CN107733820B - DS-CDMA blind symbol estimation method under the conditions of multi-path channel environment - Google Patents

Abstract

The invention belongs to blind symbol estimation technical field, a kind of DS-CDMA blind symbol estimation method under the conditions of multi-path channel environment is particularly related to.The present invention is by the multipath DS-CDMA signal modeling received at matrix form, then according to the Toeplitz special construction of information code matrix and ± 1 characteristic, receipt signal matrix are decomposed using ILSP algorithm, obtain the estimated matrix of the combined channel matrix of the Sequence composition obtained by user's frequency expansion sequence and channel parameter convolutionIt finally de-spreads to obtain user information code matrix using combined channel matrix.The beneficial effects of the present invention are: the invention proposes a kind of DS-CDMA blind symbol estimation methods under the conditions of multi-path channel environment, even and if method of the invention still there is preferable performance under Low SNR.

Description

A Blind Estimation Method for DS-CDMA Signals under Multipath Channel Environment Conditions

technical field

The invention belongs to the technical field of blind estimation of DS-CDMA (Direct-Sequence Code-Division Multiple Access), and in particular relates to a blind estimation method of DS-CDMA signals under multi-path channel environment conditions based on Toeplitz matrix structure.

Background technique

Direct Sequence Spread Spectrum (DSSS, Direct Sequence Spread Spectrum) is one of the most commonly used communication technologies in modern communication systems. At the signal sending end, the information code sequence is multiplied by a high-rate spread spectrum code sequence, so that the signal spectrum is expanded, which can reduce the power spectral density of the transmitted signal, and has the characteristics of low intercept probability. The DSSS communication system cooperates with the receiver to use the known spread spectrum sequence to despread the received signal cooperatively, which can suppress interference and recover the transmitted information. For the cooperative receiver, the transmitted information code sequence can be despread from the received signal by using the spreading sequence of the sender, but for the non-cooperative receiver, the received signal needs to be processed to extract the signal spreading sequence, Then use the estimated spreading sequence to despread to obtain the transmission information code sequence. For DS-CDMA signals, different users use different spread spectrum sequences, and the spread spectrum code sequences between users are orthogonal to each other, so that it has multiple access characteristics. DS-CDMA signal has the advantages of low probability of interception, strong anti-interference ability, code division multiple access, etc., and is widely used in civil, military and satellite communications and other fields. Therefore, it is more meaningful to study the blind estimation of DS-CDMA signal.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies in the prior art, propose a kind of DS-CDMA signal blind estimation method under the multipath channel environment condition based on Toeplitz matrix structure, the method that the present invention proposes is applicable to the multipath channel environment condition DS-CDMA signal blind estimation problem.

Technical scheme of the present invention is: the DS-CDMA signal blind estimation method under multipath channel environment condition, it is characterized in that, comprises the following steps:

S1. Constructing the DS-CDMA signal matrix model Y:

Express the received DS-CDMA signal via multipath as:

Among them, R represents the number of users, A _r is the signal amplitude of the rth user, b _r is the information code sequence of the rth user, M is the number of information codes, h _r is the spreading code of the rth user Convolution sequence of sequence and multipath channel parameters, v(n) is Gaussian white noise with variance σ ² ;

The matrix form of the above DS-CDMA signal is:

Y=HAS ^T +N (1)

Among them, JR×JR dimensional diagonal matrix A=diag(A ₁ ,...,A ₁ ,..., _AR ,..., _AR ), J is the information of intersymbol interference caused by multipath The number of codes, the L×JR dimensional matrix H is a matrix constructed from the convoluted sequence h and zero of the spread spectrum sequences of R users and the multipath coefficients, and the (M+J-1)×JR dimensional matrix S is formed by The Toeplitz matrix constructed by the elements of the M×R dimension information code matrix B, N is a Gaussian white noise matrix with a mean value of 0 and a variance of ^σ2 ;

Information code matrix of a single user The structure is:

S2. Obtain the estimated matrix of matrix H

According to the description in step S1, the matrix S is a Toeplitz structure, and the multiplication of the matrix H and the matrix S can be multiplied by the Toeplitz structure of the matrix H and the non-Toeplitz matrix form of the matrix S, namely:

Among them, the H matrix can be written as [H ₁ H ₂ ... H _JR ], H _i is the i-th column of the H matrix;

s _r =[S _(r-1)J+1 S _(r-1)J+2 ...S _J(r-1)+J ] represents the Toeplitz matrix structure composed of the information code of the rth user;

It is the Toeplitz form of the H matrix, and the B matrix is the multi-user information code matrix sent by the signal transmitter, and the specific form is:

According to formula 3, we can get The size of the matrix is (M+J-1)×MR dimension, and the specific form of its Toeplitz structure is:

The matrix can be divided into R (M+J-1)×M-dimensional Toeplitz matrices, according to formula 1:

Then get the estimated matrix Specific methods include:

S21, let i=0, randomly initialize the M×R dimensional matrix And by Get the Toeplitz form matrix

S22, let i=i+1, calculate Eliminate scale effects;

