Modification of Multichannel Reconstruction Algorithm ... - IEEE Xplore

3050

IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, VOL. 7, NO. 7, JULY 2014

Modification of Multichannel Reconstruction Algorithm on the SAR With Linear Variation of PRI Xiulian Luo, Robert Wang, Member, IEEE, Wei Xu, Yunkai Deng, Member, IEEE, and Lei Guo

Abstract—This paper focuses on the signal processing for synthetic aperture radar (SAR) with fast linear variation of PRI which was introduced to settle the blind range problem in conventional SAR with constant PRI. Since periodic pulse loss is resulted from the variation of PRI, the distribution of the completely received pulses strongly deviates from the ideal uniform one. To settle the problem of nonuniform sampling, multichannel reconstruction algorithm is employed. As the reconstruction requires a priori knowledge of the precise distribution of the samples, this paper first derives the position of the lost pulses. Further, in order to reduce the nonuniformity, an optimal PRI variation scheme is designed. Moreover, considering the drastic degradation of the AASR and the SNR caused by the conventional multichannel reconstruction, we propose a modification where the number of processed frequency bands is reduced, and then the increased degrees of freedom (DOF) are exploited to minimize the power of the residual ambiguities and the noise via a linear constraint minimum power (LCMP) method. Compared to the conventional reconstruction, the modified one dramatically improves the ISLR, the AASR, and the SNR, which is validated by simulation experiments. Index Terms—Multichannel reconstruction algorithm, nonuniform sampling, PRI variation, synthetic aperture radar (SAR).

I. INTRODUCTION IGH-RESOLUTION wide-swath synthetic aperture radar (SAR) enables a shortened revisit time for frequent global mapping with a fine resolution. This initiated lots of researches concentrating on resolving the inherent limitation of wide swath and high azimuth resolution [1]–[7]. In conventional SAR, blind ranges occur when transmit and receive events coincide, hence blocking the continuous reception [1]. The minimum continuous swath width results in an upper bound to the pulse repetition frequency (PRF), thus confining the azimuth resolution. In order to improve the azimuth resolution, a typical method is splitting the antenna into multiple azimuth subapertures to collect additional samples and then increase the equivalent PRF [4]. However, the better the azimuth resolution is, the larger the number of sub-apertures is required, thereby

H

Manuscript received August 29, 2013; revised December 16, 2013; accepted December 29, 2013. Date of publication January 27, 2014; date of current version August 21, 2014. X. Luo and L. Guo are with the Graduate University, Chinese Academy of Sciences, Beijing 100039, China, and also with the Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China (e-mail: [email protected]; [email protected]). R. Wang, W. Xu, and Y. Deng are with the Department of Space Microwave Remote Sensing System, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTARS.2014.2298242

increasing the cost of the hardware and the complexity of the signal processing. A multibeams ScanSAR mode [3, 4] can expand the swath width without blind ranges. However, this is paid for by the impaired azimuth resolution and other inconveniences related to the burst modes. An alternative approach to settle the problem of blind ranges is the periodic linear variation of PRI which was first proposed in [5] and further investigated in [4] and [7]–[9]. Among them, the system design was more concerned about in [4] while the signal processing was more focused on in [7] and [9]. Further, the effects on the image quality were analyzed in [8]. This PRI variation technique combined with multiple elevation beams (MEBs) [4] or orthogonal waveforms [6] can achieve ultrawide continuous swath imaging on a single azimuth aperture and without azimuth resolution loss.Essentially, this technique is to distribute the discrete blind ranges over the whole swath, which, however, results in periodic azimuthgapwherethepulsesarelost[7].Thepositionofthegapwas pointed out in [7]. However, only one gap position was presented without any derivation process. In fact, there are two gaps in one cycle. This paper detailedly derives the positions of both gaps. Due to periodic pulse loss and PRI variation, the distribution of the completely received pulses strongly deviates from the ideal uniform one. Although nonuniform sampling is advantageous over uniform sampling for sparsely distributed targets focused by compressed sensing [10], for conventional imaging scenes focused by conventional imaging algorithms, uniform sampling is required [11]. Among the available signal processing approaches to recover the uniformly sampled signal, one was the interpolation method [7]. Nevertheless, paired echoes (ambiguities) of nearly were generated after compression in this method. Another was the multichannel reconstruction method suggested in [9]. However, an SNR scaling of 8 dB was introduced by the reconstruction even for a very fast variation of PRI. This paper also focuses on the signal processing for a fast linear variation of PRI as in [9]. Nevertheless, the multichannel reconstruction algorithm is modified by reducing the number of processed frequency bands. Then underdetermined equations other than well-determined equations in conventional multichannel reconstruction algorithms [11]–[18] are formed to determine the reconstruction matrix. Afterward, the increment of the degrees of freedom (DOF), stemming from the difference between the number of channels and the number of processed frequency bands, is exploited to minimize the power of the ambiguities and the noise, thus possibly decreasing the SNR scaling and the AASR degradation caused by the reconstruction. This minimization problem, known as linear constraint minimum power (LCMP) [19] in mathematics, has been employed to form antenna beams pointed at certain directions in [20]. Herein, we

