CFAR DETECTION IN MIMO RADARS USING FUZZY FUSION RULES IN HOMOGENEOUS BACKGROUND

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1 CFAR DETECTION IN MIMO RADARS USING FUZZY FUSION RULES IN HOMOGENEOUS BACKGROUND Faycal Khaldi 1 ad Faouzi Soltai 2 1,2 Départemet d électroique, Uiversité des Frères Metouri Costatie Costatie 25, Algeria ABSTRACT I this paper, we propose to use fuzzy fusio rules to improve the performaces of the Cell Averagig Costat False Alarm Rate (CA-CFAR) detector for MIMO (Multiple Iput Multiple Output) radars i homogeous backgroud modeled by a Pareto distributio. We compute the membership fuctio for each idividual detector. The global membership fuctio at the fusio cetre is a combiatio of the membership fuctios collected from idividual detectors usig four fusio rules, amely; the MIN, MAX, algebraic product ad the algebraic sum. By meas of Mote Carlo simulatios, we evaluated the performace of the global system. The obtaied results showed that for a umber of odes equal to four, the performace is the best for a high umber of receivers ad a low umber of trasmitters. For the best case ad i homogeous backgroud, the algebraic product fusio rule gives the best result whe SNR >4 db whereas the algebraic sum is the best whe SNR <4 db for the CA-CFAR. KEYWORDS Radar detectio, MIMO, Fuzzy rules, Homogeeous clutter, CFAR 1. INTRODUCTION A MIMO radar structure is a multi-atea radar system which cosists of usig multiple ateas at the trasmitter ad the receiver. It is therefore a geeralizatio of the cocept of multi-static radars [1]. This techique was first used i commuicatios ad has recetly bee exteded to radars where the received sigals are joitly processed at the multiple receivig ateas. It has the advatage of improvig radar performace, i terms of the regulatio of the false alarm rate ad the maximizatio of the probability of detectio [2]. MIMO radars are, geerally divided ito two types; the coheret MIMO radar co-located ad the statistical MIMO radar widely separated. The statistical MIMO radar takes advatage of the spatial diversity i the trasmit ad receive agles to ehace the detectio performace. The differece betwee the two cofiguratios is the sigal model: For Widely Separated ateas, the spatial properties of exteded targets are exploited while the target is modelled as a poit with o spatial property for coheret MIMO radars [3]. Nataraja Meghaatha et al. (Eds) : NeTCoM, CSEIT, GRAPH-HOC, NCS, SIPR pp , 217. CS & IT-CSCP 217 DOI : /csit

2 96 Computer Sciece & Iformatio Techology (CS & IT) I radar automatic detectio system, the mai goal is to desig a algorithm that set the threshold adaptively to deal with the chagig power of the clutter ad to keep the false alarm rate costat ad at a desired value. The performaces of the CA-CFAR approaches those of the optimum detector if the referece cells are Gaussia, idepedet ad idetically distributed (iid). T R R T T (a) Statistical MIMO R x (b) Coheret MIMO Figure. 1 MIMO radar cocept. I practical situatios, the clutter may ot be homogeeous. This o homogeeity is caused by either the presece of iterferig targets or a exteded clutter edge. I this case, the performace of the CA-CFAR degrades seriously. I order to overcome this problem, several modified versios of the CA-CFAR detector were proposed ad are geerally based o the order statistic techique: the OS-CFAR [4], the GOSCA-CFAR [5], the OSGO-CFAR ad the OSSO-CFAR [6]. Several works dealig with target detectio i MIMO radars i the Neyma-Pearso sese [7, 8] or usig the Geeralized Likelihood Ratio [9] have bee reported i the literature. I [1], Jaatia geeralized the CA-CFAR, the SO-CFAR, the OS-CFAR ad the ACMLD (Automatic Cesored Mea-Level Detector) for a Gaussia backgroud. Widely Separated MIMO radars were used i homogeeous ad o-homogeeous clutter (presece of iterferig targets). Usig INGARA database, Weiberg [11] showed that the Pareto distributio offers a good fittig performace as a model for high-resolutio high-grazig agle sea clutter. This paper deals with the aalysis of the performace of Widely Separated MIMO radars where the idividual detectors are the CA-CFAR detector. Istead of usig biary fusio rules, we propose to exted this techique to the use fuzzy fusio rules at the fusio cetre. The clutter is assumed to follow a Pareto distributio. The rest of the paper is orgaized as follow: sectio 2 describes the sigal model i MIMO radars. I sectio 3, we aalyze the fuzzy CA-CFAR detector i MIMO radars i a Pareto clutter. The results cocerig the performace of the MIMO structure i homogeeous clutter are preseted ad commeted i sectio 4 ad followed by some cocludig remarks i sectio 5.

