Joint multi-target detection and localization with a noncoherent statistical MIMO radar

Joint multi-taret detection and localization with a noncoherent statistical MIMO radar Yue Ai*, Wei Yi*, Mark R. Morelande and Linjian Kon* *School of Electronic Enineerin, University of Electronic Science and Technoloy of China E-mail: {kussoyi, linjian.kon}@mail.com Melbourne Systems Lab, University of Melbourne, Australia E-mail: mrmore@unimelb.edu.au Abstract In this paper, the problems of simultaneously detectin and localizin multiple tarets are considered for noncoherent multiple-input multiple-output (MIMO) radar with widely separated antennas. By assumin a prior knowlede of taret number, an optimal solution to this problem is presented first. It is essentially a maximum-likelihood (ML) estimator searchin parameters of interest in a hih-dimensional space. owever, the complexity of this method increases exponentially with the number of tarets. Besides, without the prior information of taret number, a multi-hypothesis test stratey on taret number is required, which further complicates this method. Therefore, we split the joint maximization into disjoint optimization problems by clearin the interference from previously declared tarets. In this way, we derive two fast but robust suboptimum solutions which allow tradin performance for a much lower implementation complexity which is almost independent of the number of tarets. In addition, the multihypothesis test detector is no loner required when taret number is unknown. Simulation results show the proposed suboptimum alorithms can correctly detectin and accurately localizin multiple tarets even when tarets share common rane bin in some paths. Keywords noncoherent statistic MIMO radar; maximumlikelihood estimation (MLE); multitaret detection and localization; hih-dimensional estimation I. INTRODUCTION Recently, multiple-input multiple-output (MIMO) radar, whose concept is brouht from wireless communication field, has drawn more and more attention from researchers. Due to the different mode of placement of antennas, enerally MIMO radar can be classified into two cateories. The first cateory co-located MIMO radar with closely spaced antennas is similar to conventional phase array radar []. The second cateory, known as statistical MIMO radar, employs widely separated antennas. It has been shown that contributin to both transmitted waveforms and spatial diversity, statistical MIMO radar can mitiate the performance deradations caused by the radar cross-section fluctuations []-[3], and thus provin both diversity ain and eometry ain leadin to the improvement of localization performance [4]. As for statistical MIMO radar, basically there are two kinds of taret localization methods, one is based on the measurements of the estimated propaated delay or the anle of arrival at the receiver [5], and the other one is based on received radar sinal before detection process for maximumlikelihood estimation (MLE) [6]-[9]. The methods belonin to the latter roup make the most use of taret information, and thus lead to a potentially hiher accuracy especially for weak tarets. Its basic idea is to obtain the estimated location of taret by searchin for the coordinate position that maximize the likelihood ratio based on raw received sinal, in the data plane. These methods are valid under the assumption that there is one and only one taret in the data plane. As for multi-taret scenario, simply expandin the searchin dimension which increases exponentially in the number of tarets is computationally prohibited, otherwise the lobal maximum derades to local maximum, which calls for a detection process to decide the existence of these tarets. Thus, a joint detection and localization alorithm is needed for multi-taret. orri [] has proposed a multiple-hypothesis (M)- based alorithm for multi-taret localization. In [], we attempt to propose a fast multi-taret localization alorithm without multiple hypothesis testin. With the utilization of connected reion, the tarets are localized in parallel in the oriinal dimension of sinle taret and thus reducin complexity. owever, the assumption that tarets are isolated in all the path is not always hold in realistic application and the multi-taret localization performance relies on the settin of threshold which is not simply only a detection threshold but also a key point to separate the searchin rane of each taret. Thus, the difficulty to obtain an appropriate threshold restricts its practical application. This method also requires a stron assumption that tarets are always completely resolved. In this paper, we deal with the problem of multi-taret joint detection and localization for statistical MIMO radar. To this end, we start with an optimal hih dimension localization method based on joint MLE and then derive a suboptimal alorithm by splittin the joint maximization into several

