodic long code direct sequence spread spectrum (NPLC-DSSS), and such signals have been used in practical communication systems, such as Tracking and Data Relay Satellite System (TDRSS). A non-periodic long code direct sequence spread spectrum signal code division multiple access system (NPLC-DSSS-CDMA) modulates the sending waveforms of different users by adopting different pseudo-random codes and then superposes and transmits the modulated sending waveforms, and a received signal is shown as the superposition of NPLC-DSSS signals of a plurality of random symbol initial positions. The core of DSSS signal analysis is to estimate the spreading codes, and it is assumed in a large number of research works that the time delay of each user is known, and actually for third-party reception, the user power and the pseudo code sequence are unknown under multi-user conditions, and in addition to the random modulation of symbols and the low signal-to-noise ratio environment, the time delay estimation is not simple.
Research on SC-DSSS and PLC-DSSS signal synchronization technologies has been carried out for many years, and mature methods such as a Frobenius norm method (hereinafter referred to as an F norm), an autocorrelation envelope method, a eigenvalue decomposition method and the like exist. The principle based on the autocorrelation matrix F norm method can be summarized as that different desynchronization times correspond to different correlation matrix F norms, and the matrix F norm reaches the maximum when synchronization is performed. For NPLC-DSSS signals, because waveforms in a pseudo code period are randomly modulated by information symbols, when the period is segmented, the correlation matrix F norm of the signals under the same symbol cannot be accumulated, so that the method cannot be directly applied, and the research results of the conventional asynchronous multi-user blind synchronization technology are very limited, and a reliable scheme which is enough to cope with the large-capacity NPLC-DSSS-CDMA system blind synchronization is not available.
Disclosure of Invention
Therefore, the invention provides a non-periodic long code direct sequence spread spectrum signal time delay estimation method and system based on norm fitting, which can realize time delay estimation of a large-capacity asynchronous NPLC-DSSS-CDMA system under a non-cooperative receiving condition, and can effectively reduce the operation complexity of the system while ensuring good estimation precision.
According to the design scheme provided by the invention, the method for estimating the time delay of the aperiodic long code direct spread spectrum signal based on norm fitting comprises the following contents:
carrying out carrier synchronization and timing synchronization on the received signal to obtain a non-periodic long code direct sequence spread spectrum CDMA baseband waveform;
modeling a long code direct sequence spread spectrum signal into a short code direct sequence spread spectrum signal containing missing observation, rearranging a baseband waveform into a missing data matrix according to the code element width of an information code, and acquiring the square of an F norm curve of the missing data matrix;
setting an equivalent period of a non-periodic long code direct-spread CDMA signal by combining the information code element width and the spread spectrum pseudo code sequence length in a baseband waveform, representing a missing data matrix as a cyclic repeated representation of a cell matrix, and obtaining a screening matrix of the cell matrix by judging the positions of elements with the same symbol in the cell matrix so as to obtain a user signal F norm curve square template;
and modeling the F norm curve of the user signal as the cyclic convolution of a template curve according to the standard fitting norm curve, and solving the model by using least square to obtain the step-out time parameters of each user.
The non-periodic long code direct sequence spread spectrum signal time delay estimation method based on norm fitting further comprises the steps of rearranging a baseband waveform, segmenting a long code direct sequence spread spectrum signal according to an information code period to serve as a matrix column, determining the dimension of the matrix according to the number of user information codes and the length of a spread spectrum pseudo code sequence to obtain an equivalent short code direct sequence spread spectrum signal matrix representation, and performing point multiplication on the equivalent short code direct sequence spread spectrum signal matrix representation and a 0-1 matrix to obtain a missing data matrix representation; and obtaining the F norm representation according to the autocovariance matrix of the missing data matrix.
The non-periodic long code direct sequence spread spectrum signal time delay estimation method based on norm fitting further sets the equivalent period of the non-periodic long code direct sequence spread spectrum CDMA signal as the least common multiple of the code element width of the information code and the sequence length of the spread spectrum pseudo code, and defines a cell matrix with the dimension size of the least common multiple of the code element width of the spread spectrum pseudo code multiplied by the code element length of the information code and the sequence length of the spread spectrum pseudo code.
The non-periodic long code direct sequence spread spectrum signal time delay estimation method based on norm fitting further defines a screening matrix which has the same dimension with a cellular matrix and corresponds to the cellular matrix time delay, the element position of each column and the designated row element of the matrix which are positioned under an information code element at the same time is 1, and the rest positions are 0; and (3) through screening the matrix, correlating the pseudo codes under different information code elements in the matrix to 0 so as to judge the same symbol positions of the specified row elements in the cellular matrix.
As the non-periodic long code direct sequence spread spectrum signal time delay estimation method based on norm fitting, further, according to the period length of a pseudo code, the repetition times of a cellular matrix are determined, the absolute value of each position in a correlation matrix of a signal missing data matrix is only related to the user step-out time, and the F norm of the correlation matrix is represented by a function of the user step-out time; and fitting a functional relation according to the numerical value represented by the function to obtain a square template of the F norm curve of the user signal.
As the non-periodic long code direct sequence spread spectrum signal time delay estimation method based on norm fitting, further, under the condition of a single user, the out-of-step time corresponding to the maximum value of an F norm curve is used as time delay estimation; and under the condition of multiple users, performing model modeling on the F norm curve under the condition of the multiple users to obtain the time delay estimation of the out-of-step time of each user.
