APPLICATION OF COMPLETE COMPLEMENTARY SEQUENCE IN ORTHOGONAL MIMO SAR SYSTEM

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1 Progress In Eletromagnetis Researh C, Vol. 13, 51 66, 2010 APPLICATION OF COMPLETE COMPLEMENTARY SEQUENCE IN ORTHOGONAL MIMO SAR SYSTEM S. F. Li, J. Chen, L. Q. Zhang, and Y. Q. Zhou 201 Lab, Shool of Eletroni and Information Engineering Beihang University Beijing , China Abstrat The Complete Complementary Sequene CC-S) onsists of several omplementary orthogonal sequenes and has optimal sidelobe level performane, whih is satisfied with the requirement of the orthogonal Multiple Input Multiple Output MIMO) radar signals. Aimed at the diffiulty of high sidelobe level in Syntheti Aperture Radar SAR) imaging proessing in range dimension, an approah of depressing sidelobe level based on CC-S in MIMO SAR system was proposed. The transmitter model for orthogonal MIMO SAR system using CC-S and the orresponding mathed filter MF) were established in this paper. In addition, the MIMO SAR imaging results were simulated. The simulation results demonstrate that the performane of CC-S employed in orthogonal MIMO radar system is muh better than that with traditional Linear Frequeny Modulation LFM) signal, by whih the feasibility and validity of CC-S applied in orthogonal MIMO SAR system are justified. 1. INTRODUCTION MIMO radar is a new onept proposed in reent years [1 7]. The waveforms requirements differ between MIMO and multi-hannel antenna system. In MIMO radar, there are several transmitters whih are transmitting multiple orthogonal or non-oherent waveforms and several reeivers whih are reeiving the ehoes refleted by the targets, while the traditional multi-hannel antenna system transmits multiple oherent waveforms in the transmitter. MIMO radar systems are mainly divided into two important ategories. In the first ategory, different transmit and reeive antenna elements are lose to eah other, so that the system an exploit the waveform diversity offered Corresponding author: S. F. Li shufeng 2004@163.om).

2 52 Li et al. by orthogonal signals to ahieve oherent proessing, inrease the degree of freedom and improve the parameter estimation performane. We refer to the system as orthogonal MIMO radar [8 12]. In the seond ategory, transmitter and reeiver elements are far from eah other relative to the transmitted wavelength. In this ase, the MIMO radar system utilizes the widely separated antennas to obtain nonoherent proessing to obtain target detetion and estimation of various parameters [13 16]. The system in this ategory is mostly known as statisti MIMO radar [17 19]. This paper fouses on the MIMO radar based on CC-S whih is ategorized as the orthogonal MIMO radar. Orthogonal MIMO radar transmits orthogonal signal set, and the reeivers extrat the orresponding eho by mathed filter. The design of transmitted signal impats on the orthogonal MIMO radar system performane diretly. In order to onstrit interferene and enhane the target resolution, the signal employed in orthogonal MIMO radar should have good auto- and ross- orrelations, even have ideal orrelation property the sidelobes of aperiod auto- and ross- orrelations are zero). Orthogonal MIMO radar mainly utilizes orthogonal phase oding and orthogonal frequeny oding in preeding literature [20 23]. The sidelobe levels of above two odes will deteriorate the imaging result, while CC-S utilizes the omplementary pair to anel the sidelobe and to improve the imaging quality. The CC-S opens a new diretion for the signal design of orthogonal MIMO radar. The advantage of SAR tehniques is that they are independent of the weather ondition, day and night, whih plays ritial roles in imaging sensors. With the development of the MIMO radar, drawing the onept of MIMO into SAR domain beomes an interest topi for MIMO radar [24 27]. Through a deterministi array and spatial parallel sampling proedure, the problem of motion ompensation was solved in [24]. The orrelation among distribution of transmitter/reeiver antenna, imaging performane and spatial spetral domain filling is analyzed in [25]. The above referenes mainly refer to the ground-based radar. This paper mainly presents the researh of airborne MIMO SAR. The orthogonal signals are required in MIMO SAR system, so exploring the available orthogonal signals determines the pratial appliation of MIMO SAR. The MIMO SAR imaging algorithm based on CC-S is analyzed in this paper. Owing to the zero sidelobe level orrelation funtion of CC-S, the system an obtain the high peak sidelobe level ratio PSLR) and integration sidelobe level ratio ISLR) without depressing sidelobe level, while traditional SAR system aquire the high PSLR through applying

