Superimposed training synchronization for Widely Linear systems

In this paper, the training sequence synchronization (TSS) problem for Widely Linear (WL) system estimation is addressed. This problem appears when superimposed training (ST) is considered as the methodology to perform the identification of WL systems. The proposed method exploits the ciclostationarity induced in the process at the output of the WL system when training sequences generating circulant augmented matrices are employed. Unlike strictly linear (SL) systems, where the delay required to achieve synchronization is unique, for WL systems two possible solutions appear. It is here shown that the correct synchronization delay can be distinguished if further characteristics of the WL system are known in advance.