A Novel Range Compression Algorithm for The Resolution Enhancement in GNSS-SAR

Passive Global Navigation Satellite System (GNSS)-based Synthetic Aperture Radar (SAR), known as GNSS-SAR, is a new passive radar imaging system. However, compared with conventional SAR, range resolution of GNSS-SAR is significantly lower. To improve range resolution of GNSS-SAR is an interested topic for investigation. In this paper, a novel range compression algorithm for enhancing range resolutions of GNSS-SAR is proposed. In the proposed scheme, at first, range compression is conducted by correlating the received reflected GNSS signal of intermediate frequency (IF) with the synchronized direct baseband GNSS signal in range domain. Then spectrum equalization is applied to the compressed results to suppress side lobes. Both theoretical analysis and simulation results have demonstrated that significant range resolution improvement in GNSS-SAR can be obtained by the proposed range compression algorithm, compared to the conventional range compression algorithm.


Introduction
Passive GNSS (Global Navigation Satellite System)-based SAR (Synthetic Aperture Radar), known as GNSS-SAR, is a developing synthetic aperture radar (SAR) technique for remote sensing in recent years [1,2].Unlike conventional SAR techniques, GNSS-SAR is a passive SAR receiver which uses the signals from Global Navigation Satellite System (GNSS) such as GPS, Galileo, GLONASS or Beidou as transmission of opportunity.Due to the fact that there is no need to construct SAR transmitter, GNSS-SAR has a higher flexibility together with lower expenses than conventional SAR under various applications.However low range resolution is one of the main problems that affects the current development of GNSS-SAR [1,2,13,14,16].
However, a shortcoming of the approaches [13,14,16] is that multi-statistic image processing method is time consuming as they are applied after generating multiple full GNSS-SAR images.
The main contribution in this paper is to propose a new range compression algorithm for GNSS-SAR signal processing to improve range compressed resolution.In the proposed algorithm, the received intermediate frequency (IF) reflected GNSS signal is correlated with the synchronized direct baseband GNSS signal at range domain for each azimuth bin for range compression.Then spectrum equalization [11] is applied to suppress side lobes of the compressed result to enhance range resolution.
The rest of the paper is organized as follows.Resolution of the conventional range compression algorithm is analyzed in section 2. Resolution of the proposed range compression algorithm is analyzed in section 3. The simulation tests are provided in section 4. Section 5 discusses the future development of this research and Section 6 provides conclusions of the paper.

Resolution of The Conventional Range Compression Algorithm
Based on the analysis in [1][2][3][4][9][10][11][12]14,16], the overall view of the conventional range compression algorithm at GNSS-SAR receiver can be illustrated as Figure 1.In Figure 1  and reflected baseband signal can be expressed as where A d and A r denotes magnitudes of the direct and reflected signals respectively; C (•) denotes PRN code; D (•) denotes the navigation bits; t denotes the range domain; u denotes the azimuth domain; τ denotes the received direct signal delay relative to the transmitted signal; τ R denotes the received reflected signal delay relative to the direct signal; f d denotes Doppler frequency; φ d denotes direct signal phase, and φ r denotes reflected signal phase, which can be regarded as constant values within each range domain; j denotes the symbol of complex number; n d denotes the background noise at direct channel and n r denotes the background noise at reflected channel.
Thereafter signal synchronization based on received direct IF signal as ( 1) is performed, and the synchronized direct baseband signal is severed as imaging matched filter, which can be modeled as follows Range compression is conducted through correlating baseband reflected signal s r 2 with imaging matched filter s m at range domain, which result with respect to the noise absence term can be expressed as follows.
where Λ (•) indicates triangle function and its duration is determined by PRN code chip rate of GNSS signal; * denotes the conjugate.In (4), because s r 2 and s m are with the same frequency f d , the frequency component after performing range correlation for the compression is canceled.Assuming the chip rate of PRN code C (•) is B, then the half pulse duration of the triangle function Λ (•) is derived as 1 2B .Because the terms A r and exp (jφ r (u)) are constants with respect to t, the duration of (4) will be determined by the term Λ (•).Thus the attainable range resolution with respect to pulse duration can be expressed as [1][2][3][4][6][7][8][9][10][11]14,17] where c denotes transmission velocity of GNSS signal, β represents bi-static angle and δ R 1 represents the achievable range resolution by the conventional algorithm.According to (5), it can be seen that for the conventional range compression algorithm in GNSS-SAR, if bi-static angle β is fixed, the range resolution improvement can only be accomplished by employing GNSS signals with a higher PRN code chip rate C (•).

Resolution of The Proposed Range Compression Algorithm
However according to [21], we can derive that for quadrature modulated signals of exp (j (•)) shape, if the two signals for performing correlation have the same basedband components shaped as rectangular function but different frequencies, compared the case with the same frequencies, pulse duration of the correlated result will be shortened in the main lobe.Inspired by this, to develop a universal scheme for improving range resolution among GNSS-SAR, a new range compression algorithm is proposed, which is modeled in Figure .2.
In Figure 2, the signals (both direct and reflected) are converted to IF band at front end GNSS receiver as well.But comparing with the conventional range compression algorithm, the proposed  new algorithm directly uses the received reflected IF GNSS signal to correlate with the synchronized direct baseband signal s m at range domain for performing range compression, where the reflected IF GNSS signal s r (•) is given as follows And the intermediate range compressed result can be expressed as follows Based on the intermediate range compressed result (7), to suppress the compressed side lobes, spectrum equalization [11] is performed.Concerning applying spectrum equalization technique in this paper, the detailed procedure in the module 'Spectrum Equalization' in Figure 2 can be further presented as Figure 3.
As we can see that in Figure 3, Fourier transform of intermediate range compressed signal as ( 7) is conducted.The transformed result is expressed as follows where T denotes one GNSS PRN code period; ω denotes the frequency range of the triangle function Λ (•) in ( 7) with an interval of [−B, B].Meanwhile spectrum equalization window is designed, which is based on the reciprocal of the spectrum with respect to the correlation between the synchronized  direct IF signal s m IF and the synchronized direct baseband signal s m .In Figure 3, the synchronized direct IF signal is given as follows the correlated result between s m IF and s m is given as and the spectrum of the correlated result is the Fourier transform of (10), which can be expressed as Then the equalization window is designed as follows The key step of spectrum equalization is performed as follows The equalized result is a rectangular function at frequency domain, where the rising edge appears at the frequency f IF − B and the falling edge appears at the frequency f IF + B. And due to the fact that spectrum equalization is conducted at frequency domain, side lobes of the reflected signals at different range positions can be suppressed simultaneously.
To obtain the final range compressed signal, Inverse Fourier transform based on the spectrum equalized result shown in ( 13) is conducted.To extract the sharper pulse duration component, the  2 and Figure 3 is expressed as follows In (14), the pulse duration is determined by the component f IF + B of the sinc (•) function term, and can be derived as 1 f IF +B .Thus the attainable range resolution with regard to pulse duration is expressed as where δ R 2 denotes the range resolution obtained by the proposed algorithm.It can be seen that ( 15) is 1 1+ f IF /B times superior than (5) provided by conventional range compression algorithm.Meanwhile, from ( 14), we can see that the reflected magnitude and phase information are still preserved.
However GNSS receivers have their certain sampling frequencies, which should be considered when determine the IF value for performing range compression.Denoting the sampling frequency of GNSS receiver as f s , according to sampling theory [22], the condition f IF + B ≤ 1 2 f s should be satisfied.And to make the proposed algorithm because effective, the condition f IF + B > B should be satisfied at the same time as well.Therefore, all in all, the determination of f IF value should satisfy the following constraint Finally, azimuth compression is conducted for forming the full GNSS-SAR image based on ( 14) with different phase value φ r (u) in azimuth domain.

The Simulation Experiment
To test the proposed algorithm for enhancing range resolution, simulations of the GNSS-SAR based on the standard GPS C/A code signal receiver configuration of ground moving mode is carried out in this section as examples.Since GPS receiver works in ground moving mode, the field of version (FOV) is mostly in horizontal, which can be considered as quasi-monostatic, the bi-static angle β can be considered as zero [2].Thus range resolutions of the conventional algorithm and the proposed algorithm are expressed as and respectively.The parameter values of the standard GPS C/A code receiver is given in Table 1.2×(5.115×10 6 +1.023×10 6 ) ≈ 25 m for f IF 1 and f IF 2 respectively.The verdict will be verified by the result with respect to range compressed pulse and the corresponding point spread function [11] shown in Figure 4.
From Figure 4, we can see that based on a standard GPS C/A code signal receiver, the range compressed pulse based on the proposed algorithm is around 3 times thinner and 6 times thinner than the conventional algorithm with f IF 1 and f IF 2 , respectively.
To verify the proposed range compression algorithm, a simulation test is carried out.The simulation experiment is set out as shown in Figure 5.
In Figure 5, four strong reflection surfaces with 400 m long and 20 m width are arranged with 200 m along the azimuth direction and 108 m with the range direction.The direct and reflect signal antennae are moving along the azimuth direction with a constant speed to perform aperture synthetic.The GPS data are simulated using parameters listed in Table 1.Based on the considered scenarios, the GNSS-SAR images generated by both the proposed range compression scheme and the conventional range compression scheme are shown in Figure 6.
As can be seen in Figure 6(a) and (b), due to the fact that the proposed scheme can offer a superior range resolution, the four scattering areas in Figure 5 can be well separated.Through the comparisons, Figure 6(b) has a less range ambiguity because a higher IF value is employed at the GPS receiver.In Figure 6(c), the two scatters located at different range domain cannot be separated on the GNSS-SAR image with the conventional range compression algorithms as the resolution of this approach is 150 m according to (17) with B = 1.023MHz.
In summary, the simulation results in this section has demonstrated that the proposed range compression algorithm can provide a superior range resolution than the conventional range compression algorithm.
Furthermore through tests, the proposed range compression algorithm is also applicable for the GNSS-SAR receiver based on the other GNSS signals of opportunity.Since for most GNSS signals receiver, the IF values are typically higher than the baseband frequency (which equals to PRN code chip rate), a superior range resolution should be achieved by employing the proposed algorithm.However because GNSS receivers differ in the PRN code types and IF values for signals receiving, the achievable range resolutions after improving will be different.

Discussion
Although the proposed algorithm can significantly improve range resolution of GNSS-SAR, according to Figure 4 to Figure 6, it can be seen that the magnitude decreases with respect to f IF values.This is because when performing spectrum equalization, Signal-to-Noise Ratio (SNR) will decrease with respect to the selected cutoff frequency [11].
Meanwhile due to the fact that spectrum equalization is employed, range compressed delay of the proposed algorithm is supposed to be higher than convention range compression algorithm.According to machine running time, range compressed delay per azimuth bin with respect to the two algorithms is given as Table 2.

Figure 1 .
Figure 1.The conventional range compression algorithm.

Figure 2 .
Figure 2. The proposed range compression algorithm.

Figure 3 .
Figure 3.The proposed range compression algorithm.

Figure 4 .
Figure 4. (a) Range compressed pulse based on the conventional range compression algorithm; (b) Range compressed pulse based on the proposed range compression algorithm with f IF 1 = 2.092MHz; (c) Range compressed pulse based on the proposed range compression algorithm with f IF 2 = 5.115MHz;(d) The point spread function of (a); (e) The point spread function of (b); (f) The point spread function of (c).
, under the conventional range compression algorithm, both direct and reflected signals are quadrature converted to IF (Intermediate Frequency) band by multiplying the component exp (−j2π • ( f c − f IF ) • t) at first, where f c denotes the transmission frequency, f

Table 1 .
The parameter values of the standard GPS receiver configuration based GNSS-SAR

Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 23 March 2017 doi:10.20944/preprints201703.0179.v1
Peer-reviewed version available at Sensors 2017, 17, 1496; doi:10.3390/s17071496Based on the sampling frequency value in Table 1 and the constraint (16), two different IF frequencies f IF 1 = 2.092 × 10 6 Hz and f IF 2 = 5.115 × 10 6 Hz are employed in the simulation tests.Theoretically the range resolution for the conventional algorithm can be achieved at c 2B = ≈ 150 m, while with the proposed algorithm in this paper, the resolution can improved to

Table 2 .
The average range compressed delay per azimuth binThe conventionalThe proposed range compression The proposed range compression range compression algorithm algorithm with f IF 1 = 2.092MHz algorithm with f IF 2 = 5.115MHz