A Mathematical Model for Designing a Multiple MTI

Transcription

1 Int. J. Contep. Math. Sciences, Vol. 5, 200, no. 5, A Matheatical Model or Designing a Multiple MTI Filter Using MIMO Radar Signals Waleed Khalid College o Engineering, Al-Mustansiryha University, Baghdad, Iraq Ali Khalid Jassi College o Engineering, Al-Mustansiryha University, Baghdad, Iraq alianar2004@yahoo.co.in Abstract A ground clutter cancellation in ulti-channel noise radar is presented. The radar syste under consideration consists o independent noise transitters working in the sae requency band and n receivers. Independent cancellation o clutter echoes originating ro successive transitters is not ully eective thereore joint cancellation o all clutter echoes is proposed. MIMO (Multiple-input ultiple-output) extensions radar systes are enable to nuber o advantages copared to traditional approaches. These advantages include iproved angle estiation and target detection. Keywords: MIMO Radar, Linear Frequency Modulation, waveor design, Matheatical odeling Introduction The ter noise radar reers to a group o radars using a rando waveor or target illuination [, 2]. This type o radar can be used in a relatively wide range o applications. It is possible to construct surveillance, iaging [3], tracking, guidance, collision warning, subsurace and other types o radar using a noise waveor. Noise

2 2538 Waleed Khalid and Ali Khalid Jassi radars have several advantages over classical pulse, pulse-doppler and FMCW radars. Literature survey o a noise waveor ensures the absence o range and Doppler abiguity and low peak power. One o the crucial probles o the noise radar is the asking eect [4, 5, 8], which consists in hiding weak target echoes in the side lobes o strong returns ro clutter and near targets. This proble can be solved by using adaptive ethods or strong echoes cancellation [6, 7]. Current research on the noise radar is ocused on two ain conigurations: ultistatic (netted) coniguration and MIMO (ultiple output ultiple inputs) coniguration. The concept o netted noise radars oring a ence along a border has been proposed in [9]. The noise MIMO radar has been described in [0]. In the case when all netted or MIMO transitters are eitting signals in separated bands there is no intererence between the and the whole signal processing can be perored as in a ono-static noise radar. However, requency resources are very valuable and it is diicult to allocate separate requency bands or each transitter, especially when using wideband signals. An alternative solution is to transit independent noise waveors ro each transitter using the sae requency band. For ininite transitting tie, the transitted noise signals are orthogonal to each other. However, or liited tie intervals soe correlations between the signals have been presented. It degrades the perorance o the whole syste. It is possible to orthogonally the inite-length signals beore transission; however, tie-delayed and Doppler shited versions o those signals will be correlated. The lack o orthogonally between received coponents originating or dierent transitters decreases the sensitivity o the syste, especially in the case o strong ground clutter, which can copletely ask weak echoes o oving targets [, 2]. This paper presents an eective ethod o ground clutter reoval in ultistatic or MIMO noise radars. The clutter reoval procedure utilizes a ulti-diensional lattice predictor or signal orthogonalisation. The received signal is then projected onto orthogonalised clutter subspace. Fig.. Syste concept or = 3 transitters and n = 3 receivers.

3 Model or designing a ultiple MTI ilter Syste concepts It is assued that the signal eitted by the radar is band-pass continuous noise. There are K transitters and L receivers in the syste, located in dierent positions. The transitters send independent noise signals x (t) in the sae requency band. The receivers have access to the signals y (t), y 2 (t)... n sent by all transitters. This can be achieved by the use o a separate channel with an antenna directed towards the transitter or by transission o the signal saples by a coputer network. The concept o the syste or = 3 and n = 3 is presented in Fig.(). The signal received by the n-th receiver originating or the -th transitter can be expressed by the ollowing orula: Q R P q R p V p Y = + j t n, ( t) aq X t bp X t exp 2D () q= C P C λ where x (t) is the signal transitted by the -th transitter, a q, bp are the coplex signal aplitudes, R q, R p are the biostatic ranges, V p is the target biostatic velocity, λ is the wavelength, Q is the nuber o stationary targets, P is the nuber o oving targets. The irst ter on the right-hand side o equation () corresponds to the relections ro stationary targets. The second ter represents contributions ro oving targets. The signal received by the nth receiver coprises contributions or each transitter and it can be expressed as ollows: M Yn ( t) = Yn, ( t) + W ( t) (2) = where w(t) is an additive white Gaussian noise odeling environent and receiver noise. The detection procedure is based on the atched iltering concept. In order to take into account dierent Doppler shits o target echoes, a bank o ilters is used, in which each ilter is atched to a dierent requency shit: * R V ψ, n ( R, V ) = Yn ( t) X t exp j2d t dt (3) C n λ The signal x (t) correlates only with the corresponding ter y (t), n o the signal y n (t). However, signals originating ro other transitters act as additional noise sources. This causes the raise o the noise loor on the range-doppler surace calculated by (3), which leads to the reduction o syste sensitivity. In addition, the returns ro stationary targets, i.e. clutter, can ask weaker oving targets.

