This document presents a direction of arrival estimation method for monostatic multiple-input multiple-output radar systems with arbitrary array configurations. The method uses manifold separation and polynomial rooting techniques to offer low computational complexity and improved resolution for closely spaced sources, compared to conventional spectral MUSIC. It analyzes the steering vectors and wavefield modeling for monostatic MIMO radar, and examines the number of modes selection for the proposed method. Simulation results are presented to investigate the performance of the proposed algorithm.

1. Published in IET Radar, Sonar and Navigation
Received on 25th May 2011
doi: 10.1049/iet-rsn.2011.0362
ISSN 1751-8784
Direction of arrival estimation for monostatic
multiple-input multiple-output radar with arbitrary
array structures
Y. Cao Z. Zhang F. Dai R. Xie
National Key Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, People’s Republic of China
E-mail: cyh_xidian@163.com
Abstract: Compared with other systems with a single transmit antenna, multiple-input multiple-output (MIMO) radar systems
have additional degrees of freedom that can enhance space resolution, improve parameter identifiability and enhance
flexibility for transmit beam pattern design. The computational complexity for direction of arrival (DOA) estimation using
sensor arrays increases very rapidly with the number of channels. The polynomial-rooting version of multiple signal
classification algorithm (root-MUSIC) is computationally more efficient than spectral MUSIC. However, this algorithm can
only be applied to uniform linear arrays. The manifold separation technique allows arrays of any geometry to be used with
fast DOA estimators designed for linear arrays. In this study, a DOA estimation method that uses manifold separation and
polynomial rooting technique is presented for monostatic MIMO radar with arbitrary array configuration. The algorithm offers
a low computation complexity and an improved resolution capability for closely spaced sources as compared to conventional
spectral MUSIC. Moreover, the wavefield modelling for monostatic MIMO radar and the number of mode selection of the
proposed method are also analysed in the study. Finally, the simulation results are presented and the performances of the
proposed algorithm are investigated and discussed.
1 Introduction
Recently, there has been considerable interest in a novel class
of radar systems called multiple-input multiple-output
(MIMO) radar, where the MIMO refers to the use of
multiple-transmit as well as multiple-receive antennas. The
MIMO radar system allows transmitting orthogonal
waveforms in each of the transmitting antennas [1, 2].
These waveforms can be extracted by a set of matched
filters in the receiver. Each of the extracted components
contains the information of an individual transmitting path.
By using the information of all of the transmitting paths, a
better spatial resolution [2] can be obtained. It has been
shown that this kind of radar system has many advantages
such as excellent interference rejection capability [3],
improved parameter identifiability [4] and enhanced
flexibility for transmit beam pattern design [5].
The multiple signal classification (MUSIC) method is
introduced in [6] to estimate direction of arrival (DOA), but
it needs multi-dimension search for multiple targets
identification and location. In order to avoid angle search,
estimation of signal parameters via rotational invariance
techniques (ESPRIT) [7] is proposed for its high-resolution
and low computation burden. The ESPRIT algorithm is
applied to bistatic MIMO radar by exploiting the invariance
property of the transmit and receive arrays [8]. However, an
additional pair matching between the DOAs and direction
of departures (DODs) of targets is required. The
interrelationship between the two 1D ESPRIT is exploited
to obtain automatically paired DOAs and DODs estimation
without deteriorating the performance of angle estimation
[9, 10]. In [11], an angle estimation method employing the
ESPRIT and singular value decomposition of cross-
correlation matrix of the received data from two transmit
subarrays is developed. In [12], a direction finding method
for monostatic MIMO radar using the ESPRIT and Kalman
filter is developed. Another low-complexity DOA estimator
such as root-MUSIC [13, 14], using polynomial rooting
instead of searching technique, reduces significantly
computation cost and enhances resolution capability for
closely spaced sources as compared to spectral MUSIC.
