CN110808760A - ILSP-CMA-based synchronous DS-CDMA signal pseudo code sequence and information sequence joint blind estimation - Google Patents

ILSP-CMA-based synchronous DS-CDMA signal pseudo code sequence and information sequence joint blind estimation Download PDF

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CN110808760A
CN110808760A CN201911022213.3A CN201911022213A CN110808760A CN 110808760 A CN110808760 A CN 110808760A CN 201911022213 A CN201911022213 A CN 201911022213A CN 110808760 A CN110808760 A CN 110808760A
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signal
pseudo code
sequence
information
code sequence
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张天骐
喻盛琪
赵健根
张刚
李鑫凯
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Chongqing University of Post and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69—Spread spectrum techniques
    • H04B1/707—Spread spectrum techniques using direct sequence modulation
    • H04B1/7073—Synchronisation aspects
    • H04B1/70735—Code identification
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/0001—Systems modifying transmission characteristics according to link quality, e.g. power backoff
    • H04L1/0036—Systems modifying transmission characteristics according to link quality, e.g. power backoff arrangements specific to the receiver
    • H04L1/0038—Blind format detection
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0045—Arrangements at the receiver end
    • H04L1/0047—Decoding adapted to other signal detection operation
    • H04L1/005—Iterative decoding, including iteration between signal detection and decoding operation

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Abstract

The invention requests to protect a synchronous DS-CDMA signal pseudo code sequence and information sequence combined blind estimation based on ILSP-CMA, belonging to the technical field of signal processing. Constructing a received synchronous DS-CDMA signal model by using the known number of users, a pseudo code column period and an information code sequence period, then performing eigenvalue decomposition on a covariance matrix of the signal to obtain a corresponding eigenvector, namely a signal subspace, projecting the received signal to the signal subspace, establishing a log-likelihood function model, finally solving the information matrix and the pseudo code matrix by using an iterative least square projection constant modulus algorithm, and finally realizing the joint blind estimation of the pseudo code sequence and the information sequence. The method can accurately estimate the pseudo code sequence and the information sequence of the synchronous DS-CDMA signal under a lower signal-to-noise ratio, is easy to operate and has important engineering practical significance.