S23. Will rewritten in Toeplitz form calculate Then by the matrix Get the Toeplitz form matrix

S24. Repeat steps (2) to (3) until the algorithm converges or reaches the maximum number of iterations. The algorithm convergence condition is:

Where ε is the threshold value of convergence;

S25. Repeat steps (1) to (4) multiple times, and select the one with the best iteration effect as the final result;

S3, using the estimated matrix of the final H matrix Perform despreading to obtain the estimated matrix of the information matrix S matrix

In the general technical scheme of the present invention, the received multipath DS-CDMA signal is modeled into a matrix form, and then according to the Toeplitz special structure and ±1 characteristics of the information code matrix, the ILSP algorithm is used to decompose the received signal matrix, and the received signal matrix is obtained by the user. The estimation matrix of the joint channel matrix formed by the sequence obtained by the convolution of the spreading sequence and the channel parameter Finally, the user information code matrix is obtained by despreading the joint channel matrix.

The beneficial effects of the present invention are: the present invention proposes a DS-CDMA signal blind estimation method under multi-path channel environment conditions, and the method of the present invention still has better performance even under the condition of low signal-to-noise ratio.

Description of drawings

Fig. 1 is a kind of specific implementation flow chart of the DS-CDMA signal blind estimation method propagated under the multipath channel environment condition of the present invention;

Fig. 2 is in the embodiment 1 of the present invention, the bit error rate of the information code matrix estimation matrix when the number of users is 3 is the comparative schematic diagram of the variation curve of the signal-to-noise ratio and CRB (Cramer-Rao Bound);

Fig. 3 is a schematic diagram of the comparison between the normalized mean square error of the joint channel matrix estimation matrix and the variation curve of the signal-to-noise ratio when the number of users is fixed in the embodiment 2 of the present invention and the CRB;

Fig. 4 is a schematic diagram comparing the normalized mean square error curve of the joint channel matrix estimation matrix with the signal length and the CRB when the number of users is fixed in Embodiment 3 of the present invention.

Detailed ways

The technical solutions of the present invention will be described in detail below in conjunction with the accompanying drawings and examples.

Example 1

FIG. 1 is a flow chart of a specific embodiment of DS-CDMA signal blind estimation under multipath channel environment conditions in the present invention. As shown in Figure 1, the present embodiment realizes the DS-CDMA signal blind estimation method under multipath channel environment conditions and includes the following steps:

Step 1: The received DS-CDMA signal via multipath propagation can be expressed as

Among them, R represents the number of users, this implementation is R=3, a _r is the signal amplitude of the rth user, which is a random number in this implementation, b _r is the information code sequence of the rth user, this time In the implementation, both the information code sequence and the spreading code sequence are ±1 sequences, and M is the number of information codes. In this implementation, M=100, the spreading gain L=31, and the multipath channel parameters of each user are all [1,0.9 ,0.7,0.5,0.3,0.15], h _r is the convolution sequence of the spreading code sequence of the rth user and the multipath channel parameters, the signal-to-noise ratio is -5dB to 0dB, and n(n) is the variance σ ² Gaussian white noise.

Step 2: According to step 1, the matrix form of the DS-CDMA signal propagated by multipath can be written as

Y=HAS ^T +N

Among them, JR×JR dimensional diagonal matrix A=diag(A ₁ ,...,A ₁ ,..., _AR ,..., _AR ), J is the information code of the intersymbol interference caused by multipath number, the L×JR dimensional matrix H is a matrix constructed from the convoluted sequence h and zero of the spread spectrum sequences of R users and the multipath coefficients, and the (M+J-1)×JR dimensional matrix S is composed of M × Toeplitz matrix constructed from elements of R-dimensional information code matrix B, N is Gaussian white noise matrix with mean value 0 and variance σ ² .

Information code matrix of a single user The structure is shown in the following formula

Step 3: For the DS-CDMA signal matrix model Y introduced above, due to the special structure and ±1 characteristic of the Toeplitz matrix of the matrix S, if there is a fuzzy matrix, the Toeplitz structure of the matrix S will be destroyed, and the matrix A is a diagonal matrix, that is, only It will have a scale effect on each column of the matrix H, which can be eliminated by normalizing each column of H, so the matrix Y can be decomposed directly using the ILSP algorithm to obtain the estimated matrix of the S matrix and the H matrix and

Specific implementation steps:

(1). Let i=0, randomly initialize the M×R dimensional matrix And by Get the Toeplitz form matrix

(2). Make i=i+1, calculate Eliminate scale effects;

(3). Will rewritten in Toeplitz form calculate Then by the matrix Get the Toeplitz form matrix

(4). Repeat steps (2) to (3) until the algorithm converges or reaches the maximum number of iterations. The algorithm convergence condition is:

Where ε is the convergence threshold, which is usually taken as 1×10 ^-9 . In this algorithm, the maximum number of iterations is set to 50.

(5). In order to improve the performance of the algorithm, repeat steps (1) to (4) multiple times (this method is selected as 40 times), and select the one with the best iteration effect as the final result.