Direction finding for monostatic and bistatic MIMO radar
employing polynomial rooting are presented in [15, 16],
respectively.
Unfortunately, both the ESPRIT and the root-MUSIC
methods are designed for uniform linear arrays (ULA).
Later, techniques known as array interpolation [17, 18] and
beamspace transform [19] have been developed to map the
steering vector of a planar array onto steering vector of a
ULA-type array in order to apply low-complexity root-
MUSIC technique. These preprocessing techniques often
introduce mapping errors in the form of bias and excess
variance in the DOA estimates.
The MIMO radar often transmits orthogonal waveforms in
each of the transmitting antennas in order to detect the whole
3608 in the azimuth angle simultaneously. An ULA steering
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2. vector will be ambiguous when the sum of two arrival angles
is p. Therefore two dimensional (2D) array geometry should
be used in this situation. Array interpolation method
transforms 2D array to a virtual ULA-type array. Angular
sectors should be divided for array interpolation method
because of ambiguous steering vector over the whole 3608.
In contrast to interpolation and mapping techniques,
manifold separation approach [20–22] does not require
any division into angular sectors and it provides a
significantly smaller fitting error than the other techniques
commonly used over the whole 3608 coverage area. The
algorithm is suitable for DOA estimation of monostatic
MIMO radar with arbitrary array configuration over 3608
coverage. It is a key problem for the manifold separation
approach to select the number of modes. The usual array
signal processing model [20–22] selects a large value
(typically larger than the dimension of the steering vectors)
to guarantee that the approximation error is negligible.
However it is still an unsolved problem for the MIMO radar
model. The number of modes should be larger than M2
(M elements array) if following the same rule for the
monostatic MIMO radar. This will lead to a very large
computation load. We derived the steering vectors of the
monostatic MIMO radar and put the usual array and the
MIMO model to unite. By the analyses and simulation
results, it can be seen that the monostatic MIMO radar has
a good DOA estimation performance even if the number of
modes is smaller than (M2
/2).
The remainder of this paper is organised as follows. In
Section 2, we describe our monostatic MIMO radar scheme
and the associated data model. In Section 3, we first present
a steering vector and wavefield modelling analysis for
monostatic MIMO radar, and then a DOA estimation
method using the polynomial rooting instead of spectrum
searching for monostatic MIMO radar with ULA
configurations and arbitrary array configurations are
presented. Moreover, we explain how to select the number
of modes in order to alleviate the complexity burden and
maintain the algorithm performance for monostatic MIMO
radar. The simulation results of the proposed algorithm
are presented and the performance are investigated and
discussed in Section 4. Finally, Section 5 contains our
conclusions.
2 Signal model
Consider a monostatic MIMO radar system consisting of M
elements with arbitrary array configuration, M different
narrow-band waveforms are emitted simultaneously, which
have identical bandwidth and centre frequency but are
temporally orthogonal. By applying matched filters for each
transmitted waveform on each receiver, the system is
capable of isolating each transmitted signal making transmit
degrees-of-freedom available in the receiver. A block
diagram of the receiver processing is shown in Fig. 1.
Assume that the effect of Doppler frequencies on the
orthogonality of the waveforms and the variety of phases
within repetition intervals can be ignored. P targets with
different Doppler frequencies are assumed to locate at the
same range bin. The direction of the pth target with respect
to the array normal is denoted by up.
Then the MIMO steering vector [3, 4, 8–12] corresponding
to the pth target is
a(up) = ar(up) ⊗ at(up) (1)
where ar(u) and at(u) are steering vectors of the receive and
transmit arrays, respectively. ⊗ is the Kronecker product.
For monostatic MIMO radar, ar(u) ¼ at(u).