1939-1404 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

LUO et al.: MODIFICATION OF MULTICHANNEL RECONSTRUCTION ALGORITHM

extend it to the multichannel reconstruction algorithm to improve the reconstruction performance. Before the reconstruction, this paper presents a PRI variation scheme, as it is indispensable for the multichannel reconstruction. Succeeding sections are organized as follows. In Section II, the characteristics of the echo data with PRI variation are presented and a fast variation scheme is designed. Section III presents the modified multichannel reconstruction algorithm. In Section IV, the 1-D simulation is performed to show the advantages of the proposed algorithm. II. LINEAR VARIATION OF PRI For slow linear variation of PRI, Gebert and Krieger [7] presented the position of the gap where the pulses were not completely received. However, an additional gap caused by the periodic jump from the highest to the lowest PRF was not discussed in [7], as it was much shorter than the presented one. Nevertheless, for very fast variation of PRI, the influence of this gap cannot be ignored as the first gap is also very short. Since the multichannel reconstruction algorithm only deals with the completely received pulses, the distribution of the lost pulses has a big influence on the reconstruction performance. This section first analyzes the characteristics of the echo data, where the exact positions of both gaps are derived in mathematics. Then an optimal PRI variation scheme based on the gap distribution is designed to reduce the deviation of the distribution of the completely received pulse from the ideal uniform one.

3051

Fig. 1. Timing diagram of the transmission. The shaded bars represent the transmit instances.

coincides with the transmit of the ( )th pulse. Therefore, the distribution of the blind area is determined by (2). Equation (2) is easily rewritten as

is the sum of the th element to the where element in the vector given by

For the first cycle, if

th

, then

If there exists a positive integer value of

satisfying

A. Characteristics of the Echo Data Assume a variation cycle of samples and a pulse duration of . The timing diagram of the transmission is shown in Fig. 1, where the difference of two consecutive PRIs and within one sweep period is set to a constant which is calculated as

where

defines the geometric PRF mean and represents the PRF span. For the th transmitted pulse, the range time distribution of its th ( ) blind area satisfies

where represents the range time. In fact, the th blind area of the th pulse is the area where the reception of the th pulse’s echo

where with the concerned slant range gate, then the th pulse is lost and located in its th blind area. By applying (4) and to (6), we can derive the indices of the lost pulses which are integers within and and , , , and are calculated as (7) at the bottom of the page, where we can see that there are two gaps in one cycle. Furthermore, in order to better show the echo characteristics and the positions of the gaps, the blind area distribution diagram is illustrated in Fig. 2, where the horizontal axis denotes the index of the transmitted pulse, while the vertical axis represents the slant range. The blind area, shaded in dark gray, periodically moves with the pulse index. With referring to (2), the time width of the dark-gray region is . In addition, for a slant range gate of located in the spanning blind range, two bold lines indicate the positions of the two gaps in one cycle. Projecting the two lines onto the horizontal axis, the indices of the lost pulses are acquired. Furthermore, the region shaded in light gray represents the th spanning blind range, and its width is .

3052


which enables a widest spanning blind range of

Fig. 2. Blind area distribution versus the pulse index.