disjoint optimization problems after eliminatin the interference in all the paths from previously declared tarets. This allows information of each taret to be extracted one-byone from the oriinal received sinal minled with information of all tarets, and then performin sinle taret detection at each estimated location. Unlike our previous alorithm in [], the threshold can be obtained based on theory of taret detection and the alorithms declare tarets serially. In addition, they remain efficient without the utilization of multi-hypothesis testin utilized in [] when the prior knowlede of the number of tarets is not available. In the scenario with completely resolved tarets, the proposed alorithm is simplified further. Finally, numerical examples are provided to assess detection and localization performances of the proposed two multitaret localization alorithms. II. MODELS AND NOTATIONS We assume a typical MIMO radar scenario with N t t transmitters located at ( xk, yk),( k =,,..., N), and M receivers r r located at ( xl, y l ), ( l =,,..., M) respectively, in a twodimensional Cartesian coordinate system. The antennas of both transmitters and receivers are widely separated to ensure the space diversity. A set of mutually orthoonal sinals are transmitted, with the lowpass equivalent E Nsk() t, k =,,..., N where E denotes the total transmitted enery for transmit antennas. The focus in this paper is on simultaneously detectin and localizin tarets, therefore only static tarets are considered. Suppose that ( > ) static tarets appear in the radar surveillance reion, with the th taret located at ( x, y ).For convenience, we define a two-dimensioned vector θ of the unknown location of the th taret θ [ x, y ] T () For noncoherent MIMO radar, the received sinal reflected from the th taret at lth receiver due to the sinal transmitted from kth transmitter (defined as the th path) is iven by (Considerin the orthoonality of transmitted sinals, an assumption is introduced that raw sinal has been separated to N channels first, and each channel refers to the sinal transmitted from a certain antenna): E r () t = sk ( t ) n (), t t T N α τ + < < () where the reflection coefficient α = α exp( jβ ) of the th path is a complex random variable. T is the observation time interval. n () t represents additive complex white aussian random noise. The propaation time between the kth transmitter and the lth receiver is τ = ( x x ) + ( y y ) + ( x x ) + ( y y ) c t t r r k k l l (3) with c the speed of liht. Note that, to accommodate the more eneral case of movin tarets, the sinal model with taret velocity taken into account can be found in [6]. After samplin, the continuous sinal of () can be written in a vector form where r = E N α s + n (4) r [ r [], r [],..., r [ N ]] T (5) T [ [], [],..., [ N ]] T (6) T with a samplin interval Ts = T ( NT ), thus the sampled sinal is r[ n] = r ( nts ), [ n] = sk ( nts τ ). Note that is the function of unknown location of taret. The noise vectors n are normally distributed with zero mean and scaled identity covariance matrixσ I. avin taken all the reflections of the tarets into consideration, the vector form of the received sinal of the th path in noncoherent processin is iven below E r n (7) = N α + = where n are mutually independent across different path and normally distributed with zero mean and a covariance matrix R =σ I. III. MULTI-TARET DETECTION AND LOCALIZATION As discussed in [], the MLE of the unknown parameter vector can be found by examinin the likelihood ratio for the hypothesis pair, with correspondin to the taret presence hypothesis and correspondin to the noise only hypothesis. As for multi-taret estimation, the observation vector r is related to the parameters of all tarets ( θ, =,,..., ), thus a hih dimensional parameter vector θ= [ θ T, θ T,..., θ T ] T S is introduced for the joint estimation of all tarets. Before proceedin, it is necessary to introduce the followin Definition which is instrumental to the development of the subsequent alorithms. Definition : Consider a scenario with tarets and a M N MIMO radar, the th ( =,,..., ) taret is said to be completely resolved, if the time difference of arrivin between this taret and any other jth ( j =,,...,, j ) taret in any of the M N paths is larer than the radar effective pulse width. That means, τ τj > τc (8) where τ is the propaation time of th taret between the kth transmitter and l the receiver, and τ c is the effective duration of

