# Blind Estimation of Spreading Code Sequence of QPSK-DSSS Signal Based on Fast-ICA

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## Abstract

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## 1. Introduction

- This paper mainly focuses on the spreading code sequence estimation problem of QPSK- DSSS signals modulated by two different spreading code sequences with the same period. A blind estimation method of QPSK-DSSS signal spreading code sequences based on Fast-ICA algorithms is proposed.
- The proposed estimation method of spreading code sequences mainly includes signal whitening, separation matrix calculation, and spreading code extraction.
- The computational complexity of the algorithm is analyzed in Section 3.4 and is compared with other algorithms.
- In Section 4, we make experiments to study the influence of different spreading code lengths, information code lengths, frequency offsets, and different SNR on the spreading code estimation method. Finally, it is compared with the existing spreading code estimation method of QPSK-DSSS signal.

## 2. QPSK-DSSS Signal Model

**R**as the following:

## 3. Spreading Code Estimation Based on Fast-ICA Algorithm

#### 3.1. Signal Whitening

**R**, are correlated, before using the Fast-ICA algorithm to estimate the spreading code sequence, the received signal needs to be whitened [16]. The new vector after whitening,$\tilde{\mathit{v}}$, must satisfy $E\left\{\tilde{\mathit{v}}{\tilde{\mathit{v}}}^{T}\right\}=\mathit{I}$. Whitening can remove the correlation between the received signal data, and it can simplify the blind separation algorithm, and then to improve the separation performance of the signal blind separation algorithm [17]. This process can be achieved by doing eigendecomposition, which is shown in the following:

- (1)
- The first step is calculating the covariance matrix of the received signal, r(t), ${\mathit{R}}_{r}=\frac{1}{M}\mathit{R}{\mathit{R}}^{H}$. The larger $M$ means, the richer the information of the spreading sequence contained in the received signal. Therefore, theoretically, under the same condition of the SNR, the longer the information code length, $M$, means the better the estimation effect of the spreading sequence;
- (2)
- Then, the eigendecomposition should be performed on ${\mathit{R}}_{r}$, as shown in Equation (6).$${\mathit{R}}_{r}=[\begin{array}{cc}{\mathit{U}}_{s}& {\mathit{U}}_{n}\end{array}]\left[\begin{array}{cc}{\mathit{\Lambda}}_{s}& \\ & {\mathit{\Lambda}}_{n}\end{array}\right]{\left[\begin{array}{cc}{\mathit{U}}_{s}& {\mathit{U}}_{n}\end{array}\right]}^{H}$$
- (3)
- Finally, the received signal should be whitened using ${\mathit{U}}_{s}$ and ${\mathit{\Lambda}}_{s}$.

#### 3.2. Calculate the Separation Matrix

#### 3.3. Calculate the Spreading Code Sequence

#### 3.4. Algorithm Complexity Analysis

## 4. Simulation Experiment and Result Analysis

#### 4.1. Relationship between BER and Spreading Code Length

#### 4.2. Relationship between BER and Message Code Length

#### 4.3. Relationship between BER and Residual Carrier

#### 4.4. Comparison Experiment with Different Methods

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Step 1: Use ${\mathit{R}}_{r}=E\left\{\mathit{R}{\mathit{R}}^{H}\right\}$ to calculate the covariance matrix of the received signal. Then, the eigendecomposition of this matrix is used to get ${\mathit{U}}_{s}$ and ${\mathit{\Lambda}}_{s}$; |

Step 2: Compute the whitened signal Z by Equation (7); |

Step 3: Set initial values for the separation vector ${\mathit{W}}_{j}$, and normalize it by using Equation (12); |

Step 4: Iterate according to Equation (11), and use Equation (12) to unitize the iterative result for each iteration; |

Step 5: Determine whether the separation vector ${\mathit{W}}_{j}$ converges, if not, return to step 4; |

Step 6: Orthogonalize the separation vector ${\mathit{W}}_{j}$ by Equation (13); |

Step 7: Determine whether all source signals have been completely separated.That is to judge whether j is less than the number of spreading sequences, if not, return to Step 4 until all spreading sequences are separated; |

Step 8: The estimated spreading code sequence $\left[\begin{array}{cc}{\tilde{\mathit{P}}}_{1}& {\tilde{\mathit{P}}}_{2}\end{array}\right]$ is calculated by Equation (15). |

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**MDPI and ACS Style**

Xu, L.; Liu, X.; Zhang, Y.
Blind Estimation of Spreading Code Sequence of QPSK-DSSS Signal Based on Fast-ICA. *Information* **2023**, *14*, 112.
https://doi.org/10.3390/info14020112

**AMA Style**

Xu L, Liu X, Zhang Y.
Blind Estimation of Spreading Code Sequence of QPSK-DSSS Signal Based on Fast-ICA. *Information*. 2023; 14(2):112.
https://doi.org/10.3390/info14020112

**Chicago/Turabian Style**

Xu, Lu, Xiaxia Liu, and Yijia Zhang.
2023. "Blind Estimation of Spreading Code Sequence of QPSK-DSSS Signal Based on Fast-ICA" *Information* 14, no. 2: 112.
https://doi.org/10.3390/info14020112