sensors Article

A Channelization-Based DOA Estimation Method for Wideband Signals Rui Guo *, Yue Zhang, Qianqiang Lin and Zengping Chen Science and Technology on Automatic Target Recognition Laboratory (ATR), National University of Defense Technology, Changsha 410073, China; [email protected] (Y.Z.); [email protected] (Q.L.); [email protected] (Z.C.) * Correspondence: [email protected]; Tel.: +86-731-8457-4453 Academic Editor: Vittorio M. N. Passaro Received: 4 May 2016; Accepted: 28 June 2016; Published: 4 July 2016

Abstract: In this paper, we propose a novel direction of arrival (DOA) estimation method for wideband signals with sensor arrays. The proposed method splits the wideband array output into multiple frequency sub-channels and estimates the signal parameters using a digital channelization receiver. Based on the output sub-channels, a channelization-based incoherent signal subspace method (Channelization-ISM) and a channelization-based test of orthogonality of projected subspaces method (Channelization-TOPS) are proposed. Channelization-ISM applies narrowband signal subspace methods on each sub-channel independently. Then the arithmetic mean or geometric mean of the estimated DOAs from each sub-channel gives the final result. Channelization-TOPS measures the orthogonality between the signal and the noise subspaces of the output sub-channels to estimate DOAs. The proposed channelization-based method isolates signals in different bandwidths reasonably and improves the output SNR. It outperforms the conventional ISM and TOPS methods on estimation accuracy and dynamic range, especially in real environments. Besides, the parallel processing architecture makes it easy to implement on hardware. A wideband digital array radar (DAR) using direct wideband radio frequency (RF) digitization is presented. Experiments carried out in a microwave anechoic chamber with the wideband DAR are presented to demonstrate the performance. The results verify the effectiveness of the proposed method. Keywords: digital array radar; direction of arrival (DOA) estimation; wideband signal; digital channelization receiver

1. Introduction The problem of locating wideband emitters with sensor arrays is of growing interest in many applications such as sonars, radars, advanced satellites and cellular communication systems. Unfortunately, we cannot apply narrowband signal subspace methods such as multiple signal classification (MUSIC) [1] and estimation of signal parameters via rotation invariance techniques ESPRIT [2] on wideband sources because the phase difference between sensor outputs is no longer just dependent on the direction of arrival (DOA) alone, but also depends on the temporal frequency, which has a wide range. The incoherent signal subspace method (ISM) [3] decomposes wideband signals into many narrowband signals and uses narrowband methods on each decomposed narrowband signals. Then, the results from all the frequency bins are combined to create the final DOA estimation. The ISM method is simple and effective, but it cannot resolve coherent sources and suffers from low signal noise ratio (SNR). The coherent signal-subspace method (CSM) [4] uses a transformation matrix to transform the correlation matrices from many frequency bins into one general correlation matrix at one focusing frequency. Then narrowband signal subspace methods can be applied to estimate the DOA. Sensors 2016, 16, 1031; doi:10.3390/s16071031

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Although this method has been extended in [5,6] to decrease the resolution threshold and reduce the estimation bias, the method still requires initial DOA estimations and its estimation performance is very sensitive to these initial values. The test of orthogonality of projected subspaces (TOPS) [7] and the test of orthogonality of frequency subspaces (TOFS) [8] are newly introduced methods which estimate DOA by checking the orthogonality between the signal and noise subspaces of different frequency components of the sources. Both TOPS and TOFS are incoherent methods. The performance of TOPS is between that of the coherent and the incoherent methods in the whole SNR range. Recently, TOPS was extended in [9,10] to deal with coherent signals and achieve a higher accuracy. These algorithms perform satisfactorily when the received signals are simple, but this requirement is not guaranteed in real environments. Important parameters including density of signals, dynamic range, frequency range and bandwidth should be taken in consideration. That is why studies in which these algorithms are used in real environments are rare. The DOA estimation is transformed into a sparse reconstruction problem in recent research [11–14]. These algorithms have a number of advantages, including increased resolution and improved robustness to noise. However, it is necessary to utilize iteration to achieve a prescribed accuracy in these methods. The intractable computational complexity for sparse recovery makes it difficult to implement on hardware platforms. To the best of our knowledge, there are no wideband DOA estimation methods based on sparse reconstruction that have been validated on hardware platforms. The main purpose of this paper is to present a hardware-efficient wideband DOA estimation method. The digital channelization receiver shows several desirable characteristics, including high broadband instantaneous frequency coverage, good sensitivity and dynamic range, simultaneous signal detection, arbitration and parameter encoding, and fine frequency measurement [15]. Digital channelization receivers play an important role in radar and electronic warfare applications. The channelization receiver partitions the received signal into a number of sub-channels and arbitrates which sub-channels the signal truly resides in. Afterwards, the parameters of the arbitrated channels including signal center frequency, pulse width and amplitude are then estimated, which is very important for DOA estimation. The channelization receiver architecture was first used to estimate DOA of ultra-wideband signal in [16–18]. It splits the array output into multiple frequency channels and down-converts each channel into much lower frequency. Each channel can then be sampled at a lower sampling rate. Each branch of the proposed channelization receiver architecture consists of a mixer, Bessel band-pass filter and low sampling rate analog-to-digital converter (ADC). However, the frequency split and down-convert are implemented before digitization. The performance is highly sensitive to environmental factors, for example, the temperature. With the development of high-speed ADCs, direct sample to wideband intermediate frequency (IF) signal conversion is possible. Recently, the Science and Technology for Automatic Target Recognition (ATR) Laboratory developed a digital array radar (DAR) test-bed using direct wideband radio frequency (RF) digitization [19,20]. The test-bed works at the IF of 0.6–3.0 GHz. It can achieve an instantaneous bandwidth of 500 MHz. Based on this test-bed, a new DOA estimate flow including IF digitization, digital channelization, channel selection and DOAs estimation is proposed. Firstly, the digital channelization receiver is used to split the wideband array output into multiple narrowband sub-channels. Secondly, the sub-channels within the bandwidth of wideband signals are selected out among the output sub-channels and signal parameters are estimated accurately. Finally, a channelization-based ISM method (Channelization-ISM) and a channelization-based TOPS (Channelization-TOPS) are proposed to estimate the DOA of wideband signals. Channelization-ISM first estimates the DOAs of each sub-channel independently by exploiting the narrowband signal subspace method. Then the estimated DOAs from each sub-channel are averaged to yield the final result. Channelization-TOPS measures the orthogonality between the signal and the noise subspaces of the output sub-channels to subsequently estimate DOAs. Based on the accurate signal parameters estimation, signals with different bandwidths are isolated reasonably. The output SNR is improved by removing the noises from the bandwidth of signals. The proposed channelization method outperforms