Step 4: Use the estimated matrix of the final H matrix Perform despreading to obtain the estimated matrix of the information matrix S matrix

Compare the obtained estimated matrix with the original data matrix, calculate the bit error rate, and compare it with the CRB in the same situation, and draw the curve of the bit error rate versus the signal-to-noise ratio. In this implementation, 100 Monte Carlo experiments are carried out, and the finally obtained information code matrix bit error rate versus SNR (Signal Noise Rate, signal-to-noise ratio) variation curve is shown in FIG. 2 . It can be seen from the figure that the blind despreading method proposed by the present invention has excellent performance in the case of low SNR, and gradually approaches the CRB curve as the SNR increases, which is consistent with the theory.

Example 2

The purpose of this embodiment is to simulate the change of the normalized mean square error rate of the joint channel matrix with the SNR under the condition of a certain number of users. The implementation conditions of this implementation are the same as those of implementation 1, the signal-to-noise ratio is -5dB to 5dB, and the normalized mean square error of the joint channel is calculated by the following formula:

100 Monte Carlo experiments were performed, and the finally obtained joint channel matrix normalized mean square error versus SNR curve is compared with CRB as shown in Figure 3. It can be seen from the figure that the blind despreading method proposed by the present invention has good performance in the case of low SNR, and the normalized mean square error of the joint channel decreases with the increase of SNR, and gradually approaches CRB, which is consistent with the theoretical match.

Example 3

The purpose of this embodiment is to simulate the change of the normalized mean square error rate of the joint channel matrix with the signal length under the condition of a certain number of users. This implementation condition is fixed at -3dB, the signal length is changed from 100 to 500, and the other conditions are the same as in implementation 2. The normalized mean square error of the joint channel is calculated by the following formula:

100 Monte Carlo experiments were carried out, and the finally obtained joint channel matrix normalized mean square error curve with signal length is compared with CRB as shown in Figure 4. It can be seen from the figure that the normalized mean square error of the joint channel obtained by the blind despreading method proposed by the present invention decreases with the increase of the signal length, and gradually approaches the CRB, which is consistent with the theory.

Claims (1)

1. the DS-CDMA blind symbol estimation method under the conditions of multi-path channel environment, which comprises the following steps:

S1, building DS-CDMA signal matrix model Y:

The DS-CDMA signal through multipath transmisstion received is indicated are as follows:

Wherein, R indicates the number of user, A_rFor the signal amplitude of r-th of user, b_rFor the information code sequence of r-th of user, M is Information code number, h_rFor the spread spectrum code sequence of r-th user and the convolution sequence of multi-path channel parameters, v (n) is that variance is σ²'s White Gaussian noise, L are spreading gain；

The matrix form of above-mentioned DS-CDMA signal are as follows:

Y=HAS^T+N (1)

Wherein, JR × JR ties up diagonal matrix A=diag (A₁,...,A₁,...,A_R,...,A_R), J is the intersymbol due to caused by multipath The information code number of interference, L × JR tie up the frequency expansion sequence and sequences h and zero structure after multi-path coefficients convolution that matrix H is R user Matrix made of making, (M+J-1) × JR dimension matrix S are the Toeplitz matrixes constructed by the element of M × R dimension information code matrix B, N be mean value be 0, variance σ²White Gaussian noise matrix；

The information code matrix of single userStructure are as follows:

S2, the estimated matrix for obtaining matrix H

According to step S1, matrix S is Toeplitz structure, and can obtain that matrix H is multiplied with matrix S can be with transformed matrix H's Toeplitz structure is multiplied with the non-Toeplitz matrix form of matrix S, it may be assumed that

Wherein, H-matrix can be written as [H₁ H₂ ... H_JR], H_iFor the i-th column of H-matrix；

s_r=[S_(r-1)J+1 S_(r-1)J+2 … S_J(r-1)+J] indicate r-th of user information code character at Toeplitz matrix structure；

For the Toeplitz form of H-matrix, B matrix is the multi-user information code matrix that signal transmitting terminal issues, concrete form Are as follows:

According to formula (3), can obtainThe size of matrix is (M+J-1) × MR dimension, the concrete form of Toeplitz structure are as follows:

Matrix can be divided into the Toeplitz matrix of R (M+J-1) × M dimensions, can be obtained according to formula (1):

Then obtain estimated matrixSpecific method include:

S21, i=0, random initializtion M × R is enabled to tie up matrixAnd byObtain Toeplitz formal matrices

S22, i=i+1 is enabled, calculated1≤r≤R, eliminating scale influences；

S23, generalIt is rewritten as Toeplitz formIt calculatesAgain by matrix To Toeplitz formal matrices

S24, repetition step S21~S23 until algorithmic statement or reach maximum number of iterations, algorithmic statement condition are as follows:

Wherein ε is convergent threshold value；

S25, it repeats step S21~S24 more times, selects best primary as final result of iteration effect；

S3, with the estimated matrix of finally obtained H-matrixIt is de-spread to obtain the estimated matrix of information matrix s-matrix