At each receiver the received signals are fed into a bank of
matched filters that are designed to separate the orthogonal
components of the transmitted signals. Taking noise into
consideration, the outputs of all the matched filters in all the
receivers can be expressed in a matrix form as
x(t) = As(t) + n(t) (2)
where x(t) is an M2
× 1 vector; A ¼ [a(u1), a(u2), . . ., a(uP)]
is an M2
× P matrix composed of P steering
vectors; s(t) ¼ [s1(t), s2(t), . . ., sP(t)]T
is a column vector
consisting of the phases and amplitudes of the P non-
coherent narrowband signal sources at time t, say,
sp(t) = bpej2pfdpt
with fdp being the Doppler frequency and
bp the amplitude which is influenced mainly by the radar
cross section (RCS), the transmit and the receive antenna
gain in the target direction, the propagation loss and so on;
n(t) is the noise output of all the matched filters. We know
that there are M independent and identical white Gaussian
noise sources among receivers and M orthogonal transmit
signals. Therefore the noise outputs of all matched filters
are orthogonal. Here n(t) can be thought as a stationary,
second-order ergodic, spatially and temporally Gaussian
white noise vector of zeros mean and covariance matrix
s2
I, where s2
is a scalar and I is the identity matrix.
The array covariance matrix can be written as
Rx = E{x(t)xH
(t)} (3)
where [.]H
denotes Hermitian transpose and E{} denotes the
statistical expectation.
Fig. 1 Monostatic MIMO radar processing
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3. Substituting x(t) from (2) into (3) results in
Rx = ARsAH
+ s2
I (4)
where Rs ¼ E{s(t)sH
(t)} is the source covariance matrix. The
eigenvalue decomposition of R yields
Rx =
M2
m=1
lmemeH
m (5)
where l1 ≥ l2 ≥ · · · ≥ lP+1 ≥ · · · ≥ lM2 are the
eigenvalues of Rx and em (m ¼ 1, . . . , M2
) are the
corresponding eigenvectors. The matrices
Es = [e1, . . . , eP] (6)
En = [eP+1, . . . , eM2 ] (7)
are composed of the signal and the noise subspace
eigenvectors of the exact array covariance matrix,
respectively.
In practical situations, the exact array covariance matrix Rx
is unavailable and its sample estimate
ˆRx =
1
L
L
l=1
x(l)xH
(l) (8)
is used, where L is the number of snapshots.
The eigendecomposition of the sample covariance matrix
(8) yields [22]
ˆRx = ˆEs
ˆLs
ˆEH
s + ˆEn
ˆLn
ˆEH
n (9)
where the sample eigenvalue are sorted in non-ascending
order ( ˆl1 ≥ ˆl2 ≥ · · · ≥ ˆlP+1 ≥ · · · ≥ ˆlM2 ) and the matrices
ˆEs = [ˆe1, . . . , ˆeP] and ˆEn = [ˆeP+1, . . . , ˆeM2 ] contain in
their columns the signal-subspace and noise-subspace
eigenvectors of ˆRx, respectively. Correspondingly, the
diagonal matrices ˆLs = diag{ ˆl1, . . . , ˆlP} and ˆLn =
diag{ ˆlP+1, . . . , ˆlM2 } are built from the signal-subspace and
noise-subspace eigenvalues of ˆRx, respectively.
The MUSIC null-spectrum function is defined as [6]
f (u) = ˆEH
n a(u) 2
= aH
(u) ˆEn
ˆEH
n a(u) (10)
where . denotes the vector 2-norm. The spectral MUSIC
technique estimates the signal DOAs from the minima of
this function by means of a search over u.
3 Polynomial rooting DOA estimation for
monostatic MIMO radar
3.1 Monostatic MIMO radar with ULA
configuration
Consider an ULA with at(u) ¼ ar(u) ¼ [1,ej(2p/l)dsinu
, . . .,
ej(2p/l)(M21)dsinu
]T
, where [.]T
denotes the transpose, d and l
are the inter-element spacing and the wavelength,
respectively.