As the non-periodic long code direct sequence spread spectrum signal time delay estimation method based on norm fitting, further, assuming that the pseudo code subsequences among the users are uncorrelated and the information codes are randomly independent, the missing data matrix of the CDMA mixed signal is linear superposition of the missing data matrix of the signal component of each user, and the F-norm square curve of the mixed signal correlation matrix corresponds to the superposition of the F-norm curve squares of each user.
As the non-periodic long code direct sequence spread spectrum signal time delay estimation method based on norm fitting, further, cyclic shift weighted addition of F norm curve square corresponding to standard fitting F norm curve square is obtained to obtain a matrix product model of F norm curve square to represent Fm＝T[Fs]ξ in which T [ F ]s]Is a matrix formed by standard fitting norm curve, xi is a column vector with the length of the code element width of the information code and the t th thereofiAn element is Ai 4，AiThe amplitude of the signal of the ith user is the amplitude of the signal sent by each user, and the diagonal element of the amplitude of the signal is the amplitude of the signal sent by each user; solving xi in the model by using a least square algorithm; based on the solution result, taking out
Acquiring the out-of-step time parameter tau of each user at the position corresponding to the middle and front K maximum values1～τK。
As the method for estimating the time delay of the aperiodic long code direct sequence spread spectrum signal based on norm fitting, further, the least square solution of ξ is represented as:
further, the present invention provides a system for estimating a time delay of a non-periodic long code direct sequence spread spectrum signal based on norm fitting, comprising: a data preprocessing module, a data processing module I, a data processing module II and a modeling solving module, wherein,
the data preprocessing module is used for carrying out carrier synchronization and timing synchronization on the received signals to acquire a non-periodic long code direct sequence spread spectrum CDMA baseband waveform;
the data processing module I is used for modeling the long code direct sequence spread spectrum signal into a short code direct sequence spread spectrum signal containing missing observation, rearranging the baseband waveform into a missing data matrix according to the code element width of the information code and acquiring the square of an F norm curve of the missing data matrix;
the second data processing module is used for combining the code element width of the information code in the baseband waveform and the length of the spread spectrum pseudo code sequence, representing the missing data matrix as the cyclic repetition representation of the cellular matrix according to the equivalent period of the non-periodic long code direct spread CDMA signal, and obtaining the screening matrix of the cellular matrix by judging the positions of the elements with the same symbol in the cellular matrix so as to obtain a square template of an F norm curve of the user signal;
the modeling solving module is used for modeling the square of the F norm curve of the user signal into the circular convolution of the square of the standard F norm curve according to the standard fitting norm curve; and solving the model by using least square to obtain the out-of-step time parameter of each user.
The invention has the beneficial effects that:
the method analyzes the F norm curve under the single-user NPLC-DSSS signal missing data matrix, utilizes the cell matrix and the screening matrix to carry out norm curve fitting, establishes a model based on the multi-user norm curve, realizes time delay estimation of each user by solving model parameters, can effectively reduce the complexity of system operation while ensuring good estimation precision, can improve the utilization rate of system resources, and further verifies through simulation experiment data.
Description of the drawings:
fig. 1 is a schematic flow chart of a signal delay estimation method in an embodiment;
FIG. 2 is a schematic diagram showing comparison between a data fitting result and a measured result in the embodiment;
FIG. 3 is a morphological illustration of a missing data matrix F-norm curve under three combined loss of synchronization time parameters in an embodiment;
FIG. 4 is a square curve of norm of matrix for example 5 users in the embodiment;
FIG. 5 is an illustration of the ξ estimation results under the curve corresponding to FIG. 4 in an example;
FIG. 6 is a flow chart of algorithm implementation in the embodiment;
FIG. 7 is a graph showing the variation of the correct detection probability P with the signal-to-noise ratio under different signal parameters in the embodiment;
FIG. 8 is a graph showing the variation of the correct estimate NMSE with the signal to noise ratio under different signal parameters in the example;
FIG. 9 is a graph showing the variation of the correct detection probability P with the number of pseudo code periods for different signal parameters in the embodiment;
FIG. 10 is a graph illustrating the variation of the correct estimate NMSE with the number of pseudo-code periods under different signal parameters in an embodiment;
fig. 11 is a graph showing the variation of the detection performance with the number of users in the embodiment.
The specific implementation mode is as follows:
in order to make the objects, technical solutions and advantages of the present invention clearer and more obvious, the present invention is further described in detail below with reference to the accompanying drawings and technical solutions.
Direct Sequence Spread Spectrum (DSSS) signals have excellent characteristics of interference resistance, interception resistance and the like, and are widely applied to military and commercial communication systems. Under non-cooperative reception conditions, blind analysis of such signals has been a hot and difficult problem of research. In the prior art, most of the signals are of the conventional short code (SC-DSSS), periodic long code (PLC-DSSS) and the like, and the study on non-periodic long code (NPLC-DSSS) signals is less. Pseudo code synchronization is a fundamental problem in spread spectrum signal analysis, and blind synchronization under the condition of unknown pseudo code sequences is more difficult. To this end, referring to fig. 1, an embodiment of the present invention provides a method for estimating a time delay of an aperiodic long code direct sequence spread spectrum signal based on norm fitting, including the following steps:
s101, carrying out carrier synchronization and timing synchronization on a received signal to obtain a non-periodic long code direct sequence spread spectrum CDMA baseband waveform;
s102, modeling a long code direct sequence spread spectrum signal into a short code direct sequence spread spectrum signal containing missing observation, rearranging a baseband waveform into a missing data matrix according to the code element width of an information code, and acquiring the square of an F norm curve of the missing data matrix;
s103, setting an equivalent period of a non-periodic long code direct-spread CDMA signal by combining the information code element width and the spread spectrum pseudo code sequence length in a baseband waveform, representing a missing data matrix as cyclic repeated representation of a cellular matrix, and obtaining a screening matrix of the cellular matrix by judging the positions of elements with the same symbol in the cellular matrix so as to obtain a user signal F norm curve square template;
and S104, modeling the user signal F norm curve into a cyclic convolution of a template curve according to a standard fitting norm curve, and solving the model by using least square to obtain the step-out time parameters of each user.
