Blind velocities mitigation for MIMO GMTI radar with Doppler division multiple access waveforms

Accepted Manuscript Regular paper Blind velocities mitigation for MIMO GMTI radar with Doppler division multiple access waveforms Fuyou Li, Feng He, Zhen Dong, Manqing Wu PII: DOI: Reference:

S1434-8411(17)31564-9 https://doi.org/10.1016/j.aeue.2017.10.023 AEUE 52101

To appear in:

International Journal of Electronics and Communications

Received Date: Accepted Date:

28 June 2017 14 October 2017

Please cite this article as: F. Li, F. He, Z. Dong, M. Wu, Blind velocities mitigation for MIMO GMTI radar with Doppler division multiple access waveforms, International Journal of Electronics and Communications (2017), doi: https://doi.org/10.1016/j.aeue.2017.10.023

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Blind velocities mitigation for MIMO GMTI radar with Doppler division multiple access waveforms Fuyou Lia, Feng Hea,*, Zhen Donga, Manqing Wua,b a

School of Electronic Science and Engineering, National University of Defense Technology, De Ya Road, Changsha, China, 410073

b

China Academy of Electronics and Information Technology, China Electronics Technology Group Corporation (CETC), Beijing, China, 100846

Correspondence author: Feng He, National University of Defense Technology, School of Electronic Science and Engineering, De Ya Road, Changsha, China, 410073, E-mail: [email protected], +86 13607485198

Abstract

Multiple-input multiple-output (MIMO) radar with multiple transmitters and multiple receivers can achieve a larger virtual antenna array and more system degrees of freedom; thus applying it to ground moving target indication (GMTI) radar can improve the performance of GMTI. Doppler division multiple access (DDMA) waveforms are approximately orthogonal providing good minimum detectable velocity (MDV) performance. However, in such DDMA systems, a sufficient

(PRF) design

freedom is required. Furthermore, these waveforms suffer from blind velocities which

MIMO GMTI radar mitigate blind

mitigate blind MIMO GMTI radar

Keywords: blind velocities mitigation; DDMA MIMO GMTI radar;

1. Introduction

Multiple-input multiple-output (MIMO) radar has recently become a hot research area with the rapid development of array antennas. MIMO radar with multiple transmitting antennas and multiple receiving antennas has potential advantages in target detection and angle estimation compared to single-input multiple-output (SIMO) radar [1-3]. The returned signals of MIMO radar are separated by matched filters or/and bandpass filters, and then processed together; thus the length of the virtual array and the number of the system degrees of freedom are greater than those for SIMO radar. MIMO radar has a potentially important application in

ground moving-target indicator (GMTI) radar. A decreased minimum detectible velocity (MDV) can be achieved due to the longer baseline by the MIMO GMTI radar [1]. Doppler division multiple access (DDMA) waveforms can achieve high performance from the approximately ideal MIMO radar [4, 5]. By applying a modulation in slow time, the echoes from different transmitting waveforms can be separated in the Doppler domain. In a GMTI radar system, the moving targets are detected based on the difference in between moving targets and static ground clutter. Space time adaptive processing (STAP) is an optimum filter to cancel out the clutter and enhance the target detection.

in the space time

The temporal samplings play a key role in the detection performance related to the ambiguous level. These problems in GMTI systems are so-called blind velocities, i.e., when the STAP outputs drop to zero. Blind velocities correspond to the radial velocities of moving targets where the grid of clutter patches is positioned [10]. For reference, the radar system parameters are listed in Table 1. Therefore, the blind velocities of SIMO GMTI radar are represented as

vblind  n f r / 2

(1)

where n is an integer. The blind velocities of moving targets are only relative to the variation

of the PRF and the carrier frequency. Furthermore, DDMA waveforms suffer from blind velocities more seriously than those in SIMO radar, especially in

NT

DDMA MIMO GMTI

NT NT  1

NT velocities

f r / NT

fd

vblind  n

 fr

(2)

2 NT

where n is an integer

n 1 1 / NT To detect the moving targets in GMTI radar, the blind velocities should be mitigated. Some researchers have proposed methods to mitigate the blind velocities based on the influencing factors from equation (1). Different carrier frequencies correspond to different blind velocities, so the

