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An Improved Processing Scheme of Digital Beam-Forming in Elevation for Reducing Resource Occupation Wei Wang, Robert Wang, Senior Member, IEEE, Yunkai Deng, Timo Balz, Member, IEEE, Feng Hong, and Wei Xu Abstract—For the next generation of spaceborne synthetic aperture radar remote sensing satellites, high resolution and wide coverage are important goals. Digital beam-forming (DBF) with multichannels in elevation is a great and promising candidate to cover wide swaths. In this letter, we focus on onboard digital processing for DBF in elevation. It is generally believed that the onboard processing for DBF is challenging due to the limitations in flight-hardware availability, the heavy computational load, and the high resource occupation. In order to reduce the computational load of DBF, one novel processing scheme is proposed. This proposed scheme performs a modified time-variant weighting on a real intermediate frequency signal of each subchannel, and the weighted signals of all channels are summed to two real data streams. To obtain a correct DBF output, a modified quadrature demodulation process is presented. Then, the scheme is extended to apply FIR filters for overcoming pulse extension loss. Furthermore, improved time-variant weighting coefficients are derived to compensate the phase errors brought by the FIR filtering process. Compared with the present processing flow, the proposed scheme could significantly reduce the computational load and resource occupation. Index Terms—Digital beam-forming (DBF), intermediate frequency (IF) signal, resource occupation, synthetic aperture radar (SAR).
I. I NTRODUCTION
S
YNTHETIC aperture radar (SAR) is an important imaging tool which has the capacity of obtaining high-quality images in day or night under almost all-weather conditions. It is applied for numerous Earth observation missions, e.g., wide area surveillance, disaster management, Earth dynamic monitoring, etc. [1], [2]. Currently, high-resolution wide-swath has become the trend of future spaceborne SAR systems. In this Manuscript received October 30, 2015; accepted December 9, 2015. Date of publication January 12, 2016; date of current version February 24, 2016. This work was supported in part by the Hundred Talents Program of the Chinese Academy of Sciences, by the National Science Fund for Excellent Young Scholars under Grant 61422113, and by the National Science Fund under Grant 61172122. W. Wang and F. Hong are with the Department of Space Microwave Remote Sensing System, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China, and also with the University of Chinese Academy of Sciences, Beijing 100039, China (e-mail:
[email protected]). R. Wang, Y. Deng, and W. Xu are with the Department of Space Microwave Remote Sensing System, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China (e-mail:
[email protected]). T. Balz is with the State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing, Wuhan University, Wuhan 430079, China (e-mail:
[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/LGRS.2015.2508098
context, digital beam-forming (DBF) is regarded as a promising candidate for future Earth observation missions to enhance the imaging capacity [3]–[6]. The main innovative characteristic of this promising concept is the use of multichannels in elevation and/or azimuth where the receiving antenna is split into multiple subapertures with independent receiver channels. SAR with DBF in elevation could form an equivalent highgain and sharp pattern, which could steer a real-time beam for scanning and following the pulse echoes arriving from different directions as a function of time [7]–[9]. All of the channels distributed in elevation are separately amplified, downconverted, and digitized onboard. Then, the data of each channel are processed by digital processing resources of the radar system. Digital receiver architectures [11] are generally adopted in radar systems. Therefore, the received signals are all downconverted to the intermediate frequency (IF) band and digitized. For the present DBF processing flow scheme, the sampled real data of each channel are digitally downconverted to baseband complex data by quadrature demodulation before combination for DBF. Therefore, the number of quadrature demodulators needed is proportional to the number of channels. Then, the time-variant weighting is performed for each channel. At last, the echo data of all channels are summed to one complex data stream as the output of DBF [10]–[15]. However, the resource occupation of this processing scheme is high, which would restrain the applications of DBF in elevation for spaceborne SAR systems. In this letter, an improved processing flow scheme is proposed for reducing the computational load and saving resource occupation. The sampled real IF data of each channel are first multiplied by two groups of time-variant real coefficients based on the principle of DBF. Then, the weighted signals of all channels are summed to two real data streams. In order to obtain the complex data output of DBF, a modified quadrature demodulation is presented. Then, the scheme is extended to apply FIR filters for overcoming pulse extension loss (PEL), and improved time-variant weighting coefficients are derived to compensate the phase errors brought by the FIR filtering process. This proposed processing flow has only one quadrature demodulator, and the multipliers consumed by the real data weighting process are less than complex data weighting. Therefore, the resource occupation of the proposed scheme is significantly lower than the present one. This letter is organized as follows. In Section II, the present digital processing scheme is described. In Section III, the proposed digital processing scheme is derived in detail. In Section IV, the simulation results validate the feasibility of the proposed scheme, and the analysis shows that the improved
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Fig. 1. Quadrature demodulation of IF signals.
