In traditional orthogonal frequency-division multiple access passive optical networks (OFDMA PON) or time-division multiplexing access (TDMA) based OFDM PONs, analog-to-digital converters (ADCs) with a high sampling rate are required to demodulate high-speed aggregated OFDM data in order to receive a small portion of the downstream data at optical network users (ONUs). Meanwhile, OFDM signal has a higher peak-to-average power ratio (PAPR) than the single carrier signal, which can result in the nonlinear effect. The resulting nonlinearity reduces the received signal performance. To enhance practicability of the present PONs, according to the sub-Nyquist sampling theory, we propose and detail a delay-division-multiplexing (DDM) scheme to enable a FDMA PON with low-sampling-rate ADCs. Based on pre-allocated relative time delays among the ONUs and discrete Fourier transform spread (DFT-S) technique, pre-processed signals sent from an optical line terminal (OLT) can be detected as different downstream signals following spectral aliasing caused by ADCs operating at a sub-Nyquist sampling rate. In the proposed scheme, as the signal distortion introduced by the propagation, aliasing and time shifted sampling is pre-compensated, the DFT and inverse discrete Fourier transform (IDFT) are unnecessary for de-mapping and picking out the signal at ONUs. Therefore, the proposed DDM scheme greatly enhances cost efficiency and enables a reduction in computational complexity. Meanwhile, DFT-S FDMA signal has low PAPR, which relieves the nonlinear effect in signal E/O conversion and transmission. As a result, the proposed scheme benefits the power budget of the OLT and power consumption of the ONUs. In experiment, we demonstrate that each ONU with an ADC operating at 1/2-1/32 of the Nyquist sampling rate is able to receive 1/2-1/32 of the downstream data, with an insignificant performance penalty. Furthermore, the details of the matrices that include channel response, aliasing and time delay are first analyzed. In addition, training symbol is very important for estimating the channel response, and how to derive and design training symbols is the first study to outline the details of this issue. The effects of fiber dispersion and the sampling instant of an ADC on signal performance are also studied. The results show that the signal performance has some degree of tolerance to sampling instant deviation and the power penalty is less than 0.5 dB to achieve a forward error correction limit of 10-3 after 25 km fiber transmission. The theoretical analysis and experimental results indicate that the proposed scheme can simplify the ONU and reduce the cost of the PON.