It should be noted that the virtual indices of the lost pulses are integers within and , which vary with the slant range. However, the maximum number of lost pulses in the two gaps for the th spanning blind range is fixed and, respectively, determined by and , where represents the ceil operation. As the more the lost pulses are, the stronger the nonuniform sampling might be, the following variation scheme is designed to acquire the fewest lost pulses in the two gaps with minimum PRF span. B. Variation Scheme With referring to (1) and (7), the total width of the two gaps is calculated as

without overlap. The steps of choosing the variation parameters are shown in Fig. 3. First, the geometric PRF mean is usually determined to be with the processed Doppler bandwidth, considering that the effective PRF is smaller than due to the pulse loss. Second, the range of is decided by the coverage, where and represent the nearest and furthest slant ranges, respectively. Then, we suggest choosing to acquire nearly identical width of the two gaps. Third, the initial PRF span is acquired by minimizing (10). Since the PRF span and the pulse duration have a significant impact on the gap width, the two parameters can be adjusted to acquire no more than one pulse in each gap as well as minimum PRF span as follows. If the width of the larger gap with the initial PRF span and the initial pulse duration is smaller than 1, the PRF span can be further decreased until . On the other hand, if it is greater than 1, there might be two consecutive lost pulses in one gap, thus resulting in much stronger nonuniform distribution than when . Under the situation of , it is needed to reduce the pulse duration until . The above design of the PRI variation scheme is to reduce the nonuniformity of the sampling and then improve the focusing performance after multichannel reconstruction [16].

III. MODIFICATION

where and represent the width of the two gaps, respectively. In order to attain an arbitrary coverage, is set to be greater than considering that no echo pulses will be received for slant range

if

[9]. As a result, the width of the two gaps calculated by (8) is certainly positive. Furthermore, according to (5) and Fig. 2, the width of the th spanning blind range is

OF

MULTICHANNEL RECONSTRUCTION

In order to recover the uniformly sampled signal, the interpolation method was applied in [7]. Nevertheless, very strong ambiguities appeared after compression in this method. Another available method was the multichannel reconstruction adopted in [9]. However, it resulted in strong SNR scaling and serious degradation of AASR. In this section, a modified multichannel reconstruction algorithm is proposed to improve AASR and SNR over the conventional one [11]–[16]. The reconstruction principle, the modification strategy, and the calculation of the reconstruction performance are presented as follows. A. Reconstruction Principle

It is observed from (8) and (9) that when is greater, the width of the gaps are smaller and the spanning blind range is wider, thus leading to more uniform distribution of the completely received pulses. However, when the spanning blind range is too wide, there appears an overlap between adjacent blind ranges, which then causes doubled number of gaps and stronger nonuniform sampling within the overlapped part. Therefore, the upper bound to the PRF span is

The indices of the lost pulses are derived in Section II. They are integers within and . The completely received ( , where is the number of the lost samples in one cycle) samples within one cycle are regarded as channels. Provided that the first channel is the reference channel, the sampled signal of the th channel is represented by

where is the time delay of the th channel relative to the reference channel, is the original time-continuous signal, is the Dirac delta function, and is the noise. After sampling, the spectrum of is the superimposition


3053

Fig. 3. Flowchart of PRI variation design.

of a number of sub-bands limited to the cycle repetition frequency

represents the sweep period. Therefore, the spectrum where of each channel can be represented as

where denotes the discrete frequency after sampling, the phase ramp term

is the is to realize time shift in frequency domain and noise spectrum. For the time-continuous signal, the relationship between the original Doppler frequency and the instantaneous squint angle can be expressed as

Therefore, the spatial–temporal spectra of the time-continuous signal can be illustrated in Fig. 4(a), while that of the sampled signal can be illustrated in Fig. 4(b). As not all the superimposed sub-bands can be reconstructed by exploiting the multichannel structure, they are divided into two groups. One can be reconstructed, and the other cannot. The first group is represented by oblique solid lines and the second group by oblique dashed lines in Fig. 4(b). Further, the antenna pattern is also presented in the two figures to indicate the amplitude of the sub-bands. If sub-bands are contained in the first group, the sum of the second group of sub-bands can be expressed as

Fig. 4. Spatial–temporal spectrum: (a) for continuous signal, (b) for sampled signal, and (c) after reconstruction.