Description

ILSP-CMA-based synchronous DS-CDMA signal pseudo code sequence and information sequence joint blind estimation
Technical Field
The invention relates to direct sequence spread spectrum communication signal processing, in particular to a synchronous DS-CDMA signal pseudo code sequence and information sequence combined blind estimation method based on an iterative least square projection constant modulus (ILSP-CMA) algorithm.
Background
Direct Sequence Spread Spectrum (DSSS) communication signals are transmitted after original narrowband digital signals are Spread to a very wide spectral range by using a pseudo-code Sequence (or called PN code) technology, so that the signal Spectrum is broadened and the signal power spectral density is reduced, and the DSSS communication signals can work in a negative signal-to-noise ratio environment, i.e., signals are submerged in noise, have the advantages of strong anti-interference, anti-multipath, low interception probability, multiple access multiplexing and the like, and are widely applied to the civil and military communication fields. CDMA systems, such as those in third generation communications, employ direct sequence spread spectrum techniques, and in the latest joint tactical distribution system (JTIDS) in the united states, a hybrid of direct sequence spread spectrum and frequency hopping is used for communications.
For a synchronous direct sequence code division multiple Access (DS-CDMA) signal, different users use different pseudo code sequences, and the pseudo code sequences between the users are orthogonal to each other, so that the signal has a multiple-Access (MA) characteristic. In non-cooperative communication, to analyze a received DS-CDMA signal, a pseudo code sequence and an information sequence in the signal need to be acquired. Therefore, the research on the pseudo code sequence and the information sequence of the DS-CDMA signal is significant.
The DSSS signal can be divided into a single-user direct sequence spread spectrum signal and a multi-user direct sequence spread spectrum signal according to the number of users. The blind estimation problem of the pseudo code sequence and the information sequence of the single-user signal has been widely and deeply researched, and the main methods include a feature decomposition method, a third-order correlation method, an information subspace estimation method, a neural network algorithm and the like. For the research of multi-user signals, document (Yao Y, Poor V. Eave dropping in the synchronous CDMA channel: an EM-based adaptive [ J ]. IEEE Transactions on Signal Processing,2015,49(8):1748-1756.) proposes a DS-CDMA Signal blind estimation algorithm based on EM algorithm, which is also a blind estimation algorithm more effective for synchronous DS-CDMA signals at present, but the algorithm needs to use the estimated pseudo-code sequence to despread the Signal to obtain information sequence estimation, and the complexity of the algorithm increases exponentially with the increase of the number of users. The literature (Avitzour D.detection of asynchronous CDMA with unknown user waves [ J ]. IEEE Signal processing Letters,2004,11(2):209-211.) proposes to estimate the spreading matrix and the information matrix by iterative iteration using the Iterative Least Squares Projection (ILSP) algorithm, but the information sequence estimation performance is limited in the case of unknown spreading sequences.
In view of the above, the invention applies the ILSP-CMA algorithm to the DS-CDMA signal estimation, and can directly estimate and obtain the pseudo code sequence and the information sequence through iterative computation.
Disclosure of Invention
The invention aims to solve the technical problem that joint blind estimation is difficult to carry out on a pseudo code sequence and an information sequence under the condition of low signal-to-noise ratio of a current DS-CDMA signal, and provides an estimation method based on an ILSP-CMA algorithm. The method does not need to utilize the estimated pseudo code sequence to de-spread the signal to obtain the information sequence, and utilizes the constant modulus characteristic of the information sequence to minimize the modulus change of the output signal, can quickly converge to a threshold, and solves the problem of the combined blind estimation of the pseudo code sequence of the signal and the information sequence under the condition of low signal-to-noise ratio.
The implementation method of the technical scheme provided by the invention for solving the technical problems comprises the following steps: firstly, carrying out characteristic decomposition on a covariance matrix of a received signal, obtaining a signal subspace according to the number of users, then projecting the received signal to the signal subspace, establishing a log-likelihood function related to an information matrix and a pseudo code matrix, and finally solving the function by using an iterative least square method to finally obtain an information sequence and a pseudo code sequence.
After synchronization and baseband processing, the received DS-CDMA signal can be expressed as:
Figure RE-GDA0002321881520000021
wherein, K represents the number of users, M represents the number of information codes and is also the number of pseudo code sequence periods, AkRepresenting the signal amplitude of the kth user, v (n) representing zero mean and σ variance2White Gaussian noise, L and TCRespectively representing the length and chip width of the pseudo-code sequence. { bk(m)∈±1,m∈Z+Is the symbol width as TsC, and obeying an equal probability distributionk(t) denotes a pseudo code waveform of the kth user, N is a signal sample length, and N is ML. (1) The formula is written in a matrix form
Y＝CAB+V (2)
Wherein C ═ C1,c2,…,cK]∈RL×KIs a pseudo code matrix, A ═ diag (A)1,A2,…,AK) For a diagonal matrix of signal amplitudes, B ═ B1,b2,…,bK]T∈RK×MFor the information code matrix, V represents variance σ2Gaussian white noise matrix.
From equation (2), a covariance matrix of Y can be constructed as
RY＝E[YmYH m]＝CA2CH+σ2I (3)
The covariance of the sample for equation (3)An approximation is obtained. Then to
Figure RE-GDA0002321881520000032
Decomposing the eigenvalue to obtain the signal subspace U represented by the eigenvector corresponding to the first K maximum eigenvaluesSIs estimated value ofK represents the number of users.
Projecting an observation matrix Y into its signal subspace
Figure RE-GDA0002321881520000034
Subjecting Y to dimensionality reduction to obtain
Wherein X ∈ RK×M,
Figure RE-GDA0002321881520000036
Still a gaussian white noise matrix.
The log-likelihood function of X can be given by
Figure RE-GDA0002321881520000037
When the last term of the equation (5) takes the minimum, corresponding H and B are the maximum likelihood estimates corresponding to the likelihood function, and at this time, it is equivalent to solving the following minimum problem:
wherein | · | purple sweetFThe Frobenius norm of the matrix is represented.
For the solution of equation (6), the general idea is to perform the solution by using the least square method. Order to
Figure RE-GDA0002321881520000039
First, an initial value of H is given
Figure RE-GDA00023218815200000310
Is obtained by least square method
Figure RE-GDA00023218815200000311
Corresponds to the minimum value of
Figure RE-GDA00023218815200000312
And will be
Figure RE-GDA00023218815200000313
Each element bk(m) projection onto unit circle to ensure bk(m) is a unit length. Is fixed to obtain
Figure RE-GDA00023218815200000314
Again using least square method to solve
Figure RE-GDA00023218815200000315
H corresponds to the minimum value of (d). This process is repeated until convergence or a maximum number of iterations is reached.
Drawings
FIG. 1 is a schematic ILSP-CMA algorithm flow diagram of the present invention;
FIG. 2 is a diagram of performance of blind estimation of pseudo code sequences with respect to signal-to-noise ratio variation in different users according to the present invention;
FIG. 3 is a diagram of performance of information sequence blind estimation varying with signal-to-noise ratio for different users according to the present invention;
FIG. 4 is a graph of the convergence rate of the algorithm of the present invention;
Detailed Description
The invention is further described with reference to the following drawings and specific examples.
FIG. 1 is a schematic diagram showing the ILSP-CMA algorithm flow of the present invention, which comprises the following steps:
(1) initialization H0∈RK×KP is 0, and the convergence threshold is threshold;
(2) p +1, update B matrix:
Figure RE-GDA0002321881520000041
and B ispProjection:
(3) updating the H matrix:
Figure RE-GDA0002321881520000043
(4) computing
Figure RE-GDA0002321881520000044
(5) And (4) judging that iteration is stopped when th is less than threshold (or the maximum iteration number is reached), and otherwise, repeating the steps (2), (3) and (4).
Finally obtaining the estimation of the information code sequence B through ILSP-CMA algorithm
Figure RE-GDA0002321881520000045
Estimation of H
Figure RE-GDA0002321881520000046
And deriving therefrom the amplitude of the kth user signal
Figure RE-GDA0002321881520000047
And pseudo code sequence
Figure RE-GDA0002321881520000048
Estimation of (2):
Figure RE-GDA0002321881520000049
wherein the subscript p denotes the result of the p-th iteration, the symbol
Figure RE-GDA00023218815200000410
Represents the pseudo-inverse of the matrix, sgn {. cndot.) represents the sign-finding operation.
Fig. 2 and 3 are diagrams of pseudo code sequence and information sequence estimation performance in different users. Both are error rate curve diagrams obtained by 300 Monte Carlo simulations when the number of information codes is 200, the number of users is 4, 5 and 6 respectively, and the signal-to-noise ratio is-10 dB-0 dB. As can be seen from FIG. 2, the algorithm provided by the invention can realize correct estimation of the pseudo code sequences of 4-path users and 7-path users under the signal-to-noise ratios of-6 dB and-2 dB. As can be seen from FIG. 3, the algorithm provided by the invention can realize correct estimation of information sequences of 4-path users and 7-path users under the signal-to-noise ratios of-4 dB and-2 dB. Meanwhile, under the same signal-to-noise ratio, the smaller the number of users is, the lower the error rate is, and the performance of the algorithm is enhanced.
Fig. 4 is a graph of algorithm convergence rate for different numbers of users. The experimental conditions are that the number of information codes is 100, the maximum iteration time is 40 times, the signal-to-noise ratio is-5 dB, the number of users is 2, 4, 6, 8 and 10 respectively, and Monte Carlo simulation is 300 times. As can be seen from fig. 4, when the number of users is 2, the convergence value reaches 0 only by 5 iterations. As the number of users increases, although the corresponding iteration number increases, the corresponding iteration number tends to be stable finally, and the convergence value can reach 0 at the maximum iteration number of 20, which shows that the algorithm has a faster convergence speed.
The method constructs a correlation matrix of a received signal by modeling a synchronous DS-CDMA signal, obtains a signal subspace by utilizing characteristic decomposition, projects the received signal to the signal subspace, and finally realizes the joint blind estimation of an information sequence and a pseudo code sequence by utilizing an ILSP-CMA algorithm. The algorithm has better estimation performance when fewer observation samples are used, is simpler, is easy to realize in engineering, can adapt to the working condition of low signal-to-noise ratio, and has good application prospect in the aspect of blind processing of direct sequence spread spectrum signals.

