## 1 Introduction  
With the rapid development of wireless communication, such as wireless access networks, 5G, and 6G, ultrahigh-speed data can be realized by using high-frequency millimeter waves (MMWs). The radio over fiber (ROF) system is a key part of wireless communication [1; 2; 3; 4]. In the ROF system, the generation of MMW signals beyond 100 GHz in electronic domains faces a serious challenge because of restrictions on the frequency responses of electronic modules and components [5]. This limitation can be overcome by generating MMWs in the optical domain [6]. The MMWs generated in the optical domain is referred to as optical MMWs. Optical MMWs consist of two coherent beams of light with a frequency interval of 30 GHz to 3000 GHz, with which the electrical MMW signal can be generated by beating these beams in a photodetector. It is important to note that the optical MMWs are different from electrical MMW signals; they comprise optical wave signals, which is a key technical term used in ROF systems. The generation of optical MMWs is a key technique to realize low cost and high transmission performance in ROF systems [7]. Many schemes to generate optical MMW have been proposed, such as optical heterodyning methods [8], optoelectronic oscillator methods [9], mode-locked lasers methods [10], external modulator methods [11; 12; 13; 14], and optical nonlinear effect methods [15; 16]. Among the above methods, the external method with MZMs offers several advantages, such as a high frequency multiplication factor (FMF), a greater tunability, a higher reliability, a higher conversion efficiency, and receiver sensitivity. It is the most commonly used and proven method and has been widely exploited. The first proposal to utilize photonic frequency multiplication techniques for mm wave signal generation was made by [PERSON]. [17]. The principle of photonic frequency multiplication techniques is as follows: firstly, the nonlinear property of an external modulator is utilized to generate multi-order sidebands, and the two sidebands, spaced at the desired millimeter wave, are extracted by various optical methods, which are called the optical millimeter wave. At the same time, it is necessary to suppress the other sidebands as much as possible. Then, these two extracted sidebands are injected into the photodetector for photo-electronic conversion to generate the desired millimeter-wave signals; in most cases, symmetrical \(\pm\)n\({}^{\text{th}}\)-order sidebands are extracted and injected into the photodetector to generate the millimeter-wave with a frequency of 2n/\(f_{RF}\), where \(f_{RF}\) is the frequency of the RF driving signal loaded into the external modulator, and 2n is called the frequency multiplication factor (FMF). In order to obtain high-frequency millimeter-waves, either the FMF or the \(f_{RF}\) should be increased. Due to the limitations of the frequency of the RF driving signal and the frequency response of the external modulator, the general method to obtain high-frequency millimeter-waves is to increase the FMF. To improve the FMF, it is necessary to select the higher-order sidebands while suppressing the lower-order sidebands; this can be realized through cascading external modulators. External modulator methods, as well as frequency doubling [18; 19], quadrupling [20], octupling [21], 12-tupling [22], and 16-tupling [23]. The highest FMF reached 24 [24; 25] and 32 [26; 27; 28] in recent years. In general, the higher the FMF, the more complex the structure of the system. The data modulation format is an important issue for ROF. It will greatly affect the transmission performance of the ROF system. The conventional data modulation formats for the optical MMW in an ROF are single-sideband (SSB) modulation, double-sideband (DSB) modulation, and optical carrier suppression (OCS) [29; 30; 31; 32].