And (3) performing numerical fitting on an F-norm curve of the NPLC-DSSS-CDMA signal covariance matrix under the missing data model, constructing a model of the F-norm curve under the asynchronous multi-user condition, and finally realizing the solution of model parameters by a least square estimation method so as to obtain the time delay estimation value of each user. The method has low complexity and excellent performance, and can realize stable performance in a large-capacity system with a large number of users.
The long code DSSS signal is modeled into a short code DSSS signal by adopting a missing data model, received signals are segmented and rearranged according to information code width, a pseudo code chip under the same information symbol is used as observation data of a pseudo code period, and the other pseudo code chips are regarded as missing data, so that the long code DSSS signal and the short code DSSS signal are unified in a statistical angle, an F norm method can be expanded and applied to the long code DSSS signal under the missing data model, and the method achieves good performance under the conditions of single users and synchronous multiple users. However, under the asynchronous multi-user condition, since the signals are the superposition of a plurality of long code signals, the F-norm curve traversing the out-of-step time is also expressed as the superposition of each user component, and if the curves are not modeled and separated, the out-of-step time of each user is difficult to interpret, so that the reliability of the estimation result cannot be ensured. Especially, when the number of users is large and the time delays of different users are close to each other, the manual interpretation method based on the F-norm curve form is basically difficult to perform, so that the time delay estimation problem of the multi-user NPLC-DSSS signal is very necessary to study. The method adopts a serial estimation offset (SEC) thought based on a covariance matrix to solve the blind synchronization problem of asynchronous short code CDMA signals, firstly estimates time delay, power and a spread spectrum pseudo code sequence of signals with larger power by adopting an F norm and matrix eigenvalue decomposition method, and subtracts the component in a correlation matrix of the signals to carry out next estimation.
It is assumed that the signals have achieved down-conversion and timing synchronization, and at the same time, the number of users and the period of the pseudo code have been accurately estimated. The baseband NPLC-DSSS-CDMA signal sampled at the pseudo-code chip period can be represented as
Wherein K is the number of users, and f is a residual carrier; a. thei，ci(n)，τi,
Respectively sending amplitude, a pseudo code sequence, information code waveform time delay and an initial phase of a signal for the ith user; bi(j) For observing the jth information symbol of the ith user in the time period, the DSSS usually adopts BPSK modulation without loss of generality, and assume bi(j) Obtaining + -1 at equal probability; m is the number of pseudo code sequence periods;
the number of the information codes of the ith user is satisfied
q (n) is over miningThe information code waveform (rectangle) of (2); g is the code element width of the information code; l is the length of the spread spectrum pseudo code sequence; v (n) is a Gaussian white noise sequence.
The missing data model is to regard the long code direct-spread signal as a short code direct-spread signal containing 'missing observation', and the short code direct-spread model can be expressed as
The short code direct spread signal is segmented according to periods to be used as a column of a matrix, and the short code direct spread signal can be arranged into dimensions
Matrix of sizes
At this time, the missing data matrix XτCan be expressed as
Wherein [ ] represents a dot product of the matrix, i.e., a Hadamard product; wτIs a 0, 1 matrix with the element W of the m-th row and the n-th column τ,(mn)1 if and only if m has the value of formula (4)
mod represents the remainder operation. The missing data matrix carries out segment rearrangement on the received signals according to the symbol length, and tau is equal to 2,L＝7,For example, G-3, the missing data matrix of the received signal can be expressed as
In the progressive sense, when τ ═ τiTime, matrix XXHHas a maximum F norm. The characteristic enables the out-of-step time estimation problem under the condition of a single user to be a maximum value search problem, but the specific form of an F-norm curve is not given, so that the optimization model cannot be guided to accelerate convergence theoretically. Meanwhile, the situation under the multi-user condition is not analyzed, so that the application of the algorithm is very limited. In the embodiment of the scheme, an NPLC-DSSS signal covariance matrix F norm curve under a missing data model can be analyzed to obtain a specific curve form, and modeling is attempted to be carried out on the multi-user condition so as to realize popularization and application of the scheme.
