## 1 Introduction  
Ocean waves are small-scale wind-gravity waves that occur on ocean surfaces, including sea and swell, and are also an important ocean dynamic process. For many situations, it is necessary to understand their internal structures, such as marine transportation, offshore platforms, and ocean wave parameters at specific locations for ports and ocean engineering [1]. The common methods for obtaining ocean wave information include numerical models, field observations, and remote sensing observations. A numerical model uses mainly mathematical operations to calculate and predict the sea state. Although the model can obtain the results of ocean wave parameters of long-term sequences, it is affected by multiple conditions, such as initial condition settings, observation data assimilation and water depth. Field observations mainly consist of sea state measurements from buoys [2]. Buoys are recognized as more accurate means in the field observation of ocean waves; however, buoy locations are sparse, and the data records at each position may be discontinuous [3]. Buoys can verify the ocean wave parameters obtained by numerical models and remote sensing [4]. Remote sensing obtains the sea state by means of a synthetic aperture radar (SAR), altimetry and scatterometry. Altimeters and scatterometers are highly susceptible to the underwater terrain when observing waves. Although altimeters provide uniform, repetitive measurements of the significant wave height (SWH), other wave parameters, such as the mean wave period, cannot be observed by altimeters [5,6]. Scatterometers are most prominent for the observation of surface winds over global oceans instead of ocean waves [7]. Compared with numerical models and in situ buoy measurements at a single location, SARs are effective and of great interest because of the high spatial resolution and the almost instantaneous observation potential of large ocean areas [8]. As a powerful instrument to measure ocean waves, a SAR can work all day under almost any weather condition [9]. A SAR has multiband and multipolarization characteristics, which allow the estimation of the spatial distributions of the investigated characteristics [10]. Especially important, the ocean observation results provided by SARs are not affected by the underwater terrain. Therefore, this paper intends to use SARs to achieve the observation of ocean waves. However, it is known that SAR images of oceanic scenes include velocity bunching caused by the orbital motions of ocean waves. Velocity bunching leads to a nonlinear imaging mechanism in ocean SAR images [11]. Accordingly, ocean SAR images become blurred, especially in the azimuth direction (the direction parallel to the SAR flight direction is the azimuth direction, and the SAR look direction is defined as the range direction) [12]. This phenomenon is known as the azimuth cutoff wavelength or simply the azimuth cutoff, and affects only the azimuthally traveling waves [13]. This phenomenon leads to information on SAR observations that mainly contains low-wavenumber swell, and only waves with a wavelength greater than the azimuth cutoff wavelength can be observed [14]. This condition is a fatal flaw in the observation of ocean waves by a single SAR satellite, which greatly limits the observation capability and integrity of SAR. The azimuth cutoff wavelength is an inherent drawback of SAR and has not received much attention as a helpful sea state parameter. In 1996, [PERSON] et al. proposed evidence of the azimuth cutoff dependency on the wind speed and SWH [15]. In 2014, [PERSON] et al. proposed two models to directly retrieve the SWH uWHW Wsing the azimuth cutoff [16]. In 2015, [PERSON] et al. estimated the wave orbital velocity from the azimuth cutoff wavelength using Envisat advanced synthetic aperture radar (ASAR) measurements [17]. Most of the above studies focus on the mutual estimation of the azimuth cutoff wavelength and parameters such as the SWH and wind speed.