the time-correlation of the transmitted waveform sk ( t ), k =,,..., N [] (for example, if a rectanular pulse train is employed, then τ c T p ). Besides, the two tarets and j which satisfy (8) for the th path are referred as two isolated tarets in the th path. Conversely, the th taret is called unresolved if (8) is not satisfied, indicatin that the th taret shares with the jth taret one rane bin in the th path. By parity of reasonin, that any two of the tarets are mutually isolated in each of the M N paths is defined as all the tarets are completely resolved, otherwise is defined as the tarets are partially resolved. Take an M N = MIMO radar as an example, of which each antenna is monostatic, and also receivin sinals transmitted from other antennas. A scenario with two unresolved tarets is plotted in Fi. in which only two of the total four paths are plotted. It shows that the two tarets are isolated in the AA path but unresolved in the BB path. p ( r θ, α, ) p ( r θ, α, ) p( r ) E = exp r R α N = () E + α R r = N E α R α N = = where α is a parameter related to the Radar Cross-Section (RCS) of the th taret, and is unknown before localization in most cases. Thus, the eneral likelihood ratio is utilized to solve the problem [6]. For any θ, the likelihood () is maximized by α l n p ( r θ, α, ) = = (), α αˆ ML To simplify the problem, we consider a scenario with completely resolved tarets first. From Definition and the fact that R is a diaonal matrix, we have (3) R s =, thus () can be rewritten as follows Fi.. Sketch map of a scenario with tarets and a MIMO radar, wherein tarets are unresolved in the BBth path. A. Optimal hih-dimensional method In order to simplify the problem, we assume that the taret number is known before localization. Assumin that represents the sinal presence hypothesis as modeled in (7) and represents the noise-only hypothesis, the likelihood functions of r under additive aussian white noise environment is and E p ( r θ, α, ) = C exp l, k r α = N E R rl, k α = N p( r ) = C exp rl, kr r l, k () where C and C are constants irrelevant to θ. Up to the fact that p( r ) is not a function of θ, the likelihood function is rewritten as likelihood ratio: (9) E p ( r θ α, ) exp{ r R s l, k, α N = E + α = N R r E α R } N = Pluin (4) into (), the ML estimation of α ˆ α ML = R r E R N Substitutin the ML estimation of the likelihood function (4), we have N = σ α and is - (4) (5) R = σ I into E ln p ( r θ, ) r (6) Employin the assumption that n are independent across different paths (indexed by ), the ML joint estimation of locations all the tarets is θˆ = s r = F( θ ) (7) ML N M ar max ar max ( θ, θ) S k= l = = σ ( θ, θ) S = Definin F( θ ) as follows F( θ ) = r (8) N M k= l= σ

owever, the assumption that all the tarets are completely resolved is usually too strinent for realistic problems. For the more eneral cases, tarets located arbitrarily may share rane bins with each other in one or more transmit-receive paths, i.e., unresolved. In this case, the likelihood of the th path is still formulated as (), however, because of the existence of some cross-product term R,, it is difficult to et close-form solution of the ML estimation ofα. For purpose of obtainin a close-form expression of eneral likelihood, (5) is still in use as an approximate solution of ˆML α, and thus the ML estimation of θ remains the same as (7). In this case, we refer to the hih dimensional method formulated in (7) as optimal and can be seen as a theoretical upper bound compared with the followin described suboptimal alorithms which may have further performance loss. The implementation of (7) is involved with a hihdimensional joint maximization. In order to find the lobal maximum, a -dimensional rid search is employed throuh the whole data plane to find an approximate maximum point, then