Fig. 3. Block diagram of the proposed processing scheme for direct DBF.
would consume three to four real multipliers. Therefore, with increasing number of channels, the resource occupation increases rapidly. III. D ERIVATION OF THE P ROPOSED D IGITAL P ROCESSING S CHEME Fig. 2. Block diagram of the present processing scheme for direct DBF.
processing flow scheme could reduce the computational load so as to reduce the resource occupation. Finally, the conclusion is drawn in Section V. II. P RESENT D IGITAL P ROCESSING S CHEME This section describes the present digital processing scheme for basic DBF, which can be called scan-on-receive. For radar systems, the received radio frequency (RF) signals should be first downconverted to IF signals before digital sampling by analog-to-digital converters. Using the digital process resources (such as FPGA and DSP) of radar system, the sampled real IF digital signals can be band-shifted to obtain complex baseband signals by a quadrature demodulation process which can be called digital downconverting, as shown in Fig. 1. In Fig. 1, IF(t) and f1 represent the sampled IF signals and the IF, respectively. The module LPF represents a low-pass filter. For a DBF-SAR system with N channels in elevation, the received signals from all subchannels are separately downconverted and digitized. Then, in order to form an equivalent scanning high-gain and sharp pattern, the received signals of the N channels are all weighted by time-variant weighting factors and then combined. The theory of DBF [7], [15] shows that time-variant weighting and summing are both performed with complex signals. Therefore, before weighting, the signal of each channel should be quadrature-demodulated to a complex baseband signal. The block diagram of the processing scheme of a DBF-SAR system is shown in Fig. 2. In Fig. 2, IFn (t) and ωn (t) represent the sampled IF signals and the complex time-variant weighting coefficients of the nth receiving channel, respectively. From Fig. 2, it can be seen that the resource occupation of such a system is nearly proportional to the number of channels in elevation. For the digital downconverting part, the resource occupation is very large due to the low-pass digital filtering, which is a very resource-consuming process. While performing time-variant complex weighting, one complex multiplication
For saving the digital resources of the DBF-SAR system, an improved digital processing scheme is proposed in this section. A. Basic DBF First, the basic DBF is considered, which neglects the PEL and is the same as the one considered in Section II. In order to facilitate understanding, the block diagram of the improved digital processing flow is illustrated in Fig. 3 first, and then, the detailed derivations are shown in the following part. In Fig. 3, pn (t) and ϕn (t) represent the amplitude and phase of the complex time-variant weighting coefficients ωn (t). IFC and IFS represent the weighted real signals, and they will be expressed in formulas (5) and (6). Considering a linear FM waveform, the transmitting RF real signal pulse can be expressed as t s(t) = rect (1) cos 2πfc t + πKr t2 Tp where Tp and fc represent the pulse length and the carrier frequency, respectively. t and Kr are fast time and chirp rate. After being scattered by a point target, the received echo of the nth channel is t−tn cos 2πfc (t−tn )+πKr (t−tn )2 +ψ . RFn (t) = rect Tp (2) The variable ψ represents the phase change caused by the scattering process upon reflection from the surface. tn is the two-way time delay of the echo received by the nth channel. The RF real received signal is downconverted to an IF signal that can be expressed as t − tn IFn (t) = rect cos 2πf1 t+πKr (t−tn )2 −2πfc tn +ψ Tp (3) where f1 represents the IF. It should be noted that the amplitude coefficients of the signals in (1)–(3) are omitted because they have no effect on the processing flow scheme.