More transmitters are required to transmit multiple waveforms, and the bandwidth for the receivers is increased. blind velocities related to the PRFs

mitigating blind

MIMO GMTI radar mitigate blind

modulation with linear phases is applied in each transmitter. For different PRFs, different modulation factors in slow time are employed. The

modulation corresponding to the

employed.

blind

Table 1 DDMA MIMO GMTI radar system parameters Parameter

Symbol

Value

number of transmitters

NT

4

number of receivers

NR

4

number of pulses per CPI

M

128

radar carrier frequency

fc

10GHz

speed of light

c

3 108 m/s

radar wavelength

  c / fc

0.03m

f r  f r1  6600 Hz, f r 2  7100 Hz

PRF

f r , f r1 , f r 2

PRI

Tr  1/ f r

1.5152 104 s

sub-PRF in DDMA MIMO

f rc  f r / NT

1650Hz

dT

0.015m

receiving subarrays separation

dR

0.06m

platform velocity

va

70m/s

GMTI radar system transmitting subarrays separation

2. DDMA MIMO GMTI Radar

2.1. DDMA MIMO GMTI Radar Signal Model

In MIMO radar, some literature focuses on the fast-time waveforms transmitting from each of the NT transmitters. Waveform orthogonality is achieved in fast time so that the echoes can be separated by matched filters or bandpass filters. However, it is difficult to achieve a good GMTI performance in fast-time MIMO systems [15]. DDMA waveforms achieve orthogonality in the Doppler domain by modulating different linear phases in each transmitter. The DDMA MIMO GMTI radar transmits NT identical waveforms with the same carrier frequency f c . To ensure that the NT transmitting waveform can be separated in Doppler domain, consider dividing the full PRF into NT orthogonal sub-PRFs f rc satisfying

f rc  f r / NT , which is more than the highest Doppler frequency of interest. DDMA MIMO GMTI radar emits different Doppler-shifted pulse sequences from each transmitter. Assume

that the starting phase of each waveform is varied with the slow-time pulse

m  0  m  M  1 . Then the starting phase   l , m  from the l-th  l  0,1,

, NT  1

transmitter at slow time m can be represented as

  l , m   l mTr where Tr is

(3)

 l is the phase modulated coefficient. l  

f rc  NT  1  2l  2

(4)

Consider a 4  4 broadside-looking MIMO GMTI radar with a Nyquist virtual array [4]. The simulation parameters are shown in Table 1. And we assume that the clutter is Gaussian, and ignore the variation from different range. The range-Doppler image for a receiver is shown in Fig. 1. Here, there are 4 stripes corresponding to 4 transmitters. Thus each of the echoes for the different transmitters can be extracted by an inverse Fourier transform of each stripe. Finally, space-time adaptive processing (STAP) can be applied to detect the moving targets [6].

Fig. 1 Range-Doppler image for a DDMA MIMO system

2.2. Analysis of Blind

DDMA MIMO GMTI Radar

In the DDMA MIMO GMTI radar system, to ensure the orthogonality of the DDMA waveforms, we require that the PRF satisfies

f r / NT  BD

(5)

where BD is the Doppler bandwidth of both the clutter and targets. In a DDMA MIMO GMTI radar system, as shown in Fig. 2, for a moving target with the radial velocity vr and the cone angle t of the look direction from the target to the antenna phase center, the Doppler frequency f d of this moving target for the carrier frequency f c is fd 

2vr f c 2va f c  cos t c c

(6)

where 2vr f c / c is caused by target motivation, and 2va cos t fc / c is caused by platform motivation. In a DDMA system, when the

fast

is greater than

the sub-PRF, the fast moving target will

nf r / NT f d  nf r / NT

fd

the

functional relations between the ambiguous Doppler frequency and the radial velocity can be represented as f d  nf r / NT 

2(vr  vblind ) f c 2va f c  cos t c c

(7)

where n is an integer, and vblind is the blind velocity. Based on equations (6) and (7), the

vblind  n

 fr 2 NT

n

cf r 2 NT f c

(8)