standard optimization methods can be utilized to refine the estimation [7]. In addition, the approximation of ˆML α may lead to considerable performance loss when tarets share common rane bins in more than a few of the M N paths. Besides, this alorithm suffers from the followin two problems: When the number of tarets increases, the hihdimensional rid search process becomes computationally prohibited due to the curse of dimensionality. The number of tarets has to be predetermined before implementin the multi-taret detection and localization, otherwise a multi-hypothesis testin [] detector is required which further increases the alorithm complexity. The above problems heavily restrict the applications of the hih-dimensional method. ence, suboptimum alorithms are also investiated in the subsequent sections to trades alorithm performance for implementation complexity. B. Suboptimum alorithm for partially resolved tarets The aim of this section is to derive reduced-complexity strateies for implement of the MLE (7). The main idea is to split the joint maximization into disjoint optimization problems by clearin the interference from previously declared tarets, which allows information of each taret to be extracted one-by-one from the oriinal received sinal minled with information of all the tarets. Based on the pairwise independence amon θ, =,,..., (Assume the number of tarets is predetermined before localization), we define θ ( θ, θ) S ( θ, θ ) S = = J = max F( ) = max F( θ ) (9) The suboptimum solution relies on the fact that J can be lower bounded as follows in view of the possibility that some tarets are not isolated in each path N M J max F( θ ) F ( θ ) max ( ) d = F θ θ S θ S = d = k= l= = () where F ( θ ) is the objective function of the th taret and F ( θ ) d is defined as modified term related to the previously declared taret d in the th path. ˆ d ˆ r θ Rd ( θ ) d = σ θ ˆ Rd F () R is defined as the rane containin the interference from the previously declared taret d. Takin the estimation error of θ ˆ into consideration, the correctness of the decision of rane bins in each path is not uaranteed, thus, R ˆ d is defined as follows: ( ( t ) ( t ) ( r ) ( r ) x k k + l + l ) Rˆ = {( x, y) [ x + y y c x x y y c τ d c () ˆ τ τ ] } d c where ˆ τ d is the time delay of the taret located at θ ˆ in the d th path, τ c is the effective duration of the time-correlation function of the transmitted waveform and i is the maximum inteer not reater than i. The inequality in () simply follows the fact that the locations ˆθ,, θ ˆ are contained in the maximization set of (7) and all the modified terms ( F ( θ ) d ) are reater than zero. From the definition above, it is obvious that the modified term indicates the information belonin to the paths in which the search point and previously declared tarets are not isolated. Thus, the redefined objective function F ( θ ) only contains the information of the paths in which tarets are isolated. Now we have the estimation of θ that θˆ = ar max F ( θ ) (3) θ S The implementation of (3) is involved with an optimization in the oriinal -dimensional space, and thus reducin the searchin dimension sinificantly compared with the optimal hih dimensional method. In order to solve the multi-taret localization problem from (), an iterative way of which the spirit is similar to the CLEAN alorithm [3] is introduced. Without loss of enerality, the localization process starts with the stronest taret (defined as taret ), and the remainin ( ) tarets are localized one by one from the stronest taret to the weakest one by repeatin the searchin process formulated in (3). In this case, the multi-taret problem is deenerated to several sinle taret localization problems, since the local peaks caused by echoes from other undetermined tarets (say taret q, q> ) are rearded as backround noise in the

