Communication system mismatch represents a major influence in the losses of both speech quality and speaker recognition system performance. Although microphone and handset differences have been considered for speaker recognition e.g., NIST SRE, nonlinear communication system differences, such as modulation/demodulation Mod/DeMod carrier mismatch, have yet to be explored. While such mismatch was common in traditional analog communications, today, with the diversity and blending of communication technologies, it is reconsidered as a major distortion. This paper is focused on estimating and correcting the frequency-shift distortion resulting from Mod/DeMod carrier frequency mismatch in high-frequency single sideband HF-SSB speech. To overcome the drawbacks of existing solutions, a two-step algorithm is proposed to improve estimation performance. In the first step, the offset of speech is scaled to a small frequency interval, which eliminates or reduces the nonuniqueness issue due to the periodicity within the spectrum; the second step performs fine tuning within the estimated predetermined uniqueness interval UI. For the first time, a statistical framework is developed for UI detection, where an innovative acoustic feature is proposed to represent alternative frequency shifts. Additionally, in the estimation process, statistical techniques such as GMM-SVM, i-Vector, and deep neural networks are applied in the first step to improve the estimation accuracy. An evaluation using DARPA RATS HF-SSB data shows that the proposed algorithm achieves a significant improvement in the estimation performance up to +35.6% improvement in accuracy, speech quality measurement up to +27.3% relative improvement in the PESQ score, and speaker verification up to +59.9% relative improvement in equal error rate.