3 Computer Sciece & Iformatio Techology (CS & IT) SIGNAL MODEL IN MIMO RADARS The structure uder cosideratio is a MIMO radar system that has M trasmit ateas ad N receive ateas. The ateas are assumed to be widely separated as show i Fig. 1.a. It is also E M sm t, where E is the total trasmitted assumed that the m th trasmitter delivers a sigal ( ) 2 power ad sm ( t ) 1. That is, systems with a reduced umber of odes (couples Tx-Rx) have a icreased available power per ode. I other words, each of the M trasmitters provides a power equal to M E. The th received sigal is modelled as follows: r m, ( t) ( ) s t + e ( t) M m 1 R α m, σ m. (1) c Where s m (t) is the m th trasmitted sigal, e(t) is a additive thermal oise, α m, is a complex coefficiet icludig the amplitude ad the phase of the received sigal ad is give by the followig expressio. E M G G t σ π exp j 2 rλ 2 R m m, ( ) π R R λm m. (2) If the trasmitted waveforms are assumed to be orthogoal i such a way that they ca be separated i each receiver, the received sigal after the matched filterig ca be expressed as: q m, m, + m, α. (3) The MIMO radar detectio problem ca be formulated i terms of the biary hypothesis test as follow:, Q α +, Uder hypothesis H, the target is declared abset i the received sigal ad the sigal is costituted of clutter oly. Uder hypothesis H 1, a is target declared preset ad the received sigal is the sum of both target ad clutter sigals. The classical Neyma-Pearso detector uses the Likelihood ratio test ad is give by: ( q H1) ( q H ) P T ( q ) Log γ. (4) P Where P(q H 1 ) ad P(q H ) are the probability desity fuctios of the observatio vector uder the hypothesis H 1 or H respectively. The threshold γ is determied by a prescribed probability of false alarm. The Likelihood ratio test i (4) is equivalet to the followig test [2]: H H 1. 2 Q γ. (5) Where Q is the matched filter output of the cell uder test (CUT). For a CA-CFAR detector, Q 2 is the sum of the CUT powers, γt*z is the detectio threshold, Z is the oise power level estimatio ad T is a factor that adjusts the P fa at a desired value.

4 98 Computer Sciece & Iformatio Techology (CS & IT) The structure of the received data is show i Fig. 2. The rage gatig method is employed i oly oe agular-resolutio cell (Fig. 2.a). Each receiver ca sese the echoes of all trasmitters ad therefore, this structure ca be formulated as a matrix with M*N colums ad each colum cotais a CUT (grey cells) plus 2*L referece cells as show i Fig. 2.b. (a) MIMO radar resolutio cells (b) MIMO radar simplified cofiguratio Figure 2 MIMO Radar Cocept 3. FUZZY CA-CFAR DETECTOR FOR MIMO RADARS 3.1. Fuzzy CA-CFAR Detector i Pareto Clutter A block diagram of the fuzzy CA-CFAR detector uder cosideratio is show i Fig. 3.The received sigal is sampled i rage by the rage resolutio cells. The statistics which is the membership fuctio is compared to a threshold to decide about the presece or the absece of a target. The clutter is assumed to be modeled by a Pareto distributio which is defied as follows: (6) Where α is the shape parameter ad β the scale parameter. I the CA-CFAR detector, the membership fuctio to the false alarm space is give by [12 ]