localization process, and the information of previously declared tarets have been eliminated from the objective function F ( θ ). Unlike sinle taret localization, a detection process is utilized to decide whether the local peak F ( ˆ θ ) is caused by the echo from a taret or backround noise. When all of the estimated locations have been determined, a joint decision is made as follows = ( ˆ F θ) λ (4) where λ is a set threshold related to the backround noise in the whole search space and the required false alarm probability with correspondin to the tarets presence hypothesis located at { θ, θ,..., θ } respectively and correspondin to the noise only hypothesis. To simplify the detection, we transform (4) into disjoint sinle taret detection problem. Owin to the fact that the statistical function ( F ( ˆ θ )) of each taret only consists of paths havin been removed of the interference of declared tarets, sinle taret detection is reasonable based on F ( θˆ ). F ( ˆ θ ) λ, =,,..., (5) where λ is the threshold for taret. The threshold is determined by the backround noise in neihborin rane of θˆ and the required false alarm probability with correspondin to the taret presence hypothesis located at θ ˆ and correspondin to the noise only hypothesis. Notin that λ is in relation to the number of paths contained in the correspondin statistical function F ( ˆ θ ), λ is also related to θ ˆ. owever, the number of tarets is usually unknown before the localization, thus (4) is no loner realizable, instead, we are faced with a multi-hypothesis testin problem with difficulty to compute. Luckily, the disjoint detection remains valid because we jude every taret separately, and the statistical function of each taret only consists of paths havin been removed of the interference of declared tarets. Noticin that the threshold of each detection chanes with the taret location, the no taret determination in the th estimated location does not uarantee that F ˆ ( θ ) ( > ) is lower than the correspondin threshold λ althouh we determine the tarets from the stronest one to the weakest one. To solve this problem, we set an upper bound of the number of the potential tarets max depends on the maximum handlin capacity of the processor, thus the iteration ends when max estimated locations have been obtained. To summarize, this proposed suboptimum alorithm works in an iterative way which has an estimation step (containin an elimination process and an optimization process) and a detection step in each iteration. It extracts the information of each taret one-by-one from the raw sinal wherein the stroner taret is dealt with earlier until meetin the aforementioned terminal condition. In this way, we refer to this joint detection and localization alorithm as successiveinterference-cancellation (SIC) multi-taret localization alorithm and the procedures of the alorithm are shown in TABLE I. In fact, the idea of joint detection and parameter estimation for statistical MIMO radar was mentioned before in [7]. owever, it only dealt with a sinle extended taret instead of multi-taret. Moreover, considerin the difference between the proposed SIC multi-taret localization alorithm and the SIC alorithm used in communication problems such as multipath and multi-user, the former subtracts the contribution of the estimated tarets from the objective function (or the statistical function) whereas the latter cancels the interference in the received sinal. TABLE I. TE PROCEDURES OF SIC MULTI-TARET LOCALIZATION ALORITM ) Initialization: =, for all θ S, objective function F ( θ) = F( θ). ) Eestimation step: Elimination process: remove the interference of the extracted taret. Optimization process: for all θ S, obtain the maximum likelihood estimation θˆ = armax F ( θ) (6) θ S and the threshold λ correspondin to θ ˆ. 3) Detection step: if F ( ˆ θ) > λ, Add the estimation of the th taret θ ˆ in the declared taret collection, Determine the removin rane by () based on the declared taret collection. o to step ) and = +. 4) If max, repeat step ) and step 3). C. Suboptimal alorithm for completely resolved tarets When tarets are completely resolved, the proposed SIC multi-taret localization alorithm can be simplified further. For this scenario, a different lower bound of J can be obtained below J max F( θ ) (7) θ S\ u = where u ˆ ˆ ˆ = { R, R,..., R }. And R ˆ contains the reions defined in () for all the M N paths. The estimation of the location of a certain taret is determined by

