As an innovative multiple-input-multiple-output (MIMO) technology, optical spatial modulation (OSM) resolves antenna interference and synchronization challenges in MIMO systems by selecting a single antenna to carry information and collectively transmits the antenna index as additional information. However, existing OSM research predominantly adheres to the orthogonal transmission criterion, and imposes limitations on enhancing the transmission rate of the system although the research is effective in avoiding inter-symbol interference. To this end, the introduction of non-orthogonal transmission via Faster-Than-Nyquist (FTN) technology compresses symbol intervals during pulse shaping, enabling an increase in transmission rate within the same bandwidth per unit time. As a result, we propose a novel Faster-Than-Nyquist rate optical spatial pulse position modulation scheme that combines OSM with FTN to further enhance the transmission rate and spectrum efficiency of the system. Additionally, in response to the highly complex receiver issue, a multiclassification neural network (MNN) decoder is proposed to significantly reduce computational complexity and achieve approximate optimal detection.

At the transmitting end, the input binary bit stream is divided into two groups of data blocks after serial/parallel transformations. The first group of data blocks is mapped to the index of the selected lasers for each symbol period, while the second group is mapped to pulse position modulation (PPM) symbols. An FTN shaping filter is employed to compress the PPM symbols. Then, the compressed PPM-FTN signals are loaded onto the chosen lasers for transmission. The signal traverses the Gamma-Gamma channel, and it is received by photodetectors (PDs) and converted into an electrical signal for further signal processing at the receiving end. Initially, downsampling is conducted to obtain a signal with the same dimensionality as the input signal. The downsampled signal is then classified based on its effective features, with each class being assigned the corresponding label. Subsequently, different samples with varying signal-to-noise ratios (SNRs), along with their associated label values, are utilized as input and output for offline training of a neural network model. The objective is to achieve optimal decoding accuracy by defining average loss and learning rate parameters to construct an MNN, which helps determine the number of hidden layers and neurons. Finally, the well-constructed MNN is employed for online signal detection. Then, inverse mapping is conducted on output label values from the decoder to recover the corresponding modulation symbols and laser index.

Monte Carlo simulations are conducted to evaluate the proposed scheme in a Gamma-Gamma channel. We first derive an upper bound of the average bit error rate (ABER) of the system and provide a comparison of the simulated BER with the ABER in Fig. 3. The results show that the two curves asymptotically coincide at high SNRs, which demonstrates the correctness of the derived ABER. Then, an analysis is performed on the influence of various parameters such as the number of lasers, the number of detectors, and modulation order on the error performance of the OSPPM-FTN system. The findings reveal that an increase in these parameters can enhance both the transmission rate and BER performance of the system, despite at varying costs. Furthermore, in Fig. 5, we compare the transmission rate, spectrum efficiency, and BER performance of the proposed system with traditional OSPPM. The results indicate that under the acceleration factor of 0.9, compared to the OSPPM system, the proposed system shows a 17% increase in spectrum efficiency and a 5.5% increase in transmission rate with only 1 dB SNR lossy. As the acceleration factor decreases from 0.9 to 0.7, the spectrum efficiency and transmission rate of the OSPPM-FTN system rise by 73% and 21.5% respectively. Thus, the proposed scheme demonstrates a significant improvement in both transmission rate and spectrum efficiency with the reduction of the acceleration factor. Through the comparison with the maximum likelihood (ML) algorithm, Figs. 7 and 8 illustrate the computational complexity reduction and BER performance of the proposed MNN decoder. The results show that the MNN decoder achieves near-optimal decoding performance, and as the detectors increases, the computational complexity of the MNN decoder is significantly lower than that of ML. For instance, when there are 8 or 16 PDs, our decoder can reduce computational complexity by 69.75% and 89.95% respectively.

A Faster-Than-Nyquis rate optical spatial pulse position modulation scheme is proposed by combining optical spatial pulse position modulation with the FTN technique, which effectively improves the transmission rate and spectrum efficiency of the system. Compared to traditional optical spatial modulation, simulation results show that the proposed scheme achieves a significant improvement in transmission rate and spectrum efficiency with the decreasing acceleration factor. Simultaneously, increasing the modulation order, the number of lasers, and the number of detectors can improve the transmission rate and error performance of the system. However, the cost associated with each parameter varies, and the selection of these parameters should be contingent on specific circumstances. Additionally, the MNN decoder proposed for the OSPPM-FTN scheme achieves near-optimal decoding performance while substantially reducing computational complexity. It is noteworthy that this advantage is particularly pronounced in large-scale MIMO systems.