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the conventional ISM method and TOPS method, especially in real environments. Moreover, the output signals in a channelization receiver are in a parallel format, making it easy to implement on hardware. 2. The Wideband Signal Model Assuming a uniform linear array (ULA) of K omnidirectional sensors receives PpP ď Kq wideband signals s p ptqpp “ 1, 2, ¨ ¨ ¨ Pq from unknown directions tθ1 , θ2 , ¨ ¨ ¨ , θ P u. The kth sensor output xk ptq is: xk ptq “

P ÿ

s p pt ´ τk pθ p qq ` nk ptq k “ 1, 2, ¨ ¨ ¨ K

(1)

p“1

where nk ptq is the additive white Gaussian noise of kth sensor which is assumed to be statistically independent with signal sources. τk pθ p q is the propagation delay of the kth sensor: τk pθ p q “ pk ´ 1qdsinθ p {c

(2)

where c is the speed of the signal propagation, d is the spacing between adjacent sensors. The discrete-time Fourier transform (DTFT) of the kth sensor output is: Xk pωq “

P ÿ

S p pωqe´ jωτk pθ p q ` Nk pωq

(3)

p “1

Decomposing the sensor outputs into several narrowband signals using a filter bank or the discrete Fourier transform (DFT), the output can be written in vector format at J frequencies as: Xpωi q “ Apωi qSpωi q ` Npωi q i “ 0, ¨ ¨ ¨ , J ´ 1

(4)

Xpωi q “ rX1 pωi q, X2 pωi q, ¨ ¨ ¨ , XK pωi qsT

(5)

Spωi q “ rS1 pωi q, S2 pωi q, ¨ ¨ ¨ , SP pωi qsT

(6)

where:

[¨ ]T denotes the transpose operator. Apωi q is the K ˆ P steering matrix. Its columns are the K ˆ 1 array manifolds apωi , θ p q: Apωi q “ rapωi , θ1 q, apωi , θ2 q, ¨ ¨ ¨ , apωi , θ P qs

(7)

” ıT apωi , θ p q “ e´ jωi τ1 pθ p q , e´ jωi τ2 pθ p q , ¨ ¨ ¨ , e´ jωi τK pθ p q

(8)

3. The Proposed Method Inspired by the digital channelization receiver, we propose a new DOA estimate flow shown in Figure 1, which is composed of IF digitization, digital channelization, channel selection and DOAs estimation. Detailed descriptions of each procedure are presented below. In the DOAs estimation, the channelization-based ISM method and channelization-based TOPS method are proposed.

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Figure 1. Flow of the proposed method. Figure 1. Flow of the proposed method.

3.1. IF Digitization and Digital Channelization Figure 1. Flow of the proposed method.

wideband radar returns are directly digitized. A digital quadrature demodulation 3.1.IFIFThe Digitization andDigital DigitalChannelization Channelization 3.1. Digitization and system [21–23] is applied to get the amplitude and phase information of the received signals. A The wideband radar returns are directly digitized. A digital quadrature demodulation system [21–23] The wideband radar returns are directly digitized. A digital quadrature demodulation channelization receiver typically employs digital filter banks to extract multiple narrowband is applied to get the amplitude and phase information of the received signals. A channelization system [21–23] is applied to get the amplitude and phase information of the received signals. Ain sub-channels from the received wideband signals [24–26]. The architecture can be illustrated receiver typically employs digital filter banks to extract multiple narrowband sub-channels from channelization typically employs digital filter banks narrowband Figure 1. xk ( nreceiver ) represents the digitization of kth sensor outputtoxkextract (t ) withmultiple the sampling rate the fs , received wideband signals [24–26]. The architecture can be illustrated in Figure 2. x pnq represents killustrated in sub-channels from the received wideband signals [24–26]. The architecture can be where f s is greater than twice of bandwidth of the input wideband signal.  means decimation. the digitization kth sensor xk ptq with thesensor sampling rate fxs , (where f s the is greater thanrate twicef of Figure 1. x ( n) of represents theoutput digitization of kth output with sampling k t ) carrier s , The array k of output is channelized into JÓ means frequency channels. of the i-th bandwidth the input wideband signal. decimation. TheThe array outputfrequency is channelized into J f is greater than twice of bandwidth of the input wideband signal. means decimation. where  channels is channels. at: frequency The carrier frequency of the i-th channel is at: The array output is channelized into J frequency channels. The carrier frequency of the i-th 2 i channel is at: i 2πi (9) (9) ωi “ J J 2 i i  (9) hLP (n) is a low-pass filter. J h LP pnq is a low-pass filter. hLP (n) is a low-pass filter.

e j0n

xk (n)

e j0n

xk (n)

e j1n

yk0 (m)

hLP (n)

yk0 (m)

hLP (n)

e j1n

y1k (m)

hLP ( n)

y1k (m)

hLP ( n)

e jJ 1n e jJ 1n

ykJ 1 ( m)

hLP ( n)

y J 1 ( m)

h ( n)

k LP Figure receiver Figure 2. 1. Digital channelization channelization receiver architecture. architecture.