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In SAR systems, the IF signals are digitized first. Then, before digital downconverting, the first step of the proposed processing flow is a real weighting of the IF digital signals as illustrated in Fig. 3. The real weighting factors are based on the complex time-variant weighting coefficients that can be expressed as
where LPF(·) represents the low-pass filtering process. From (7), it can be seen that the real and imaginary parts of the baseband signals of the DBF are obtained successfully with this modified digital downconverting process approach.
ωn (t) = pn (t) · exp (j · ϕn (t)) .
For SAR with DBF in elevation, if the pulse extension is larger than the 3-dB coverage of the receiving beam, PEL would occur and reduce the receiving gain. In order to compensate the gain loss, [13]–[15] have proposed efficient approaches for combining signals with improved receiving gain. The basic principle of the improved approach is combining the timevariant weighting with FIR filters which are constructed for specific time delays in time domain. For the present processing flow, the FIR filtering should be performed after digital downconverting and time-variant weighting [13]. However, after digital downconverting, the signal of each channel has two data streams (real and imaginary parts), and both data streams should be filtered with FIR filters. In this section, the digital processing scheme proposed in Section III-A is extended to apply the FIR filtering for overcoming PEL. In order to reduce the computational load, the filtering process could be performed after digital sampling and before other steps in the proposed scheme. Therefore, for each channel, there is only one data stream that should be filtered with an FIR filter. The filtered signal of the nth channel can be expressed as
(4)
With the proposed processing scheme, the weighting results are t − tn IFCn (t) = rect pn (t) Tp ×cos 2πf1 t+πKr (t−tn)2−2πfc tn +ψ cos(ϕn(t)) t − tn 1 pn (t) = rect 2 Tp × cos 2πf1 t+πKr (t−tn )2 −2πfc tn +ψ+ϕn (t) + cos 2πf1 t+πKr (t−tn )2−2πfc tn +ψ−ϕn (t) (5) t − tn IFSn (t) = rect pn (t) Tp 2 ×cos 2πf1 t+πK r (t−tn ) −2πfc tn +ψ sin(ϕn (t)) t − tn 1 = rect pn (t) 2 Tp × sin 2πf1 t+πKr (t−tn )2 −2πfctn +ψ+ϕn (t) −sin 2πf1 t+πKr (t−tn )2−2πfc tn+ψ−ϕn (t) . (6) After weighting the real signals, the next step should be combining the signals of all N channels and the quadrature demodulation process. However, from (5) and (6), it can be seen that the weighted real signals cannot be downconverted directly because the second cosine term of (5) and the second sine term of (6) are undesired terms that cannot be eliminated by the digital downconverting process using the quadrature demodulator in Fig. 1. In order to obtain correct complex baseband signals of DBF, as illustrated in Fig. 3, a modified quadrature demodulation process could be presented as
N N IFCn (t) · cos(2πf1 t)+ IFSn (t) · sin(2πf1 t) I = LPF 1
1
N t − tn 1 = rect pn (t) 2 1 Tp × cos πKr (t−tn )2 −2πfctn +ψ+ϕn(t) N IFCn (t) · (−sin(2πf1 t)) Q = LPF 1
N + IFSn (t) · cos(2πf1 t) 1
=
N t − tn 1 rect pn (t) 2 1 Tp × sin πKr (t − tn )2 −2πfctn +ψ+ϕn (t) (7)
B. Combination of Weighting and FIR Filters
IFn (t) = IFn (t − Δtn )
(8)
where Δtn represents the time delay quantity of the nth channel. The next step is weighting the IF digital signals for DBF. The time-variant weighting coefficient for the nth channel should be modified as ωn (t) = pn (t − Δtn ) exp (j · ϕn (t − Δtn )) .
(9)
The following steps are the same as the scheme proposed in Section III-A. The results are N t − tn − Δtn 1 rect pn (t − Δtn ) I = 2 1 Tp · cos −2πf1 Δtn + πKr (t − tn − Δtn )2 − 2πfctn + ψ + ϕn (t − Δtn )) Q =
N t − tn − Δtn 1 rect pn (t − Δtn ) 2 1 Tp · sin −2πf1 Δtn + πKr (t − tn − Δtn )2 − 2πfctn + ψ + ϕn (t − Δtn )) . (10)
From (10), it can be seen that the phase −2πf1 Δtn is an undesired term that is brought by the delay filtering process occurring in the real and imaginary parts. In order to eliminate it, the time-variant weighting coefficient in (9) can be modified as ωn (t) = pn (t − Δtn ) exp (j · (ϕn (t − Δtn ) + 2πf1 Δtn )) . (11)
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Fig. 4. Whole block diagram of the proposed processing scheme with FIR filters for overcoming PEL. TABLE I S YSTEM PARAMETERS
Fig. 5. System geometry of the SAR system with DBF in elevation.