Z

Tx

Rx

t

va

Y X

Moving targets

Iso-range ring

Fig. 2 Geometry of airborne antenna arrays Taking the parameters in the previous section into consideration, the sub-PRF is

f r / NT  6600 / 4  1650 Hz, so the first blind velocity ( n  1 ) is 24.75 m/s. In a SIMO system, first blind velocity ( n  1 ) is 99 m/s. This means there will be NT  1 new “blind velocities” (24.75 m/s, 49.5 m/s and 74.25 m/s) caused by the DDMA waveform when compared to the SIMO system with the first blind velocity at 99 m/s. The SCNR (signal to clutter plus noise ratio) loss is shown in Fig. 3. The result shows that there are 4 notches (i.e., blind velocities) with high SCNR loss formed by STAP processing. Therefore, the mitigation of the blind velocities is the key point for DDMA MIMO GMTI radar systems.

Fig. 3. SINR Loss after STAP for DDMA MIMO GMTI radar

3. Methods of Blind Velocities Mitigation Based on the analytical expression (8), the key factors influencing on blind velocities are the velocities [16,17]. To mitigate the blind velocities caused by DDMA MIMO GMTI radar,

PRF/PRI to mitigate the blind velocities.

3.1. In a DDMA MIMO GMTI radar system with a fixed carrier frequency, the blind velocities depend on the different PRFs. Blind velocities can be mitigated by the To compare it with the traditional DDMA system in a relatively fair circumstance, we assume that the

number of coherent pulses. Thus,

the number of coherent pulses of each PRF is changed into M / 2 . The method is shown in Fig. 4. Using the multi-PRF DDMA method, the echo data are sampled at sampling rate f r1 at slow-time pulses from 0 to M / 2  1 , and sampled at sampling rate f r 2 at slow-time pulses from M / 2 to M  1 . For moving targets at the same cone angle, the difference of

the blind velocities (an example for n=1) based on equation (8) between different PRFs can be represented as

c  f r 2  f r1  2 f c NT

 vr  vblind 1  vblind 2 

(9)

where vblind 1 and vblind 2 are the first blind velocities corresponding to PRFs f r1 and f r 2 , respectively. The Doppler resolution of a radar system is f r / M . For the multi-PRF DDMA, the number of the coherent pulses for each PRF is M / 2 , so the lowest distinguishable radial velocity is

vr min 

c min  f r1 , f r 2  2 fc M /2

(10)

When the difference of the blind velocities in (9) is more than the lowest distinguishable radial velocity in (10), the blind velocities can be mitigated, i.e.

 vr  vr min f r 2  f r1 

min( f r1 , f r 2 ) NT M /2

(11)

Slow time PRI1

PRI1

PRI2

PRI2

M/2 slow-time samples M/2 slow-time samples for PRF1 for PRF2

Fig. 4 samples in slow time for Different from the traditional DDMA GMTI radar, the

DDMA MIMO

GMTI radar must change the slow-time modulated phases with the variable PRFs. Then, the

starting phase   l , m  from the l-th transmitter at slow time m  0  m  M / 2  1 can be represented as

  l , m   l1mTr1 , 0  m  M / 2  1

(12)

 l1 is the phase modulated coefficient.

where Tr1  1/ f r1 is

 l1  

f r1  NT  1  2l  2 NT

(13)

In the slow-time pulses from M / 2 to M  1 , the starting phase   l , m  from the l-th transmitter at slow time m  M / 2  m  M  1 can be represented as

  l , m   l 2  m  M / 2  Tr 2 , M / 2  m  M  1 where Tr 2  1/ f r 2 is

(14)

 l 2 is the phase modulated coefficient. l 2  

fr 2  NT  1  2l  2 NT

(15)

On the receiving end, the flowchart of the signal processing for a single receiver based on the DDMA method is shown in Fig. 5. First, the matched filter should be applied to the echoes data. Second, the echo data with different PRFs are moved to the range-Doppler domain by FFT in the slow-time domain respectively. Then, the echoes from different transmitters can be extracted via Doppler domain bandpass filters. Next, an inverse FFT is applied to acquire the outputs of MIMO GMTI radar. Last, the echoes of MIMO GMTI radar are jointly processed by STAP.