The output output of of i-th i-th sub-channel sub-channel can be be expressedas: as: Figure 1. Digital channelization receiver architecture. The can expressed  j i ( n  r ) y i ( m )  [ xk (´ n )  en ji n ]  hLP ( n) n  mJ  ř xk ( n  r )e´ h q ( r ) n  mJ jωi pn´rLP The output of i-th“ksub-channel expressed as: i s ˚be yik pmq rxk pnq ¨ e jωcan h LP pnq|n“mJ “ x pn ´ rqe h LP prq|n“mJ r k r  j  ( mJ  r ) ř i  ji n jω  j i ( n  r ) xk (emJ (r ) ´rq hprq  yki “ ( m ) x[kxpmJ ]r)i pehmJ hLP ( r ) n  mJ rqe´ k ( n )´ LP ( n ) hnLP  mJLP  xk ( n  r ) e

r

r

r

(10) (10)

(10)   xkfilter ( mJ is r )e D and hLPD(  r ) L  J  1 , where L is a positive integer. By The order orderofof prototype The prototype filter is D and D “ L ˆ J ´ 1, where L is a positive integer. By polyphase r polyphase decomposition with thefilter, prototype filter, Equation (10) can be decomposition with the prototype Equation (10) can be rewritten as:rewritten as: The order of prototype filter is D and , where is a positive integer. By D  L  J  1 L yki (ř m)   xk (mJ  r )e ji ( mJ  r ) hLP (r ) polyphase decomposition with the prototype filter, Equation (10) can be rewritten as: i ´ jω p mJ ´ r q i yk pmq “ xk pmJ ´ rqe h LP prq r r J L  1  1 (11) i ( mJ  r )  j(ir( mJ ´1 yki (mJ)ř r )e jlJ heLP ) lJ  p ) h (lJ  p) Lř ´1xk (mJ (11) xk  (mJ  p)´  jωi pmJ ´l J ´ pLPq h pl J ` pq r “ LP p 0 x l k0pmJ ´ l J ´ pqe 10L 1 (11) p“0 Jl “  ji ( mJ lJ  p ) hLP (lJ  p)   xk (mJ  lJ  p)e  ji ( mJ  r )

p 0 l 0

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p p

mJ `ppq. ) . Then: (mJ ´  pq p) and Definexkxpmq andh phpmq Define pmJ p ( m )“ hhLP LP ( k (m)“xxkkpmJ J 1 L 1

yik pmq

´1 Lř ´1  ji ( mJ  lJ ) i Jř y“ xk (mJ p)´ejω  p)e ji pjω p qh k ( m)   LP (lJ i pmJ ´l Jh x pmJ ´ lJ lJ ´ pqe LP pl J ` pqe i p  0 l k0

“

p “0 l “0 1 L 1 Jř ´1 LJř ´ 1  ji ( m  l ) J ip r [ x p pm xkp (´ m lqe  l )´ejω )]e jjω i pm´l q Jhhp (lplqse ip p k p 0 l 0 p“0 l “0



(12) (12)

Substituting Equation (9) into Equation (12), we can rewrite yki (m) as: Substituting Equation (9) into Equation (12), we can rewrite yik pmq as: J 1 L 1

 ji ( m  l ) J p yki (mJř )´1  hp (l )]e ji p Lř ´[1pxk ( m  l )e ´ jω p m ´ l q J h plqse jωi p i i p l  0  0 xk pm ´ lqe yk pmq “ r p

“ “ “

p“0 Jl“ 2 i 2 i 1 0L 1 j p ( m l ) J j J J Jř ´ 1 Lř ´[1 px p ( m  l )e 2πi h ( l )] e k j 2πi p ´ j J pm´l q J p h p plqse J rp  0 l x0k pm ´ lqe p“0 l “0 2 i J 1 L 1 j p Jř ´1 Lř J  ´[1 pxkp (m  l )hp (l )]ej 2πi p rp  0 l x0k pm ´ lqh p plqse J p “0 l “0 2 i j p Jř ´1 J 1 p j 2πi Jp  rx p[pmq xk (m )hp hpmqse p ( m)]e J ˚ k p “0 p  0



(13) (13)

 

p where  represents convolution operation. Replacingp xkp (m)  hp (m) as p xˆ k ( m ) , then: where ˚ represents convolution operation. Replacing xk pmq ˚ h p pmq as xˆ k pmq, then: i

p

y k ( m )  J  IDFT (pxˆ k ( m )) (14) yik pmq “ J ¨ IDFTpxˆ k pmqq (14) Figure 2 shows the optimized digital channelization receiver architecture, which is realized by Figure 3 shows the optimized digital channelization whichmodule. is realized implementing one low-pass filter and an inverse discretereceiver Fourier architecture, transform (IDFT) The by implementing filter inverse discrete Fourier (IDFT) module. J low-pass down sampling byone is moved to the and left ofanthe filtering operation. h0 (mtransform ) to hJ 1 (m ) represent the The down sampling by J is moved to the left of the filtering operation. h pmq to h pmq represent the 0 J ´ 1 polyphase components of the low-pass filter hLP (n) . This requires fewer components and is a more polyphase components of the low-pass filter h LP pnq. This requires fewer components and is a more realistic architecture. realistic architecture.

xk (n)

h0 (m)

yk0 (m)

h1 (m)

y1k (m)

hJ 1 (m)

ykJ 1 (m)

z 1

z 1

Figure 3. The optimized digital channelization receiver architecture. Figure 2. The optimized digital channelization receiver architecture. ii The (m) can The output output of of digital digital channelization channelization receiver yykkpmq canbe beregarded regardedasasaanarrowband narrowbandsignal signal sampled with a sampling rate of f {J. Assume that N is the number of snapshots of x pnq and M s k M sampled with a sampling rate of f s / J . Assume that N is the number of snapshots of xk ( n) andthat of yik pmq, then we have the conclusion that M “ N{J. The bandwidths of the output sub-channels i that of yk (m) , then we have the conclusion that M  N / J . The bandwidths of the output are same. Different output bandwidths are required to deal with more complicated situation in real sub-channels where are same. Different output bandwidths are required to deal more complicated environments signals with different unknown bandwidths coexist. Thewith digital channelization situation in real environments where signals with different unknown bandwidths coexist. receiver architecture can be extended to isolate channels with different bandwidths based onThe a digital channelization receiver architecture can be extended to isolate channels with different multistage DFT filter [27,28]. bandwidths based on a multistage DFT filter [27,28].

