Optical OFDM index modulation (O-OFDM-IM) is a new multicarrier modulation technique that can achieve remarkable improvements in transmission rate and bit error rate (BER) performance by carrying additional information through the index of subcarriers. Currently, in the field of optical communication, O-OFDM-IM has triggered a research boom for potential improvements in system error performance and spectrum efficiency. However, existing O-OFDM-IM schemes require complex channel estimation at the receiver to obtain channel state information, which not only increases the complexity of the receiver but also brings a large spectrum resource overhead. This study proposes a differential index shift keying DC-bias optical OFDM (DISK-DCO-OFDM) scheme that avoids complex channel estimation while ensuring BER performance. Additionally, a multiclassification detector based on radial basis function (RBF) neural network is suggested to address the high complexity of the receiver.

By considering a single subcarrier block as an example at the transmitter side, an initial transmission matrix that does not carry information is first prepared at the transmitter before the differential operation is performed. Then, the input binary bits are mapped into a time-frequency dispersion matrix that satisfies the difference operation, i.e., the matrix has only one non-zero element in each row and column. For difference operation, the time–frequency dispersion matrix of the current moment is multiplied with the transmission matrix of the previous moment to obtain the true signal matrix of the current moment. Next, the real signal matrix is transmitted by the laser after the Hermitian symmetry and inverse Fourier transform. On the receiver side, the received signal matrix of the previous moment was first inverted and then multiplied with the received signal matrix of the current moment, and the characteristic matrix of the received signal can be obtained. Then, the real and imaginary parts of the feature matrix were used to construct a one-dimensional feature vector, which was used as the input of the RBF neural network. Finally, the trained neural network was used as a multiclassification detector to complete the decoding work at the receiver side. The proposed scheme completely avoids complex channel estimation.

The DISK-DCO-OFDM system was established in this study and the BER performance of the system was simulated under different turbulence intensity and received aperture conditions. First, we derived an upper bound of the average bit error rate (ABER) of the system and compared the simulated BER with the ABER (Fig. 2). The two curves asymptotically coincided at high signal-to-noise ratios, which demonstrated the accuracy of the derived ABER. Then, we compared the BER performance of the proposed scheme with that of the conventional subcarrier index shift keying DCO-OFDM (SISK-DCO-OFDM) system, and the corresponding results are shown in Fig. 3. The BER performance of the proposed scheme is substantially better than that of the SISK-DCO-OFDM system when the subcarrier block length is 2 under weak turbulence condition. When the subcarrier block length is 4, the BER curves of the proposed scheme and the SISK-DCO-OFDM system coincided at high SNR. Therefore, the proposed scheme guarantees the BER performance while effectively avoiding the channel estimation. The computational complexity reduction rate and BER performance of the proposed multiclassification detector for the receiver side compared with the differential maximum likelihood (DML) detection algorithm are shown in Fig. 6 and Fig. 7, respectively. The computational complexity of the proposed detector is reduced by 16.67% and 70% for subcarrier block lengths of 2 and 4, respectively, compared with the DML. The difference in the BER performance between the two detection algorithms does not exceed 2 dB under weak turbulence.

This study proposes a DISK-DCO-OFDM scheme. The main feature of this scheme is the use of a time-frequency dispersion matrix that satisfies the differential process. Simulation results show that the proposed scheme not only effectively avoids the channel estimation process but also guarantees better BER performance than all current optical OFDM index modulation systems in a weak turbulence environment. Meanwhile, the proposed multiclassification detector can considerably reduce the decoding complexity at the receiver side, and the difference in BER performance compared with DML does not exceed 2 dB. In particular, the method of constructing the received signal feature vector provides an effective reference for future decoding using machine learning or deep learning methods at the receiver side for differential-type systems. Therefore, the proposed scheme can provide a reference for the application of optical OFDM index modulation in complex channel environments, and the proposed multiclassification detector can contribute to future research on reducing the decoding complexity at the receiver side.