Receiving subarray matched filter

slow-time pulses from 0 to M/2-1

slow-time pulses from M/2 to M-1

PRF1

PRF2

FFT

FFT

Bandpass filters in Doppler domain

Bandpass filters in Doppler domain

… IFFT

… IFFT

IFFT

IFFT

MIMO outputs

Fig. 5 Flowchart of the signal processing for a single receiver based on the

DDMA

method

3.2.

In the PRI-dithered DDMA method, the random dithers are added to the constant PRI. The PRIs between adjacent slow-time pulses are variable in a CPI. Assume that the PRI is Tr ; then, the normalized Doppler frequency of a moving target in traditional DDMA system is f d _ norm 

f d _ norm  0, 1, 2,

2vr



NT Tr

(16)

correspond to the nulls of the STAP output, and the radial velocities of

moving targets with these Doppler frequencies are blind velocities. When PRIs are varied, velocity are different; thus, the

aT  1 exp  j 2 f d Tr  exp  j 2 f d 2Tr 



T

fd

exp  j 2 f d  M  1 Tr 

T

(17)

represents the transpose of a matrix or

vector

Tri

aT  1 exp  j 2 f d ,1  exp  j 2 f d ,2 

exp  j 2 f d ,M 1 

T

(18)

where m

f d ,m  f d  Tri , m  1, 2,

, M 1

(19)

i 1

In the SIMO GMTI radar, the standard STAP can be applied to the Different from the SIMO GMTI radar, the DDMA MIMO GMTI radar must extract the MIMO outputs by bandpass filters in the Doppler domain. To adopt a method similar to the traditional DDMA system, the slow-time modulated phases in the

DDMA system are varied with

PRIs. In the

DDMA system, the starting phase   l , m  from the l-th transmitter at the slow-time pulse m can be changed from   l , m   l mTr into m

  l , m   l  Tri , m  1, 2, , M  1 i 1

(20)

where the phase modulated coefficient  l is the same as (4) in order to preserve a linear relationship between the starting phase and the slow time. We define   l ,0   0 . Suppose that the nominal PRI of the DDMA system is Tr , and the maximum dither without range ambiguity is Tmax . PRIs subject to the standard uniform distribution are employed:

Tri

U Tr  Tmax , Tr  Tmax 

where U  a, b  means the standard uniform distribution on the open interval

(21)

 a, b  .

The

processing procedures of the nonuniformly sampled MIMO radar data for a single receiver is shown in Fig. 6. First, matched filters are used on the MIMO radar echoes from each receiver. Second, we move to the range-Doppler domain by a nonuniform discrete Fourier transform (NDFT) [19, 20]. Because DDMA waveforms are utilized, there are NT stripes in the range-Doppler image. The echoes for the MIMO channels can be extracted by bandpass filters in the Doppler domain. Then, an inverse NDFT yields the nonuniformly sampled space-time snapshots, which are the outputs of MIMO GMTI radar. Finally, the MIMO echoes data are processed with STAP.

Receiving subarray matched filters NDFT Bandpass filters in Doppler domain

… inverse NDFT

inverse NDFT

MIMO outputs

Flowchart of the signal processing for a single receiver based on the

4. Simulation Results

In this section, we compare the output SINR performance of the proposed method with that of traditional DDMA MIMO GMTI radar. For the multi-PRF DDMA method, consider an airborne broadside-looking radar with the same parameters as stated in Table 1. The PRFs are

f r1  6600 Hz for the pulses from 0 to 63 and f r 2  7100 Hz for the pulses from 64 to 128, which satisfy the condition of expression (11). For the PRI-dithered DDMA method, consider an airborne broadside-looking radar with the same parameters as the previous except the nominal PRF