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3.2. Channelization Selection and Parameter Estimation The frequency of received signals is not known in a real environment. Sometimes only part of the output sub-channels are within the wideband signal bandwidth. Before estimating the DOA, we need to find the sub-channels in which the wideband signals exist. The output sub-channels within the bandwidth of wideband signals always result in higher power output. The sub-channel power is a criterion to determine whether there signals exist in the sub-channel. We can compare the power of all the sub-channels to select out the sub-channels within the wideband signal bandwidth. Assume that xk pnq consists of a wideband signal sk pnq and white Gaussian noise nk pnq „ Np0, σn2 q. sk pnq has a power of A2 and the power spreads on SpS ă Jq sub-channels equally. The input SNR is: SNRin “

A2 σn2

(15)

The output yik pmq is composed of the response due to the noise yikn pmq and the signal yiks pmq, respectively. The noise response is a complex filtered baseband noise with an autocorrelation function γykn [29]: N ÿ “ ‰ σ2 γykn “ E ykn ¨ y˚kn “ σn2 |hk pmq|2 « n (16) J n “0

Only the S sub-channels within the wideband signal bandwidth are expected in further processing. The SNR of these sub-channels are: A2 J (17) SNRout “ 2 σn S The SNR is improved approximately J{SpJ{S ą 1q times. The signal parameters of each selected sub-channel, including frequency, bandwidth and amplitude must be determined. The DOA of a narrow signal can be estimated with the only sub-channel which the signal resides in. However, wideband signals always span a number of sub-channels. We will introduce how to estimate the DOA of wideband signals in the next section. 3.3. Channelization-Based ISM Method Assume that a total of S sub-channels within the wideband signal bandwidth are selected. Firstly, we use narrowband methods to estimate the DOAs of every selected sub-channel. In practice, the estimated K ˆ K covariance matrix can be expressed as: M ÿ ˆ iq “ 1 ypωi , mqyH pωi , mq, i “ 0, 1, ¨ ¨ ¨ , S ´ 1 Rpω M

(18)

m“1

T

where r¨sH denotes the complex conjugate transpose ypωi , mq “ ry1i pmq, y2i pmq, ¨ ¨ ¨ , yiK pmqs . ˆ i q, the eigenvalues λ1 , λ2 , ¨ ¨ ¨ , λK in descending order Performing an eigendecomposition on Rpω and their associated eigenvectors u1 , u2 , ¨ ¨ ¨ , uK can be obtained. Define matrices Fpωi q “ ru1 , ¨ ¨ ¨ , uP s and Upωi q “ ruP`1 , ¨ ¨ ¨ , uK s, the columns of Fpωi q and Upωi q span the signal subspace and the noise subspace respectively. DOAs of every sub-channels can be estimated via the spatial spectrum function: PSUB pωi , θq “

1 ||UT pω

2 i qapωi , θq||

(19)

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Then we combine the estimated DOA θi for the different sub-channels, and we can find the final DOA estimation. The first estimator exploits the arithmetic mean metric both for the individual sub-channels and the combination over the frequency range, which can be expressed as: PChannelized´ ISM1 pωi , θq “

1 1 ř S ´1 1 S i“0 PSUB pωi ,θ q

(20)

The second estimator uses the arithmetic mean metric for the individual sub-channels and the geometric mean metric for the combination over the frequency range: PChannelized´ ISSM2 pωi , θq “ ´ ś S ´1

1

1 i“0 PSUB pωi ,θ q

¯1{S

(21)

The first estimator shows higher accuracy and lower resolution than the second one. 3.4. Channelized Based TOPS Method Following the standard TOPS approach introduced in [7], we first perform an eigendecomposition ˆ i q and obtain the noise subspace Upωi q. Select one output sub-channel as reference to obtain on Rpω the reference signal subspace Fpω0 q. Define a diagonal unitary transformation matrix whose size is k ˆ k and diagonal elements are rTpωi , θi qsk,k : rTpωi , θi qsk,k “ expt´jωi pk ´ 1qdsinθi {cu (22) rTpωi , θi qsk,k can transform the array manifold of one frequency into that of another frequency without changing the DOA. Define a K ˆ P matrix Fi pφq: Fi pφq “ Tp∆ωi , φqFpω0 q, i “ 1, 2 . . . , S ´ 1

(23)

where ∆ωi “ ωi ´ ω0 , φ is a hypothetic arrival angle of signal: Dpφq “ rF1H Upω1 q|F2H Upω2 q| . . . FSH´1 UpωS´1 qs

(24)

Dpφq is a full rank matrix if φ is not equal to the arrival angle of signal otherwise Dpφq loses its rank. This theorem holds as long as the source signals are not fully correlated. The estimation of DOA can be obtained through a one-dimensional scan on φ, i.e., θˆ “ argmax φ

1 σmin pφq

(25)

where σmin pφq is the smallest singular value of Dpφq. 3.5. Discussion The channelization receiver shows several appealing characteristics such as wideband frequency coverage, high sensitivity and dynamic range, and accurate measurement of frequency resolution. The digital channelization receiver splits the wideband array output into multiple narrowband sub-channels and meanwhile estimates the parameters of the selected sub-channels. The estimation of the parameters including signal center frequency, pulse width and amplitude is very helpful to DOA estimation. Firstly, signals with different frequencies can be separated into different sub-channels. The DOA estimations of signals in different sub-channels can be obtained accurately without any influence of other signals. Secondly, to estimate the DOA of a signal, the knowledge of the signal parameters such as signal center frequency, pulse width and amplitude is necessary. The channelization

