This paper focuses on digital signal processing techniques compensating the non-linear effects inherent to optical modulation or amplification within a coherent optical orthogonal frequency division multiplexing (CO-OFDM) transmitter featuring a semiconductor optical amplifier (SOA). Two complementary approaches are specifically considered: crest factor reduction and linearization using a digital baseband predistortion. Two possible implementations are presented for the digital predistortion block. One is the basic solution of static compensation; the other consists in a parallel two-box digital polynomial predistorter (PTB) combining, in parallel, a static nonlinear block with a memory polynomial predistorter. Moreover, we show that a linearization of the dynamic behavior of the transmitter, in addition to peak-to-average power ratio (PAPR) reduction, offers better performance. The robustness of the predistorters or of the combined predistorter/PAPR reduction blocks is assessed for various scenarios. Finally, we propose solutions to improve robustness via multipoint identification or switching strategies for predistortion.