On MIMO Radar Transmission Schemesfor Ground Moving Target Indication

Ming Xue†, Duc Vu†, Luzhou Xu†, Jian Li†, and Petre Stoica‡†Department of Electrical and Computer Engineering

University of Florida, Gainesville, FL‡Department of Information Technology, Uppsala University, Uppsala, Sweden.

Abstract— We compare several multiple-input multiple-output(MIMO) radar transmission schemes, including code division,time division and Doppler frequency division multiplexing ap-proaches, for ground moving target indication (GMTI). Toutilize probing waveforms with low sidelobe levels for rangecompression, we transmit sequences specifically designed to havelow correlation levels. At the receiver side, we apply the iterativeadaptive approach (IAA), which uses only the primary data,to form high resolution angle-Doppler images. To mimic realworld scenarios, we apply our algorithms to a simulated datasetwhich contains high-fidelity, site-specific, simulated ground clut-ter returns. By combining the usage of intelligent transmissionschemes, probing waveforms with good correlation properties,and the adaptive angle-Doppler imaging approach, we show thatslow moving targets can be more clearly separated from theclutter ridge in the angle-Doppler images and potentially moreeasily detected by MIMO radar than by its conventional single-input multiple-output (SIMO) counterpart.

I. INTRODUCTION

Recently, much attention in the literature has been paid to

multiple-input multiple-output (MIMO) radar [1]–[4]. Unlike a

standard phased-array radar, which transmits scaled versions of

a single waveform, MIMO radar can transmit via its antennas

different or orthogonal waveforms. Consider a MIMO radar

system with LT transmit antennas and LR receive antennas,

where the receive array is a filled (i.e., with 0.5-wavelength

inter-element spacing) uniform linear array (ULA) and the

transmit array is a sparse ULA with LR/2-wavelength inter-

element spacing (see, e.g., Figure 1). When orthogonal wave-

forms are transmitted by the MIMO radar, its virtual array

is a filled (LTLR)-element ULA, i.e., the virtual array has an

aperture length LT times that of the receive array [1]. This

increased virtual aperture afforded by the MIMO radar system

enables many advantages, including better spatial resolution,

This work was supported in part by the Office of Naval Research (ONR)under Grant No. N00014-07-1-0293, the U.S. Army Research Laboratoryand the U.S. Army Research Office under Grant No. W911NF-07-1-0450,the National Science Foundation (NSF) under Grants No. CCF-0634786 andNo. ECCS-0729727, the Swedish Research Council (VR), and the EuropeanResearch Council (ERC). The views and conclusions contained herein arethose of the authors and should not be interpreted as necessarily representingthe official policies or endorsements, either expressed or implied, of the U.S.Government. The U.S. Government is authorized to reproduce and distributereprints for Governmental purposes notwithstanding any copyright notationthereon.

Please address all correspondence to: Dr. Jian Li, Department of Elec-trical and Computer Engineering, P. O. Box 116130, University of Florida,Gainesville, FL 32611, USA. Phone: (352) 392-2642. Fax: (352) 392-0044.E-mail: li@dsp.ufl.edu.

improved parameter identifiability, and enhanced performance

for ground moving target indication (GMTI). We focus herein

on the advantage of using MIMO radar for GMTI.

Chirp-like sequences, such as the Golomb [5] and Frank

[6] sequences, can be used in GMTI for range compression.

However, the aperiodic auto-correlation functions of these

sequences have high sidelobe levels. We use herein the CAN

(cyclic algorithm - new) sequences or sequence sets [7] [8]

synthesized by cyclically minimizing the integrated auto-

correlation sidelobe levels or a related metric concerning both

the auto- and cross-correlations. The CAN sequence initialized

by the Golomb or Frank sequence can have a much lower

integrated sidelobe level (ISL) compared to its initializing se-

quence. Probing sequences with low auto-correlation sidelobe

levels provide better range compression and enhance the sub-

sequent space-time adaptive processing (STAP) performance.

Conventional STAP used for GMTI requires secondary data

(data from range bins adjacent to the range bin of current

interest) to estimate the clutter-and-noise covariance matrix

of the primary data (data from the range bin of current

interest); see, e.g., [9]–[11]. However, high quality secondary

data may be hard to get, especially for an inhomogeneous

clutter environment. We consider herein using a weighted

least-squares based iterative adaptive approach (IAA) [12]–

[15] for angle-Doppler imaging in conjunction with several

MIMO transmission schemes. IAA is a robust, user parameter-

free and nonparametric adaptive algorithm that can work with

even a single data snapshot (e.g., only the primary data),

arbitrary array geometries, and random slow-time samples.