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receiver offers us a good way to obtain these parameters. Thirdly, the channelization receiver removes noises beyond the bandwidth of signals and selects the sub-channels within the bandwidth of signals with a high accuracy. The output SNR is improved approximately J{SpJ{S ą 1q times. Finally, the channelization receiver can be implemented in a parallel processing architecture, consequently it is able to tackle real-time processing on hardware platforms [29,30]. In virtue of these advantages, the proposed channelization-based method shows a better performance over the conventional ISM and TOPS methods. Compared with the method described in [16], the ADC in the proposed method is closer to the antenna, which can significantly reduce the complexity and hardware cost. The performances of the proposed method may degrade when the array manifold is affected by mutual coupling, sensor position errors and gain or phase uncertainties. Many calibration algorithms have been developed to compensate these uncalibration impairments [31–33] In this paper we assume that the array manifold is deterministic and constant in time. Similar to TOPS, the proposed method works with arbitrary 1-D or 2-D arrays when the array manifolds are linearly independent. Only ULAs are used in the simulation for convenience. In the DOA estimation procedure, we present the channelization-based ISM method and channelization-based TOPS method. The difference between these two methods is similar to that between the ISM method and TOPS, which is presented in [31]. In this paper, we only focus on the improvement of the proposed channelization-based method instead of the conventional ISM method and TOPS method. 4. Simulation In this section, some computer simulations are conducted to demonstrate the performance of proposed algorithm for DOA estimation of wideband signals. Consider a ULA composed of eight sensors. The maximum number of resolved sources is 7 (K ´ 1). Suppose two wideband signals with the same power located at θ1 “ 22˝ and θ2 “ 28˝ impinging on the ULA. The two sources have the same center frequency f 0 “ 2.65 GHz and the same bandwidth B “ 400 MHz. The sampling frequency is chosen to be f s “ 1.2 GHz. The sensor noise is complex Gaussian noise. The average root mean square error (RMSE) of the estimates from 200 Monte Carlo trials is defined as: g f ÿ f 1 200 RMSE “ e pθw ´ θq2 (26) 200 t “1

where θw is the DOA estimation value of the incident signal at the w-th Monte Carlo trial. In the first simulation, the accuracy performances of the ISM method [3] and the proposed Channelization-ISM method are compared. We also present the Cramér-Rao lower bound (CRLB) for the DOA estimations. The first estimator in Equation (17) is applied to yield the final results. The number of sub-channels in the Channelization-ISM method is the same as that of frequency bins in the ISM method, which is 64. The RMSEs against the SNR and the number of snapshots are plotted in Figures 4 and 5, respectively. In Figure 4, the SNR varies from 0 to 20 dB with a step size of 2 dB and the number of snapshots is 500. In Figure 5, the number of snapshots varies from 50 to 1000 and the SNR is fixed at 10 dB. It is clear that with the increase of the SNR and the number of snapshots, the performances of both methods improves. The performance of the proposed method asymptotically approaches CRLB. The proposed Channelization-ISM method shows a better performance than the ISM method at an arbitrary level of SNR and an arbitrary number of snapshots. This is mainly because the channelization receiver has a higher frequency resolution. Signal parameters can be obtained accurately, which is very helpful for DOA estimation. The output SNR is improved by removing by removing the noises beyond the bandwidth of the signals. This result supports the discussions in Section 3.5 and demonstrates the efficiency of our proposed method. The second simulation considers the same scenario as the first simulation to compare the performances of the TOPS method [7] and the proposed Channelization-TOPS method. Similar to the

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result of the first simulation, Figures 6 and 7 show that the proposed Channelization-TOPS method always outperforms the TOPS method at any level of SNR and any number of snapshots. The proposed Sensors 2016, 16, 1031 18 channelization-based method has a better DOA estimation accuracy than the conventional ISM99of and Sensors 2016, 16, 1031 of 18 TOPS methods. 1

10 1 10

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To study the detection capability of week signal with the proposed Channelization-ISM Tostudy studythethe detection capability of week with the proposed Channelization-ISM To detection capability of week signalsignal with the proposed Channelization-ISM method, method, the resolution probabilities versus SNR for the proposed Channelization-ISM and ISM method, the resolution probabilities versus SNRproposed for the proposed Channelization-ISM ISM the resolution probabilities versus SNR for the Channelization-ISM and ISM and method method are calculated. By definition, a signal is resolved successfully ˆwhen | ˆˆk   k | is smaller   k | isthan |  ksmaller smaller method are calculated. By definition, is resolved successfully are calculated. By definition, a signal ais signal resolved successfully when |θkwhen ´ θk | is 0.5, ˆ and therepresent ˆk where  than 0.5, the estimated and true directions for the kth incident signal, where θ and θ represent estimated and true directions for the kth incident signal, respectively. ˆ k k than 0.5, wherek  k and  k represent the estimated and true directions for the kth incident signal, respectively. This simulation considers the scenario where there are two sources with one source respectively. This simulation considers the scenario where there are two sources with one source (weak source) being weaker than the other one by 20 dB. The simulation parameters are the same (weak source) being weaker than the other one by 20 dB. The simulation parameters are the same with those of the second simulation. Figure 7 shows the resolution probability of the two sources with those of the second simulation. Figure 7 shows the resolution probability of the two sources versus SNR that corresponds to the strong source with ISM and Channelization-ISM method. versus SNR that corresponds to the strong source with ISM and Channelization-ISM method. Source 1 is the weak source. The resolution probability for the weak source with ISM method is Source 1 is the weak source. The resolution probability for the weak source with ISM method is

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This simulation considers the scenario where there are two sources with one source (weak source) being weaker than the other one by 20 dB. The simulation parameters are the same with those of the second simulation. Figure 8 shows the resolution probability of the two sources versus SNR that corresponds to the strong source with ISM and Channelization-ISM method. Source 1 is the Sensors 2016, 16, 1031 10 of 18 Sensors 2016, 16, 1031resolution probability for the weak source with ISM method is unsatisfactory, 10 of 18 as weak source. The it remains low even though the SNR increases to 6. Thewith proposed can obtain Channelization-ISM can obtain obtain similar performance lower Channelization-ISM SNR. ISM ISM suffers suffers from from bad Channelization-ISM can similar performance with lower SNR. bad similar performance with lower SNR. ISM suffers from bad performance degradation for the The weak performance degradation for the weak source while the proposed Channelization-ISM doesn’t. performance degradation for the weak source while the proposed Channelization-ISM doesn’t. The source while the proposed Channelization-ISM doesn’t. method The results illustrate theaspect proposed results illustrate that the the proposed proposed channelization-based performs better that on the the of results illustrate that channelization-based method performs better on aspect of channelization-based method performs better on the aspect of dynamic range. Figure method 9 which shows dynamic range. Figure 8 which shows the comparison between the TOPS and dynamic range. Figure 8 which shows the comparison between the TOPS method and theChannelization-TOPS comparison betweenalso the supports TOPS method and Channelization-TOPS also supports the conclusion. the conclusion. conclusion. Channelization-TOPS also supports the 0