3 Progress In Eletromagnetis Researh C, Vol. 13, window funtion, thus result in the broadening of mainlobe and the derease of the resolution; the MIMO SAR system based on CC-S guarantee the high PSLR and high resolution at the same time. The outline of this paper is arranged as follows: Setion 2 presents the orthogonal signal model of the MIMO SAR and the onept of CC-S. This is done in order to introdue ideas and notation to be used later in imaging algorithm based on CC-S. The reeiver design and mathed filter based on CC-S are proposed in Setion 3. In Setion 4, the imaging results is briefly disussed and displayed via the results of simulation. A summary inluding onlusions is presented in Setion SIGNAL MODEL OF AIRBORNE MIMO SAR The model of MIMO SAR is shown in Fig. 1, where we see that the platform is supposed to fly along the x-axis at height h and veloity v during the onstant altitude aquisition time, the M transmitters and N reeivers of the linear array are equally spaed along the x-axis, where d and l is the inter-element spaing of transmitters and reeivers respetively, θ is the squint angle of the first transmitter, γ is the pith angle, the loation of the target is x T, y T ). When t = 0, the instant slant range between the swath enter 0 and antenna phase enter is R m t) for m-th transmitter and R n t) for the n-th reeiver. z d V θ γ l h R ) m t R ) n t 0 x y Transmitter Array Reeiver Array Figure 1. Model of the antenna array.

4 54 Li et al. At time t, R m t) and R n t) are expressed as follows: R m t) = vt + md x T ) 2 + yt 2 + h2 R n t) = vt + nl x T ) 2 + y 2T + 1) h2 Using a Taylor series expansion, 1) an be written as: ) R m t) R m + md x T R m vt R m md x T ) 2 v 2 t 2 Rm 3 ) 2) R n t) R n + nl x T R n vt R n nl x T ) 2 v 2 t 2 Rn 3 where t T s 2, T s denotes the syntheti aperture time, in expression 2), R m = md x T ) 2 + yt 2 + h2 R + m2 d 2 2mdx T 2R, R n = nl x T ) 2 + yt 2 + h2 R + n2 l 2 2nlx T 2R. Where R = x 2 T + y2 T + h2, under the ondition of far field, the length of antenna an be omitted with the distane between antenna and the target, the 2) an be approximated as: R m t) R + m2 d 2 2mdx T 2R R n t) R + n2 l 2 2nlx T 2R + md x T 1 R md x T ) 2 R vt R nl x T ) 2 + nl x T R vt ) R 3 ) R 3 v 2 t 2 v 2 t 2 3) where R = h/os γ os θ) is the distane between target and the first transmitter, the phase delay during the flying is: φ mn t) = 2π λ [R mt) + R n t)] 4) The Doppler frequeny is: f dmn t)= 1 dφ mn t) md xt = + nl x T 2π dt λr λr 2 λr md x T ) 2 +nl x T ) 2 λr 3 where the Doppler entroid frequeny: f dmn = f dmn t) md xt t=0 = λr The Doppler modulation frequeny: f rmn = f d mn t) t=0 = ) v ) v 2 t = f dmn +f rmn t 5) + nl x T λr 2 λr md x T ) 2 + nl x T ) 2 λr 3 ) v 6) ) v 2 7)