Tri

f r  6600 Hz. Assume the maximum dither is Tmax  0.2Tr , and

U  0.8Tr ,1.2Tr  . The extracted MIMO output data via bandpass filtering in Doppler

domain and inverse NDFT are processed with STAP. The SCNR loss for MIMO GMTI radar using the multi-PRF DDMA and PRI-dithered DDMA methods is shown in Fig. 7, which illustrates the impact of multi-PRF and PRI-dithered techniques applied to DDMA. As seen in this figure, the SCNR losses located at blind velocities have been substituted with small losses by using multi-PRF DDMA and PRI-dithered DDMA methods compared to the traditional DDMA MIMO GMTI radar. The multi-PRF and PRI-dithered DDMA are both effective methods for the mitigation of blind velocities for DDMA systems. Utilizing the multi-PRF DDMA method, the SCNR loss cannot decline at the location without the blind velocities, and the SCNR loss at the

location of the first blind velocities is about -3 dB. The SCNR losses of the PRI-dithered DDMA method located at blind velocities have been substituted with a small loss expanding over the whole Doppler space. The blind velocities have been nearly mitigated by PRI-dithered DDMA at the cost of smaller SCNR losses in the entire Doppler space.

Fig. 7 SCNR loss for MIMO GMTI radar using the Multi-PRF DDMA and PRI-dithered DDMA methods versus the traditional DDMA radar Both the

mitigate blind

velocities compared with traditional DDMA systems. The implement, but its performance is limited for systems with a smaller number of coherent pulses. In addition, the ambiguity mitigation method of the performance sensitive to the PRF error. The SCNR loss for the

a small

PRF error is shown in Fig. 8. When one of the PRFs has a small error, although the blind velocities can be mitigated, the result may have a relatively large error without any warning. If the real Doppler of a moving target is f dt , and the measured Doppler corresponding to

PRFs f r1 and f r 2 are f d 1 and f d 2 , respectively, then f dt  mod  f di , f ri  , i  1, 2 , where

mod  a, b  returns the modulus after division of a by b . Thus, PRF error has a large effect on the real Doppler of the moving target. For the maximum dither is a key factor influencing on the performance. maximum dithers

the maximum

dither Tmax , the better the performance of mitigating blind velocities. However, the maximum dither is limited in the

due to the range ambiguities;

thus the unambiguous swath decreases. In addition, the relatively complex system control and implementation, and it has Both these

are useful when a wide range of detectable

velocities is required in the GMTI systems, which is important in DDMA MIMO GMTI radar system.

Fig. 8 SCNR loss for

a small PRF error

Fig. 9 SCNR loss at the first blind velocity for different maximum dithers

5. Conclusions

In this paper, two methods to mitigate the blind velocities of DDMA MIMO GMTI systems are proposed. Both of the methods were demonstrated to be capable of mitigating the blind velocities. The

influencing the blind velocities in DDMA MIMO GMTI radar.

These

should be necessary when a wide

range of detectable velocities is required especially in DDMA MIMO GMTI radar with small . velocities mitigation.

demonstrated the validity of the blind

Acknowledgments The work described in this paper was supported by the Major Research Plan of the National Natural Science Foundation of China [Grant number 91438202]. The authors would like to thank the reviewers for their constructive comments and suggestions.

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Fuyou Li is working toward his PhD degree at the National University of Defense Technology, Changsha, China. He received his BS and MS degree in information engineering from the National University of Defense Technology in 2012 and 2014, respectively. His current research interests include MIMO GMTI radar waveform design and space-time adaptive processing. Feng He received BS and PhD degrees in signal processing from the National University of Defense Technology, Changsha in 1998 and 2005, respectively. He is currently an associate professor with the Institute of Space Electronic and Information Technology, National University of Defense Technology. His current major research interests include SAR processing, digital beamforming, space-time adaptive processing, and inverse SAR. Zhen Dong received the PhD degree in electrical engineering from the National University of Defense Technology, Changsha, China in 2001. He is currently a professor with the Institute of Space Electronic and Information Technology, National University of Defense Technology. His recent research interests include SAR system design and processing, ground moving target indication (GMTI), and digital beamforming. Manqing Wu received his MS degree from the National University of Defense Technology, Changsha, China, in 1990. Currently, he is a professor with the China Electronics Technology Group Corporation, Beijing, China, and also is a member of the Chinese Academy of Engineering. His research field is radar signal processing.