Blind Estimation of LSC-DS-CDMA Signal Based on Matrix Completion and Triple Correlation

As the Long and Short Codes Direct Sequence Code Division Multiple Access (LSC-DS-CDMA) signal contains long and short PN codes of multi-user, the existing methods of PN codes blind estimation for the Direct Sequence Code Division Multiple Access (DS-CDMA) signal are no longer applicable. Then a pseudo random (PN) codes estimation method based on matrix completion and triple correlation is proposed. Firstly, LSC-DS-CDMA signal is represented as a matrix model with missing data for multi-user short code and the composite code matrix estimation is modeled as a blind source separation problem in the theory. Secondly, matrix completion theory is used to estimate the composite code subspace. A method of the composite code sequences estimation is proposed based on the singular value thresholding algorithm and Fast-ICA algorithm. Finally, the delayed triple correlation algorithm is presented to estimate the long and short PN codes from the composite code sequences based on the shift-and-add property of m sequence. Simulations show that the bit error rate of long and short codes sequences can be reduced to 0.1% when the SNR is above -2 dB.