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In this paper, preamble design for estimation and compensation of channel distortion parameters (or channel impairments) in orthogonal frequency-division multiplexing (OFDM) transmission over peak-limited channels is studied. Specifically, the designed preamble considers the estimation of frequency selective channels, carrier frequency offset (CFO), in-phase/quadrature-phase (I/Q) imbalance together with the minimization of peak-to-average power ratio (PAPR) of the transmitted signals. In the proposed design, we employ adaptive Markov chain Monte Carlo (AMCMC) techniques to select preamble sequence that minimizes the channel estimate mean-squared error while suppressing the effect of the I/Q mismatch. AMCMC algorithm is also deployed to select phase information to the designed preamble in order to minimize the PAPR of the oversampled preamble signals in time domain. To estimate CFO, maximum likelihood-based scheme that utilizes two successive OFDM preambles is employed, and the CFO is estimated by considering phase rotation between two consecutive received OFDM preambles. Numerical simulations are provided to verify the efficacy of the proposed design.