Implementing preprocessing in a delay-division multiplexing (DDM) orthogonal frequency-division multiplexing (OFDM) passive optical network (PON) requires a priori knowledge of channel responses, which need to be estimated under the constraint of sub-Nyquist analog-to-digital sampling. The localized approach allocates subcarriers in different frequency zones to training symbols in different time slots for channel estimation without spectral overlap. Unfortunately, the localized scheme is susceptible to inaccurate estimation when using an avalanche photodiode (APD), due to variations in APD saturation associated with different training symbols. Instead of localizing all subcarriers of a training symbol in a single frequency zone, we propose distributing training subcarriers through various frequency zones. This distributed scheme would prevent spectral overlap and also reduce the degree of variation in APD saturation, thereby improving the accuracy of channel estimation. Alternatively, we propose an orthogonal scheme in which each training symbol uses all of the subcarriers simultaneously. The orthogonality specified among consecutive training symbols should make it possible to estimate the channel response with low computational complexity. We conducted experiments to compare various schemes used for channel estimation in a 25-Gbps APD-based OFDM-PON. Our results revealed that the orthogonal scheme achieved the best results, and the localized scheme provided the worst channel estimates. We demonstrate the application of the orthogonal scheme in a penalty-free DDM system at 1/32 of the Nyquist rate, which provided a loss budget of 28 dB after fiber transmission over a distance of 25 km.