5 Computer Sciece & Iformatio Techology (CS & IT) 99 > / (7) Where ad Evelope Detector (8) : : ; L Q β µz L Q C A ( B β T FC or H 1 Figure. 3 Block Diagram of the fuzzy CA-CFAR detector Sice the clutter obeys to a Pareto distributio, it was show that the followig trasformatio leads to a expoetial distributio "# (9) Where follows a Pareto distributio with parameters α ad β, $ %," ad X ( follows a expoetial distributio with parameter α,,) #* % The decisio rule cocerig a fuzzy CA-CFAR detector is give by [ ] : ) - 1 /1 / /1 / >2 <2 Usig the trasformatio i (9), the decisio rule becomes : - /1 / /1 / >2." 8 <2." 8 5 (11)

6 1 Computer Sciece & Iformatio Techology (CS & IT) The membership fuctio to the false alarm space is the GHI J " DEF GHI >2 / C 12 " J Usig the results i [12], the membership fuctio reduces to Fuzzy Fusio Rules i MIMO Radars The umber of fuzzy decisios (D 1, D 2,..., D MN ) is equal to the umber of odes M.N where M is the umber of trasmitters ad N is the umber of receivers. Each ode trasmits its membership fuctio to the fusio cetre where a global membership fuctio NO is derived. The fuzzy fusio rules cosidered i this work are MIN, MAX, Algebraic sum ad Algebraic product. 1) The MIN fusio rule The membership fuctio at the fusio cetre, µ NO is defied as NO PQR S,, ST,. SUV (14) The correspodig threshold at the fusio cetre is [12] 2) The MAX fusio rule For this rule, µ NO is defied as 2 NO 1 1 $ UV (15) NO PX) S,, ST,. SUV (16) The correspodig threshold at the fusio cetre is [12] 3) The Algebraic sum fusio rule 2 NO $ UV (17) Followig the same reasoig as previously, µ NO is foud to be [\ NO 1 Y1 S/ Z (18) The correspodig threshold at the fusio cetre is obtaied from the $ expressio [13] ΓY]^,8A_ 8`abZ $ 1 [\8! (19)

7 Computer Sciece & Iformatio Techology (CS & IT) 11 4) The Algebraic product fusio rule I this case, µ NO is defied as [\ NO Y1 S/ Z (2) The correspodig threshold at the fusio cetre is obtaied from the $ expressio [13] $ ΓY]^,8A_ 8`ab Z [\8! (21) 4. RESULTS AND DISCUSSIONS To demostrate the effectiveess of usig fuzzy fusio rules i a MIMO structure, we used Mote-Carlo simulatios to assess the detectio probability (P D ) as a fuctio of the sigal-toclutter ratio (SCR). We assume that the umber of referece cells is L16, the desig P fa is equal to 1-4 ad the clutter is homogeeous. We also assume that the umber of odes MN is equal to 4 with three differet cases (M4 ad N1, M2 ad N2, M1 ad N4). For the four fusio rules cosidered, the thresholds at the fusio cetre are calculated usig expressios (15), (17), (19) ad (21). Fig. 4 shows the detectio performace with respect to M ad N. It is clear that the highest P D is obtaied for M1 ad N2. I geeral, the performace icreases as the umber of receivers icreases. Figure. 4 CA-CFAR i MIMO radars with MIN, MAX, algebraic product ad algebraic sum fuzzy fusio rules i homogeous backgroud i cases (M1, N4), (M2, N2) ad (M4, N1) Next, we compare the performace of the for fusio rules for the case of M1 ad N4. We observe that the Algebraic product fusio rule gives the best results for a SCR > 4 db ad the MIN fusio rule has comparable performace as the latter SCR > 15 db.

