# Interspectral Error Tracking and Compensation of DSDT in Satellite Internet of Things
## 1 Introduction  
With the increasing demand for interactive data services from the satellite Internet of Things, there is a shortage of spectrum resources for satellite communications [1, 2]. Recent surveys have shown that up to 80% of allocated frequency bands are under-utilized, thus resulting in a significant waste of spectrum resources [3]. Nevertheless, most of idle frequency resources are mostly scattered across multiple frequency bands, and these bandwidths of idle frequency bands are not large and not equal, which are named frequency holes in this paper.  
In order to fully utilize the frequency holes scattered across multiple frequency bands, a Direct Spectrum Transmission technology has been presented in [4, 5, 6], which divides one complete signal into multiple sub-spectrum signals with small bandwidths for frequency holes. Combined with cognitive radio technology, DSDT can dynamically use frequency holes resources to improve communication efficiency and meet the bandwidth diversity.  
The DSDT concept was initially proposed by a team of scholars led by [PERSON]. In their work [7], the feasibility of DSDT was demonstrated through the multiple transponder transmission experiments of DVB-S2X. A simple synchronization scheme based on pilots was provided for amplitude, frequency, and phase offset in [8]. Furthermore, frequency offset can be compensated by changing the filter coefficients of the combining filters sequentially based on the estimated frequency [9]. In addition, theydiscussed the issues of peak-to-average power ratio and adjacent channel interference in DSDT [10]. However, in the DSDT system, its performance depends heavily on accurate synchronization toward multiple sub-spectrums.  
Therefore, to remedy the synchronization error after using the pilot synchronization scheme, some free-pilot synchronization schemes for DSDT were provided in [11; 12], which can be used in conjunction with other schemes based on pilots [13; 14; 15]. In [11], a free-pilot amplitude compensation scheme was proposed utilizing the consistency of \(-3\) dB point at adjacent sub-spectrums, where this specific point owns identical amplitude values between neighboring sub-spectrums. Subsequently, a novel free-pilot scheme was presented in [12], which uses multiple points between adjacent sub-spectrums to estimate frequency and phase offset due to the consistency of phases of these points. As a result, its performance was better than the former [11], but it is limited by the width of transition zone between adjacent sub-spectrums. Moreover, the expansion of the width of the transition zone resulted in an increase in bandwidth. The above free-pilot synchronization schemes for DSDT only utilize the local features of adjacent spectra and do not fully exploit the correlation between all sub-spectrums; thus, there is still room for further improvement in free-pilot synchronization performance.  
In this paper, a free-pilot synchronization method based on all sub-spectrums is proposed for DSDT, which can adaptively track and compensate amplitude-frequency-phase errors among sub-spectrums by utilizing the focusing nature of constellations. All sub-spectrums are weighed by the minimum Euclidean distance of the constellation to compensate for amplitude-frequency-phase errors simultaneously. This operation can be also regarded as an equalizer, as the combined spectrum with synchronization error exhibits characteristics similar to frequency selective fading. Meanwhile, the least squares iterative structure is adopted for improving its synchronization error convergence and tracking speed. Finally, some simulations are provided for analysis of the synchronization performance. Compared with the methods proposed in [11; 12], our method exhibits a lower synchronization error under the same signal-to-noise ratio conditions, and it is not limited by FFT resolution. In addition, we build a DSDT test system using the Universal Software Radio Peripheral (USRP) platform to verify the feasibility of our method.