A Blind Estimation Method for Synchronous Long Code DSSS Signal Based on Coupled Tensor Decomposition

Abstract

The present invention belongs to the field of communication technology, and in particular to a method for blind estimation of synchronous long code DSSS signals based on coupled tensor decomposition. The present invention first models the DSSS signal intercepted by multiple antennas as a tensor, and then decomposes it into multiple sub-tensors with a coupling relationship, and obtains the estimation of the spread spectrum sequence and information symbols after coupling tensor decomposition. Compared with the traditional method, it is simpler and has better performance. Computer simulation results show that the present invention still has good performance under low signal-to-noise ratio conditions.

Description

Technical Field

[0001] The invention belongs to the field of communication technology, and in particular relates to a synchronous long code DSSS signal blind estimation method based on coupled tensor decomposition. Background Art

[0002] As a typical low probability of intercept signal, direct sequence spread spectrum (DSSS) signal is widely used in many fields such as radar, satellite communication, mobile communication, speed measurement, navigation and tracking. For non-cooperative communication receivers, there is no prior knowledge of parameters such as the spread spectrum sequence, so it is necessary to estimate the spread spectrum sequence to despread the direct spread signal and further obtain the information code sequence. The spread spectrum sequence period and spread spectrum gain of the long code direct spread signal are different, and the ratio of the two is generally a non-integer multiple, which increases the difficulty of estimating the spread spectrum sequence. Therefore, the blind estimation of the non-periodic long code DSSS signal of multiple users is more meaningful. In the scenario of multi-antenna reception, the intercepted synchronous long code DSSS signal can be modeled as a coupled tensor model, and the coupled tensor decomposition is further used to realize the blind estimation of the signal. Summary of the invention

[0003] In view of the above problems, the present invention proposes a blind estimation method for synchronous long code DSSS signals based on coupled tensor decomposition.

[0004] The technical solution of the present invention is:

[0005] A blind estimation method for synchronous long code DSSS signal based on coupled tensor decomposition, such as Figure 1 As shown, the following steps are included:

[0006] S1. Define the sample of the non-periodic long code DSSS signal intercepted by the i-th antenna as y i (n), the signals intercepted by I antennas are arranged as Tensor

[0007] S2. Construct D row selection matrices P with dimensions G×L d , that is, select G rows from L rows, and construct D dimensions as The column selection matrix Q d , G is the spreading gain, L is the spreading sequence length, is the number of information code elements, M d is the number of selected columns in the dth mode, D = L / Δτ, Δτ = gcd(L,G) represents the number of modes;

[0008] S3. Arrange the signals corresponding to the same mode, that is, the same spread spectrum sequence symbol, into D sub-tensors, such as Figure 2 As shown, the CP decomposition of each sub-tensor is:

[0009]

[0010] in Represents G×M d ×I-dimensional subtensor, A=[a 1 a 2 ...a R ] is an I×R dimensional gain matrix, C=[c 1 c 2 ... c R ] is the spreading sequence matrix, B=[b 1 b 2 ... b R ] is the information code element matrix;

[0011] S4. Convert each sub-tensor into three matrix slices:

[0012]

[0013]

[0014]

[0015] where ⊙ represents the Kronecker product, The dimension is GM d ×I, The dimension is GI×M d , The dimension is M d I×G;

[0016] S5. The coupling tensor decomposition process is as follows:

[0017] S51, let k = 0, randomly initialize the spread spectrum sequence and information codeword to obtain C (0) ,B (0) ;

[0018] S52, Order

[0019]

[0020] Get A's update A (k) =((F H F) -1 F H Y') H ;

[0021] S53, let A Cd =A (k) ⊙(P d C (k) ),use Get B d =BQd Update

[0022]

[0023] Will Combine to get B (k+1) ;

[0024] S54, Order use Get C d =P d Update of C

[0025]