5 Progress In Eletromagnetis Researh C, Vol. 13, The next will introdue the model of transmitted signals. We assume that the M transmitting signal is in the same frequeny, meeting the orthogonality, the m-th signal is s m τ), define the orrelation funtion by: { s m τ)s 1, m = n nτ)dτ = 8) m,n, m n where τ is the fast time, m,n denotes the ross-orrelation value of different transmitted signals, if the ondition m,n 0m n) is satisfied, the transmitted signals are orthogonal. There are no omplete orthogonal signal in the single ode field, while the CC-S meet the ondition of orthogonality, and need the multiple hannels in the pratial appliation. Thus we employ the CC-S in the MIMO SAR system for exploiting the above property to analyze the MIMO SAR imaging based on CC-S. We will present the onept of CC-S in the next setion. Definition 1 Supposing that {A m, B m } onsists of M pairs of omplementary sequene, the length of A m and B m is L. {A m, B m } is alled CC-S if both the following orrelation funtion onditions are satisfied: i) For every i = 1, 2,..., M, it holds that { 2L τ = 0 R Ai A i τ) + R Bi B i τ) = 0 τ = ±1, ±2,..., ±L 1) ii) For every 1 m, n M, m n, it holds that R Am A n τ) + R Bm B n τ) = 0 τ = 0, ±1, ±2,..., ±L 1) 10) where R Am A n τ) denotes the aperiod orrelation funtion between A m and A n, and R Bm B n τ) denotes the aperiod orrelation funtion between B m and B n. The 9) desribes the auto-orrelation funtion ACF) and 10) shows the ross-orrelation funtion CCF) of the CC- S respetively. The orthogonal MIMO radar transmitter model based on CC-S is shown in Fig. 2. From Fig. 2, we an see that A m and B m 0 m M) onstitute a omplementary pair, T denotes the delay time, and f is the arrier frequeny. {A m, B m } is given as: { Am = a 0 m, a 1 m,..., a L 1 9) The definition of M pairs of omplementary sequene m ) B m = b 0 m, b 1 m,..., b L 1 m ) 11) where {A 0, B 0 ), A 1, B 1 ),..., A M, B M )} meet the omplete orthogonality and make up a family of CC-S. A m and B m are transmitted in

6 56 Li et al. CC-S A 0 A 1 A 2 A M-1 f f f f.. Σ Σ Σ Σ St) 0 St) 1 St) 2 S M-1 Tx 1 Tx 2 Tx 3 Tx M t) Rx 1 Rx 2.. Rx N f T B 0 f T B 1 T B 2 f f.. T B M-1 Figure 2. Transmitter model based on CC-S. m-th antenna by turns, the m-th transmitted signal s m τ) is: L 1 [ ] s m τ)= a l m ret τp τ l T )+b l m ret τp τ T l T ) e j2πf τ l=0 =[s Am τ) + s Bm τ T )] e j2πf τ 12) where T also denotes the pulse repetition time, T is the subpulse time, τ p = L T is the pulse during time, and ret τp t) denotes the retangle window funtion: { 1 0 t τp ret τp t) = 13) 0 else 3. MIMO SAR IMAGING ALGORITHM BASED ON CC-S The system employs the CC-S in MIMO SAR. Due to the omplete orthogonality of CC-S, the range dimension and azimuth dimension an be proessed independently. The range dimension ompression is desribed as following:

7 Progress In Eletromagnetis Researh C, Vol. 13, The Compression of Range Dimension The eho signal y n τ, t) arrived at the n-th reeiver is: M 1 [ y n τ, t)= A r s Am τ R mt)+r n t) )+s Bm τ R )] mt)+r n t) T m=0 ) w a t t ) e j2πf τ Rmt)+Rnt) = y n,am τ)+y n,bm τ T )14) where A r denotes the omplex amplitude of the reeived signal, w a t) is the azimuth envelope, and t is beam enter offset time. The struture of reeiver is shown is Fig. 3. There are M sub-hannels in the reeiver, and the sub-hannel extrats the orresponding eho data by mathed filter. Aimed at the dual ode property of CC-S, the sub-reeiver in Fig. 3 is desribed in Fig. 4. We define: Rm, n) = m2 d 2 + n 2 l 2 2x T md + nl) 2R 15) The eho arrived at the m-th sub-reeiver of the n-th antenna an Rx 1 Rx 2 Rx N e -j2πft e -j2πft... e -j 2πft Groups of MF MF 1 MF MF M MF 1 MF 2 MF M MF 1 MF 2 MF M The Azimuth ompression of MIMO SAR Imaging Results Figure 3. Struture of MIMO radar reeiver.