Then (14) is rewritten as

In (17) and (18), full frequency interval

which is the first frequency band of the

3054


So the th frequency band can be expressed as

with . Combining the channels, one obtains a set of linear equations which can be rewritten as a matrix equation Fig. 5. Signal spectra before and after sampling: (a)

and (b)

.

where

and

Furthermore, if all channels are identical and the noise is assumed to be spectrally white, the power spectral density (PSD) of the noise can be calculated by

where indicates the expectation operator and represents the noise power of each channel before reconstruction. Next the reconstruction matrix will be derived. Before this, it is supposed to have a form as follows:

, where indicates the with reconstruction of the th sub-band, while that others are zeros implies the suppression of other sub-bands. Connecting the reconstructed sub-bands, is recovered. However, it is contaminated by the residual ambiguous spectrum and the scaling noise , as expressed in (29). After reconstruction, the spatial–temporal spectrum is shown in Fig. 4(c), where the oblique solid and dashed lines represent the reconstructed and residual unreconstructed sub-bands, respectively. Furthermore, with the consideration of the processed bandwidth , spectra components within the dark-gray and light-gray regions contribute to the unambiguous and ambiguous powers, respectively. It must be noticed that the range of in (14) and (18) is different. In fact, is recurrent with a period of according to the sampling theorem. Consequently, when is odd, the spectrum represented by (18) is identical with the one denoted by (14). As illustrated in Fig. 5(a), the spectrum in the dark-gray region is the same as that in the light-gray one. However, when is even, the two spectra are identical only after swapping the left and right halves of one spectrum, as illustrated in Fig. 5(b). Therefore, before the reconstruction, if is even, it is needed to swap the two halves of the spectrum of the sampled signal for each channel. B. Modification Strategy For conventional reconstruction algorithm [11]–[18], the number of channels equals the number of sub-bands to be reconstructed, i.e., . As a result, the solution to (30) is uniquely determined to be

where the element in the th row and th column is the reconstruction filter corresponding to the th channel and th frequency band. In the following derivation, the th column of is represented by , the th row of by where . To reconstruct the th sub-band of and suppress other sub-bands, the following equation should be satisfied:

Therefore, a set of linear constraints of

can be expressed as

Herein, we propose a modified multichannel algorithm by reducing the number of processed sub-bands. Then, (30) becomes a set of underdetermined linear equations with infinite solutions. Our objective is to find an optimum solution of to minimize the power of the interference which comprises the ambiguities and the noise. Since the power of the reconstructed spectrum is constant with reconstruction filters satisfying (30), the minimization of the interference power is equivalent to that of the total power after reconstruction. Therefore, this optimization problem can be stated as follows:


3055

TABLE I SYSTEM PARAMETERS

Fig. 6. Azimuth signal envelope and the applied PRF variation versus the pulse index. The PRF varies from 1715 to 1485 Hz periodically: (a) original and (b) amplified.

which satisfies the LCMP [19], [20] in mathematics. In (32), denotes the vector or matrix conjugate-transpose operation, and

while the ambiguous signal is not. In addition, with varying number of processed sub-bands, the ambiguity contribution changes accordingly, while the noise contribution keeps invariant [see (17) and (27)]. In fact, after focusing with a Doppler bandwidth limited to , the reconstructed spectrum outside will not contribute to the signal power or the ambiguity power, which is equivalent to weighting each row of the reconstruction matrix by a rectangular window. Then the reconstruction matrix can be expressed as

gives the channel covariance matrix. By using the method of Lagrange multipliers [19], the closed-form solution to (32) is calculated as

which collapses to (31) when , i.e., the conventional reconstruction algorithm is a special case of the modified one. Moreover, as long as no samples coincide spatially, it is easily verified that and are always invertible. Physically, the modification is realized by substituting nulls at the outer sub-bands in conventional algorithm with the minimization of the interference power. As long as the outer sub-bands are outside the processed Doppler interval where is determined by the 3-dB width of the radar beam [2], the modification will not change the azimuth resolution. However, the oversampling rate is reduced, because the number of samples within one cycle is reduced from to . Then the ambiguity contribution is increased, from which the influence on the AASR will be discussed in Section III-C. C. Reconstruction Performance The modified reconstruction filters calculated by (34) can produce minimum power of interference, which is made up of the residual ambiguities and the noise. However, compared with ideal uniform sampling, the residual ambiguities and the noise are still possibly amplified by the reconstruction. This section will calculate the amplification of AASR and SNR with additionally taking into account the processed Doppler bandwidth during focusing. It should be first underlined that amplification for the residual ambiguities and the noise is different because the noise of each channel is randomly distributed and uncorrelated

of which the th column is denoted by . Consequently, according to (29), the AASR after reconstruction can be calculated as