In the IAA-based MIMO STAP, we apply IAA to form a

high-resolution angle-Doppler image of targets, clutter, and

interference for each range bin of interest using the primary

data only. The so-obtained image is then used for GMTI.

In a standard MIMO scheme, orthogonal waveforms with

extremely low ISL’s are hard to obtain. Therefore, we turn

to several MIMO schemes that instead exploit the transmit

diversity in the slow-time or Doppler frequency domain in lieu

of the standard fast-time domain. The merits and limitations

of these schemes are investigated.

Our paper is organized as follows. In Section II, we intro-

duce the MIMO radar data model and various transmission

schemes. In Section III, we discuss the waveform synthesis

algorithms used in these transmission schemes and angle-

Doppler imaging via IAA. After that, we show the perfor-

mance of various transmission schemes in terms of angle-

1171978-1-4244-5827-1/09/$26.00 ©2009 IEEE Asilomar 2009

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Fig. 1. A UAV equipped with a MIMO radar.

Doppler imaging quality in Section IV. Finally, we draw our

conclusions in Section V.

II. MIMO RADAR DATA MODEL AND TRANSMISSION

SCHEMES

Consider a MIMO radar system with LT sparse transmit

antennas and LR filled receive antennas. Let aT(θ) and aR(θ),respectively, denote the transmit and receive steering vectors

for a target at azimuth angle θ:

aT(θ) =[1 ej2π

LRd

λ sin θ · · · ej2π(LT−1)LRd

λ sin θ]T

, (1)

and

aR(θ) =[1 ej2π d

λ sin θ · · · ej2π(LR−1)d

λ sin θ]T

, (2)

where d = λ2 is the inter-element distance of the receive array,

λ is the wavelength corresponding to the carrier frequency, and

(·)T denotes the transpose of a matrix or a vector. Assume a

total of P pulses are transmitted during a coherent processing

interval (CPI) to detect the Doppler frequency shift of a

moving target. For a target with Doppler frequency shift f ,

its nominal temporal steering vector aD(f) corresponding to

the P pulses can be expressed by

aD(f) =[1 e

j2π ffPRF · · · e

j2π(P−1)f

fPRF

]T

, (3)

where fPRF is the pulse repetition frequency (PRF). Let an

LT × P matrix W denote the slow-time modulation of the

waveforms emitted from different transmitters for different

pulses [16] [17]. Then, for a target located at azimuth angle

θ with Doppler frequency shift f , the steering matrix A from

LT transmitters to LR receivers for P pulses can be written as

A(θ, f) = (DaT(θ)WDaD(f)) ⊗ aHR

(θ), (4)

where Dx stands for a diagonal matrix formed from the vector

x, (·)H denotes the conjugate transpose of a matrix or a vector,

and ⊗ denotes the Kronecker matrix product.

Based on the data model in (4), we consider several

MIMO radar transmission schemes including code division,

time division, and Doppler frequency division multiplexing

schemes, and compare them with their conventional SIMO

radar counterpart. Ignoring for now the spatial and temporal

steering vector information in (4), a transmission scheme can

be described by the weighting matrix W and the transmit

waveform. To illustrate the MIMO schemes more clearly, we

show in Figure 2, for different transmission schemes, the

radian phases of the modulation matrix W mapped into the

interval [0, 2π). W is obtained from A with θ = 0◦ and f = 0Hz:

W =(DaT(θ)WDaD(f)) ⊗ aR(θ)|θ=0◦,f=0Hz (5)

=W ⊗ 1LR,

where 1L is a length-L all 1 vector. Since the spatial and

temporal aspects are separated in the two dimensions, the mod-

ulations across the virtual aperture versus slow-time become

visually more intuitive.

First, when all the LT antennas transmit orthogonal wave-

forms simultaneously, we refer to this scheme as the fast-

time code division multiple access (FT-CDMA), which has

the largest virtual aperture at each slow-time (i.e., pulse

transmission), as in Figure 2(b). Since there is no slow-time

modulation, the weighting matrix W is just an all 1 matrix.

Range compression and transmit diversity are achieved by

transmitting a set of almost orthogonal waveforms with good

auto- and cross-correlation properties.

In the second transmission scheme, we consider a simple

switching strategy, where only one transmit antenna is used to

transmit a signal at each PRI. To avoid the artifacts induced

by periodic switching [15], [18], [19], we consider choosing

one antenna randomly from the LT antennas, with equal prob-

ability, to transmit at each PRI [15]. This corresponds to the

case where, for each column of W, there is only one nonzero

entry which is 1 , and it is chosen randomly from LT possible

entries. As the transmit diversity is realized by switching in

slow-time, the waveform for each active transmitter can remain

the same from one pulse to another. We refer to this scheme

as the randomized time division multiple access (R-TDMA).

An example of the resulting virtual aperture versus slow-time

is shown in Figure 2(c).