θˆ = ar max F( θ ) (8) θ S\ u Assumin that different tarets fall in different rane bins in any path, a conclusion is formulated that the location of the pth ( p ) taret will not be included in the area of R ˆ most likely. ence, eliminatin R ˆ from the searchin rane will not chane the result of θ ˆ p. Now considerin a disjoint detection, the existence of a certain taret in any estimated location is irrelevant to other tarets for the assumption that the tarets are isolated in any path. Thus make joint sinle taret detection process as follows: F( θˆ ) λ, =,,..., (9) where λ is threshold of the th taret. In most cases, these tarets are located within a relatively small rane with a backround noise differs little in the whole surveillance reion, meanin that these thresholds λ, =,,..., can be simplified into one threshold λ. As for conditions that the number of tarets is not available before localization, the localization process can be terminated if the th estimated location is determined as no taret. It simply relies on the fact that F( θ ˆ + ) F( θ ) is efficient, and thus F( θ ˆ + ) F( θ ) < λ, meanin that every point in the remained search space is decided as. We refer to this joint detection and localization alorithm as successivesearch-space-removin (SSR) multi-taret localization alorithm. D. Comparison of the proposed two suboptimal alorithms From the aforementioned derivation of the two proposed alorithms, when deals with completely resolved tarets, it is obvious that the SIC alorithm is equivalently efficient. On the other hand, the performance of the SSR alorithm in scenario with partially resolved tarets is not uaranteed, because the correspondin likelihood local peak may be located outside the search space in the iteration. Thus the localization precision and detection probability of this taret are exacerbated severely compared to the SIC alorithm. owever, the SSR alorithm reduces search space durin each iteration and does not need to compute the modified term. ence it has less calculation compared with the SIC alorithm. In addition, owin to the different termination stratey, the number of loops drops noteworthily when max ( is the actual number of tarets), which also decreases calculation and reduces the false alarm of SSR alorithm to some extent compared with SIC alorithm. We have already proposed a multi-taret localization alorithm in [], which localizes tarets in parallel with the utilization of connected reion. Just as aforementioned, a theoratical value of the threshold is not avaliable. If the threshold is set based on theory of taret detection, the searchin rane of different tarets may be connected with others (as shown in Fi.) and thus it is no loner able to separate tarets successfully. This phenomenon apears when the sinal-to-noise ratio (SNR) is hih, since the detection threshold under this condition is much less than the maximum in the whole data plane. On the other hand, in consideration of the resolution of MIMO radar [4], the threshold is set to be - 3dB (half) of the lobal maximum, and the searchin ranes are shown in Fi. when the proportion of the taret intensity is :.65:.5 and the SNR is db. In Fi., the weakest taret located at (5, 6) km is missin, which demonstrates that weak tarets may be covered up by stron tarets in this case. owever, accordin to the proposed numerical examples in Section IV, SIC and SSR alorithm delcared all the tarets successfully in hih SNR conditions and weak tarets are not covered up by stron tarets. y/km 9 8 7 6 5 4 3 3 4 5 6 7 8 x/km y/km 9 8 7 6 5 4 3 3 4 5 6 7 8 x/km Fi.. Ranes in which pixel value pass the threshold which is set based on theory of taret detection to be -3dB of the lobal maximum when SNR=dB As for the host taret problem mentioned in [5], which is a kind of false taret resulted from the combination of measured ranes that do not belon toether. In fact, Our previous alorithm is still faced with this problem as shown in Fi. 3 with at least three host tarets (marked by red or blue ellipse). Compared with the simulation results of the proposed two alorithms in Section IV, the alorithms declare anveraely less than one false tarets aainst SNR from -5dB to 5dB, indicatin sinificant reduction of host tarets. y/km 9 8 7 6 5 4 3 3 4 5 6 7 8 x/km Fi. 3. Likelihood in the whole data plane Ranes in which pixel value pass the threshold when SNR=5dB