One can see from (17) and (34) that both and change with reducing . Furthermore, the two changes have adverse influences on the AASR. Therefore, if the influence caused by the variation of is greater than that arising from the variation of , the AASR will be improved. However, if the adverse situation happens, the AASR will be degraded. As the variation is hard to quantify, it is difficult to judge only from (36) whether the AASR will become better or worse with reducing . Therefore, in order to acquire the best AASR, it is needed to compare the results calculated by (36) with all values of between and . Similarly, according to (29), the SNR after reconstruction can be calculated as

3056


Fig. 7. Azimuth impulse response at the slant range of 975 km: (a) without consideration of antenna side lobes and noise, (b) with antenna side lobes, (c) with noise, and (d) with both antenna side lobes and noise.

where

According to (39) and (41), (40) can be written as

where is the identity matrix which gives the noise covariance matrix. Then (37) can be rewritten as

which implies that the SNR scaling is the mean value of over . where The SNR scaling, defined as a measure for the variation of SNR from that of ideal uniform sampling with a sampling rate of [13], can be calculated as

the

. Therefore,

processed

Doppler

interval

can be regarded as

the spectral appearance of the SNR scaling.

IV. SIMULATION RESULTS AND ANALYSIS The 1-D (azimuth domain) simulation is given in this section to assess the modified reconstruction algorithm. represents the SNR of ideal uniform sampling and where is calculated as

A. Simulation Parameters The simulation parameters are listed in Table I, which are the same as the ones specified in [7] except for the PRF span and the sweep period. As a slant range of 868–1097 km leads to (see Section II-B) varying from 9 to 12, a sweep period of 21 pulses is set according to the flowchart in Fig. 3. In addition, a of 230 Hz is chosen as it produces .


Fig. 8. Spectral appearance of the SNR scaling. The dashed and solid plots correspond to the conventional reconstruction ( ) and the modified one ( ), respectively. The contributions when focusing with are shaded in gray.

B. Simulation Results For an exemplary slant range of 975 km, the simulated azimuth signal envelope and the PRF variation versus the pulse index are presented in Fig. 6, where an azimuth time extension of 3-dB width of the antenna beam is considered. Within one PRI variation cycle of 21 samples, the 11th pulse in the first gap and the 13th pulse in the second one are lost, which agrees well with the results given by (7). Herein, we consider a pulse to be fully lost as soon as it is no longer received completely. First, a band-limited signal is taken into account. The azimuth impulse responses with the interpolation and the conventional reconstruction ( ) applied are shown in Fig. 7(a) by green and red plots, respectively. One can see the ambiguities in the azimuth impulse response for interpolation are canceled by the reconstruction. This is because the spectrum recovery is perfect for a band-limited signal [14], [15]. For comparison, the compressed result for ideal uniform sampling signal is shown by blue plot. However, SAR signal is not band-limited because of the side lobes of the antenna pattern. Additionally, the system noise cannot be neglected, either. In order to show the influence of the two factors on the azimuth impulse response, the compressed results with the antenna side lobes and the noise considered are presented in Fig. 7(b) and (c), respectively. Further, the results with both factors simultaneously considered are shown in Fig. 7(d). To demonstrate the advantages of the modified reconstruction ( ) over the conventional one and the interpolation, the azimuth impulse responses for the three approaches are plotted together with different colors in the three figures. The analysis of the simulation results in Fig. 7 is presented as follows. First, both the conventional and the modified reconstruction algorithms achieve the maximum amplitude of the ambiguities nearly 14 dB lower than the interpolation [Fig. 7(b)]. Furthermore, some of the ambiguities for the modified reconstruction are much lower than for the conventional one [see the region in the dashed rectangles in Fig. 7(b)]. Since the ambiguous energy is actually the sum of all ambiguities, we can infer that the AASR is improved by the modification. In addition, the noiselevelwithconventionalreconstructionappliedis13dBhigher than that with interpolation [Fig. 7(c)]. Fortunately, the modification can reduce the noise to a level nearly equal to the one in the case of interpolation. This can be explained in Fig. 8, where the spectral

