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Nonlinear OQPSK-type (Offset Quadrature Phase Shift Keying) modulations can be designed to have almost constant envelope, making it suitable for systems requiring highly-efficient and low-cost grossly nonlinear power amplifiers. In this paper we consider the use of pseudo-random spreading sequences for channel estimation purposes in systems employing nonlinear OQPSK-type modulations. We consider Maximum-Length sequences, Kasami sequences, Gold sequences and Tomlinson, Cercas, Hughes sequences, all known to have good autocorrelation properties, making them appropriate for channel estimation purposes. The cross-correlation between different OQPSK components that constitute nonlinear OQPSK-type signals is obtained and its impact on the channel estimation performance is evaluated. It is shown that Tomlinson, Cercas, Hughes sequences outperform the other sequences in the channel estimation context.