As a non-periodic long code direct sequence spread spectrum signal time delay estimation method based on norm fitting in the embodiment of the invention, further, in baseband waveform rearrangement, long code direct sequence spread spectrum signals are segmented according to information code periods to serve as columns of a matrix, the dimension of the matrix is determined according to the number of user information codes and the length of a spread spectrum pseudo code sequence, equivalent short code direct sequence spread spectrum signal matrix representation is obtained, and the equivalent short code direct sequence spread spectrum signal matrix representation is multiplied by a 0-1 matrix point to obtain missing data matrix representation; and obtaining the F norm representation according to the autocovariance matrix of the missing data matrix. Furthermore, the equivalent period of the aperiodic long code direct-spread CDMA signal is set to be the least common multiple of the code element width of the information code and the length of the spread spectrum pseudo code sequence, and a cell matrix with the dimension size of the least common multiple of the code element width of the spread spectrum pseudo code and the length of the spread spectrum pseudo code sequence is defined. Further, a screening matrix which has the same dimension as the cellular matrix and corresponds to the time delay of the cellular matrix is defined, the element position of each column of the screening matrix, which is positioned under one information code element simultaneously with the designated row element of the matrix, is 1, and the rest positions are 0; and (3) through screening the matrix, correlating the pseudo codes under different information code elements in the matrix to 0 so as to judge the same symbol positions of the specified row elements in the cellular matrix. Further, determining the repetition times of the cellular matrix according to the period length of the pseudo code, wherein the absolute value of each position in a correlation matrix of the signal missing data matrix is only related to the user step-out time, and the F norm of the correlation matrix is represented by a function of the user step-out time; and fitting a functional relation according to the numerical value represented by the function to obtain a square template of the F norm curve of the user signal. Further, under the condition of a single user, taking the out-of-step time corresponding to the maximum value of the F norm curve as time delay estimation; and under the condition of multiple users, performing model modeling on the F norm curve under the condition of the multiple users to obtain the time delay estimation of the out-of-step time of each user.
The relationship between the missing data matrix F norm and the time to loss of synchronization is described below from a numerical analysis perspective, starting from a single-user case. It should be noted that not only the case where L and G are relatively prime is considered here, but also any other case where G ≦ L is applicable.
The autocovariance matrix of the missing data matrix may be expressed as R (τ) ═ X (τ)HThe F norm of which is defined as the value excluding the influence of diagonal elements (noise reduction effect)
Wherein
E[|Rij(τ)|]＝A2[W(τ)⊙Ψi(τ)](i)[[W(τ)⊙Ψi(τ)](j)]H (8)
Wherein [ ·](i)Representing the ith row element of the matrix. ΨiThe (tau) matrix has the same dimension as W (tau), and the element position in each column and the ith row element are simultaneously under one information code is 1, and the rest positions are 0. Passing through ΨiAnd (tau) screening the matrix, setting the pseudo code correlation under different information code elements in the autocorrelation matrix to be 0, and realizing the fitting of the theoretical value to the statistical average value.
Due to the modulation of the pseudo-random sequence by the information symbols, the equivalent period of the NPLC-DSSS signal is expanded to TeLcm (L, G), the least common multiple of L, G. According to the definition of the missing data matrix, the missing matrix form of the signal is fixed within an equivalent period, and assuming that the signal is long enough, the missing matrix form will be a cyclic repetition of the fixed unit. Defining the missing matrix unit as a cellular matrix
The dimension is L multiplied by Lcm (L, G)/G, where Lcm (L, G) represents the least common multiple of L and G. When the signal parameters (L, G) are constant,
of the form (d) is dependent only on τ, i.e.
If and only if
m＝[τ+(n-1)G+i-1 mod L]+1,i∈[1,G] (9)
The screening matrix corresponding to the cellular matrix is expressed as
Corresponding to the data length of M pseudo code periods in the signal model, the fixed unit repetition number is
At this time, the correlation matrix is defined according to equation (8)
Gcd (L, G) represents the greatest common divisor of L, G. It can be seen that, for a given data length, the absolute value of each position of the correlation matrix of the NPLC-DSSS signal missing data model is only related to the out-of-step time τ, and the F norm of the matrix is a function of τ. This functional relationship can be obtained by numerical fitting according to equation (10). Taking NPLC-DSSS signals of parameters (L, G, τ, M) (125, 60, 25, 1000) and (13, 7, 5, 1000) as examples, respectively, under the condition that the signal-to-noise ratio Es/N0 is-5 dB, the data fitting result obtained by the formula (10) and the measured result of the formula (7) are paired as shown in fig. 2, (a) represents (L, G, τ, M) ((125, 60, 25, 1000), (b) represents (L, G, τ, M) ((13, 7, 5, 1000), and shows the F-norm curve under the missing data model which can be accurately fitted under the condition of two signal parameters and a lower signal-to-noise ratio, in the form of symmetry, and both sides of the true value τ with respect to the step time0And (4) symmetry. Under the condition of a single user, the out-of-step time corresponding to the maximum value of the norm curve can be used as the estimation of the true value, which is already applied in practice. Under the condition of multiple users, the power, the time delay and the like of each user are different, the form of the norm curve becomes complex, and the desynchronizing time of each user is difficult to judge morphologically.
As the non-periodic long code direct sequence spread spectrum signal delay estimation method based on norm fitting in the embodiment of the present invention, further, assuming that the pseudo code subsequences between users are uncorrelated and the information codes are randomly independent, and the missing data matrix of the CDMA mixed signal is linear superposition of the missing data matrix of the signal component of each user, the F-norm square curve of the mixed signal correlation matrix corresponds to superposition of the F-norm curve squares of each user. Further, the F norm curve squared is added in a cyclic shift weighting mode corresponding to the standard fitting F norm curve squared to obtain a matrix product model of the F norm curve squared to represent Fm＝T[Fs]Xi, itIn, T [ F ]s]Is a matrix formed by standard fitting norm curve, xi is a column vector with the length of the code element width of the information code and the t th thereofiAn element is Ai 4，AiThe amplitude of the signal of the ith user is the amplitude of the signal sent by each user, and the diagonal element of the amplitude of the signal is the amplitude of the signal sent by each user; solving xi in the model by using a least square algorithm; based on the solution result, taking out
Acquiring the out-of-step time parameter tau of each user at the position corresponding to the middle and front K maximum values1～τK. Further, the least squares solution of ξ is represented as:
taking 5 users as an example, fig. 3 shows the form of the F-norm curve of the missing data matrix under three combined out-of-step time parameters, and it is very difficult to directly interpret the out-of-step time parameters from the curve. When the number of users is larger, and the power of each user is different, the method relying on the curve morphology basically fails. Therefore, modeling of the curve is necessary, and a method for realizing accurate estimation of the out-of-step time of each user can be explored through solving of model parameters. The modeling of the F-norm curve under multi-user conditions will be discussed below to explore the contribution of each user component therein.