Denoting z ¼ ej(2p/l)d sinu
, the MUSIC null spectrum
function can be expressed as
f (z) = ˆEH
n a(z) 2
F = aT
(1/z) ˆEn
ˆEH
n a(z) (11)
where a(z) = at(z) ⊗ ar(z) = [1, . . . , z(M−1)
, z, . . . , zM
, . . . ,
z(M−1)
, . . . , z(2M−2)
]T
1×M2 . Obviously, (11) represents a
polynomial of degree 2(2M 2 2).
If we define
b(z) = [1, z, . . . , z(2M−2)
]T
(12)
The steering vector can be denoted as
a(z) = Tb(z) (13)
where
T =
IM 01×M · · · 01×M
01×M IM · · · 0M−2×M
0M−2×M 0M−2×M · · · IM
⎡
⎣
⎤
⎦
T
2M−1×M2
IM and 0i×j are M × M identity matrix and i × j zero matrix,
respectively.
Substituting a(z) from (13) into (11), one obtains
f (z) = bT
(1/z)TH ˆEn
ˆEH
n Tb(z) (14)
This allows applying fast polynomial rooting algorithms
instead of exhaustive search to obtain DOA of the targets,
for example, root-MUSIC method.
3.2 Monostatic MIMO radar with arbitrary array
configurations
We cannot distinguish angles of arrival between u and p 2 u
for the monostatic MIMO radar of ULA configuration. Here
we use 2D array configuration and the manifold separation
technique to estimate DOA of the targets over the whole
3608 coverage area.
3.2.1 Wavefield modelling for monostatic MIMO
radar: Based on the model in [23], we write the array
manifold for arrays with arbitrary configuration having
omnidirectional sensors as
at(u) = ar(u)
= [ejkr1 cos(b1−u)
· · · ejkrm cos(bm−u)
· · · ejkrM cos(bM −u)
]T
(15)
where k ¼ 2p/l is the wavenumber, u is a wavefront
impinging direction, rm is the distance from the centroid of
the array and bm is the angular position (counted
counterclockwise from the x-axis) of the mth array element
in polar coordinates.
The array manifold for MIMO radar can be written as the
Kronecker product of at(u) and ar(u)
a(u) = ar(u) ⊗ at(u) (16)
The [(p 2 1)M + q]th element of the monostatic MIMO
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4. manifold can be written as
[a(u)](p−1)M+q = ejkrp cos(bp−u)
ejkrq cos(bq−u)
= ejk[rp cos(bp−u)+rq cos(bq−u)]
= ejk[cos u(rp cos bp+rq cos bq)+sin u(rp sin bp+rq sin bq)]
= ejkrl cos (cl−u)
(17)
where p, q ¼ 1, . . . , M, l ¼ (p 2 1)M + q, cl ¼ a tan((rp sin
bp + rq sin bq)/(rp cos bp + rq cos bq))
rl = (rp cos bp + rq cos bq)2
+ (rp sin bp + rq sin bq)2
= r2
p + r2
q + 2rprq cos(bp − bq)
The monostatic MIMO radar can be seen as the array radar
with M2
element located at (rl, cl), so that the wavefield
modelling for monostatic MIMO radar can be obtained in
the same way as array radar. By using the Jacobi–Anger
expansion, we can mathematically express (17) as [20, 23]
ejkrl cos(cl−u)
=
+1
n=−1
jn
Jn(krl)ejn(cl−u)
=
+1
n=−1
jn
Jn(krl)ejncl e−jnu
=
+1
n=−1
[Gs]l,ne−jnu
(18)
where
[Gs]l,n = jn
Jn(krl)ejncl (19)
is the (l, n)th element of the sampling matrix Gs and Jn(.) is
the Bessel function of the first kind of order n.
The idea of wavefield modelling is to write the signal-
dependent part of the array output as the product of a
sampling matrix Gs (independent from the wavefield) and a
coefficient vector ds(u) (independent from the array) [23].