4 2540 Waleed Khalid and Ali Khalid Jassi 3 Algorith Description A single channel ground clutter reoval can be achieved using a standard intererence canceller based on the Wiener iltering theory, well described in [3, 7]. According to the general structure o the canceller, the clutter estiate is subtracted ro the received signal in order to obtain an estiate o the desired non-zero Doppler echo. The clutter estiate, in turn, is obtained at the output o a linear ilter excited by the reerence signal. This ilter can be realized either as a transversal ilter or as a well known joint process estiator. The joint process estiator consists o two parts [3, 7]: a lattice predictor and a linear cobiner (regression ilter). An iportant eature o the lattice predictor is that it ay be viewed as an orthogonalisation transor. Feeding the input o a ultistage predictor with the sequence o saples o the reerence signal, a corresponding sequence o orthogonal backward prediction errors at the output o each stage is obtained. Prediction errors are then used by a linear cobiner to reove the intererence ro the received signal. The act that they are orthogonal to each other sipliies the solution to the proble o inding optial coeicients o the linear cobiner. This idea o clutter reoval was presented in [5, 8] in context o the noise radar and FM radio-based radar, respectively. In both publications the intererence canceller was ipleented as a single channel (scalar) joint process estiation ilter. In the case o ultiple sources considered in this paper, the useulness o such solution is restricted since the single channel version o the joint process estiator can be applied only to each single channel independently instead o joint reoval ro all channels. For this reason, eective clutter suppression in radar syste with ultiple sources requires the use o the ulti-channel version o the joint process estiation ilter. The ulti-channel lattice prediction algorith has the ollowing or [3]: + ( n) = ( n) Γ+ b ( n ) (4) b b + ( n) = b ( n ) Γ+ ( n) (5) where (n), b (n) denote orward and backward prediction errors (M vectors) at the output o the -th stage. The (M M) atrices o PARCOR (Partial b Correlations), coeicients Γ +, Γ + and the (M M) covariance atrices P, the prediction errors are deined as ollows: H b Γ = E ( n) b ( n P (6) [ ][ ] + ) P o b Γ H [ ( n ) ( n ][ P ] b + = E b ) b b P b + = I Γ + Γ + P (7) (8)

5 Model or designing a ultiple MTI ilter 254 b P + = I Γ+ Γ + P (9) The recursions (4) (9) are repeated in a loop or = 0 to M with initial conditions: T n) = b ( n) = X ( n) = [ X ( n), X ( n)... X ( n)] (0) o ( o 2 b = Γ = R xx (0) Rxx () b b P = ( I Γ Γ ) Rxx (0) X (n Γ () P = (2) where ) are sapled versions o the transitted signals and, H R ( ) = E[ X ( n) X ( n )] (3) xx is the (M M) autocorrelation atrix o the vector reerence signal. To coplete the joint process estiation, the coeicients o the linear cobiner are deterined and calculated or = 0 to M: b H h ( n) = [ P ] E[ b ( n) e ( n)] (4) H ( n) = e ( n) h b ( n e + ) (5) * For =0, the e o ( n) = Y ( n) and h ( n) = [ R ( n)]. E[ X ( n). Y ( n)] o xx where Y l (n) is the sapled version o the signal received by the n-th receiver. The inal estiate o the non-zero Doppler echo ro () is given by e +! (n), i.e. the output o the linear cobiner. The expectation E[ ] in the above orulas is replaced in calculations by a saple ean. Fig.(2), depicts a block diagra o the lattice joint process estiator used or ground clutter reoval. l Fig.2. Joint process estiator

6 2542 Waleed Khalid and Ali Khalid Jassi 4 Siulation Results The algoriths presented in this paper were tested by eans o coputer siulations. The transitted signal was a band liited Gaussian noise. The targets were siulated by adding tie-delayed and Doppler shited versions o the transitted signal to the received signal. The sapling requency was equal to 200 khz and the length o the signal blocks was equal to The range-doppler suraces were obtained by correlating appropriate signals using (3). Beore correlation a Haing window was applied to the signals in order to reduce side lobes. In the irst siulation scenario, it was assued that there are three transitters and one receiver. Soe stationary targets were present to siulate ground clutter. In addition, three oving targets were siulated. The environent and receiver noise were neglected. The results presented below were obtained or the irst channel but the results o processing o other channels are coparable. The values o the correlation were clipped at the ean noise loor level. In the igure, only ground clutter at zero Doppler requency is visible. The noise loor level is approxiately at 30 db (arbitrary scale). To reove zero Doppler coponents, the single-channel lattice ilter was used. The input o this ilter was the signal ro the irst transitter x (t). The echoes originating ro ground clutter were reoved and the noise loor level was decreased to 28 db. However, the oving targets still cannot be observed, because the signals ro other transitters present in the easureent signal y (t) keep the noise loor at a high level. In the next step, a single-channel lattice ilter was used to reove signals originating ro all transitters separately. This led to urther reduction o the noise loor to the level o ( 5 db). The siulated oving targets start to be visible. However, the lattice ilters did not reove zero Doppler coponents copletely because were used independently or each channel. The use o the ulti-channel lattice ilter described in this paper yielded the results. The ground clutter was reoved copletely and the noise loor level was reduced to -24 db. The siulated oving targets are clearly visible above the noise loor. In the second siulation scenario, the inluence o the nuber o transitters on the radar detection perorance was investigated. The received signal consisted o the signals originating ro all transitters and additive noise. The signals generated by the transitters contained zero-doppler coponents representing clutter. The power o each o those signals was the sae. Additional noise siulating disturbance at the receiver was 40 db below the level o the useul signals. Dierent ethods or clutter cancellation were used in presented situation. Figure (3) below, showed the noise loor level versus nuber o transitters or dierent versions o the cancellation algorith. It can be observed that joint cancellation ethod using ulti-diensional lattice ilter yields constant noise loor

