This paper proposes an improved carrier frequency offset (CFO) and sampling frequency offset (SFO) estimation scheme for orthogonal frequency division multiplexing (OFDM) based broadcasting system with cyclic delay diversity (CDD) antenna. By exploiting a periodic nature of channel transfer function, cyclic delay and pilot pattern with a maximum channel power are carefully chosen, which helps to enable a robust estimation of CFO and SFO against the frequency selectivity of the channel. As a performance measure, a closed-form expression for the achievable mean square error of the proposed scheme is derived and is verified through simulations using the parameters of the digital radio mondiale standard. The comparison results show that the proposed frequency estimator is shown to benefit from properly selected delay parameter and pilot pattern, with a performance better than the existing estimator.