The previously reported hybrid orthogonal frequency division multiplexing-digital filter multiple access (OFDM-DFMA) PONs offer promising solutions for seamlessly converging optical and mobile networks for 5G. However, the hybrid OFDM-DFMA PONs based on intensity-modulation and direct-detection (IMDD) convey double sideband (DSB) signals at different sub-wavelengths, this halves the spectral efficiency and signal transmission capacity. In this paper, hybrid single sideband (SSB) OFDM-DFMA PONs are proposed and explored, for the first time, where multiple SSB OFDM channels produced without employing the Hilbert transform operation are multiplexed using orthogonal digital filtering in ONUs, and demultiplexed/demodulated by a single FFT operation in OLT without incorporating matching filters. It is shown that similar to the DSB PON, the proposed SSB PON has excellent robustness against digital filter characteristic variations and channel interferences. More importantly, it decreases peak-to-average power ratios (PAPRs) of digitally-filtered OFDM signals by >2dB, thus leading to >2dB reductions in optimum signal clipping ratio and >1 bit reductions in minimum required DAC/ADC resolution bits. For fixed spectral bandwidths, the SSB PON almost doubles the maximum upstream transmission capacity without considerably degrading its differential ONU optical launch power dynamic range compared to the DSB PON. While for fixed upstream signal transmission capacities, compared to the DSB PON, the SSB PON not only halves the overall signal transmission bandwidth, but also leads to >2.5dB (>1.2dB) improvements in power budget (differential optical launch power dynamic range for ONUs locating at high frequency regions). Index Terms— Digital orthogonal filtering, single sideband (SSB), intensity modulation and direct detection (IMDD).