With this new weighting coefficient in (11), the final process results of the whole scheme are N t − tn − Δtn 1 rect pn (t − Δtn ) I= 2 1 Tp · cos πKr (t − tn − Δtn )2 − 2πfc tn + ψ + ϕn (t − Δtn )) Q=
N 1 t − tn − Δtn rect pn (t − Δtn ) 2 1 Tp · sin πKr (t − tn − Δtn )2
− 2πfc tn + ψ + ϕn (t − Δtn )) . (12)
The signals in (12) are the same as the DBF output end in [13], thereby realizing a coherent combination to overcome the PEL. The whole block diagram is illustrated in Fig. 4. In Fig. 4, Dn is the FIR filter which represents the delay module of the nth channel. IV. S IMULATION AND A NALYSIS In this section, the proposed process approach is simulated considering a wide-swath spaceborne DBF-SAR system. Then, the computational load is analyzed to demonstrate the advantages of the proposed scheme. A. Simulation With DBF-SAR System A DBF-SAR system is considered, and the system parameters are listed in Table I. The looking angle of the selected swath ranges from 28◦ to 33.65◦, and the ground swath width is about 100 km.
Fig. 6. Simulation results. (a) Real part of the DBF output with the present processing scheme. (b) Compression result of the DBF output with the present processing scheme. (c) Real part of the DBF output with the proposed processing scheme. (d) Compression result of the DBF output with the proposed processing scheme.
Three point targets are located along the swath and distributed at the borders and center of the swath. The system geometry is illustrated in Fig. 5. In Fig. 5, θ1 = 28◦ , θ2 = 30.83◦, θ3 = 33.65◦. All of the receiving channels receive the echoes reflected by the three point targets. In order to validate the equivalence between the present scheme and the proposed one, the sampled data streams of all of the subchannels are processed with the present DBF scheme combined with FIR filters and the proposed one that is illustrated in Fig. 4. The results are shown in Fig. 6. From Fig. 6, it can be seen that the output of the proposed processing scheme for DBF is identical to the present one. Therefore, the correctness of the proposed digital processing scheme is validated.
WANG et al.: IMPROVED PROCESSING SCHEME OF DBF IN ELEVATION FOR REDUCING RESOURCE OCCUPATION
Fig. 7. Number of real multiplications of the present scheme and the proposed scheme for the basic DBF (M = 32).
B. Analysis of Computational Load In order to analyze the computational load of the proposed processing flow and compare it with the present one, the amount of real multiplications needed is derived in this section. Assuming M order low-pass filter for digital quadrature demodulation, the number of real multiplications of the present processing scheme for the basic DBF illustrated in Fig. 2 can be expressed as T1 = N · (2 + 2 · M + 3).
(13)
In (13), the third term 3 in the bracket represents the optimized number of real multiplications for one complex multiplication. For the proposed processing flow in Fig. 3, the number of real multiplications of the basic DBF is P1 = N · 2 + 4 + 2 · M.
(14)
The comparison between T1 and P1 is illustrated in Fig. 7. Considering the DBF with L order FIR filters for overcoming PEL, the FIR filter of each channel is put behind the timevariant weighting for the present processing flow in [13]. In this way, the number of real multiplications of the present processing scheme for the DBF with FIR filters can be expressed as T2 = N · (2 + 2 · M + 3 + 2 · L).
(15)
For the proposed processing flow with FIR filters in Fig. 4, the number of real multiplications is P2 = N · (L + 2) + 4 + 2 · M.
