In this paper, we propose a novel cross domain iterative detection for unitary modulated symbols transmissions, e.g., OFDM. Particularly, signal spaces before and after the unitary modulation are conceptualized as two domains and the proposed scheme performs iterations across these two domains for signal detection. More specifically, a tunable-sized linear minimum mean square error (LMMSE) estimator is adopted in one domain, complemented by a reduced-complexity sum-product algorithm (SPA) in the other. Heuristic state evolution of the proposed scheme is derived, which reveals that a reduced-sized LMMSE estimator will introduce performance degradation that cannot be compensated by the cross domain iteration. However, it is advantageous for complexity reduction. Our numerical results verify our conclusions and show that the proposed scheme can achieve error performance comparable to that of the standard SPA while requiring lower complexity.