Consider an ambient modulated backscatter communication (AmBC) system adopting binary phase shift keying modulation that the receiver is to decode the backscatter device induced message without knowledge of the channel state information, the statistical channel covariance matrices, and the noise variance at the receiver antennas. In this paper, we apply the fact that the ambient orthogonal frequency-division multiplexing (OFDM) signals with a large number of subcarriers contain repetitive elements inducing time correlation. We propose a simple sample covariance matrix distance based rule that does not need to invert the estimated covariance matrices. The results show that the developed method enables the receiver to detect the backscatter symbol over one ambient OFDM symbol period applying the time correlation induced by the wideband ambient OFDM transmission which contains repetitive elements.