(16)
The comparison between T2 and P2 is illustrated in Fig. 8. From Figs. 7 and 8, it can be seen that the proposed processing flow could significantly reduce the computational load so as to reduce the resource occupation. V. C ONCLUSION Real-time processing of DBF in elevation poses a challenge to the onboard hardware of spaceborne SAR systems. In order to mitigate the heavy computational load, a novel processing scheme is proposed in this letter. Compared with the present approach, the proposed scheme only needs one quadrature demodulator, and complex multiplications are avoided. Therefore,
313
Fig. 8. Number of real multiplications of the present scheme and the proposed scheme for the DBF with FIR filters (L = 8 and M = 32).
the computational load and resource occupation are significantly reduced. The simulation results demonstrate the validity of the proposed scheme. Therefore, the proposed scheme can promote the applications of DBF-SAR in elevation for the development and implementation of a new generation of SAR systems. R EFERENCES [1] J. C. Curlander and R. N. McDonough, Synthetic Aperture Radar Systems and Signal Processing. Hoboken, NJ, USA: Wiley, 1991. [2] F. Henderson and A. Lewis, Manual of Remote Sensing: Principles and Applications of Imaging Radar. New York, NY, USA: Wiley, 1998. [3] N. Gebert, G. Krieger, and A. Moreira, “Digital beamforming on receive: Techniques and optimization strategies for high-resolution and wide-swath SAR imaging,” IEEE Trans. Aerosp. Electron. Syst., vol. 45, no. 2, pp. 564–592, Apr. 2009. [4] G. Krieger, N. Gebert, and A. Moreira, “Multidimensional waveform encoding: A new digital beamforming technique for synthetic aperture radar remote sensing,” IEEE Trans. Geosci. Remote Sens., vol. 46, no. 1, pp. 31–46, Jan. 2008. [5] M. Younis, S. Huber, A. Patyuchenko, F. Bordoni, and G. Krieger, “Performance comparison of reflector–and planar-antenna based digital beam-forming SAR,” Int. J. Antennas Propag., vol. 2009, Jun. 2009, Art. ID 614 931. [6] C. Gao et al., “Large-scene sliding spotlight SAR using multiple channels in azimuth,” IEEE Geosci. Remote Sens. Lett., vol. 10, no. 5, pp. 1006–1010, Sep. 2013. [7] M. Süß, B. Grafmüller, and R. Zahn, “A novel high resolution, wide swath SAR,” in Proc. IEEE IGARSS, Sydney, NSW, Australia, 2001, vol. 3, pp. 1013–1015. [8] M. Suess, M. Zubler, and R. Zahn. “Performance investigation on high resolution wide swath SAR system,” in Proc. EUSAR, Cologne, Germany, 2002, pp. 187–190. [9] F. Bordoni, M. Younis, V. Makhaul, and G. Krieger. “Adaptive scanon-receive based on spatial spectral estimation for high-resolution wideswath SAR,” in Proc. IEEE IGARSS, Cape Town, South Africa, 2009, pp. I-64–I-67. [10] X. Xu et al., “The realization of digital beamforming based on FPGA and DSP,” in Proc. Int. Conf. ISDEA, Oct. 13–14, 2010, vol. 2, pp. 713–716. [11] C. Fischer, C. Heer, and R. Werninghaus. “X-band HRWS demonstrator digital beamforming test results,” in Proc. 9th Eur. Conf. Synthetic Aperture Radar, Nuremberg, Germany, 2012, pp. 1–4. [12] C. Fischer, C. Heer, and R. Werninghaus, “Development of a high resolution wide-swath SAR demonstrator,” in Proc. EUSAR, Aachen, Germany, 2010, pp. 1–4. [13] F. Feng, H. X. Dang, X. M. Tan, and G. T. Li, “An improved scheme of digital beam-forming in elevation for spaceborne SAR,” in Proc. IET Int. Radar Conf., Xi’an, China, Apr. 2013, pp. 1–6. [14] F. Feng, S. Li, W. Yu, and S. Wang, “Study on the processing scheme for space-time waveform encoding SAR system based on two-dimensional digital beamforming,” IEEE Trans. Geosci. Remote Sens., vol. 50, no. 3, pp. 910–932, Mar. 2012. [15] M. Süß and W. Wiesbeck, “Side-Looking Synthetic Aperture Radar System,” EP Patent EP 1 241 487, Sep. 18, 2002.