3057

Fig. 9. Position and number of lost pulses for exemplary slant ranges.

appearance of the SNR scaling for the two reconstructions is presented. From Fig. 8, it is indicated that the strong SNR scaling in conventional reconstruction is significantly reduced by the modification. Furthermore, when taking both the side lobes of antenna pattern and the system noise into account, the conventional reconstruction does not show any dramatical advantages over the interpolation method, but the modified one does [Fig. 7(d)]. C. Performance Analysis The position and the number of the lost pulses vary with the slant range, as shown in Fig. 9. Therefore, the nonuniformity of the sampling, defined as [17]

also varies with the slant range. Since the performance is related to the nonuniformity, the performance analysis over the whole coverage is needed. In fact, the nonuniformity defined in (43) is equal to the SNR scaling with and . The nonuniformity over the whole coverage is shown in Fig. 10(a). Then, azimuth resolution, ISLR (the energy within the main lobe related to the energy outside this region), AASR (the energy of the ambiguities related to the energy of the real signal), and SNR scaling are calculated and presented in Fig. 10(b)–(e), respectively. The results in Fig. 10 are summarized and analyzed as follows. First, the azimuth resolution scarcely varies with the processing approaches and is nearly independent of the slant range or the nonuniformity [Fig. 10(b)]. This is because the processed Doppler bandwidth for different approaches is identical. As for the ISLR [Fig. 10(c)] and the AASR [Fig. 10(d)], both of them achieved by multichannel reconstruction (conventional and modified) are much better than by interpolation. Further, both of them for the modified reconstruction ( ) are better than for the conventional one. However, the SNR scaling [Fig. 10(e)] achieved by the conventional reconstruction is much worse than by interpolation. Fortunately, the modified one can reduce the SNR a lot, though it is still worse than for interpolation. Moreover, combing Fig. 10(c)–(e)

3058


Fig. 10. Reconstruction performance: (a) nonuniformity, (b) resolution, (c) ISLR, (d) AASR, and (e) SNR scaling.

with (a), it is generally acquired that the stronger the nonuniformity is, the worse the performances (ISLR, AASR, and SNR scaling) achieved by the multichannel reconstruction are, and the three performances are greater improved by the modified reconstruction over the conventional one. In addition, starting from with conventional reconstruction, the modified reconstruction can be applied repeatedly, while lowering , until no further performance increase is achieved. At this point, there is no benefit of further reducing . For the designed PRI variation scheme in this paper, is chosen as the number of processed frequency bands. V. CONCLUSION This paper analyzed the echo characteristics with linear variation of PRI and presented some considerations on the choice of PRF span and sweep period. Then, a modified multichannel reconstruction algorithm was proposed to deal with the nonuniform sampling problem. In this algorithm, in order to ensure that the number of processed frequency bands can be reduced without degrading the

azimuth resolution, the oversampling rate of the original signal should be great enough. However, this is worthy of paying for an arbitrary large swath width. Furthermore, compared to the conventional one, ISLR, AASR, and SNR scaling were 2.5, 4, and 10.5 dB improved, respectively. Nevertheless, the AASR in some slant ranges was still drastically deteriorated. Fortunately, there have been a lot of approaches to improve the AASR [22], [23]. In a very simple approach, one could just enlarge the dimension of the antenna yielding a narrower pattern, but this comes at the expense ofresolution[13]. A bigger antenna in combination with an adapted tapering was investigated in [13] to provide an improved suppression of the ambiguous energy without degrading the azimuth resolution, which, however, is at the cost of a decreased SNR. An alternative approach is to employ the reflector antenna with higher gain and lower side lobes [3], [20], which is under intense investigation. In fact, the modification of the multichannel reconstruction algorithm can also be applied to other recurrent strong nonuniform sampling SAR systems, such as the multistatic SAR and DPCA SAR, to improve the focusing performance.