In the multi-user case, the F-norm of the correlation matrix R can be considered in two ways. The introduction of the F norm model is obtained based on an eigenvalue decomposition theory. The embodiment can start from the initial eigenvalue decomposition theory.
The missing data model converts the NPLC-DSSS-CDMA signal to an SC-DSSS-CDMA signal model. At the moment, a classic pseudo code period length segmented signal model can be adopted
Wherein b isi(n) the nth transmission symbol of the ith user, ci1,ci2Individual watchShowing the front and back subsequences of the ith user pseudo code,
τ＝[τ1,τ2...τK]，C(τ)＝[c11,c12,c21,c22...cK1,cK2]，A＝diag{A1,A2,...AKthe diagonal matrix is used, and the diagonal elements are the amplitude of signals sent by each user. b (n) ═ b1(n)b1(n+1)...bK(n)bK(n+1)]TIs a transmit symbol matrix.
In this case, the correlation matrix can be obtained by equation (12)
R＝E[s(n)s(n)T]＝E[C(τ)Ab(n)b(n)TAC(τ)T] (12)
Based on the assumption that the pseudo-code sub-sequences are uncorrelated and the information codes are randomly independent among users
In the formula (14), tr (-) represents a matrix tracing operation, and the square of the F norm of the correlation matrix R is
Equation (15) illustrates that, from the eigenvalue decomposition theory perspective, the correlation matrix F-norm square curve of the signal in the multi-user case corresponds to the superposition of the F-norm curve squares of each user.
Eigenvalue decomposition is a relatively macroscopic view because the equivalence of the missing data model and the short code CDMA model is "statistical," and not exactly equal for each segment. To prove the above conclusion more accurately, the relationship between the mixed signal F-norm curve and each independent component is obtained from the missing data matrix.
The missing data matrix of the CDMA mixed signal obtained by the construction mode of the missing data matrix is linear superposition of the missing data matrix of each user signal component, i.e.
The autocorrelation matrix R (τ) is obtained
Considering the missing data matrix product between any two users, the transmitted information symbols of different users are independent and random, i.e.
E[bi(m)bj(n)]0, i ≠ j or m ≠ n (18)
The following can be concluded
Thus, it is possible to provide
Equation (20) illustrates that the F-norm matrix of the hybrid signal is actually the sum of the autocovariance matrices of the components, and the F-norm of the hybrid signal can be calculated by
Equation (21) illustrates that the F-norm squared of the multi-user composite signal is substantially equal to the linear superposition of the F-norm squares of the users.
From the above, the square of the autocorrelation matrix F-norm curve of the NPLC-DSSS-CDMA signal under the missing data model is substantially the superposition of the square of the F-norm curves of the user components. Under the condition of single user, the square of the NPLC-DSSS signal F norm curve is obtained by fitting a standard curve to perform cyclic shift. Under the condition of multiple users, different time delays may exist among the users, so on the basis of accurately modeling a single-user F-norm curve, the obtained F-norm curve square is added in a weighted manner corresponding to the cyclic shift of the standard fitting F-norm curve square, which can be expressed as:
wherein the content of the first and second substances,
represents the standard fitting F norm curve cyclic shift tauiThe latter corresponding value. The form of equation (22) is similar to a convolution model, which is equivalent to the form of matrix multiplication shown in equation (23)
Fm＝T[Fs]ξ (23)
Where ξ is the column vector of length G, its τ thiAn element is Ai 4。T[Fs]The matrix formed for the standard fitting norm curve can be expressed as
Since the power of each user is unknown, similar to the channel estimation problem, the least squares solution of ξ is
The estimation result of ξ reflects the out-of-step time information and the power information of each user, wherein the existence of noise is considered, the size is difficult to directly and accurately estimate, the accuracy of the signal power information is disturbed to a certain extent, but the out-of-step time parameter is irrelevant to the noise and is more stable. Taking 5-user (125, 60) NPLC-DSSS-CDMA system as an example, fig. 4 is a norm square curve thereof, and it is basically difficult to distinguish information such as time delay of each user from the curve morphology. Fig. 5 corresponds to the ξ estimation result under the curve of fig. 4, and there is a significant energy component at the time delay position, and under the condition that the number of users is known, the desynchronization time of each user can be effectively obtained (the position corresponding to the first K maximum values is the time delay position). The method can obtain more reliable results when the number of users is large, and is a choice with low complexity and excellent performance.