In addition, we also consider two MIMO schemes that

exploit the transmit diversity associated with slow-time mod-

ulation. For these two schemes, all the transmitters are active

and transmit a single version of a waveform for the entire

CPI. From pulse to pulse, we apply slow-time modulations

by multiplying a coefficient in W with the waveform for a

corresponding transmitter and pulse number [20] [21]. In the

first scheme, the coefficients in W induce different Doppler

carrier frequencies into the waveforms from different transmit-

ters over slow-time to achieve transmit diversity. Therefore,

this strategy is referred to as the Doppler division multiple

access (DDMA) [17], [20], [21]. Its modulation diagram is

shown in Figure 2(d). Notice that, in DDMA, the maximum

Doppler frequency shift should not go beyond fPRF/LT to

avoid Doppler ambiguity. Motivated by DDMA, we also

consider another MIMO scheme where, instead of frequency

division as in DDMA, code division is employed in slow-time

to achieve orthogonality among the transmitted waveforms.

We use unimodular orthogonal waveforms with relatively flat

spectra to induce the slow-time modulation, and by doing so

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(d)

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(e)

Fig. 2. The radian phases of the modulation matrix W mapped into theinterval [0, 2π), across virtual array aperture vs. slow-time, with LT = 3,LR = 6, and P = 32, for (a) SIMO, (b) FT-CDMA, (c) R-TDMA, (d)DDMA, and (e) ST-CDMA schemes.

we avoid the maximum Doppler limitation imposed by DDMA

without incurring Doppler ambiguity [22]. This scheme is

referred to as the slow-time CDMA (ST-CDMA). The ST-

CDMA modulation diagram is provided in Figure 2(e). Notice

that, for the latter two schemes, since the orthogonality of

the transmit waveforms is accomplished by the slow-time

modulation, a single waveform with good auto-correlation is

sufficient to achieve transmit diversity.

Finally, notice that if only one transmit antenna is active for

the entire CPI without slow-time modulation, then the MIMO

scheme reduces to its SIMO counterpart. This implies that, in

W, only one row is all one, and all other elements of W are

zero. The aperture versus slow-time for the SIMO scheme is

shown in Figure 2(a).

To guarantee that the total transmitted power is the same for

all the transmission schemes introduced above, whenever there

is only one transmitter active in one PRI, the instantaneous

power for that transmitter is PT; and for those schemes with

all the transmitters active in one PRI, the instantaneous power

for each transmitter is PT/LT.

III. TRANSMIT WAVEFORM SYNTHESIS AND

ANGLE-DOPPLER IMAGING USING IAA

Notice that, for the MIMO transmission schemes, the trans-

mit diversity is realized by different strategies: FT-CDMA

employs fast-time waveform orthogonality, R-TDMA employs

transmitter switching, while DDMA and ST-CDMA make use

of slow-time modulation via W by Doppler frequency division

and spread spectrum code division, respectively.

With respect to the transmit waveform, there is some

literature on MIMO radar waveform set synthesis and an

extensive literature on a single radar waveform design. We

focus herein on using the newly proposed CAN algorithm [7]

[8] to design a waveform set or a single waveform with good

correlation properties. CAN minimizes the ISL by cyclically

updating the waveform in the time and the frequency domains.

As the basic operation involved is FFT, the CAN algorithm

is quite fast. Indeed, it can be used to design very long

sequences, e.g., sequences with N ∼ 105 and LT ∼ 10, which

can hardly be handled by other algorithms suggested in the

previous literature. The CAN algorithm can be used to design

a set of multiple orthogonal waveforms with good auto- and

cross-correlation properties for the FT-CDMA scheme, and a

single waveform with good auto-correlation properties for all

the other transmission schemes. An introduction to the CAN

algorithm and the examples of so-generated waveform set or

single waveform can be found in [22]. We will see in the

Numerical Examples Section that the FT-CDMA using the

sequences designed here fails due to the high sidelobe levels,

which are also different for different waveforms, making it

impossible to exploit the MIMO virtual aperture for sidelobe

suppression. Nevertheless, the other MIMO schemes, which

do not rely on the fast-time waveforms to achieve transmit

diversity, provide better spatial resolution than their SIMO

counterpart due to the much longer MIMO virtual aperture

length.

Given a transmission scheme W, transmit waveform X, and

received signal Y, we need to form 3-D range-angle-Doppler

images. We first perform range compression by matched

filtering (MF), and then form the angle-Doppler image for

each ROI by applying IAA [12] to the primary data only.

