In this paper, training symbol designs for estimation of frequency selective channels and compensation of in-phase (I) and quadrature (Q) imbalances on orthogonal frequency division multiplexing (OFDM) transmitters and receivers are studied. We utilize cross entropy (CE) optimization techniques together with convex optimization to design training sequences having low channel estimate mean squared error (MSE) and minimum effects of I/Q mismatch, while lowering the peak power of the training signals. The proposed design provides better channel estimate MSE and bit error rate (BER) performances and is applicable to OFDM systems with and without null subcarriers. The efficacies of the proposed designs are corroborated by analysis and simulation results.