We study one-dimensional ergodic operator family with sampling function $\{x\}$ and some its generalizations. The general result by Damanik and Killip implies that they cannot have absolute continuous spectra. We show that for almost all frequencies and all coupling constants these operators have pure point spectrum of positive Lebesgue measure, and that singular continuous spectrum is supported on a closed set of measure zero. In addition, there is no singular continuous spectrum for large coupling. The results are joint with Svetlana Jitomirskaya.