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In the the last last simulation, simulation, the the performances performances of of the the proposed proposed Channelization-ISM Channelization-ISM method method and and In Channelization-TOPS method method against against the the number number of of sub-channels sub-channels are are studied. studied. The The SNR SNR is is fixed fixed at at Channelization-TOPS 10 dB and the number of snapshots is 256. Figure 9 shows that with the increase of the number of 10 dB and the number of snapshots is 256. Figure 9 shows that with the increase of the number of sub-channels, the the performances performances of of the the proposed proposed methods methods improves. improves. This This is is mainly mainly because because the the sub-channels, sub-channel bandwidth becomes narrower with the increase of the number of sub-channels. Then, sub-channel bandwidth becomes narrower with the increase of the number of sub-channels. Then, the influence influence over over the the phase phase difference difference between between sensor sensor outputs outputs from from the the temporal temporal frequency frequency of of the

sub-channels becomes weaker. These will lead to a better performance of the DOA estimation. sub-channels becomes weaker. These will lead to a better performance of the DOA estimation. However, the increase of the number of sub-channels may result an increase of the computational However, the increase of the number of sub-channels may result an increase of the computational complexity. The number of channels used generally is limited when digital channelization is complexity. The number of channels used generally is limited when digital channelization is implemented on a hardware platform. implemented on a hardware platform.

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In the last simulation, the performances of the proposed Channelization-ISM method and Channelization-TOPS method against the number of sub-channels are studied. The SNR is fixed at 10 dB and the number of snapshots is 256. Figure 10 shows that with the increase of the number of sub-channels, the performances of the proposed methods improves. This is mainly because the sub-channel bandwidth becomes narrower with the increase of the number of sub-channels. Then, the influence over the phase difference between sensor outputs from the temporal frequency of sub-channels becomes weaker. These will lead to a better performance of the DOA estimation. However, the increase of the number of sub-channels may result an increase of the computational complexity. The number of channels used generally is limited when digital channelization is implemented on a hardware platform.

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5. Experiments Experiments 5.5.Experiments In this section, we present experiments carried out in a microwave anechoic chamber to further thissection, section,we wepresent presentexperiments experimentscarried carriedout out in a microwave anechoic chamber to further InInthis demonstrate the performance of the proposed algorithm.in a microwave anechoic chamber to further demonstrate the performance of the proposed algorithm. demonstrate the performance of the proposed algorithm. 5.1. The Architecture of DAR Test-Bed 5.1.The TheArchitecture ArchitectureofofDAR DARTest-Bed Test-Bed 5.1. Figure 10 shows the architecture of the wideband DAR test-bed, which is composed of Figure11 10 shows the architecture the wideband DAR test-bed, which is of composed Figure shows the architecture of theof wideband DAR test-bed, which is composed widebandof wideband antennas, RF front modules, digital receiver, digital signal processor, built-in calibration wideband RF front modules, digital receiver, digital signal processor, built-in calibration antennas, RFantennas, front modules, digital receiver, digital signal processor, built-in calibration circuitry and circuitry and data recorder. circuitry and data recorder. data recorder.

Figure 11. The architecture of the wideband DAR test-bed. Figure 10. The architecture of the wideband DAR test-bed. Figure 10. The architecture of the wideband DAR test-bed.

The wideband wideband antenna antenna is is realized realized using using eight eight tapered tapered slot slot antennas antennas (TSAs) (TSAs) shown shown in in Figure Figure 11. 12. The The wideband antenna is realized using eight tapered slotisantennas (TSAs) shown inamplifier Figure 11. Figure 13 shows the architecture of the RF front-end, which composed of low noise Figure 12 shows the architecture of the RF front-end, which is composed of low noise amplifier Figureprogrammable 12 shows the architecture of the RF front-end, which is composed of Signals low noise amplifier (LNA), splitter and RFRF switch. from thethe RF (LNA), programmableattenuator, attenuator,band bandpass passfilters, filters,power power splitter and switch. Signals from (LNA), programmable attenuator, band pass filters, power splitter and RF switch. Signals from the front-end are directly digitized by the digital receiver. As shown in Figure 14, the 13, digital RF front-end are directly digitized bywideband the wideband digital receiver. As shown in Figure the RF front-end are directly digitized by the wideband digital receiver. As shown in Figure 13, the receiver receiver consists ofconsists ADC, large-scale programmable array (FPGA)gate and multichannel digital of ADC,field large-scale field gate programmable array (FPGA)optical and digital receiver consists of ADC, large-scale field programmable gate array (FPGA) and modules. It isoptical capable of directly input signals up 3 GHz at theup sampling of multichannel modules. It issampling capable offour directly sampling fourtoinput signals to 3 GHzrate at the multichannel optical modules. It is capable ofThe directly sampling four input signals up to 315GHz at the 1.2 GHz utilizing band-pass sampling theories. digital signal processor shown in Figure is based sampling rate of 1.2 GHz utilizing band-pass sampling theories. The digital signal processor shown sampling rate of 1.2 GHz utilizing band-pass sampling theories. The digital signal processor shown in Figure 14 is based on the latest generation of high-performance multicore fixed and floating-point in Figure 14 is based on the latest generation of high-performance multicore fixed and floating-point

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DSP TMS320C6678 and Xilinx Virtex-6 Virtex-6 family’s family’s high-density, FPGA, which which is applicable applicable and for on theTMS320C6678 latest generation of high-performance multicorehigh-density, fixed and floating-point DSP TMS320C6678 DSP and Xilinx FPGA, is for DSP TMS320C6678 and Xilinx Virtex-6 family’s high-density, FPGA, which is applicable for high-speed data communication, processing. The data recorder is designed to store kinds of data for Xilinx Virtex-6 family’s high-density, FPGA, which is applicable for high-speed data communication, high-speed data data communication, communication, processing. processing. The The data data recorder recorder is is designed designed to to store store kinds kinds of of data data for for high-speed system test test and and post-processing. processing. The post-processing. data recorder is designed to store kinds of data for system test and post-processing. system system test and post-processing.