Consequently, by writing (18) in matrix form, we can
express the concept of manifold separation technique by
a(u) = Gsds(u) (20)
The nth component of ds(u) is
[ds(u)]n = e−jnu
(21)
We define a truncated matrix G [ CM2
×N
as
[G]m,n = [Gs]m,n (22)
for m ¼ 1, . . ., M2
and n ¼ 2(N 2 1/2), . . ., (N 2 1/2).
Consequently, the manifold separation technique
approximates the steering vector as
a(u) = Gd(u) + W (23)
where W is the error owing to truncation. Observe that for
sufficiently large N, we have W 2
0 and
d(u) = [ej((N−1)/2)u
, . . . , e−j((N−1)/2)u
]T
(24)
is an N × 1 Vandermonde vector which depends on the
steering angle and the parameter N. The accuracy of the
approximation (23) increases with increasing the value of
N. Note that in order to preserve the uniqueness of the roots
associated with the true DOAs and avoid spurious roots on
the unit circle, the following condition has to be met
a(ui) = a(uj)
Gd(ui) = Gd(uj)
(25)
for ui = uj and ui,uj [ [0 2p).
3.2.2 Polynomial rooting DOA estimation: We use the
notation z′
¼ eju
and substitute a(z′
) from (23) into (10), the
MUSIC null-spectrum function can be written as
f (z′
) ≃ dT
(1/z′
)GH ˆEn
ˆEH
n Gd(z′
) (26)
Obviously, the polynomial function has 2N 2 2 roots which
appear in conjugate reciprocal pairs. The azimuth
estimations are computed from the argument of the P roots
z′
p(p = 1, . . . , P) closest to the unit circle, that is,
ˆup = arg (z′
p), in a way similar to that used in the
conventional root-MUSIC algorithm.
The matrix G may be derived from the following
minimisation
arg min
G
K
k=1
|a(uk) − Gd(uk)|2
(27)
where u1, . . ., uK [ [0 2p), K (K ≫ M2
) is the number of
calibration points.
The response of the monostatic MIMO radar to a far-field
source can be modelled by measuring the directional
characteristic of the array in an anechoic chamber. We may
measure the array response to a far-field source by moving
the source around the monostatic MIMO radar at a fixed co-
elevation angle, for example, at 908 in the azimuthal range
u1, . . ., uK [ [0 2p). Alternatively, the same result can be
obtained by fixing the source location and rotating the
monostatic MIMO radar about its centroid [20].
We form the calibration matrix with the steering vectors of
the monostatic MIMO radar
Ac
= [a(u1), a(u2), . . . , a(uK)] (28)
Similarly, we can form the matrix D
D = [d(u1), d(u2), . . . , d(uK)] (29)
The matrix G can be obtained by the least squares (LS)
approach
G = Ac
DH
(DDH
)−1
(30)
where (.)21
denotes the matrix inversion.
3.2.3 Selection of the number of modes N: In order to
minimise the modelling error, a larger number of excitation
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5. modes N should be selected. This leads to a smaller array
manifold reconstruction error and, consequently, to a
smaller error in the DOA estimates. The parameter N
should be taken to be large enough [typically larger than
the dimension of a(u)] for array radar to obtain an
acceptable DOA estimation performance [20–22]. The
value of N should be larger than M2
for the monostatic
MIMO radar if following the same rule. This will lead to a
very large computation load.
From (17), the monostatic MIMO radar can be seen as an
array radar with M2
elements located at (rl, cl). It has been
suggested in wavefield modelling [23] to use as a rule
of thumb
N ≃ 4kR (31)
where R is the radius of the smallest circle centred at the
origin of the array and enclosing all the physical components.
Rewriting the distance between the centroid of the array
and the lth element
rl = r2
p + r2
q + 2rprq cos(bp − bq) ≤ rp + rq
≤ 2 max(rp) (32)
R can be shown as
R = max(rl) = 2 max(rp) (33)
The maximal error of W owing to truncation can be written as
[23]
|1G(N)| ