A Novel Range Compression Algorithm for Resolution Enhancement in GNSS-SARs

Transcription

1 sensors Artile A Novel Range Compression Algorithm or Resolution Enhanement in GNSS-SARs Yu Zheng, Yang Yang and Wu Chen Department o Land Surveying and Geo-inormatis, The Hong Kong Polytehni University, Hung Hom, Kowloon, Hong Kong, China; yyang118@gmail.om (Y.Y.); wu.hen@polyu.edu.hk (W.C.) * Correspondene: yuzheng175@gmail.om; Tel.: Reeived: 23 Marh 217; Aepted: 22 June 217; Published: 25 June 217 Abstrat: In this paper, a novel range ompression algorithm or enhaning range resolutions o a passive Global Navigation Satellite System-based Syntheti Aperture Radar (GNSS-SAR) is proposed. In the proposed algorithm, within eah azimuth bin, irstly range ompression is arried out by orrelating a releted GNSS intermediate requeny () signal with a synhronized diret GNSS base-band signal in the range domain. Thereater, spetrum equalization is applied to the ompressed results or suppressing side lobes to obtain a inal range-ompressed signal. Both theoretial analysis and simulation results have demonstrated that signiiant range resolution improvement in GNSS-SAR images an be ahieved by the proposed range ompression algorithm, ompared to the onventional range ompression algorithm. Keywords: GNSS-SAR; global navigation satellite system; syntheti aperture radar; range ompression; range resolution 1. Introdution The passive Global Navigation Satellite System (GNSS)-based Syntheti Aperture Radar (SAR), also known as GNSS-SAR, is a tehnique or remote sensing that has been developing in reent years [1,2]. Unlike onventional SAR tehniques, the GNSS-SAR is a passive SAR reeiver whih uses the signals rom Global Navigation Satellite Systems (GNSSs) suh as the global positioning system (GPS), Galileo, GLONASS or Beidou or transmission o opportunity. Due to the at that there is no need to onstrut a SAR transmitter, the GNSS-SAR has a higher lexibility and implies lower expenses than a onventional SAR under various appliations. However, low range resolution is one o the main problems that aets the urrent development o GNSS-SARs [1 5]. With a onventional GNSS-SAR imaging algorithm that inludes both range and azimuth ompression, range resolution is determined by GNSS signal bandwidth and bi-stati angle or sensing, while azimuth resolution is determined by Doppler requeny shit [1,2,4,6 17]. However, when the system is onsidered as a quasi-monostati ase, in whih the bi-stati angle is and range and azimuth domain are orthogonal, range resolution is mainly deided by the GNSS signal bandwidth [1,2,4,7 17]. I shape ators o a wave orm are not onsidered, potential range resolution identially equals the reiproal o doubled signal bandwidth value. For GNSS signals, the bandwidth value is equal to the pseudo-random noise (PRN) ode hip rate [1,2]. For instane, beause the hip rate o GPS Coarse Aquisition Code (C/A) ode signal is 1.23 MHz, the potential range resolution is obtained at the level o 15 m [1,2,16]. A GLONASS P ode signal, where the hip rate is 5.11 MHz, with GPS P ode signal and Beidou signal, where the hip rate is 1.23 MHz, were used in works [1,2,4,6 1,12,13,17], respetively. The potential range resolution or [1,2,1,12,13] was obtained at the level o 3 m and 15 m in [4,6 9,17]. Galileo signals were employed in [11] (single Galileo E5) and [14,15] (joint Galileo E5), in whih a single Galileo E5 signal ould provide potential range resolution at the level o 15 m with Sensors 217, 17, 1496; doi:1.339/s

2 Sensors 217, 17, o 13 a hip rate o 1.23 MHz and 3 m or joint Galileo E5 signal with a joint hip rate o 51 MHz based on a bandwidth extension tehnique [18]. In total, aording to [1,2,6 16], as we an see, use o GNSS signals with relatively higher hip rates is urrently preerred, beause relatively improved range resolutions an be obtained. Looking at the azimuth resolution o the GNSS-SAR, the level less than 1 m an be potentially ahieved or moving reeiver [1], while or ixed reeiver, a level 3 4 m an be potentially obtained by 3 s integration [11]. Meanwhile, besides the aorementioned works, spatial resolution enhanement o the GNSS-SAR was studied in [3 5]. Typially, in works [4,5], the spatial resolution improvements were arried out based on multi-stati image proessing method with lean tehniques [19,2] or extrating a sene-sattering enter, in whih both range and azimuth resolutions were improved. Based on GLONASS enrypted preision ode (P ode) signal and Beidou signal as soure o opportunity as examples, spatial resolutions in [4,5] were improved to a level o 6 7 m. It an be seen that under a onventional GNSS-SAR range ompression algorithm, with a given bi-stati topology, the signal hip rate is the main ator that restrits improvements o range resolution. Although a multi-statisti image proessing method with lean tehniques [4,5] an enhane spatial resolution o various GNSS-SARs, a shortoming o the approahes is that the methods are time onsuming as they are applied ater generating multiple ull preliminary GNSS-SAR images. In ontrast to [4,5,13], the objetive in this researh is to enhane range resolution in the GNSS-SAR imaging proedure. To ahieve the objetive, the main ontribution in this paper is to propose a new range ompression algorithm or GNSS-SAR imaging signal proessing to improve range-ompressed resolution. In the proposed algorithm, within eah azimuth bin, at irst, the reeived intermediate requeny ()-releted GNSS signal is orrelated with the synhronized diret baseband GNSS signal at the range domain or eah azimuth bin or perorming range ompression. Then spetrum equalization [14] is applied to suppress side lobes o the ompressed result or ahieving the inal range-ompressed signal. The theoretial derivation and simulation results show that the proposed range ompression algorithm an improve range resolution in the GNSS-SAR signiiantly, ompared to onventional range ompression algorithm. Also, the proposed range ompression algorithm is less time onsuming than multi-stati image proessing [4,5] or enhaning range resolution as there is no neessity or obtaining multiple ull preliminary GNSS-SAR images. The rest o the paper is organized as ollows. Resolution o the onventional range ompression algorithm is analyzed in Setion 2. Resolution o the proposed range ompression algorithm is analyzed in Setion 3. The simulation tests are provided in Setion 4. Setion 5 disusses the assoiated issues o this researh as well as uture developments. Setion 6 provides the inal onluding remarks o the paper. 2. Resolution o the Conventional Range Compression Algorithm Based on the analysis in [1,2,4 7,12 15], the low diagram o the onventional range ompression algorithm at the GNSS-SAR reeiver an be illustrated as Figure 1. In Figure 1, under the onventional range ompression algorithm, both diret and releted signals are quadrature, onverted to an intermediate requeny () band by multiplying the omponent exp ( j2π ( ) t) at irst, where denotes the transmission requeny, denotes the intermediate requeny () o the employed GNSS reeiver, denotes arithmeti multipliation and denotes arithmeti orrelation. The reeived signals (both diret and releted signal) are urther down-onverted to baseband by multiplying the omponent exp ( j2π t). The down-onverted diret baseband signal an then be expressed as: s d2 (t, u) = A d (t, u) C [t τ (u)] D [t τ (u)] exp (j (2π d (u) t + φ d (u))) (1) +n d (t, u)

3 Sensors 217, 17, o 13 and the releted baseband signal an be expressed as: s r2 (t, u) = A r (t, u) C [t τ (u) τ R (u)] D [t τ (u) τ R (u)] exp (j (2π d (u) t + φ r (u))) +n r (t, u). (2) where A d and A r denote magnitudes o the diret and releted signals, respetively; C ( ) denotes PRN ode; D ( ) denotes the navigation bits; t denotes ast time [1,2], whih represents the range domain and is onstrained by one GNSS PRN ode period; u denotes slow time [1,2], whih represents the azimuth domain and is limited by the duration or perorming aperture synthesizing; τ denotes the reeived diret signal ode delay relative to the transmitted signal; τ R denotes the reeived releted signal ode delay relative to the diret signal; d denotes Doppler requeny; φ d denotes diret signal phase, and φ r denotes releted signal phase, whih an be regarded as onstant values within eah range bin; j denotes the imaginary unit; n d denotes the bakground noise at diret hannel and n r denotes the bakground noise at a releted hannel. exp j 2 t exp j 2 t Diret Reeived Diret Synhronization Diret Baseband s d 2 Synhronized Diret Baseband s m * Range Compressed Releted Baseband s r2 Releted exp j 2 Reeived Releted t exp j 2 t Figure 1. The low diagram o the onventional range ompression algorithm. Thereater signal synhronization [1,2,12] based on down-onverted baseband diret signal as (1) is perormed. A noise-ree replia s m o baseband diret signal is generated using the parameter diret ode delay τ, Doppler requeny d, and diret signal phase φ d traked rom the synhronization proedure and served as an imaging mathed ilter. The replia an be mathematially modeled as ollows: s m (t, u) = C [t τ (u)] D [t τ (u)] exp (j (2π d (u) t + φ d (u))). (3) Range ompression is onduted through orrelating baseband releted signal s r2 with imaging mathed ilter s m at eah range domain, with a duration onstrained by the PRN ode period although it is not neessarily equal. The range-ompressed result with respet to the noise absene term an be expressed as ollows: s r2 s m (4) = A r Λ (t τ (u) τ R (u)) exp (j (φ r (u) φ d (u))) where Λ ( ) indiates triangle untion and its duration is determined by the PRN ode hip rate o the GNSS signal; and denotes the onjugate. In (4), beause s r2 and s m are with the same requeny

4 Sensors 217, 17, o 13 d, the requeny omponent ater perorming range orrelation or the ompression is aneled. Assuming the hip rate o PRN ode C ( ) is B, then the eetive pulse duration o the triangle untion Λ ( ) is derived as.586 1B, where.586 represents shape ator o waveorm [2]. Beause the terms A r and exp (j (φ r (u) φ d (u))) are onstants with respet to t, the duration o (4) is determined by the term Λ ( ). Thus, the attainable range resolution with respet to pulse Λ ( ) duration an be expressed as [1,2,4,6,7,9 14,17] δ R1 =.586 (5) os (β/2) B where denotes the speed o light, β represents bi-stati angle and δ R1 represents the ahievable range resolution by the onventional algorithm. Aording to (5), it an be seen that or the onventional range ompression algorithm in the GNSS-SAR, i bi-stati topology is given prior, the range resolution is limited by signal hip rate, and improvement an only be aomplished by employing the GNSS signals with a relatively higher PRN ode hip rate as expeted by end users. 3. Resolution o the Proposed Range Compression Algorithm Aording to [21], we an derive that or the digital ommuniation signals strutured similarly or the same as GNSS signals, i the two signals or perorming orrelation dier in requeny, pulse duration o the orrelated result will be sharpened in the main lobe, ompared to the ase with the same requenies. Inspired by this, to develop a GNSS-SAR imaging algorithm or improving range resolution, a new range ompression algorithm is proposed, whih is modeled in Figure 2. exp j 2 Diret t Reeived Diret exp j 2 t Synhronization Synhronization Diret Baseband s d 2 Synhronized Diret Baseband * s m Intermediate Range Compressed * s r s m Releted exp j 2 Reeived Releted s r t Spetrum Equalization Range Compressed Figure 2. The low diagram o the proposed range ompression algorithm. In Figure 2, the signals (both diret and releted) are onverted to the band at the ront-end GNSS reeiver as well. However, in ontrast to onventional range ompression algorithms, at the irst step, the proposed new algorithm diretly uses the reeived releted GNSS signal to orrelate with the synhronized diret base-band signal s m in the range domain or perorming range ompression. The releted GNSS signal s r ( ) is expressed as ollows: s r (t, u) = A r (t, u) C [t τ (u) τ R (u)] D [t τ (u) τ R (u)] exp (j (2π ( + d (u)) t + φ r (u))) +n r (t, u) (6)

5 Sensors 217, 17, o 13 and the intermediate range-ompressed result (i.e., the result ater perorming s r s m) an be expressed as ollows: s r s m = A r Λ (t τ (u) τ R (u)) (7) exp (j (2π t + (φ r (u) φ d (u)))). Based on the intermediate range-ompressed result (7), to suppress the ompressed side lobes, spetrum equalization [14] is perormed. When applying spetrum equalization tehnique in this paper, the detailed proedure in the module spetrum equalization in Figure 2 an be urther presented as Figure 3. Synhronized Diret Baseband s m Reeived Diret Synhronization Synhronized Diret s m Fourier Transorm * Spetrum o s s m m Intermediate Range Compressed s * r s m Reiproal Fourier Transorm Spetrum o s * r s m Equalization Window Inverse Fourier Transorm Range Compressed Figure 3. The low diagram o spetrum equalization module o the proposed range ompression algorithm. As we an see in Figure 3, Fourier transorm o intermediate range-ompressed signal as (7) is onduted. The transormed result is expressed as ollows: F [s r s m] = Ts 2 A Ts r Λ (t τ (u) τ R (u)) 2 exp (j (2π t + (φ r (u) φ d (u)))) exp ( jω t) dt = A r exp (j (φ r (u) φ d (u))) sin 2 (2π ω) (8) where T s denotes the onsidered duration or perorming range ompression and ω denotes the requeny range o the triangle untion Λ ( ) in (7) with an interval o [ 2π B, 2π B]. Meanwhile, the spetrum equalization window is designed, whih is based on the reiproal o the spetrum with respet to the orrelation between the synhronized diret signal s m and the synhronized diret base-band signal s m. In Figure 3, the synhronized diret signal is given as ollows: s m (t, u) = C [t τ (u)] D [t τ (u)] exp (j (2π ( + d (u)) t + φ d (u))) (9)

6 Sensors 217, 17, o 13 the orrelated result between s m and s m is given as: s m s m = Λ (t τ (u)) exp (j2π t) (1) and the spetrum o the orrelated result is idential to the Fourier transorm o (1), whih an be expressed as: F [s m s m] = sin 2 (2π ω). (11) Then the equalization window is designed as ollows: { 1 W = F[s m s m] = 1 sin 2 (2π ω), when requeny ɛ [ B, + B]. (12), Otherwise The key step o spetrum equalization is perormed as ollows: F [s { r s m] W A = r exp (j (φ r (u) φ d (u))), when requeny ɛ [ B, + B]., otherwise (13) The equalized result is a retangular untion at requeny domain, where the rising edge appears at the requeny B and the alling edge appears at the requeny + B. Due to the at that spetrum equalization is onduted at requeny domain, side lobes o the releted signals at dierent range positions an be suppressed simultaneously. To obtain the inal range-ompressed signal, inverse Fourier transorm based on the spetrum equalized result shown in (13) is onduted. To extrat the sharper pulse duration omponent, the lower requeny omponent B is iltered out. The inal range-ompressed signal module o Figures 2 and 3 with regard to noise absene term is expressed as ollows: F 1 {F [s r s m] W} = A r exp (j (φ r (u) φ d (u))) ( + B) sin [2π ( + B) (t τ (u) τ R (u))]. (14) In (14), the pulse duration is determined by the omponent + B o the sin ( ) untion term, 1 and an be derived as +B. Thus, the attainable range resolution with regard to pulse duration is expressed as: δ R2 =.586 (15) os (β/2) ( + B) where δ R2 denotes the range resolution obtained by the proposed algorithm. It an be seen that (15) is 1 1+ /B times superior than the range resolution (5) provided by the onventional range ompression algorithm. Meanwhile, rom (14), we an see that the releted phase inormation φ r φ d is still preserved. For seleting the value in the proposed algorithm, sampling requeny o the employed GNSS reeiver should be taken into onsideration. Denoting the sampling requeny o the GNSS reeiver as s, aording to sampling theory [22], the ondition + B 1 2 s should be satisied. To make the proposed algorithm eetive, the ondition + B > B should be satisied at the same time as well. Thereore, the determination o value should satisy the ollowing onstraint: < 1 2 s B. (16)

7 Sensors 217, 17, o 13 Finally, azimuth ompression is onduted or orming the ull GNSS-SAR image based on (14) with dierent dierential phase value φ r (u) φ d (u) in the azimuth domain [2,12]. 4. The Simulation Experiment To test the proposed algorithm or enhaning range resolution, simulations o the GNSS-SAR based on the standard GPS C/A ode signal reeiver oniguration are arried out in this setion as an example. We onsider that the system works in quasi-monostati mode where range and azimuth diretions are orthogonal. Thus, the bi-stati angle β an be onsidered as zero [2]. Based on the system mode, range resolutions o the onventional algorithm and the proposed algorithm are expressed as ollows, respetively, δ R 1 =.586 (17) B and δ R 2 =.586 ( + B). (18) The parameter values o the standard GPS C/A ode reeiver are given in Table 1. Table 1. The parameter values o the standard global positioning system (GPS) reeiver oniguration-based Global Navigation Satellite System-Syntheti Aperture Radar (GNSS-SAR). PRN: pseudo-random noise; C/A: Coarse Aquisition Code. Parameters Supported signals type PRN ode hip rate B transmission requeny transmission speed The duration o eah ode period Sampling requeny Values GPS C/A ode signal 1.23 MHz MHz (L1 band) m/s 1 ms MHz Constrained by the sampling requeny value in Table 1, two dierent requenies 1 = 2.92 MHz and 2 = MHz are employed in the simulation tests. Theoretially based on (17), range resolution or the onventional algorithm an be ahieved at the level o 171 m. For the proposed algorithm, based on (18), range resolution an be obtained at the levels o 56 m and 28 m with 1 and 2, respetively. Firstly the verdit will be veriied by the result with respet to the range-ompressed pulse [3,14] o the onventional range ompression algorithm, intermediate range-ompressed result and the inal range-ompressed result (the result ater perorming spetrum equalization) o the proposed range ompression algorithm, whih are shown in Figure 4. From Figure 4, we an see that based on a standard GPS C/A ode signal reeiver, the main lobe o the range-ompressed result based on the proposed algorithm is around 3 and 6 times thinner than the onventional algorithm with 1 and 2, respetively. In the proposed algorithm, it an be seen that the side-lobes an be signiiantly suppressed by perorming spetrum equalization. Thereater, to urther veriy the proposed range ompression algorithm, a simulation test is arried out. The simulation experiment is set out as shown in Figure 5. In the experiment, a moving reeiver ase and a short-range geometry is onsidered, where the quasi-monostati assumption is held. In Figure 5, our strong reletion suraes with length o 4 m and width o 2 m are arranged with 2 m along the azimuth diretion and 18 m with the range diretion. The diret and relet signal antennae are moving along the azimuth diretion with a onstant speed to perorm syntheti aperture. The GPS data are simulated using parameters listed in Table 1. Based on the onsidered senarios, the GNSS-SAR images (both 2-D and 3-D view) generated by both the proposed range ompression algorithm and the onventional range ompression algorithm are shown in Figure 6.

8 Sensors 217, 17, o Intensities 6 4 Approximated 171 m Intensities 6 4 Approximated 56 m (a) (b) Intensities 8 6 Intensities 15 1 Approximated 56 m 4 2 Approximated 28 m () (d) Intensities Approximated 28 m (e) Figure 4. (a) Range-ompressed pulse based on the onventional range ompression algorithm; (b) Intermediate range-ompressed result based on the proposed range ompression algorithm with 1 = 2.92 MHz; () Intermediate range-ompressed pulse based on the proposed range ompression algorithm with 2 = MHz; (d) Final range-ompressed result based on the proposed range ompression algorithm with 1 = 2.92 MHz; (e) Final range-ompressed result based on the proposed range ompression algorithm with 2 = MHz. As an be seen in Figure 6a,b (Figure 6d,e), due to the at that the proposed range ompression algorithm an oer a superior range resolution, the our sattering areas in Figure 5 an be well separated. Through the omparisons, Figure 6b (Figure 6e) has a less range ambiguity beause a higher value is employed at the GPS reeiver. In Figure 6 (Figure 6), the two satters loated at dierent range positions annot be separated on the GNSS-SAR image with the onventional range ompression algorithms, as the resolution o this algorithm is around 171 m aording to (17) with B = 1.23 MHz.

9 Sensors 217, 17, o 13 GPS satellite Diret signal Diret antenna Releted The 4 Ground Sattering Areas Figure 5. The simulation senario. In summary, the simulation results in this setion have demonstrated that the proposed range ompression algorithm an provide a superior range resolution to the onventional range ompression algorithm Azimuth Distane (m) Azimuth Distane (m) (a) (b) Azimuth Distane (m) () (d) Figure 6. Cont.

10 Sensors 217, 17, o 13 (e) () Figure 6. (a) GNSS-SAR image generated by the proposed range ompression algorithm with 1 = 2.92 MHz; (b) GNSS-SAR image generated by the proposed range ompression algorithm with 2 = MHz; () GNSS-SAR image generated by the onventional range ompression algorithm; (d) Three-dimensional image o (a); (e) Three-dimensional image o (b); () Three-dimensional image o (). Furthermore through tests, the proposed range ompression algorithm is also appliable or the GNSS-SAR reeiver based on the other GNSS signals o opportunity. In the GNSS reeiver, the value is typially higher than baseband requeny (whih equals the PRN ode hip rate) o the orresponding ompatible signal. For instane, in the onsidered GPS C/A ode signal reeiver in this simulation, 1 and 2 values are obviously higher than baseband requeny o GPS C/A signal. Thereore, a superior range resolution should be ahieved by employing the proposed range ompression algorithm. However, beause the GNSS reeivers dier in the PRN ode types and values or signal reeption, the ahievable range resolutions ater improving will be dierent as well. 5. Disussion 5.1. Disussion on the Assoiated Issues Based on the theoretial derivation and simulation experiment, it has been demonstrated that the proposed range ompression algorithm enhanes range resolution signiiantly more than the onventional range ompression algorithm during the GNSS-SAR imaging proedure. For instane, in joint Galileo E5 signal reeiver-based GNSS-SARs (where the original range resolution is 3 m [14,15]), the range resolution an be potentially obtained at a level less than 1 m using the proposed range ompression algorithm. For the bistati GNSS-SAR where range and azimuth diretion are not orthogonal [3,6], although imaging perormane will be largely impated by other ators, suh as the angle between range and azimuth diretion, besides range and azimuth resolution indiators, using the proposed range ompression algorithm or obtaining superior range resolution value an still help in ahieving higher quality images. However, aording to Figure 4, it an be seen that the sene illumination level dereases with respet to values. This is beause when perorming spetrum equalization, signal-to-noise ratio (SNR) will be dereased with respet to the seleted uto requeny [14], whih is the main assoiated problem o the proposed range ompression algorithm ompared to multi-stati image proessing [4,5]. Sine the mathematial expression o SNR loss aused by spetrum equalization is introdued in [14], it is omitted at here. Aording to the orresponding mathematial expression in [14], ombining the experimental results in this paper, it an be seen that spetrum equalization auses around 5 times more SNR degradation and 3 times more SNR degradation with 1 and 2 beore perorming azimuth ompression, respetively. Sine GNSSs are low-equivalent isotropially radiated power (EIRP) soures, losses in SNR annot be so easily

11 Sensors 217, 17, o 13 tolerated. However, using lengthened integration when perorming imaging will help to improve sene illumination level. In some speii operative senarios suh as the permanent monitoring o bridges or mines by employing a lose reeiver, the losses in SNR an be aeptable. Conerning another assoiated issue, time onsumption, we study it based on judging the load with regard to the number o operations. For multi-stati image proessing [4,5] or improving resolution, we an easily see that the method is more time onsuming than the proposed algorithm beause it is applied based on generating multiple ull preliminary GNSS-SAR images. Also, the availability o a multiple perspetive exploiting multiple transmitter is not intended or the range resolution improvement only, but provides the apability o exploiting spatial diversity in dierent ways. Thereore we do not ompare the works [4,5] with this paper in detail. Comparing the proposed range ompression algorithm with a onventional range ompression algorithm, the ormer has a higher omputational load due to the at that spetrum equalization is used. To quantiy the omputational load, the orresponding analysis is provided as ollows. Assume or reeived GNSS signal (both diret and releted), there are N samples at the range domain, M samples at the azimuth domain (eah azimuth sample represents 1 milliseond) and azimuth resolution ell size is M s samples. For GNSS-SAR imaging based on the onventional range ompression algorithm, there is O ( N 2 M ) number o operations throughout the range ompression state, O (M s M N) number o operations or azimuth ompression per resolution ell and O ((M M s ) M s M N) number o operations throughput whole azimuth ompression state. Thus, the aumulated number o operations during imaging is: ( ) O N 2 M + (M M s ) M s M N. (19) For GNSS-SAR imaging based on the proposed range ompression algorithm, or range proessing o eah azimuth bin, there additionally exists O ( N 2) number o operations or perorming (1), O (N log (N)) number o operations or perorming (8), (11) and (14) respetively, as well as O (N) number o operations or perorming (13). Fourier transorm does not hange the sample quantity. The numbers o operations or designing a spetrum equalization window is very small, whih an be negleted when ompared with imaging omputations. For azimuth proessing, the numbers o operations are the same as GNSS-SAR imaging based on the onventional range ompression algorithm. Thereore the aumulated number o operations during imaging an be derived as: (( ) ) O 2N 2 + 3N log (N) + N M + (M M s ) M s M N where O (( 2N 2 + 3N log (N) + N ) M ) is or range proessing. It an be seen that the value o (2) is higher than (19). This indiates that the proposed range ompression algorithm has a higher proessing delay than the onventional range ompression algorithm. Although the proposed range ompression algorithm has been demonstrated in GNSS-SAR in this paper, due to the signal struture dierene, the easibility o the proposed algorithm in the passive radar system using other signals o opportunity besides GNSS still needs to be urther studied Future Development Based on the analysis above, in our uture work, irstly, we will test the easibility o the proposed range ompression algorithm in the passive radar system using other soures o opportunity besides GNSS, and modiy the proposed algorithm based on the orresponding signal strutures. Seondly, we would like to develop a mehanism or GNSS-SAR reeivers or trade-o among range resolution, range-ompressed SNR degradation and ompressed delay together with the orresponding ield experimental studies. (2)

12 Sensors 217, 17, o Conlusions In this paper, a novel range ompression algorithm or enhaning the resolution o the GNSS-SAR is proposed. In range ompression, the reeived releted GNSS signal is orrelated with the synhronized diret baseband signal in the range domain or eah azimuth bin. Then, side lobes o the range-ompressed result are suppressed by a proper designed spetrum equalization window. Both theoretial derivation and simulation results have demonstrated that the proposed range ompression algorithm an provide a superior range resolution ompared to the onventional range ompression algorithm in the GNSS-SAR. Moreover, the proposed algorithm is less time-onsuming than multi-stati image proessing [4,5] due to the at that it is applied without the neessity or generating multiple ull preliminary images, and is in general appliable in various GNSS-SARs. At the same time, a non-negligible main limitation o the proposed range ompression algorithm is the loss in SNR. However, lengthened integration during imaging will help to enhane sene illumination level, and under the speii operative senarios suh as the permanent monitoring o bridges or mines using a lose GNSS-SAR reeiver, the SNR losses an be aeptable. Aknowledgments: The researh was substantially by unded by the grants rom The National Key Researh and Development Program o China (No. 216YFB5183). Author Contributions: Yu Zheng proposed the idea, onduted the theoretial derivation and simulations, and arried out the writing the paper. Yang Yang helped to disuss the related tehnial issues. Wu Chen revised the manusript. Conlits o Interest: The authors delare no onlit o interest. Abbreviations The ollowing abbreviations are used in this manusript: GNSS GPS SAR SNR C/A ode P ode EIRP PRN Global Navigation Satellite System global positioning system Syntheti Aperture Radar intermediate requeny signal to noise ratio Coarse Aquisition Code Enrypted Preision Code equivalent isotropially radiated power pseudo-random noise Reerenes 1. Zuo, R. Bistati Syntheti Aperture Radar Using GNSS as Transmitters o Opportunity. Ph.D. Thesis, University o Birmingham, Birmingham, UK, Zeng, Z. Passive Bistati SAR with GNSS Transmitter and a Stationary Reeiver. Ph.D. Thesis, University o Birmingham, Birmingham, UK, Santi, F.; Antoniou, M.; Pastina, D. Point spread untion analysis or GNSS-based multistati SAR. IEEE Geosi. Remote Sens. Lett. 215, 12, Zeng, T.; Zhang, T.; Tian, W.; Hu, C. Spae-Surae Bistati SAR Image Enhanement Based on Repeat-Pass Coherent Fusion With Beidou-2/Compass-2 as Illuminators. IEEE Geosi. Remote Sens. Lett. 216, 13, Santi, F.; Buiarelli, M.; Pastina, D.; Antoniou, M.; Cherniakov, M. Spatial resolution improvement in GNSS-Based SAR using multistati aquisitions and eature extration. IEEE Trans. Geosi. Remote Sens. 216, 54, Daout, F.; Shmitt, F.; Ginolha, G.; Fargette, P. Multistati and multiple requeny imaging resolution analysis-appliation to GPS-based multistati radar. IEEE Trans. Aerosp. Eletr. Syst. 212, 48,

13 Sensors 217, 17, o Mikawa, Y.; Ebinuma, T.; Nakasuka, S. The study o the remote-sensing appliation using the GNSS releted signal with the aperture synthesis. In Proeedings o the 212 IEEE International Geosiene and Remote Sensing Symposium (IGARSS), Munih, Germany, July 212; pp Ebinuma, T.; Mikawa, Y.; Nakasuka, S. Quasi-monostati algorithm or GNSS-SAR. In Proeedings o the 213 IEEE Asia-Paii Conerene on InSyntheti Aperture Radar (APSAR), Tsukuba, Japan, September 213; pp Lazarov, A.; Chen, V.C.; Kostadinov, T.; Morgado, J.P. Bistati SAR system with GPS transmitter. In Proeedings o the 213 IEEE Radar Conerene (RADAR), Ottawa, ON, Canada, 29 April 3 May 213; pp Antoniou, M.; Zeng, Z.; Feieng, L.; Cherniakov, M. Experimental demonstration o passive BSAR imaging using navigation satellites and a ixed reeiver. IEEE Geosi. Remote Sens. Lett. 212, 9, Antoniou, M.; Hong, Z.; Zhangan, Z.; Zuo, R.; Zhang, Q.; Cherniakov, M. Passive bistati syntheti aperture radar imaging with Galileo transmitters and a moving reeiver: Experimental demonstration. IET Radar Sonar Navig. 213, 7, Antoniou, M.; Cherniakov, M. GNSS-based bistati SAR: A signal proessing view. EURASIP J. Adv. Proess. 213, 213, Santi, F.; Pastina, D.; Buiarelli, M.; Antoniou, M.; Tzagkas, D.; Cherniakov, M. Passive multistati SAR with GNSS transmitters: Preliminary experimental study. In Proeedings o the th European Radar Conerene (EuRAD), Rome, Italy, 8 1 Otober 214; pp Ma, H.; Antoniou, M.; Cherniakov, M. Passive GNSS-Based SAR Resolution Improvement Using Joint Galileo E5 s. IEEE Geosi. Remote Sens. Lett. 215, 12, Ma, H.; Antoniou, M.; Cherniakov, M. Passive GNSS-based SAR imaging and opportunities using Galileo E5 signals. Si. China In. Si. 215, 58, Zeng, H.C.; Wang, P.B.; Chen, J.; Liu, W.; Ge, L.; Yang, W. A Novel General Imaging Formation Algorithm or GNSS-Based Bistati SAR. Sensors 216, 16, Shi, S.; Liu, J.; Li, T.; Tian, W. Basi perormane o spae-surae bistati SAR using BeiDou satellites as transmitters o opportunity. GPS Solut. 217, 21, Bandwidth Extension. Available online: (aessed on 6 June 217). 19. Ghaemi, H.; Galletti, M.; Boerner, T.; Gekat, F.; Viberg, M. CLEAN tehnique in strip-map SAR or high-quality imaging. In Proeedings o the IEEE Aerospae Conerene, Big Sky, MT, USA, 7 14 Marh 29; pp Santi, F.; Buiarelli, M.; Pastina, D.; Antoniou, M. CLEAN tehnique or passive bistati and multistati SAR with GNSS transmitters. In Proeedings o the IEEE Radar Conerene (RadarCon), Arlington, VA, USA, 1 15 May 215; pp Sklar, B. Digital Communiations; Prentie Hall: Upper Saddle River, NJ, USA, Sukhatme, B.V. Sampling Theory o Surveys with Appliations; Iowa State University Press: Ames, IA, USA, by the authors. Liensee MDPI, Basel, Switzerland. This artile is an open aess artile distributed under the terms and onditions o the Creative Commons Attribution (CC BY) liense (