8 12 Computer Sciece & Iformatio Techology (CS & IT) Figure. 5 CA-CFAR i MIMO radars with MIN, MAX, algebraic sum ad algebraic product fusio rules i homogeous backgroud 5. CONCLUSIONS I this paper, we evaluated through Mote-Carlo simulatios, the performace of a MIMO radar where each detector is costituted of a fuzzy CA-CFAR detector. At the fusio cetre, the membership fuctio to the false alarm space from all detectors are received ad combied accordig to four fuzzy fusio rules. Differet values of the umber of trasmitters ad receivers were cosidered. The simulatio results demostrated clearly that the highest probability of detectio is attaied whe the umber of receivers icreases. I additio, the best performace was provided by the Algebraic product fuzzy fusio rule ad the MIN fusio rule for high SCR. REFERENCES [1] J. Li ad P. Stoica, MIMO Radar Sigal Processig, Wiley, New Jersey, 29. [2] E. Fishler, et al., Spatial diversity i radars- models ad detectio performace, IEEE Trasactio o Sigal Processig, vol. 54, o. 3, pp , 26. [3] C. Y. Chog, Sigal Processig for MIMO Radars: Detectio uder Gaussia ad o-gaussia eviromets ad applicatio to STAP, Ph.D. thesis, Supelec, Frace, 211. [4] H. Rohlig, Radar CFAR thresholdig i clutter ad multiple target situatios, IEEEE Trasactios o Aerospace ad Electroic Systems, vol. 19, o. 4, pp , [5] H. You, Performace of some geeralized modified order statistics CFAR detectors with automatic cesorig techique i multiple target situatios, IEE Proceedigs, Radar, Soar ad Navigatio, vol. 141, o. 4, pp , [6] A.R. Elias-Fuste, M.G. DE Mercado, ad E.R. Davo, Aalysis of some modified order statistics CFAR: OSGO ad OSSO CFAR, IEEE Trasactio o Aerospace ad Electroic Systems, vol. 26, o. 1, pp , 199.

9 Computer Sciece & Iformatio Techology (CS & IT) 13 [7] C. Y. Chog, F. Pascal, J.P. Ovarlez, ad M. Lesturgie, MIMO Radar Detectio i No-Gaussia ad Heterogeeous Clutter, IEEE Joural of Selected Topics i Sigal Processig, vol. 4, o. 1, pp , 21. [8] G. Cui, L. Kog, ad X. Yag, Multiple-iput multiple-output radar detectors desig i o- Gaussia clutter, IET Radar, Soar ad Navigatio, vol. 4, o. 5, pp , 21. [9] J. Liu, Z. J. Zhag, Y. Cao, ad S. Yag, A closed-form expressio for false alarm rate of adaptive MIMO-GLRT detector with distributed MIMO radar, Sigal Processig, vol. 93, pp , 213. [1] N. Jaatia, M. Modarres-Hashemi, ad A. Sheikhi, CFAR Detectors for MIMO Radars, Circuits Systems ad Sigal Processig, vol. 32, o. 3, pp , 213. [11] G.V. Weiberg, Assessig Pareto fit to high resolutio high grazig agle sea clutter, Electro. Lett., 211, 47, (8), pp [12] Z. Hammoudi, F. Soltai, Distributed CA-CFAR ad OS-CFAR detectio usig fuzzy space ad fuzzy fusio rules, IEE Proceedigs Part F Vol. 151 (3) (24) [13] H. A. Meziai, F. Soltai, Decetralized Fuzzy CFAR Detector i Homogeeous Pearso Clutter Backgroud, Sigal Processig Elsevier, Vol. 91 (211), AUTHORS Faouzi Soltai was bor i Costatie Algeria i October He received the Egieer degree from Algiers Natioal Polytechic i 1985, the MPhil (Eg) degree from Birmigham Uiversity (UK) i 1989 ad the Doctorat d état degree from Costatie Uiversity i 1999 all i Electroic Egieerig. He joied the departmet of Electroic Egieerig of Costatie Uiversity i 1989 as a assistat professor the as a full professor i 24. He is the head of Sigals ad Commuicatio Systems research laboratory. His mai research iterests iclude radar CFAR detectio, estimatio theory, eural etworks ad clutter modelig. Faycal Khaldi received his Master degree from Medea Uiversity, Algeria i 213. He joied Costatie uiversity as a PhD studet where he is workig o MIMO radar sigal processig i homogeeous ad o homogeeous clutter.