IV. SIMULATION RESULTS A. Simulation of SIC alorithm for partially resolved tarets In this section, a scenario with three tarets and a 5 5 MIMO radar system is desined to assess the performance of the proposed SIC alorithm. Each antenna is a transmitter and receiver at the same time. The placement of the radar antennas and tarets are shown in Fi. 4. The three tarets are located at (3.5, 3.5) km, (7, 8) km, (3.36, 6.48) km, respectively. The tarets positions are carefully chosen such that the st taret and 3rd taret are unresolved in some paths. The proportion of the taret intensity is :.65:.5 to find whether the weak taret will be covered up by stron taret in the detection process of SIC alorithm. The sinal minled with the echoes of all the three tarets are used to define SNR in the simulation. Besides, the performance measurements used are the number of valid taret detections and the root mean square (RMS) errors of estimated taret positions. To be specific, we define the declared taret with an estimated location within m of the actual taret location both in the two dimensions respectively as a valid taret. In the followin analysis, the results are athered by averain over realizations. y/km 9 8 7 6 5 4 3 MIMO radar taret taret taret3 3 4 5 6 7 8 9 x/km Fi. 4. The placement of MIMO radar system The performance of the proposed SIC alorithm is shown in Fi. 5~Fi. 6. The detection threshold is adaptive to the number of paths contained in the statistical function of each taret. The upper bound of the number of the potential tarets is set as max = 5. In Fi. 5, the performance comparison of SIC and SSR alorithms are iven. From Fi. 5, it can be seen that the SIC alorithm performs well when SNR is hih, specifically, it can correctly declared all the three tarets when SNR is reater than 5dB. The numbers of false tarets are all below.6 when SNR chanes from -5dB to 5dB. In Fi. 5, the detection probability P d of all tarets is plotted aainst SNR from -5dB to 5dB for P fa =. As expected, for SIC alorithm, the detection probability of all tarets rises towards as the SNR oes up and at the same time, the stroner taret corresponds to hiher detection probability than weaker taret. As for SSR alorithm, it is clear that the 3rd taret (which is the weakest and share common rane bins with st taret in some paths) has a reat performance loss especially in hih SNR conditions. In Fi. 6, based on SIC alorithm, the RMS position errors of all three tarets are plotted aainst SNR from -db to 5dB for both x and y dimensions. Note that the level of RMSE unnecessarily follows the intensity order of the tarets especially when taret SNR is hih. The reason is that in hih SNR condition, the RMS errors are very close to the Cram er-rao Bounds (CRB) affected by ambiuity function which strictly depends on the eometry [8]. Moreover, the RMS error chane little when SNR rises from db to 5dB because only rid search is utilized in the simulation, meanin that the rid width may restrict the localization accuracy especially when SNR is hih. The simulation results show that compared with SSR alorithm the SIC alorithm can accurately estimate the number of tarets and localizes them with quite hih precision even some tarets are not isolated in some paths. Declared Valid Tarest 3.5.5.5 SIC SSR -5 - -5 5 5 Probability of Detection.8.6.4. SIC-taret SIC-taret SIC-taret3 SSR-taret SSR-taret SSR-taret3-5 - -5 5 5 Fi. 5. The number of valid tarets The detection probability P d of all tarets are plotted aainst SNR from -5dB to 5dB RMSE in x/m 8 6 4 taret taret taret3 - -5 5 5 RMSE in y/m 8 6 4 taret taret taret3 - -5 5 5 Fi. 6. The RMS position errors in x dimension and y dimension of all tarets are plotted aainst SNR from -db to 5dB for = B. Simulation of SSR alorithm for completely resolved tarets In this section, the radar placement remains the same while the taret locations are chaned to (3.5, 3.5) km, (7, 8) km, (5, 6) km to make sure that all tarets are completely resolved. The proportion of the taret intensity is still :.65:.5. The performance of the proposed SSR alorithm is shown in Fi. 7 and Fi. 8 for P fa =. They all show the enerally same tendency of SIC alorithm as Fi. 5 and Fi. 6. Compared with the simulation results of the two proposed alorithms in scenario with partially resolved or completely resolved tarets respectively, SIC performs well even tarets are not isolated in some paths while SSR is efficient only for completely resolved tarets. P fa