7 Model or designing a ultiple MTI ilter 2543 level independently o the nuber o transitters. The ixed noise loor level results ro the noise added to the independent signal cancellation o each channel causes the noise loor to rise by several dbs in coparison with the ulti-diensional lattice ethod. When clutter reoval ethod is not used, the noise loor level increases steadily as a result o larger nuber o transitters. For ultiple transitters, the noise loor level is siilar to the case without with out clutter reoval procedure. Fig.3. Noise loor level or dierent clutter cancellation ethods versus nuber o transitters 5. Conclusions The presented algorith has been intensively tested on siulated data or dierent ultistatic and MIMO conigurations o the noise radar. The rando Gaussian band liited noise, requency shited to the carrier requency band, has been used as the transitted signal. One-diensional ilters were not able to reove ground clutter copletely. The application o the ultidiensional lattice ilter allows us or better clutter cancellation and detection o weaker targets. The presences o strong targets echoes have also a great ipact on the radar sensitivity. This proble has been pointed out in [0]. Our work shows that ethods described in [0, ] can be extended to ultistatic and MIMO noise radars.

8 2544 Waleed Khalid and Ali Khalid Jassi Acknowledgents. The authors wish to express a sincere thanks to the reerees and to Dr. M K Jasi, University o Nizwa, Sultanate o OMAN or assistance. Reerences [] S.R.J Axelsson, Iproved Clutter Suppression In Rando Noise Radar, Proc. o URSI 2005 Coission F Syposiu on Microwave Reote Sensing o the Earth, Oceans, Ice, and Atosphere, Barza d Ispra, Italy, 20-2 April (2005). [2] S.R.J. Axelsson, On the Theory o Noise Doppler Radar, Proc. IGARSS 2000, Honolulu, July, pp ,(2000). [3] B. Fahrhang-Boroujeny, Adaptive Filters. Theory and Applications, John Wiley & Sons, (998). [4] D. Garatyuk, R. M. Narayanan, Ultrawide-band noise synthetic radar: Theory and experient, IEEE Antennas Propagat. Soc. Int.Syp. vol. 3, Orlando, FL, pp , (999). [5] D.A. Gray, Multi-channel Noise Radar, Proc. O International Radar Syposiu 2006, IRS 2006,, Krakow, Poland, pp ,24-26 May (2006). [6] Liu Guosui; Gu Hong; Su Weiin, Developent o rando signal radars, Aerospace and Electronic Systes, IEEE Transactions, Vol. 35, Issue: 3,, pp , July (999). [7] S. Haykin, Adaptive Filter Theory, Prentice-Hall Inc., (996). [8] G. San Antonio, D R Fuhrann, and F C Roby, MIMO Radar abiguity unctions, IEEE Journal o selected topic in siginal processing, vol pp 67-77, June, (2007). [9] K.S. Kulpa, Z. Czekala, Ground Clutter Suppression in Noise Radar, Proc. Int. Con. RADAR, Tuluse, France, pp. 236, 8-22 Oct., ( 2004). [0] K.S.Kulpa, Z. Czekala, Masking eect and its reoval in PCL radar, Radar, Sonar and Navigation, IEE Proceedings - Volue 52, Issue 3, pp , June (2005).

9 Model or designing a ultiple MTI ilter 2545 [] K.S. Kulpa, Z. Czekala, Short Distance Clutter Masking Eects in Noise Radars, J. Applied Radio Electronics, Vol 4. No. Kharkow, Ukraine,, pp , (2005). [2] S.L. Marple, Digital Spectral Analysis, Prentice- Hall Inc., (987). [3] V.J. Salinen, T. Lensu, P. Eskelinen, S. Mertanen, Noise odulated ultistatic surveillance radar concept, Proc. o International Radar Syposiu 2006, IRS,, Krakow, Poland, pp. 3-34,24-26 May (2006). Received: June, 200