Further, an embodiment of the present invention further provides a system for estimating a time delay of a non-periodic long code direct sequence spread spectrum signal based on norm fitting, including: a data preprocessing module, a data processing module I, a data processing module II and a modeling solving module, wherein,
the data preprocessing module is used for carrying out carrier synchronization and timing synchronization on the received signals to acquire a non-periodic long code direct sequence spread spectrum CDMA baseband waveform;
the data processing module I is used for modeling the long code direct sequence spread spectrum signal into a short code direct sequence spread spectrum signal containing missing observation, rearranging the baseband waveform into a missing data matrix according to the code element width of the information code and acquiring the square of an F norm curve of the missing data matrix;
the second data processing module is used for combining the code element width of the information code in the baseband waveform and the length of the spread spectrum pseudo code sequence, representing the missing data matrix as the cyclic repetition representation of the cellular matrix according to the equivalent period of the non-periodic long code direct spread CDMA signal, and obtaining the screening matrix of the cellular matrix by judging the positions of the elements with the same symbol in the cellular matrix so as to obtain a square template of an F norm curve of the user signal;
the modeling solving module is used for modeling the square of the F norm curve of the user signal into the circular convolution of the square of the standard F norm curve according to the standard fitting norm curve; and solving the model by using least square to obtain the out-of-step time parameter of each user.
To verify the validity of the technical scheme of the present invention, the following explanation is further made through specific simulation data:
the algorithm implementation can be designed as a specific flow as shown in fig. 6, namely:
step 1: carrying out carrier synchronization and timing synchronization on the received signals to obtain baseband waveforms x (n);
step 2: sequentially making tau be 0-G-1, rearranging x (n) into missing data matrix, calculating F norm square curve to obtain Fm；
And step 3: according to the signal parameters (L, G) and the formulas (8), (9) and (10), the cell matrix is constructed by sequentially setting tau to 0-G-1
And a screening matrix
Obtaining a single user signal F norm curve square template Fs；
And 4, step 4: according to formula (24) adding FsRearrangement to T [ Fs]And is calculated according to equation (25)
And 5: taken out in turn
The positions corresponding to the first K maximum values are the out-of-step time parameter tau of each user1～τK。
Respectively selecting 5 user systems and 10 user systems, setting signal types with different information code widths as comparison signals, and performing Monte Carlo simulation experiments by adopting truncated m sequences for each user pseudo code sequence in all the signals. The signal parameters are shown in Table 1, and the parameter tau to be estimated in the experimenti(i ═ 1,2.. K) at [0, G-1]Is randomly generated.
TABLE 1 Experimental Signal parameters
It is not scientific to use the estimated mean square error alone in the multi-user delay estimation to measure the performance of the algorithm, because the estimation deviation of the signal component with smaller individual power may greatly affect the data performance. Therefore, the correct detection probability P can be adoptedcThe estimation deviation is measured and defined as the proportion of the number of correct estimation to the total number of users, wherein when the absolute value of the deviation between the estimation delay and the actual delay is less than 5% multiplied by G, the result is considered as the correct estimation quantity. Secondly, the normalized mean square error of the correct estimator is adopted to further measure the robustness of the algorithm under different signal parameters, and the method is defined as
ν in equation (26) represents the number of correct estimators. Since there is no sequential correspondence between the estimated user delays, the error calculation requires a correspondence between the estimated value and the actual value. The confidence of the estimated value is directly related to
Vector at τiThe magnitude of the position is positively correlated, therefore
And τkThe corresponding relationship is determined according to the following criteria
(1) Selecting an estimate vector
The first K maximum values in the middle are sorted according to the size
The corresponding positions are respectively recorded as
(2) According to
The actual time delay of each user is selected to be matched with
The minimum time delay value of NMSE between the two as the actual parameter tauiAnd will tauiExcluding the user time delay parameter set, and circulating until
And (5) confirming the pairing relationship.
The noise-resistant performance and the symbol performance under different data volumes of the scheme provided by the scheme are respectively inspected, the influence of the information code width on the parameter estimation performance of the out-of-step time is analyzed through the comparison of the signal I and the signal II, and the influence of the number of users on the algorithm performance is explored through the signal I and the signal III. In the experiment, a missing data model plus a morphology method (MDM + MD) and an SIC method for estimating offset are selected as comparison schemes to measure the performance of the schemes in the embodiment. It should be noted that the signal-to-noise ratio defined in this embodiment is a ratio of a sum of powers of all user components to a noise power.
The fixed signal data volume is 500 pseudo code periods, the signal-to-noise ratio interval is [ -10dB,10dB ], 2dB is stepped, 10000 monte carlo simulation experiments are performed under each signal-to-noise ratio, and the experiment result is shown in fig. 7/8.
Fig. 7 shows the variation of the correct detection probability of the delay for each algorithm with the signal-to-noise ratio under three different signal parameters. Therefore, the scheme in the embodiment of the invention has higher correct detection probability under various signal parameters compared with the other two schemes. In addition, due to the limitation of a calculation method, the performance of the other two schemes is very limited under a multi-user condition, the performance cannot be continuously improved along with the improvement of the signal-to-noise ratio, and the highest accuracy can only reach 70%, while in a 5-user scene, the signal-to-noise ratio can achieve the detection accuracy of more than 95% in the scheme, and in a 10-user scene, the detection probability of more than 80% can be achieved, and meanwhile, the performance can be continuously improved along with the signal-to-noise ratio, so that the remarkable advantages of the algorithm are explained. FromIn the embodiment of the present invention, when the performance of the scheme under three signal parameters is seen, comparing the first signal with the second signal shows that the spreading factor is smaller when the number of users is the same, the scheme in the embodiment of the present invention has higher correct detection probability and better performance, which is determined by the least square estimation algorithm
The dimensionality is correspondingly reduced, and the precision is improved; comparing the first signal and the third signal, which shows that the more the number of users is, the lower the correct detection probability is, which is mainly related to the signal-to-noise ratio, and when the number of users is increased, the increased number of users means that the signal-to-noise ratio of each user in the average sense is decreased under the definition of the signal-to-noise ratio adopted in the scheme in the embodiment of the present application, so that the delay estimation accuracy of each user is limited, and therefore, the overall correct detection probability is decreased accordingly.