Declared Valid Tarets 3.5.5.5-5 - -5 5 5 Probability of Detection.9.8.7.6.5.4.3.. taret taret taret3-5 - -5 5 5 Fi. 7. The number of valid tarets The detection probability P d of all tarets are plotted aainst SNR from -5dB to 5dB RMSE in x/m 8 6 4 taret taret taret3 - -5 5 5 RMSE in y/m 8 6 4 taret taret taret3 - -5 5 5 Fi. 8. The RMS position errors in x dimension and y dimension of all tarets are plotted aainst SNR from -db to 5dB for = V. CONCLUSION In this paper, we consider the detection and locatin of multiple tarets in a noncoherent statistical MIMO system. To combat the troublesome hih-dimensional optimization problem of simultaneously estimatin multiple tarets positions, we propose two alorithms to sub-optimally split the joint maximization into several disjoint optimization problems, i.e., one correspondin to each prospective taret. In this way, the proposed alorithms have much lower complexity compared with the oriinal hih-dimensional estimation method. Besides, durin the detection and locatin process, the proposed alorithms sequentially perform sinle taret detection at each estimated position after eliminatin the interference in all the paths from previously declared tarets, and the recursive process stops automatically if no taret estimate of current stae can exceed the detection threshold. Therefore the multi-hypothesis testin detector is no loner needed when the number of tarets is unknown. Simulation results show that the proposed alorithms can correctly estimate the number of tarets and localize them with a quite hih accuracy when the SNR is hih. In particular, the proposed SIC alorithm works well even when some tarets are not isolated in some paths. ACKNOWLEDMENT P fa This work was supported by National Natural Science Foundation of China (676, 67868 and 6366), Fundamental Research Funds of Central Universities (ZYXZ, ZYXYB4 and ZYX3J), Proram for New Century Excellent Talents in University (A98543963) and China Postdoctoral Science Foundation (4M55465 ). REFERENCES [] B. Lya and J. Abrikian. "Taret detection and localization usin MIMO radars and sonars."ieee Trans. Sinal Process., vol. 54, no., pp. 3873-3883, 6. [] E. Fishler, A. aimovich, R. Blum, D. Chizhik, L. Cimini, and R. Valenzuela, "MIMO radar: an idea whose time has come," in IEEE Radar Conf., pp. 7-78, April 4. [3] N.. Lehmann, E. Fishler, A. M. aimovich, et al. "Evaluation of transmit diversity in MIMO-radar direction findin."ieee Trans. Sinal Process., vol. 55, no. 5, pp. 5-5, 7. [4] A. M. aimovich, R. S. Blum, and L. J. Cimini. "MIMO radar with widely separated antennas."ieee Sinal Process. Ma., vol. 5, no., pp 6-9, 8. [5] J. Mason, "Alebraic two-satellite TOA/FOA position solution on an ellipsoidal Earth", IEEE Trans. Aerosp. Electron. Syst., vol. 4, no. 3, pp. 87-9, 4. [6] Q. e, R. S. Blum, and A. M. aimovich. "Noncoherent MIMO radar for location and velocity estimation: More antennas means better performance." IEEE Trans. Sinal Process., vol. 58, no. 7, pp 366-368,. [7] R. Niu, R. S. Blum, P. Varshney and A. Drozd. "Taret localization and trackin in noncoherent multiple-input multiple-output radar systems." IEEE Trans. Aerosp. Electron. Syst., vol. 48, no., pp. 466-489,. [8]. odrich, A. M. aimovich and R. S. Blum. " Taret localization accuracy ain in MIMO radar-based systems" IEEE Trans. Inform. Theory, vol. 56, no, 6, pp. 783-83,. [9] M. reco, F. ini, P. Stinco, A. Farina "Cramér-Rao bounds and selection of bistatic channels for multistatic radar systems", IEEE Trans. Aerosp. Electron. Syst., vol. 47, no.4, pp. 934-948,. [] A. A. orji, R. Tharmarasa, T. Kirubarajan "Widely Separated MIMO versus Multistatic Radars for Taret Localization and Trackin", IEEE Trans. Aerosp. Electron. Syst., vol. 49, no. 4, pp. 79 94, 3 [] Y. Ai, W. Yi,. Cui and L. Kon. "Multi-taret localization for noncoherent MIMO radar with widely separated antennas" in IEEE radar conf.(radar), 4, accepted. [] T. Schonhoff, A. A. iordano."detection and Estimation Theory and its applications". PearsonPrentice all, 6. [3] B.. Clark, "An efficient implement of the alorithm CLEAN ", Astron. Astrophs., vol. 89, pp. 377-378, 98 [4] Douhty, Shaun Raymond. "Development and performance evaluation of a multistatic radar system", Diss. University of London, 8. [5] Folster, Florian, and ermann Rohlin. "Data association and trackin for automotive radar networks."ieee Trans. Intell. Transp. Syst., vol. 6, no. 4,pp. 37 377, 5. [6] Q. e, R. S. Blum,. odrich and A. M. aimovich, "Taret velocity estimation and antenna placement for MIMO radar with widely separated antennas", IEEE J. Sel. Top. Sinal Process., vol. 4, no., pp. 79-,. [7] A. Tajer,.. Jajamovich, X. Wan and. V. Moustakides, "Optimal joint taret detection and parameter estimation by MIMO radar". IEEE J. Sel. Top. Sinal Process., vol. 4, no.4, pp. 7-45,