Figure 12. wideband antenna. 11. The Figure 11. 11. The wideband wideband antenna. antenna. Figure The

Figure 12. 12. The The RF RF front-end. front-end. Figure Figure 12. Figure 13. The The RF RF front-end. front-end.

Figure 13. 13. The The digital digital receiver. receiver. Figure Figure Figure 13. 14. The The digital digital receiver. receiver.

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Figure Figure 14. 15. The The digital digital signal signal platform. platform.

5.2. 5.2. Experiment Experiment Carried Carried Out Out in in Microwave Microwave Anechoic Anechoic Chamber Chamber The microwave anechoic chamber. As shown in Figure 15, the The experiment experimentisiscarried carriedout outinina a microwave anechoic chamber. As shown in Figure 16, antenna array is placed on a rotation platform. Wideband signals impinging on the array the antenna array is placed on a rotation platform. Wideband signals impinging on the array are are transformed intoparallel parallelwaves waves through a reflector is shown in 17. Figure There center transformed into through a reflector whichwhich is shown in Figure There16. center frequency frequency f 0 = 2.7 GHz and bandwidth B = 500 MHz. The gain-phase and mutual coupling errors are f 0 = 2.7 GHz and bandwidth B = 500 MHz. The gain-phase and mutual coupling errors are calibrated calibrated by the method given [34]. Thesignals wideband signals sampled are directly sampled the 10 bitsa by the method given in [34]. Thein wideband are directly by the 10 bitsby ADCs with ADCs withrate a sampling rateutilizing of 1.2 Figure Gsps utilizing the band-pass sampling theory. The complex signal 14. The digital signal platform. sampling of 1.2 Gsps the band-pass sampling theory. The complex signal data speed is data speed is 600 MHz after digital quadrature demodulation. Then we split the signal into 32 600 MHz after digital quadrature demodulation. Then we split the signal into 32 sub-channels with sub-channels with the FPGA digital platform. Theofoutput data speed of each sub-channel 5.2. FPGA Experiment Carried Out platform. in on Microwave Anechoic Chamber the on digital signal Thesignal output data speed each sub-channel is 18.75 MHz, which is 18.75 MHz, which is lower than the highest frequency of the Virtex-6 FPGA. Besides, the hard is lower than the highest frequency of the Virtex-6 FPGA. Besides, the hard resources consumption is The experiment is carried out in a microwave anechoic chamber. As shown in Figure 15, the resources consumption is calculated as shown in Table 1. The results illustrate that the hardware calculated as shown in Table 1. The results illustrate that the hardware platform adequately meets the antenna array is placed on a rotation platform. Wideband signals impinging on the array are platform adequately meets the resources constraint. resources constraint. transformed into parallel waves through a reflector which is shown in Figure 16. There center frequency f0 = 2.7 GHz and bandwidth B = 500 MHz. The gain-phase and mutual coupling errors are Table 1. Hardware resources consumption. calibrated by the method given in [34]. The wideband signals are directly sampled by the 10 bits ADCs with aHardware samplingResources rate of 1.2 Gsps utilizing sampling theory. The complex signal Total the band-pass Consumption Percentage data speed is 600 MHz after digital quadrature demodulation. Then we split the signal into 32 occupied Slices 49,200 2456 4.99% sub-channels with FPGA on digital 393,600 signal platform. The output data speed of each sub-channel Slicethe Registers 10,523 2.67% is 18.75 MHz, which lower than the 196,800 highest frequency of the Virtex-6 FPGA. Slice is LUTs 6618 3.36%Besides, the hard DSP48E1s 1344 in Table 1. The 477 results illustrate 35.49% resources consumption is calculated as shown that the hardware RAMB36E1/FIFO36E1s 704 56 7.95% platform adequately meets the resources constraint.

Figure 15. Experiment in a microwave anechoic chamber.

Figure Figure 15. 16. Experiment Experiment in in aa microwave microwave anechoic anechoic chamber. chamber.

Figure 16. The reflector.

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Figure 15. Experiment in a microwave anechoic chamber.

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Table1.1.Hardware Hardwareresources resourcesconsumption. consumption. Table HardwareResources Resources Hardware occupied Slices occupied Slices SliceRegisters Registers Slice Slice LUTs Slice LUTs

Total Consumption Consumption Percentage Percentage Total 49,200 2456 4.99% 49,200 2456 4.99% 393,600 10,523 2.67% 393,600 10,523 2.67% 196,800 6618 3.36% 196,800 6618 3.36%

DSP48E1s 1344 477 DSP48E1s 1344 477 Figure reflector. Figure17. 16. The The reflector. RAMB36E1/FIFO36E1s 704 RAMB36E1/FIFO36E1s 704 5656