[0026] make Z=[Z1,...,Z D ], Get C's update

[0027] C (k+1) =(ZP H (PP H ) -1 ) H

[0028] S55. Use the updated factor matrix to obtain

[0029]

[0030] S56, repeat S52 to S55 until the following convergence conditions are met

[0031]

[0032] Where ε is a given threshold, thus obtaining an estimate of the factor matrix

[0033] The beneficial effects of the present invention are as follows: the present invention is a synchronous long code DSSS signal blind estimation method based on coupled tensor decomposition, firstly the DSSS signal intercepted by multiple antennas is modeled as a tensor, then decomposed into D sub-tensors with coupling relationship, and the estimation of spread spectrum sequence and information symbol is obtained after coupled tensor decomposition. Compared with the traditional method, it is simpler and has better performance. Computer simulation results show that the present invention still has good performance under low signal-to-noise ratio conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a specific flow chart of the synchronous long code DS-CDMA signal blind estimation method proposed by the present invention.

[0035] Figure 2 It is a schematic diagram of S3 in the present invention constructing a received signal into a missing short code signal.

[0036] Figure 3 It is the curve of the estimated bit error rate of the information code sequence with different numbers of antennas changing with the signal-to-noise ratio.

[0037] Figure 4 It is the curve of the estimated bit error rate of the information code sequence with different number of users changing with the signal-to-noise ratio. DETAILED DESCRIPTION

[0038] The present invention is described in detail below with reference to the accompanying drawings.

[0039] The specific method of the present invention is:

[0040] Define the synchronous long code DSSS signal intercepted by the i-th antenna,

[0041]

[0042] The signal gain of the i-th antenna user r is A i,r , the number of antennas is I, the information code sequence of user r is The spreading sequence c of user r r =[c r (0),...,c r (L-1)] T , the spreading gain is G, the spreading sequence length is L, the number of spreading sequence periods is M = N / L, and the number of information symbols is q(n) is a rectangular function and satisfies q(n) = 1 when n∈[0,G), otherwise q(n) = 0, v(n) means that the mean is 0 and the variance is σ 2 Gaussian white noise, and define the received signal-to-noise ratio of user r In addition, it is assumed that L / G is a non-integer, that is, a non-periodic long code signal.

[0043] Arrange the signals intercepted by I antennas as Tensor Construct D row selection matrices P of dimension G×L d , that is, select G rows from L rows, and construct D dimensions as The column selection matrix Q d , G is the spreading gain, L is the spreading sequence length, is the number of information code elements, M d is the number of selected columns in the dth mode, D = L / Δτ, Δτ = gcd(L, G) represents the number of modes.

[0044] Arrange the signals corresponding to the same mode, that is, the same spreading sequence symbol, into D sub-tensors, such as Figure 2 As shown, the CP decomposition of each sub-tensor is:

[0045]

[0046] in Represents G×M d ×I-dimensional subtensor, A=[a 1 a 2 ... a R ] is an I×R dimensional gain matrix, C=[c 1 c 2 ... c R ] is the spreading sequence matrix, B=[b 1 b 2 ... b R ] is the information code element matrix.

[0047] Convert each sub-tensor into three matrix slices:

[0048]

[0049]

[0050]

[0051] where ⊙ represents the Kronecker product, The dimension is GM d ×I, The dimension is GI×M d , The dimension is M d I×G, let k = 0, randomly initialize the spread spectrum sequence and information codeword to get C (0) ,B (0) ,make

[0052]

[0053] Get A's update A (k) =((F H F) -1 F H Y') H ;

[0054] Let A Cd =A (k) ⊙(P d C (k) ),use Get B d =BQ d Update

[0055]

[0056] Will Combine to get B (k+1) ;

[0057] make use Get C d =P d Update of C

[0058]

[0059] make Z=[Z1,...,Z D ], Get C's update

[0060] C (k+1) =(ZP H (PP H ) -1 ) H

[0061] Using the updated factor matrix we get

[0062]

[0063] When the following convergence conditions are met, the estimate of the factor matrix is ​​obtained

[0064]

[0065] Where ε is a given threshold.