Although we could use IAA to form 3-D range-angle-Doppler

images directly, the computational complexity would increase

too much. The complete iterative procedure to implement IAA

can be found in Table III in [22], and it is shown that the IAA-

based angle-Doppler imaging approach is both user parameter

free and secondary data free. Also, note that IAA can be

implemented in parallel for different scanning points, and we

can exploit the Toeplitz block Toeplitz structures of the IAA

covariance matrix to save computations if the virtual array is

uniform and linear and the slow-time PRI is also uniform. The

high resolution angle-Doppler images provided by the various

MIMO schemes together with using the IAA algorithm should

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greatly enhance the subsequent target detection performance.

We show the angle-Doppler imaging of various transmission

schemes in the following section.

IV. NUMERICAL EXAMPLES

The dataset we used to evaluate the GMTI performance

is simulated based on the KASSPER data [23] with the

same main parameters for the real-world effect including

heterogeneous terrain, array calibration errors, and internal

clutter motion (ICM). We consider an airborne radar system

with LT = 3 transmit antennas and LR = 6 receive antennas,

with a carrier frequency of 1.24 GHz and a signal bandwidth

of 10 MHz. The platform is moving along the azimuth angle

of 270◦ with a velocity of 100 m/s, and the PRF is 1984 Hz.

Therefore, the position of the clutter ridge in the angle-Doppler

image can be pre-computed. We assume a total of P = 32pulses transmitted within a CPI. A range swath of interest

from 35 km to 50 km, which is divided into 1000 range bins,

is illuminated. We use the probing waveforms of length 256

designed in Section III. Like in the KASSPER data, calibration

errors, such as angle-independent phase errors and angle-

dependent subarray position errors, and ICM are included in

our simulated data, making the true steering vectors different

from the assumed ones.

Assume the targets are from the 100th range bin with an

average signal-to-clutter-and-noise ratio (SCNR) of -22 dB,

which is defined as:

SCNR =1I

I∑i=1

σ2t∑J

j=1 |α(ni, θj , fj)|2 + σ20

. (6)

In (6), i is the target index, I denotes the target number,

α(ni, θj , fj) denotes the RCS complex amplitude of the return

from the jth clutter in the nith range bin, σ2t is the target

power, and σ20 is power of the complex white Gaussian noise.

We consider the case where there are two targets with different

radial velocities from the same angle, and the maximum

Doppler shift is within the 1/LT Doppler band.

The angle-Doppler images formed by IAA for the three

cases and different radar schemes are shown in Figures 3 and

4.

In Figure 3, the angle-Doppler image of FT-CDMA is

presented. We see that the FT-CDMA fails to provide an

interpretable image, as a result of the high and different

range compression sidelobes, corresponding to the different

transmitted waveforms, from the strong clutter ridge. The

disappointing performance of FT-CDMA is induced by the

imperfect waveform set where the strong clutter energy from

adjacent range bins obscure, via leakage, the weak target in

the current range bin of interest. Since the transmitters use

different waveforms which have different sidelobes, the clutter

effects for different transmitters are different. As a result,

the virtual aperture concept is invalid for these sidelobes.

However, other MIMO schemes circumvent this problem by

resorting to multiplexing schemes in slow-time instead of fast-

time. Since FT-CDMA fails in all of the following simulations,

we will no longer show its performance.

In Figure 4, we notice that, the spatial resolution of the

SIMO scheme is rather poor, with the two targets almost

completely buried in the sidelobes of the strong clutter returns.

On the other hand, the three MIMO schemes, due to an

improved virtual aperture length, are able to form a much

more focused clutter ridge, and successfully resolve the two

moving targets.

We comment here that in the scenario where the targets are

moving more slowly than a certain velocity limit, all three

MIMO schemes are able to provide higher spatial resolution

and thus lower minimum detectable velocity (MDV) than their

SIMO counterpart. When the target velocities are not so small,

R-TDMA and ST-CDMA can afford a much larger Doppler

shift dynamic range, and become more desirable than DDMA.

In addition, when the transmit power per antenna is limited,

ST-CDMA can be used to place more power on the targets

and thus to get a higher SNR.

V. CONCLUSIONS

In this paper, we have compared several MIMO radar

schemes for GMTI applications. We have used waveforms

specifically designed to have low correlation levels. For the

receiver, we have applied the IAA algorithm to only the pri-

mary data to form high-resolution angle-Doppler images. By

using a high-fidelity, site-specific simulated dataset, we have

demonstrated that FT-CDMA collapses when the different fast-

time transmitted waveforms have different significant sidelobe

levels. Through R-TDMA and two other MIMO schemes that

use slow-time modulations, we have shown that MIMO radar

can provide higher spatial resolution in angle-Doppler images

and potentially better moving target detection performance

compared to its SIMO counterpart.

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−1 −0.5 0 0.5 1−0.5

0

0.5

sin(azimuth)

Nor

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ized

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pler

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