REFERENCES [1] A. Currie and M. A. Brown, “Wide-swath SAR,” IEE Proc. F-Radar Signal Process., vol. 139, no. 2, pp. 122–135, Apr. 1992. [2] I. G. Cumming and F. H. Wong, Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation. Norwood, MA, USA: Artech House, 2005. [3] W. Xu and Y. K. Deng, “Multi-channel SAR with reflector antenna for highresolution wide-swath imaging,” IEEE Antennas Wirel. Propag. Lett., vol. 9, pp. 1123–1127, Dec. 2010. [4] G. Krieger, N. Gebert, M. Younis, and A. Moreira, “Advanced synthetic aperture radar based on digital beam-forming and waveform diversity,” in Proc. IEEE Radar Conf., Rome, Italy, May 2008. [5] B. Grafmüller, C. Schaefer, “Hochauflösende Synthetik-Apertur-Radar Vorrichtung und Antenne für eine ochauflösende synthetik-apertur-radarvorrichtung,” Germany, Patent 102005062031, Dec. 22, 2005. [6] W. Q. Wang, “Space–time coding MIMO-OFDM SAR for high-resolution imaging,” IEEE Trans. Geosci. Remote Sens., vol. 49, no. 8, pp. 3094–3104, Aug. 2011. [7] N. Gebert and G. Krieger, “Ultra-wide swath SAR imaging with continuous PRF variation,” in Proc. EUSAR, Aachen, Germany, Jun. 2010, pp. 966–969. [8] Y. Wu, C. S. Li, W. Yang, and J. Zhou, “Effects of PRF variation on SweepSAR imaging quality,” Procedia Eng., vol. 15, pp. 2271–2275, 2011. [9] M. Villano, G. Krieger, and A. Moreira, “Staggered-SAR for high-resolution wide-swath imaging,” in Proc. IET RADAR Conf., Glasgow, U.K., Oct. 2012. [10] J. Fang, Z. Xu, C. Jiang, B. Zhang, and W. Hong, “SAR range ambiguity suppression via sparse regularization,” in Proc. IGARSS, Munich, Germany, 2012. [11] N. Gebert, “Multi-channel azimuth processing for high-resolution wideswath,” Ph.D. dissertation, IHE, Univ. Karlsruhe, Karlsruhe, Germany, 2009. [12] J. L. Brown, “Multi-channel sampling of low-pass signals,” IEEE Trans. Circuits Syst., vol. 28, no. 2, pp. 101–106, Feb. 1981. [13] N. Gebert, G. Krieger, and A. Moreira, “Digital beamforming on receive: Techniques and optimization strategies for high-resolution wide-swath SAR imaging,” IEEE Trans. Aerosp. Electron. Syst., vol. 45, no. 2, pp. 564–592, Apr. 2009. [14] Y.C.Jeng,“Perfectreconstructionofdigitalspectrafromnonuniformlysampled signals,” IEEE Trans. Instrum. Meas., vol. 46, no. 3, pp. 649–652, Jun. 1997. [15] J. L. Yen, “On nonuniform sampling of bandwidth-limited signals,” IRE Trans. Circuit Theory, vol. 3, no. 4, pp. 251–257, Dec. 1956. [16] N. Gebert, G. Krieger, and A. Moreira, “SAR signal reconstruction from non-uniform displaced phase centre sampling in the presence of perturbations,” in Proc. IGARSS, Seoul, South Korea, 2005. [17] T. Wang and Z. Bao, “Improving the image quality of spaceborne multipleaperture SAR under minimization of sidelobe clutter and noise,” IEEE Geosci. Remote Sens. Lett., vol. 3, no. 3, pp. 297–301, Jul. 2006. [18] W. Jing, M. Xing, C. Qiu, Z. Bao, and T. Yeo, “Unambiguous reconstruction and high-resolution imaging for multiple-channel SAR and airborne experiment results,” IEEE Geosci. Remote Sens. Lett., vol. 6, no. 1, pp. 102–106, Jan. 2009. [19] H. L. V. Trees, Optimum Array Processing. Hoboken, NJ, USA: Wiley, 2002. [20] S. Huber, M. Younis, A. Patyuchenko, G. Krieger, and A. Moreira, “Spaceborne reflector SAR systems with digital beamforming,” IEEE Trans. Geosci. Remote Sens., vol. 48, no. 4, pp. 3473–3491, Oct. 2012. [21] R.W. Beard,“Linearoperationequationswithapplicationsincontrolandsignal processing,” IEEE Control Syst. Mag., vol. 22, no. 2, pp. 69–79, Apr. 2002. [22] F. Bordoni, M. Younis, and G. Krieger, “Ambiguity suppression by azimuth phase coding in multi-channel SAR systems,” IEEE Trans. Geosci. Remote Sens., vol. 50, no. 2, pp. 617–629, Feb. 2012. [23] A. Moreira, “Suppressing the azimuth ambiguities in synthetic aperture radar images,” IEEE Trans. Geosci. Remote Sens., vol. 31, no. 4, pp. 885–890, Jul. 1993. Xiulian Luo received the B.S. degree in electronic information engineering from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2010. In September 2010, she enrolled in the Institute of Electronics, Chinese Academy of Sciences (IECAS). She is currently working toward the Ph.D. degree with the Department of Space Microwave Remote Sensing System, Institute of Electronics, Chinese Academy of Sciences (IECAS), Beijing, China. Her current research interests are high-resolution wide-swath spaceborne synthetic aperture radar (SAR) system design and signal processing.