Fig. 8 shows the variation curve of the correct estimate NMSE with the signal-to-noise ratio under three different signal parameters in the embodiment of the present invention, and it can be seen that the number of users increases and the NMSE of the correct estimate increases accordingly, i.e. it is illustrated that the variance of the correct estimate is also larger, which is mainly caused by the decrease of the average signal-to-noise ratio of each user.
The signal-to-noise ratio of a fixed signal is 0dB, the data volume of the signal is 50-500 pseudo code periods, the step is 50, 10000 Monte Carlo simulation experiments are carried out under each data volume, and the experiment result is shown in 9/10.
Fig. 9 shows the probability of correct detection for each algorithm with three different signal parameters as a function of signal-to-noise ratio. Compared with the MDM + MF and SIC schemes, the scheme in the embodiment has quite obvious advantages, the performance of signal estimation of the same parameter is superior to that of the other two algorithms under the condition of each data volume, and the performance is continuously improved along with the increase of the data volume. Under the condition of small data volume, the performance of the scheme is not seriously degraded, and the advantage is obvious under the condition of large data volume, thereby verifying the superiority of the scheme in the embodiment of the scheme.
Fig. 10 shows the NMSE of the correct estimator of the scheme in this embodiment as a function of the data volume for three different signal parameters. Therefore, under the condition of 0dB of the simulated signal-to-noise ratio, the normalized mean square error of the correct estimator is smaller when the number of users is less, and the estimated normalized mean square error is smaller when the number of the users is the same and the spreading factor is smaller.
In order to eliminate the influence on the detection index when the spread spectrum factor G is smaller, the experiment selects L1023 under different users,G915 NPLC-DSSS-CDMA signals, and the time delay of each user is [0, G-1 ] in each experiment]The range is randomly generated, the signal-to-noise ratio Es/N0 is 0dB, and the number of pseudo code periods is 500. The monte carlo simulation experiments are independently performed 10000 times under the condition of the number of users, the NMSE statistics of the algorithm on the correct estimation probability and the correct detection amount of the time delay under the signal parameters selected by the experiment are shown in fig. 11, (a) shows that the correct estimation probability of the time delay in the scheme in the embodiment of the scheme changes along with the number of the users, and therefore, when the number of the users is small, the correct estimation probability can reach 100%, and the detection correct probability begins to decline along with the increase of the number of the users. When the number of users reaches 14, the probability of correct estimation reaches 65%, and when the number of users is greater than 14, the ratio is basically stable. Considering the definition of the signal-to-noise ratio, i.e. the ratio of the sum of all user component powers to the noise power, when the number of users continuously increases, the signal-to-noise ratio of each user actually decreases gradually, and the detection accuracy of 65% for 20 users has demonstrated the effectiveness of the algorithm. Meanwhile, (b) shows the variation trend of the NMSE of the correct estimator with the increase of the number of users, and it can be seen that the estimated deviation is gradually increased with the increase of the number of users, which is directly related to the decrease of the signal-to-noise ratio of each user. Although the NMSE gradually increases with the number of users, since the definition of the correct detection amount in the embodiment of the present invention is strict, that is, the deviation is within ± 5% G, the result of the correct estimation amount has high reliability, and can be directly applied to the subsequent processing of the signal.
Unless specifically stated otherwise, the relative steps, numerical expressions, and values of the components and steps set forth in these embodiments do not limit the scope of the present invention.
Based on the foregoing system, an embodiment of the present invention further provides a server, including: one or more processors; a storage device to store one or more programs that, when executed by the one or more processors, cause the one or more processors to implement the system as described above.
Based on the above system, the embodiment of the present invention further provides a computer readable medium, on which a computer program is stored, wherein the program, when executed by a processor, implements the above system.
The device provided by the embodiment of the present invention has the same implementation principle and technical effect as the system embodiment, and for the sake of brief description, reference may be made to the corresponding content in the system embodiment for the part where the device embodiment is not mentioned.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the system and the apparatus described above may refer to the corresponding processes in the foregoing system embodiments, and are not described herein again.
In all examples shown and described herein, any particular value should be construed as merely exemplary, and not as a limitation, and thus other examples of example embodiments may have different values.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
In the several embodiments provided in the present application, it should be understood that the disclosed system, apparatus, and system may be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions when actually implemented, and for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection of devices or units through some communication interfaces, and may be in an electrical, mechanical or other form.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a non-volatile computer-readable storage medium executable by a processor. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the system according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (10)
1. A method for estimating a time delay of a non-periodic long code direct sequence spread spectrum signal based on norm fitting is characterized by comprising the following steps:
carrying out carrier synchronization and timing synchronization on the received signal to obtain a non-periodic long code direct sequence spread spectrum CDMA baseband waveform;
modeling a long code direct sequence spread spectrum signal into a short code direct sequence spread spectrum signal containing missing observation, rearranging a baseband waveform into a missing data matrix according to the code element width of an information code, and acquiring the square of an F norm curve of the missing data matrix;
setting an equivalent period of a non-periodic long code direct-spread CDMA signal by combining the information code element width and the spread spectrum pseudo code sequence length in a baseband waveform, representing a missing data matrix as a cyclic repeated representation of a cell matrix, and obtaining a screening matrix of the cell matrix by judging the positions of elements with the same symbol in the cell matrix so as to obtain a user signal F norm curve square template;
and modeling the F norm curve of the user signal as the cyclic convolution of a template curve according to the standard fitting norm curve, and solving the model by using least square to obtain the step-out time parameters of each user.