[0066] Simulation Example

[0067] This example uses MATLAB to simulate and demonstrate the above-mentioned blind estimation method of synchronous long code DSSS signal based on coupled tensor decomposition.

[0068] Simulation conditions and parameters: Spreading sequence length L = 63, spreading gain G = 30, information sequence length of each user M = 420, 100 Monte Carlo simulations were performed on the algorithm to obtain the bit error rate of the estimated information sequence and the bit error rate of the estimated information sequence under cooperative communication conditions when the number of antennas and users changed. The signal-to-noise ratio ranged from -10dB to 0dB. Figure 3 The simulation results are as follows when the number of users R=3 and the number of antennas I=2, 3, 4. Figure 3 The simulation results are as follows when the number of antennas is fixed at I = 3 and the number of users is fixed at R = 2, 3, and 4. Figure 3 and Figure 4 The simulation results show that the bit error rate decreases with the improvement of the signal-to-noise ratio, and the estimated bit error rate of the information sequence is close to the bit error rate under cooperative communication conditions as the signal-to-noise ratio increases, indicating that this method has good performance.

Claims

1. A method for blind estimation of synchronous long code DSSS signals based on coupled tensor decomposition, characterized in that: The following steps are involved: S1. Define the sample of non-periodic long code DSSS signal intercepted by the i-th antenna as y i (n), the signals intercepted by I antennas are arranged as Tensor G is the spreading gain, is the number of information code elements; S2. Construct D row selection matrices P with dimensions G×L d , that is, select G rows from L rows, and construct D dimensions as The column selection matrix Q d , L is the length of the spreading sequence, M d is the number of selected columns in the dth mode, D = L / Δτ, Δτ = gcd(L,G) represents the number of modes; S3. Arrange the signals corresponding to the same mode, that is, the same spread spectrum sequence symbol, into D sub-tensors, and decompose the CP of each sub-tensor into: in Represents G×M d ×I-dimensional subtensor, A=[a 1 a 2 ...a R ] is an I×R dimensional gain matrix, R is the number of users, C=[c 1 c 2 ...c R ] is the spreading sequence matrix, B=[b 1 b 2 ...b R ] is the information code element matrix; S4. Convert each sub-tensor into three matrix slices: where ⊙ represents the Kronecker product, The dimension is GM d ×I, The dimension is GI×M d , The dimension is M d I×G; S5. The coupling tensor decomposition process is as follows: S51, let k = 0, randomly initialize the spread spectrum sequence and information codeword to obtain C (0) ,B (0) ; S52, Order Get A's update A (k) =((F H F) -1 F H Y') H ; S53, Order B d =BQ d ,use Get B d Update Will Combine to get B (k+1) ; S54, Order C d =P d C. Use Get C d Update make Z=[Z1,...,Z D ], Get C's update C (k+1) =(ZP H (PP H ) -1 ) H , S55. Use the updated factor matrix to obtain S56, repeat S52 to S55 until the following convergence conditions are met Where ε is a given threshold, thus obtaining an estimate of the factor matrix 2. The method for blind estimation of synchronous long code DSSS signal based on coupled tensor decomposition according to claim 1, characterized in that: The i The specific expression of (n) is: The signal gain of the i-th antenna user r is A i,r , the number of antennas is I, the information code sequence of user r is The spreading sequence c of user r r =[c r (0),...,c r (L-1)] T , the spreading gain is G, the spreading sequence length is L, the number of spreading sequence periods is M = N / L, and the number of information symbols is q(n) is a rectangular function and satisfies q(n) = 1 when n∈[0,G), otherwise q(n) = 0, v(n) means that the mean is 0 and the variance is σ 2 Gaussian white noise, and define the received signal-to-noise ratio of user r In addition, it is assumed that L / G is a non-integer, that is, a non-periodic long code signal.

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