# A Capacity Enhancement Method for Frequency-Hopping Anti-Jamming Communication Systems
## 1 Introduction
### Related Works  
Since the late 1990s, scholars have studied and utilized modulation information on the amount of change in frequency-hopping frequency point positions, using techniques such as differential frequency hopping, etc. The United States-based organization Lockheed Sanders developed CHESS radio based on differential frequency-hopping technology [15]. With a hopping speed of up to 5000 hops/s and an information transmission rate of up to 19.2 kb/s, CHESS radio is equipped to handle tracking interference, and has considerable resistance to fading ability [16; 17]. [PERSON] et al. proposed a frequency-hopping detection method based on STFT (short-time Fourier transform) [18], which was combined with the G-function to analyze the frequency characteristics of shortwave differential frequency-hopping signals at each hop time interval, enabling the detection of hopping frequency information. [PERSON] et al. [19] proposed a multi-hop autocorrelation-based differential frequency-hopping (DFH) signal detection method for the non-periodic characteristics of DFH signal hopping sequences. In recent years, both domestic and foreign scholars in this field have focused on further optimizing security performance using algorithms such as chaotic sequence encryption, as well as the design of the principal rate transfer function and the detection of broadband high-speed frequency-hopping signals. In 2008, [PERSON] et al. proposed a FH-DFH approach that combines DFH with the traditional FH technique to eliminate the correlation between successive frequency hopping and to improve the anti-interception performance [20]. Several years later, in 2015, [PERSON], [PERSON] et al. proposed a frequency domain equalization algorithm for wideband DFH systems: the frequency domain decision feedback sliding multi-hop equalization algorithm (DF-SMH-FDE) [21], which can improve the BER performance of differential frequency-hopping (DFH) systems. In 2022, [PERSON] and [PERSON] [22] designed an encryption scheme based on pseudo-random sequences of logistic chaotic mapping to randomly scramble frequency-hopping (FH) patterns to address the poor two-dimensional uniformity of FH patterns in differential frequency-hopping (DFH) communications, which are easily intercepted. In doing so, they strengthened the anti-interception capability; however, this negatively affected the systems' performance. In 2022, [PERSON] et al. [23] proposed an enhanced differential frequency-hopping (EDFH) framework, which adds the transmission and processing processes of training signals to the traditional communication signal transmission and designs a mixed-signal matched filter (CMF) for user signals and interference signals at the receiving end. The research conducted in this field has demonstrated that differential frequency hopping conducts information modulation from the dimension of the amount of change in the frequency-hopping frequency point position, but the hardware complexity that is required for differential frequency hopping is high, and it only analyzes and utilizes the technology from the perspective of a single modulation method. The capacity-boosting modulation method proposed in this paper is based on the phase modulation and frequency hopping that are already used in anti-jamming communication systems, in which frequency-hopping dimensional modulation is performed to boost the information capacity. The multidimensional modulation system differs from single dimension modulation in terms of the demodulation method and BER performance. In frequency-hopping immunity papers, chaotic sequences are used to control frequency-hopping patterns to enhance the security of information transmission.