35.49% 35.49% 7.95% 7.95%

Figure shows theamplitude amplitude ofreceived received signalsin timedomain. domain.Eight Eight curves with different Figure 18 shows thethe amplitude ofofreceived signals inintime time domain. Eight curves with different Figure 1717shows signals curves with different colors represent the different sensor outputs of the ULA. Figure 18 depicts the received signals the colorscolors represent the different sensor outputs of the ULA. Figure 19 depicts the received signals in the represent the different sensor outputs of the ULA. Figure 18 depicts the received signals ininthe frequency domain. The spatial spectrum estimations of the received signals with different methods frequency domain. TheThe spatial spectrum estimations differentmethods methods are frequency domain. spatial spectrum estimationsofofthe thereceived receivedsignals signals with different areplotted 19and andFigure 20.The Thetrue trueDOA DOAcould couldbebemeasured measuredaccording accordingtotothe therecords are ininFigure ofof plotted in plotted Figures 20Figure and19 21. TheFigure true 20. DOA could be measured according to the records ofrecords the rotation the rotation platform with a precision of 0.05°. It is clear that the DOA estimations the with rotation platformof with of the 0.05°. It estimations is clear that the DOA estimationsmethods ofof platform a precision 0.05˝ .aIt precision is clear that DOA of channelization-based channelization-based methods are more approximate to the true DOA. The performances of the channelization-based moreThe approximate to the of true DOA. The performances of the are more approximate tomethods the trueare DOA. performances the proposed channelization-based proposed channelization-based methods are better than those of the conventional ISM and TOPS proposed channelization-based methods are better than those of the conventional ISM and TOPS methods are better than the those of the conventional ISM and methods. Rotating the data arrayare from methods. Rotating array from −50°toto50° 50°atat thestep stepTOPS 101groups groups original methods. Rotating the ˝array from −50° the ofof1°,1°,101 ofoforiginal data are ˝ ˝ ´50 toobtained. 50 at the stepestimations of 1 , 101 with groups of original dataangles are obtained. DOAusing estimations different DOA different incident arecalculated calculated differentwith methods. obtained. DOA estimations with different incident angles are using different methods. incident angles are calculated using different methods. Table 2 presents the RMSEs of 101 estimates Table 2 presents the RMSEs of 101 estimates with different methods. The proposed channelization Table 2 presents the RMSEs of 101 estimates with different methods. The proposed channelization methodsoutperform outperform theconventional conventional ISMand andTOPS TOPS methods.The Theexperimental experimental resultsare areiningood goodand with different methods. The proposed channelization methods outperform the conventional ISM methods the ISM methods. results agreement with the simulation results. TOPSagreement methods.with Thethe experimental results are in good agreement with the simulation results. simulation results.

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Figure Receivedsignals signals expressed expressed in domain. Figure 19.18. Received infrequency frequency domain.

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Figure DOA estimations with ISM method and Channelization-ISM method. Figure 20.19. DOA estimations with ISM method and Channelization-ISM method. Figure 19. DOA estimations with ISM method and Channelization-ISM method.

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Figure 21.20. DOA estimations with TOPS method and Channelization-TOPS method. Figure DOA estimations with TOPS method and Channelization-TOPS method. Figure 20. DOA estimations with TOPS method and Channelization-TOPS method. Table 2. 2. Mean deviation ofof different methods. Table Mean deviation different methods. Table 2. Mean deviation of different methods.

Method RMSE Method RMSE Method RMSE TOPS Method (degree) 0.6792 TOPS Method (degree) 0.6792 TOPS Method (degree) Channelization-TOPS Method (degree) 0.6792 0.6121 Channelization-TOPS Method (degree) 0.6121 0.6121 Channelization-TOPS Method (degree) ISM Method (degree) 3.2509 Method (degree) 3.2509 ISM MethodISM (degree) 3.2509 Channelization-ISM Method (degree) 0.9103 Channelization-ISM Method (degree) Channelization-ISM Method (degree) 0.9103 0.9103

6. Conclusions Conclusions 6. 6.Conclusions In this paper, we propose aa hardware-efficient, channelization-based DOA estimation method this paper, propose hardware-efficient, channelization-based DOA estimation method InIn this paper, wewe propose a hardware-efficient, channelization-based DOA estimation method for wideband signals. It splits the wideband array output into multiple frequency sub-channels and for wideband signals. It splits the wideband array output into multiple frequency sub-channels and for wideband signals. It splits the wideband array output into multiple frequency sub-channels estimate signal parameters of each sub-channel. The sub-channels within the wideband signal estimate signal sub-channel. The The sub-channels sub-channels within withinthe thewideband widebandsignal signal and estimate signalparameters parametersofof each each sub-channel. bandwidth are selected on the basis of the power of every sub-channel. The channelization-ISM bandwidth are selected on the basis of the power of every sub-channel. The channelization-ISM bandwidth are selected on the basis of the power of every sub-channel. The channelization-ISM method applies narrow techniques the selected channels and gets the final DOA estimate methodapplies appliesnarrow narrowtechniques techniquestoto tothe theselected selectedchannels channelsand andgets getsthe thefinal finalDOA DOAestimate estimatebyby by method averaging the results from all the selected channels. The Channelization-TOPS method measures the averaging the results from all the selected channels. The Channelization-TOPS method measures the averaging the results from all the selected channels. The Channelization-TOPS method measures the orthogonality orthogonality between between the the signal signal and and the the noise noise subspaces subspaces of of the the output output sub-channels sub-channels to to estimate estimate DOAs. The proposed channelization methods outperform the conventional ISM method and DOAs. The proposed channelization methods outperform the conventional ISM method and TOPS TOPS

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orthogonality between the signal and the noise subspaces of the output sub-channels to estimate DOAs. The proposed channelization methods outperform the conventional ISM method and TOPS method, which results from the proposed channelization method being able to estimate the signal parameters more accurately and improve the output SNR more. Besides, the parallel processing architecture makes it easy to implement on hardware. Simulations and experiments in a microwave anechoic chamber are carried out as well. The results illustrate that the proposed method can achieve better estimation accuracy and dynamic range performance than the conventional ISM method and TOPS method. Acknowledgments: The authors are thankful to the anonymous reviewers and the editors for their help in improving the manuscript and the ATR Lab for collecting the data used in this research. Author Contributions: All authors contributed extensively to this paper. Rui Guo and Yue Zhang provided the main idea of this work. Qianqiang Lin and Yue Zhang conceived and designed the experiments. Rui Guo performed the experiments and wrote the paper. Zengping Chen modified the manuscript and provided many valuable suggestions. Conflicts of Interest: The authors declare no conflict of interests.

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