# The Impact of Inter-Modulation Components on Interferometric GNSS-Reflectometry
## 1 Introduction  
Since the proposal of the PAssive Reflectometry and Interferometry System (PARIS) concept in 1993 [1], the reflection of Global Navigation Satellite System (GNSS) signals has been a option for various Earth surface remote sensing applications. This technique, also known as GNSS-Reflectometry (GNSS-R), can provide a dense spatial and temporal sampling capability over the Earth surface in a low-cost way. During the past two decades, several theoretical and experimental studies have been performed to demonstrate the feasibility of ocean altimetry using reflected GNSS signals, e.g., in [2; 3; 4; 5; 6; 7; 8; 9], and several studies have been performed on scatterometric applications, such as sea surface wind, sea ice and soil moisture. A comprehensive tutorial of GNSS-R technique and its applications can be found in [10]. As in traditional radar altimeters (RA), the delay of the return echo from the sea surface is the primary observable in GNSS-R altimetry, and its accuracy increases with the signal-to-noise ratio (SNR) and the bandwidth of the transmitted signal. Unfortunately, the transmitted power of GNSS signals is relatively low and the open-access signals have much narrower bandwidths than signals in traditional RA, which lead to the lower altimeric performance of the conventional GNSS-R approach (_c_GNSS-R). To overcome the bandwidth limitation, some alternative approaches have been proposed to exploit the wideband encrypted signals, such as those presented in [11; 12], known as reconstructedGNSS-R (rGNSS-R), and in [13], known as interferometric GNSS-R (iGNSS-R). Nevertheless, any of the aforementioned GNSS-R techniques operate at much lower bandwidths (2\(\sim\)40 MHz) than that in traditional RAs (\(\sim\)320 MHz), resulting in very different ranging precision. The iGNSS-R technique was proposed in [1] and discussed in detail in [13] for the ESA-proposed PARIS In-orbit Demonstrator (PARIS IoD) mission. In addition, it is also considered in the GNSS Reflectometry, Radio Occultation and Scatterometry candidate experiment aboard the International Space Station (GEROS-ISS) [14]. In iGNSS-R, the reflected signals are directly correlated against the direct signals, i.e., the signals that arrive through the line-of-sight path (see Figure 1), instead of a locally-generated clean replica as it is the case in cGNSS-R. It allows to extract information from the full spectrum of the transmitted GNSS signals, thus resulting in a sharper auto-correlation function (ACF) and improving the altimetric precision. Results from airborne experiments [15] show at least two-fold improvement in altimetric precision compared to the clean replica method, further theoretical analysis [16; 17; 18; 19] predicts an improvement of the ranging precision by a factor of 2\(\sim\)3. The modernized GNSS signals, such as GPS L1 signals transmitted by all block IIR-M and later design satellites, Galileo signals transmitted at E1/E6 bands and BeiDou signals transmitted at B1/B3 bands, are composed of several components modulated on to the same carrier to provide different navigation services (e.g., C/A (Coarse Acquisition) code, P (Precise) code and M (Military) code signals at GPS L1 band). In addition to these, byproduct signal components of using interplex modulation [20], known as Inter-Modulation (IM) components, are transmitted to combine all signal components on the same carrier and maintain constant envelope and saturation of the high-power amplifier. In general, the IM component is neglected in cGNSS-R and rGNSS-R as there is no correlation between them and the desired signal codes. Instead, by it's nature the interferometric processing exploits all the signals collected from the up- and down-looking antennas, the IM component in the direct and reflected chains are also cross-correlated together with the desired signals, thus impacting the characteristics of the interferometric waveform.