3059

Robert Wang (M’07–SM’13) received the B.S. degree in control engineering from the University of Henan, Kaifeng, China, in 2002, and the Dr.Eng. degree from the Graduate University of Chinese Academy of Sciences, Beijing, China, in 2007. In 2007, he joined the Center for Sensorsystems (ZESS), the University of Siegen, Siegen, Germany. He is currently working at the hybrid bistatic experiment. He was also involved in some SAR projects with Fraunhofer Institute for High Frequency Physics and Radar Techniques (FHR). Since 2011, he has been a Research Fellow with the Spaceborne Microwave Remote Sensing System Department, Institute of Electronics, Chinese Academy of Sciences (IECAS), Beijing, China, where he is currently funded by “100 Talents Programme” of the Chinese Academy of Sciences. His current research interests include monostatic and bistatic SAR imaging, multibaseline for monostatic and bistatic SAR interferometry, high-resolution spaceborne SAR system and data processing, airborne SAR motion compensation, frequency modulated continuous wave (FMCW) SAR system, and millimeter-wave SAR system. Dr. Wang has contributed to invited sessions on bistatic SAR at the European Conference on Synthetic Aperture Radar (EUSAR), 2008. He is the author of a tutorial entitled “Results and Progresses of Advanced Bistatic SAR Experiments” presented at the European Radar Conference 2009 and the coauthor of a tutorial entitled “Progress in Bistatic SAR Concepts and Algorithms” presented at EUSAR2008.

Wei Xu was born in Suzhou, China, in 1983. He received the M.S. degree from the Nanjing Research Institute of Electronics Technology (NRIET), Nanjing, China, in 2008, and the Ph.D. degree in communication and information engineering from the Graduate University of Chinese Academy of Sciences (GUCAS), Beijing, China. Since 2011, he has been with the Spaceborne Microwave Remote Sensing System Department, Institute of Electronics, Chinese Academy of Sciences (IECAS), Beijing, China. His research interests include spaceborne/airborne SAR technology for advanced modes, SAR raw signal simulation, and SAR signal processing. Dr. Xu was awarded the Special Prize of President Scholarship for Postgraduate Students from the Graduate University of Chinese Academy of Sciences, in 2011.

Yunkai Deng (M’11) received the M.S. degree in electrical engineering from Beijing Institute of Technology, Beijing, China, in 1993. In 1993, he joined the Institute of Electronics, Chinese Academy of Sciences (IECAS), Beijing, China, where he worked on antenna design, microwave circuit design, and spaceborne/airborne SAR technology. He has been the Leader of several spaceborne/airborne SAR programs and developed some key technologies of spaceborne/airborne SAR. Currently, he is a Research Scientist, a Member of the scientific board, and the Director of Spaceborne Microwave Remote Sensing System Department, IECAS. His current research interests include spaceborne/ airborne SAR technology for advanced modes, multifunctional radar imaging, and microwave circuit design.

Lei Guo was born in Gansu, China, in 1988. He received the B.S. degree in information engineering from the University of Science and Technology of China, Hefei, China, in 2010. In September 2010, he enrolled in the Institute of Electronics, Chinese Academy of Sciences (IECAS). He is currently working toward the Ph.D. degree in the field of highresolution and wide-swath synthetic aperture radar technology in the Graduate University of Chinese Academy of Science, Beijing, China.