Blind identification of second-order statistics using periodic Toeplitz system

Blind identification (BI) is a method to estimate a system of a channel with a priori knowledge of the transmitted signals and the received signals. This paper presents the method to estimate the impulse response of a channel using second-order statistics (SOS) of the cyclostationary (CS) received signals. In the paper, we consider the case in which the received signals are oversampled at the rate 1/mT (m=2,3, ···, n) when the received signals are sampled at the baud rate. We estimate the impulse response of a channel using the method in the double-sampling. Next, we estimate the impulse response of a channel using a result that extended the method in the sampling rate 1/mT(m=3, ···, n). Here, we need to calculate an inverse matrix of the matrix constructed using both the auto-correlation and the cross-correlation function in estimating the impulse response of a channel. In this paper, we take notice of the cyclic property of the matrix and apply periodic Toeplitz system (PTS) to get the inverse of the matrix