8 58 Li et al. MF -1 yn,a1 s t) * A1 Σ Z n1 T y n,b1 y nt) s t) * B1. Z n2 y n,am e π -j2 f t s * AM t) Σ Z nm MF-M T y n,bm s * BM t) Figure 4. Sub-reeiver mathed filter based on CC-S. be stated as: t+t y nm τ, t) = y n τ, t) s mτ)dτ t [ t+t M =A r w a t t ) e j2πf R i t)+rnt) s Ai τ) s A m τ)dτ t+t + t =A r 2L δ M i=1 t i=1 ] e j2πf R i t)+r nt) s Bi τ) s B m τ)dτ τ R ) mt) + R n t) w a t t ) e j 2π λ {[2R+ Rm,n)] λ 2 fdmn t λ 4 f rmn t 2 } +A r w a t t ) e [ t+t t M [ sai τ) s A m τ)+s Bi τ)s B m τ) ] i = 1 i m 2R+ i2 d 2 +n 2 l 2 2x T id+nl) j 2π 2R λ + [ ] 1 R id x T ) 2 +nl x T ) 2 v 2 t 2 2R 3 ] ] +[ id+nl 2xT R vt dτ 16)

9 Progress In Eletromagnetis Researh C, Vol. 13, The first part of 16) is the ontribution of auto-orrelation and the seond part denotes the ontribution of ross-orrelation. The omplementary property of {A m, B m } will be used to anel the sidelobe, thus the seond part beomes zero. The 16) an be summarized as: y nm τ, t) = A r 2L δ τ R ) mt) + R n t) w a t t ) e j 2π λ {[2R+ Rm,n)] λ 2 f dmn t λ 4 fr mn t 2 } 17) when m = n = 0, 17) is degenerated as the traditional monostati SAR system. For our purpose, we simplify the onst value as G in above expression, so 17) beomes: y nm τ, t) = G δ τ R ) mt) + R n t) w a t t ) e [jπf dmn t+ 1 2 πf rmn t2 )] 18) How to extrat the sattering funtion of the target from M 1, N 1 {y nm } m, n=0 is a ruial tehnique in MIMO SAR imaging domain The Compression of Azimuth Dimension We an onvert the eho in the range time domain into Range- Doppler domain by Fast Fourier Transform FFT). By using priniple of stationary phase POSP), the time-frequeny expression of azimuth time domain is: f t = 1 2 f d mn + f rmn t) 19) By substituting t = 2f t f dmn )/f rmn into 17), the data after the azimuth FFT an be expressed as: Y nm τ, f t ) = F F T t {y nm τ, t)} = G δ τ R ) mf t ) + R n f t ) W a f t f t ) e j 2π Rm,n) λ e jπ f 2 dmn 2frmn e jπ 2f2 t frmn 20) The azimuth beam pattern, w a t t ), is now transformed into W a f t f t ), with its shape preserved. Combining 19) and 3), the distane funtion beomes: R m f t )+R n f t )=2R+ Rm, n)+f dmn 2f t f dmn f rmn f 2ft f dmn r mn f rmn ) 2 21)

10 60 Li et al. The amount to orret is given by the last two terms in 21): Rf t ) = f dmn 2f t f dmn + 1 ) f rmn 2 f 2ft f 2 dmn r mn 22) f rmn The eho after range ell migration orretion RCMC) beomes: Y nm τ, f t ) = G δ τ 2R + Rm, ) n) W a f t f t ) e j 2π Rm,n) λ e jπ f 2 dmn 2frmn e jπ 2f2 t frmn 23) We an fous the azimuth data through the mathed filter. Aording to the harateristi of MIMO SAR system based on CC-S, there are two sorts of solutions to fous the azimuth data: 1. Every hannel uses Doppler parameter differently to ompress the data in azimuth dimension, thus we an get M N images whih an be utilized for interferometry proessing, lutter aneling and ground moving target indiation GMTI) and so on. 2. We an sum the data after range pulse ompression firstly, and then use the idential Doppler parameter to fous the data in azimuth dimension. The imaging quality using the first solution is muh better than the seond solution due to the different Doppler parameter. The two solutions are losely in the imaging performane under the ondition that the squint angle is small. The seond solution is applied in real-time proessing for the sake of the low omputation. We employ the first solution in this paper. The azimuth referene funtion is expressed by: H nm f t ) = e The data after azimuth pulse ompression is: 2f 2 jπ t frmn 24) y nm τ, t) = IF F T t {Y nm τ, f t )H nm f t )} =G δ τ 2R+ Rm, ) n) w a t)e j 2π Rm,n) λ e jπ f 2 dmn 2frmn e j2πf t t 25) 4. SIMULATION EXPERIMENTS To validate the effetiveness of the proposed MIMO SAR imaging algorithm based on CC-S, we arry out the following experiment. We simulated the 2-Input 2-Output system. The CC-S {A 0, B 0 ), A 1, B 1 )} onstruted in [28] is applied in MIMO SAR system. A 0 and B 0 are