2. The norm fitting-based aperiodic long code direct sequence signal time delay estimation method according to claim 1, wherein in baseband waveform rearrangement, long code direct sequence signals are segmented according to information code periods and used as matrix columns, the dimension of the matrix is determined according to the number of user information codes and the length of a spread spectrum pseudo code sequence, equivalent short code direct sequence signal matrix representation is obtained, and the equivalent short code direct sequence signal matrix representation is subjected to point multiplication with a 0-1 matrix to obtain missing data matrix representation; and obtaining the F norm representation according to the autocovariance matrix of the missing data matrix.
3. The norm fitting-based time delay estimation method for aperiodic long code direct-spread signal of claim 1, wherein the equivalent period of the aperiodic long code direct-spread CDMA signal is set to the least common multiple of the symbol width of the information code and the length of the spread-spectrum pseudo code sequence, and a cell matrix having the dimension of the least common multiple of the length of the spread-spectrum pseudo code sequence x the symbol width of the information code and the length of the spread-spectrum pseudo code sequence is defined.
4. The norm fitting-based aperiodic long code direct sequence spread spectrum signal delay estimation method according to claim 1 or 3, wherein a screening matrix which has the same dimension as a cellular matrix and corresponds to the cellular matrix delay is defined, and the element position under one information symbol at the same time as the matrix-designated row element in each column is 1, and the rest positions are 0; and (3) through screening the matrix, correlating the pseudo codes under different information code elements in the matrix to 0 so as to judge the same symbol positions of the specified row elements in the cellular matrix.
5. The norm fitting-based aperiodic long code direct sequence spread spectrum signal time delay estimation method of claim 1, wherein the repetition times of the cellular matrix are determined according to the period length of the pseudo code, the absolute value of each position in the correlation matrix of the signal missing data matrix is only related to the user step-out time, and the F norm of the correlation matrix is a function representation of the user step-out time; and fitting a functional relation according to the numerical value represented by the function to obtain a square template of the F norm curve of the user signal.
6. The norm fitting-based aperiodic long code direct sequence spread spectrum signal time delay estimation method according to claim 1, characterized in that under the condition of a single user, the time-out of step corresponding to the maximum value of the F norm curve is used as time delay estimation; and under the condition of multiple users, performing model modeling on the F norm curve under the condition of the multiple users to obtain the time delay estimation of the out-of-step time of each user.
7. The norm fitting-based aperiodic long code direct sequence signal delay estimation method according to claim 1 or 6, wherein, assuming that the pseudo code subsequences are uncorrelated among users and the information codes are randomly independent, the missing data matrix of the CDMA mixed signal is a linear superposition of the missing data matrices of the signal components of each user, and the F norm square curve of the mixed signal correlation matrix corresponds to the superposition of the F norm curve squares of each user.
8. The norm fitting-based method for estimating delay of aperiodic long code direct sequence spread spectrum signal as claimed in claim 7, wherein the F norm curve squared is added by cyclic shift weighting corresponding to the standard fitting F norm curve squared to obtain a matrix product model representing F norm curve squaredm＝T[Fs]ξ in which T [ F ]s]Is a matrix formed by standard fitting norm curve, xi is a column vector with the length of the code element width of the information code and the t th thereofiAn element is Ai 4，AiThe amplitude of the signal of the ith user is the amplitude of the signal sent by each user, and the diagonal element of the amplitude of the signal is the amplitude of the signal sent by each user; solving xi in the model by using a least square algorithm; based on the solution result, taking out
Acquiring the out-of-step time parameter tau of each user at the position corresponding to the middle and front K maximum values1～τK。
9. The method of claim 8, wherein the minimum xi is the minimum xiThe two-times solution is expressed as:
10. a system for estimating time delay of an aperiodic long code direct sequence spread spectrum signal based on norm fitting, comprising: a data preprocessing module, a data processing module I, a data processing module II and a modeling solving module, wherein,
the data preprocessing module is used for carrying out carrier synchronization and timing synchronization on the received signals to acquire a non-periodic long code direct sequence spread spectrum CDMA baseband waveform;
the data processing module I is used for modeling the long code direct sequence spread spectrum signal into a short code direct sequence spread spectrum signal containing missing observation, rearranging the baseband waveform into a missing data matrix according to the code element width of the information code and acquiring the square of an F norm curve of the missing data matrix;
the second data processing module is used for combining the code element width of the information code in the baseband waveform and the length of the spread spectrum pseudo code sequence, representing the missing data matrix as the cyclic repetition representation of the cellular matrix according to the equivalent period of the non-periodic long code direct spread CDMA signal, and obtaining the screening matrix of the cellular matrix by judging the positions of the elements with the same symbol in the cellular matrix so as to obtain a square template of an F norm curve of the user signal;
the modeling solving module is used for modeling the square of the F norm curve of the user signal into the circular convolution of the square of the standard F norm curve according to the standard fitting norm curve; and solving the model by using least square to obtain the out-of-step time parameter of each user.
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