Claims (3)

1. A synchronous DS-CDMA signal pseudo code sequence and information sequence joint blind estimation based on ILSP-CMA specifically comprises the following steps: firstly, carrying out characteristic decomposition on a covariance matrix of a received signal, obtaining a signal subspace according to the number of users, then projecting the received signal to the signal subspace, establishing a log-likelihood function related to an information matrix and a pseudo code matrix, and finally solving the function by using an iterative least square method to finally obtain an information sequence and a pseudo code sequence.
2. The estimation method according to claim 1, characterized in that: and establishing a covariance matrix model of the received signal, decomposing the characteristics of the covariance matrix model, and projecting the covariance matrix model to a signal subspace to realize the dimension reduction processing of the received signal and reduce the operation amount.
3. Method according to claims 1 and 2, characterized in that: and according to the statistical characteristics of the Gaussian white noise, establishing a log-likelihood function of the dimension reduction signal, and solving the function by using an iterative least square method to obtain the estimation of the information sequence and the estimation of the pseudo-code sequence.
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CN105490705A (en) * 2016-01-07 2016-04-13 电子科技大学 ILSP algorithm-based synchronous DS-CDMA signal blind de-spreading method
CN107124252A (en) * 2017-06-30 2017-09-01 重庆邮电大学 Synchronization DS CDMA signal pseudo-code sequence blind estimates containing residual frequency deviation
CN107733820A (en) * 2017-10-19 2018-02-23 电子科技大学 DS CDMA blind symbol estimation methods under the conditions of multi-path channel environment

Patent Citations (4)

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Publication number Priority date Publication date Assignee Title
KR20010075887A (en) * 2000-01-21 2001-08-11 김제우 Method for detecting steering metrix and signal metrix in adaptive array antena
CN105490705A (en) * 2016-01-07 2016-04-13 电子科技大学 ILSP algorithm-based synchronous DS-CDMA signal blind de-spreading method
CN107124252A (en) * 2017-06-30 2017-09-01 重庆邮电大学 Synchronization DS CDMA signal pseudo-code sequence blind estimates containing residual frequency deviation
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Application publication date: 20200218