11 Progress In Eletromagnetis Researh C, Vol. 13, transmitted in transmitter 1 by turns, while A 1 and B 1 are transmitted in transmitter 2 by turns. In the antenna geometry defined as Fig. 1, we loate nine point targets whih have the same sattering oeffiient and the geometry parameters: d = 0.5λ, l = 0.5λ, γ = 24, for simplifiation of the MIMO SAR system, we set θ = 90. The key simulation parameters of the MIMO SAR system are listed in Table 1. Table 1. MIMO SAR simulation parameters. Parameter Value Wavelength m Sub-pulse time µs Signal bandwidth 40 MHz Sampling rates 50 MHz Azimuth antenna length 2 m PRF 220 Hz Height 5 km Veloity 120 m/s Syntheti Aperture Time 0.84 s Slant Range km Azimuth antenna beamwidth the ACF of the master pair A0 B0) the sum of the two ACFs the CCF of the omplete omplementary pair A0,B0), A1,B1) real part of CCF of A0,A1) real part of CCF of B0,B1) phase shift figure a) real part of ACF of A0,A0) real part of ACF of B0,B0) normalized phase shift figure a) phase shift figure b) imag part of ACF of A0,A0) imag part of ACF of B0,B0) normalized imag part of the CCF of A0,A1) imag part of the CCF of B0,B1) phase shift figure ) phase shift figure b) Figure 5. Correlation Performane of CC-S.

12 62 Li et al. Table 2. Imaging qualities of point targets of CC-S ase. Targets Azimuth m) Range m) PSLR db) ISLR/dB Azimuth Range Azimuth Range Target Target Target a) Imaging results b) The impulse response Figure 6. Ideal impulse response of point targets. Figure 5 lists the orrelation property of the CC-S {A 0, B 0 ), A 1, B 1 )} and shows the perfet range dimension ompression property. Aording to the imaging algorithm desribed in Setion 3, we an get the imaging results desribed in Fig. 6. We selet three point targets to analyze the imaging qualities. The simulation and analytial results validate the imaging algorithm. Fig. 6b) indiates that the MIMO SAR system based on CC-S satisfies ideal range pulse ompression. Fig. 7 shows that the range impulse response of CC-S and LFM. The range PSLR and ISLR are db and db for the CC-S ase respetively, and db and db for traditional LFM ase. For imaging results, the MIMO SAR system based on CC-S keeps the original theoreti resolution and the o-hannel interferene is aneled. The phenomena an be interpreted as the ontribution of omplete orthogonality of CC-S.

13 Progress In Eletromagnetis Researh C, Vol. 13, a) Range setion plane CC-S) b) Range setion plane LFM) Figure 7. Range impulse response of CC-S and LFM. 5. CONCLUSION This paper establishes the transmitter model of MIMO SAR based on CC-S and proposes orresponding mathed filter. Unlike traditional SAR system whih employs LFM, the MIMO SAR system based on CC-S an depress the sidelobe perfetly and further improve the PSLR and ISLR under the ondition that the resolution keeps the ideal value. The above property enhanes the interferene apability. This paper only disusses the appliation of CC-S in MIMO SAR system. Given that the new system is in infany, there are still some problems whih should be resolved urgently: 1) How to inrease the bandwidth onsidering the pratial hardware and the limit of the Doppler. The above problem mainly restrits the development of the high resolution imaging and GMTI. 2) How to investigate merit and flaw of different imaging algorithms employing CC-S. Solving this problem will be helpful for the whole design of MIMO SAR system. ACKNOWLEDGMENT This work was supported by the Program for New Century Exellent Talents in University, Ministry of Eduation, China Grant No. NCET ).

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