7 Asia-Pacific Engineering and Technoogy Conference (APETC 7) ISBN: 978--6595-443- A Nove Method for Dopper and DOD- DOA Jointy Estimation Based on FRFT in Bistatic MIMO Radar System Derui Song, Li Li, Jiani Zhang, Xindi Jing and Xianghai Wang ABSTRACT *This paper studies the probem of parameter estimation jointy in bistatic Mutipe-Input Mutipe-Output (MIMO) radar system. For moving target, the echo often contains time-varied Dopper frequency. Thus, this paper proposes a new signa mode and a nove method for parameter estimation in bistatic MIMO radar system. Firsty, an extended signa mode is presented in bistatic MIMO radar. Secondy, two Dopper parameters are jointy estimated by searching the peak of the fractiona correation function. Finay, MUSIC agorithm and ESPRIT agorithm are used to estimate DODs and DOAs. Simuation resuts are presented to verity the effectiveness of the proposed method. INTRODUCTION Mutipe-Input Mutipe-Output (MIMO) system has attracted more and more attention for its abiity to enhance system performance [-4]. A MIMO radar system consists of both transmit and receive sensors. Transmit antennas emit orthogona waveforms whie echoes are orthogona, thus separabe, at the receiver. MIMO processing may be performed to achieve spatia and signa waveform diversity. The muti-target parameter estimation and ocaization is one of the most important aspects in bistatic MIMO radar. Most existing agorithms are divided into two categories. One ignores Dopper frequency and ony estimated DOA and DOD as shown in [-4]. The other estimates not ony DOA and DOD but aso timeinvariant Dopper frequency. In fact, the received signas contain time-variant Dopper frequency. In this case, these existing methods cannot effectivey sove this probem and provide an optima soution. So, this paper presents a new signa mode with time-variant Dopper frequency and proposes a new method based on FCF to estimate Dopper, DOD-DOA. Derui Song,, Li Li 3*, Jiani Zhang, Xindi Jing and Xianghai Wang Schoo of Urban and Environmenta Sciences, Liaoning Norma University, Daian 69, China Nationa Marine Environmenta Monitoring Center, Daian, 63, China 3 Information Engineering Coege, Daian University, Daian, 66, China Corresponding author: ffsimpe@63.com 39
THE PROPOSED SIGNAL MODEL We assume that there are Q cosey spaced transmit antennas and N cosey spaced receive antennas, and L targets. Fig. iustrates a bistatic MIMO radar system, with haf-waveength space between adjacent eements used for both transmit array and receive array. The transmit antennas emit orthogona waveforms xq t for q,..., Q. This paper proposes a new signa mode of bistatic MIMO radar system. The received signa from the n th antenna y ( n t ) n,..., N can be expressed as L Q y t x t exp j f t t A B w t, t T () n q q n n q Figure. Bistatic MIMO radar system. where denotes the radar cross-section corresponding to the th target. f and denote the initia Dopper frequency (IDF) and Dopper frequency rate (DFR) corresponding to the th target, respectivey. Aq( ) exp j q dt sin is the transmitter steering vector, Bn( ) exp j n d r sin is the receiver steering vector. The noise wt () is assumed to be independent, zero-mean Gaussian white noise. Since the transmitted waves are orthogona with each other, there are x, x, q k and q k q x, for k,..., Q and q,..., Q. At each receiving antenna, these orthogona waveforms can be extracted by Q matched fiters. The extracted signas from the q th matched fiter can be expressed as L y t exp j f t t A B w t, t T () qn, q n n FRACTIONAL CORRELATION FUNCTION In recent years, a new time-frequency anaysis too, the Fractiona Fourier transform (FRFT) [5-7], attracts increasingy more attention in signa processing society and is widey appied in detection, parameter estimation and direction of arriva estimation. Assume that the signa s() t is modeed as st () bexp j at at (3) where b is the signa ampitude, a is the initia frequency and a is frequency rate. 3
Fractiona correation function (FCF) Rˆss of the signa s() t is defined by R ˆ im, exp cot T ss T ss T T (4) where Rss t, t is the correation function of the signa st, denotes time deay, and is the rotation ange in FRFT domain. With the use of (3), (4) can be expressed as R ˆ im exp cot exp T ss T T j a t j a a T (5) When cot a, R ˆ ss has the best energy-concentrated property. Therefore, we can obtain the foowing expression as arc cot a (6) JOINT PARAMETER ESTIMATION BASED ON FRACTIONAL CORRELATION FUNCTION In this section, study of parameter estimation is made by taking the signa yqn t as an exampe. The signa yqn t denotes the extracted signas yqn t corresponding to the th target. t can be expressed as yqn exp y t j f t t A B w t (7) qn q n n According to (5) and (7), the fractiona correation of yqn R ˆ yy, qn im,, exp cot T T R t t jt dt T,, ( )[ ( )] where yy qn qn qn t can be written as T yy qn (8) R t t E y t y t. When cot, R ˆ yy, qn has the best energy-concentrated property. Therefore, we can obtain the foowing expression as ˆ cot (9) Define variabe y t as y t y exp j ˆ qn t t () Assumed Ry u as the Fourier transform of y t. So, the IDF f can be estimated by fˆ arg max R u () According to (), (9) and (), both receive subarrays R and R constructed in this paper can be expressed by R T y y... yl BG N () u T q q ql q R y y... y BAG N, (3) B B B, L B T B BN, A diag Aq,..., AqL, g () t g () t... g () t exp ˆ ˆ diag denote where G T L, g t j ft t, T and transpose and diagona matrix respectivey. Spatia spectrum of MUSIC can be got, which can be expressed as P( ) B H H ( ) U U B ( ) (4) N y N 3
Searching spectra peak of P( ), we can get the DOA estimator. H H We define C RRR I BR GGB and C RRR Z BAR GGB, where Z is showed as # # Z. According to C... and C, we can get A B CCB, where # denotes the Moore-Penrose pseudo-inverse. Therefore, the DOD estimator is estimated by arcsin arga q (5) where a is the eement of the principa diagona of matrix A, arga stands for the phase of a. SIMULATION RESULTS The considered bistatic MIMO radar is composed of Q 4 transmit antennas and N 6 receive antennas. Supposed the target ocates at the positions, (3, ),, (6,5 ) and Dopper parameters are f 8,., f, respectivey. The number of snapshots is. The number of Monte Caro iterations is 5 in a simuations. In the foowing simuation experiments, we study the resoution capabiity and estimation accuracy of the proposed method, Parae factor (PARAFAC) method [3] and ESPRIT using the rotationa factor produced (RFP-ESPRIT) method [8]. Simuation : Signa to Noise Ratio Fig. depicts the root-mean-square error (RMSE) as a function of Signa-to- Noise Ratio () when M. From Fig., we find that the performance of the proposed method is significanty better than that of the PARAFAC method and RFP-ESPRIT method. RMSE of Dopper Parameters Estimation(dB) - - -3-4 - -5 - -5 5 5 5 3 f f RMSE of Dopper Frequency Estimation (db) 3 5 5 5-5 - -5 Proposed method target Proposed method target PARAFAC target PARAFAC target RFP-ESPRIT target RFP-ESPRIT target - - -5 - -5 5 5 5 3 (a) (b) Figure. RMSE of Dopper parameters estimation (a) and Dopper estimation (b) versus. Fig.3 shows RMSE curves for DODs and DOAs estimation of the proposed method, the PARAFAC method and RFP-ESPRIT method versus. In this simuation, and are set. As we can see, the proposed method gives better performance than the PARAFAC method and RFP-ESPRIT method in the condition of ow. From these figures, we aso find that the estimation performance of the Dopper frequency parameters affects the estimation performances of the DOD and DOA. 3
Fig.4 iustrates the scatter grams of the DOAs and DODs estimated by the proposed method, the PARAFAC method and RFP-ESPRIT method based on independent trias under the hypothesis that is equa to 7dB and other simuation conditions are exacty the same as those described in Simuation. From Fig.4, we can observe that the proposed method provides a more precise ocation estimate than the PARAFAC method and RFP-ESPRIT method. RMSE of DOD( ) 6 5 4 3 Proposed Proposed PARAFAC PARAFAC RFP-ESPRIT RFP-ESPRIT RMSE of DOA( ) 7 6 5 4 3 Proposed Proposed PARAFAC PARAFAC RFP-ESPRIT RFP-ESPRIT - -5 - -5 5 5 5 3 - -5 - -5 5 5 5 3 (a) (b) Figure 3. RMSE of the DODs (a) and DOAs (b) estimation versus. Simuation : The estimated resut of DOAs and DODs 9 8 7 Proposed method PARAFAC RFP-ESPRIT 6 DOA( ) 5 4 3 3 4 5 6 7 8 9 DOD( ) Figure 4. Location estimation resut of two targets. CONCLUSIONS For moving target, the echo often contains time-varied Dopper frequency which resuts in difficuties in the parameters estimation. Thus, this paper proposes a nove method for estimating time-varied Dopper frequency and DOD-DOA in bistatic MIMO radar system. Firsty, Dopper parameters are estimated by the fractiona correation agorithm. Secondy, two subarray modes are constructed and two agorithms are presented to estimate DOD and DOA. Simuation resuts demonstrate that the proposed method sti has good performance when poor condition exists. The next step of research focus is how to improve the performance of parameter estimation in the impusive noise environment. This work was party supported by the Nationa Science Foundation of China under Grants 6455, and the Pubic science and technoogy research funds projects of ocean under Grants 5. The authors aso gratefuy acknowedge the hepfu comments and suggestions of the reviewers, which have improved the presentation. 33
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