Improving the spectrum efficiency (SE) is an effective method to further enhance the data rate of bandwidth-limited underwater wireless optical communication (UWOC) systems. Non-orthogonal frequency-division multiplexing (NOFDM) with a compression factor of 0.5 can save half of the bandwidth without introducing any inter-carrier-interference (ICI) only if the total number of subcarriers is large enough, and we termed it as half-spectrum OFDM (HS-OFDM). To the best of our knowledge, this is the first reported work on a closed-form HS-OFDM signal in the discrete domain from the perspective of a correlation matrix. Due to the special mathematical property, no extra complex decoding algorithm is required at the HS-OFDM receiver, making it as simple as the conventional OFDM receiver. Compared with traditional OFDM, HS-OFDM can realize the same data rate, but with a larger signal-to-noise ratio (SNR) margin. To fully use the SNR resource of the communication system, we further propose a digital power division multiplexed HS-OFDM (DPDM-HS-OFDM) scheme to quadruple the SE of conventional OFDM for the bandwidth-starved UWOCs. The experimental results show that HS-OFDM can improve the receiver sensitivity by around 4dB as opposed to conventional 4QAM-OFDM with the same data rate and SE. With the help of the DPDM-HS-OFDM scheme, the data rate of multi-user UWOC can reach up to 4.5Gbps under the hard-decision forward error correction (HD-FEC) limit of a bit error rate (BER) of 3.8×10-3. Although there is some performance degradation in comparison with single-user HS-OFDM, the BER performance of multi-user DPDM-HS-OFDM is still superior to that of conventional single-user 4QAM-OFDM. Both single-user HS-OFDM and multi-user DPDM-HS-OFDM successfully achieve 2Gbps/75m data transmission, indicating that the DPDM-HS-OFDM scheme is of great importance in bandwidth-limited UWOC systems and has guiding significance to underwater wireless optical multiple access.