A Semidefinite Relaxation Approach to Blind Despreading of Long-Code DS-SS Signal With Carrier Frequency Offset

Blind despreading of long-code direct sequence spread spectrum (DS-SS) signal with unknown carrier frequency offset (CFO) is considered. The maximum likelihood estimate (MLE) of spreading waveform is first derived, and to cope with the unknown CFO, we then use the semidefinite relaxation (SDR) technique to approximate our MLE problem as a convex semidefinite programming (SDP) problem, which can be solved efficiently using modern convex optimization methods. Simulation results demonstrate that the proposed approach significantly outperforms the dominant mode despreading estimator whether or not CFO exists at low signal to noise ratio (SNR).