Optical orthogonal frequency division multiplexing (OOFDM) technology features the advantages of high spectral efficiency and strong anti-dispersion ability and is of immense interest in optical communication. Additionally, based on the different detection methods at the receiver, optical communication systems are divided into direct detection (DD) and coherent detection systems. Compared with the coherent detection system, DD-OOFDM system has the advantages of low cost, simple structure, and insensitivity to spectral offset and phase noise. Therefore, DD-OOFDM optical communication systems have been widely used. The realization of high-speed information transmission in the DD-OOFDM communication systems ensures convenience; nonetheless, information security issues are emerging, such as illegal personnel stealing information through fiber bending and other means; therefore, securing optical communication has become crucial. Compared with traditional encryption methods, chaotic encryption is advantageous because of its hard-to-predict nature and limitless chaotic sequence values. Using chaotic mapping sequences to derive keys with no regularity can improve the security of the system. However, in a DD-OOFDM communication system supporting chaotic encryption, since the receiver needs to receive sufficient encrypted information to decrypt it correctly, higher requirements are posed on the system BER. The presence of OOFDM subcarrier beat interference (signal to signal beat interference, SSBI) at the receiver end of the DD-OOFDM system significantly increases the system BER; thus, reducing SSBI becomes the key to improving transmission performance. The traditional method is to insert a protection interval to avoid the overlap of SSBI and OFDM signals, thus eliminating SSBI. However, this decreases the spectrum utilization of the system. The Kramers-Kronig (KK) receiver has the advantages of high spectrum utilization, low hardware complexity, and simple implementation, which can solve the aforementioned problem efficiently. For this reason, the use of a KK receiver at the receiver side is recommended to eliminate SSBI.

In this study, image transmission is considered as an example; at the transmitter side, the image pixel values (range 0-255) are first converted into 8-bit binary numbers, subsequently into a string of binary bit streams, and finally scrambled into random binary bitstreams. Thereafter, a double chaotic sequence is used to encrypt the bitstreams, with two chaotic sequences set to initial values of 0.2 and 0.7, respectively, and set μ to 4.0. The first or second chaotic sequence is used for encryption based on if the corresponding pixel location is odd or even, respectively. In the encryption process, since the chaotic mapping sequence generates values distributed in the interval [0, 1], if left untreated, they will directly become 0 or 1 in MATLAB software, thereby causing the encryption accuracy to decrease and number of iterations of the chaotic sequence to increase. Therefore, in this study, each chaotic value generated is multiplied by a larger number, such as 1015, and subsequently, this chaotic value is remaindered against 256 to ensure that it is an 8-bit binary number when it is heterogeneous with the pixel value. This allows a chaotic value to be processed with a corresponding pixel value, lowering number of iterations of the chaotic encryption algorithm. Subsequently, the encrypted data are combined with OFDM modulation for optical modulation. This study proposes eliminating the SSBI existing in the receiver side of the DD-OOFDM system using the KK receiver to reduce the BER and improve the system transmission reliability on the basis of secure transmission. Specifically, this study analyzes the structure of the KK receiver and the condition of its function that the input signal is the minimum phase signal, and simulates and tests the BER of the DD-OOFDM system based on the KK receiver.

At the transmitter side, this study uses two chaotic sequences for data encryption, where the initial value x0 of the logistic chaotic mapping changes only by 10^-6 orders of magnitude, and less than 100 iterations are need to produce completely different chaotic sequences (Fig. 5). Theoretically, the initial value x0, control parameters μ, and number of iterations n all affect the key space. For example, in double chaotic sequence encryption, the data x0 has 32 bits, and the nature of chaos enables the generation of a completely different chaotic sequence even at one bit deviation in x0; thus, the key space is approximately 2⁶⁴. Combining the above factors, the overall key space of the system can reach approximately 2¹⁹², which effectively prevents brute force cracking. Most of the image pixel point values before encryption are concentrated around 250, an extremely uneven distribution, demonstrating the correlation between pixel points to a certain extent, is easy to be cracked by the eavesdropper and hence is less secure. The scrambled and encrypted image and pixel values are completely different compared with the original image, and the pixel values of the encrypted image are uniformly distributed between [0, 255], which destroys the correlation of pixel values in the original image with high security, rendering it difficult for an eavesdropper to launch the original image from it (Fig. 11). At the receiver side, when the CSPR is sufficiently large to cause the KK receiver to meet the minimum phase condition, it can eliminate the SSBI and reduce the BER (Fig. 12). The image after chaotic decryption using the KK receiver is essentially the same as the original image, with only a few noise points (Fig. 13).

To achieve a safe and reliable data transmission in DD-OOFDM systems, this study conducted specific analysis, design, and implementation. To solve the security problem in DD-OOFDM systems, chaotic encryption is proposed. Chaotic mapping has the characteristics of randomness and limit nonconvergence, rendering the key space extremely large and thereby improving the encryption security. The original data are processed by double chaotic sequence encryption at the transmitting end of the system to reduce the correlation between the data substantially and ensure data security. To improve the spectral efficiency of the system, OFDM is used to modulate the encrypted data at the transmitter side of the system. At the receiver side, the SSBI in the signal after direct detection is processed, and a KK receiver is proposed to solve this interference. The structure of the KK receiver and the minimum phase signal conditions that render it successful are analyzed at the receiver side. Thereafter, the optical carrier power is changed by controlling the DC bias voltage of the laser driver so that the signal input to the KK receiver meets the minimum phase. With a CSPR of 11 dB, the system performs efficiently, with the KK receiver below the forward error correction threshold of the unutilized KK receiver.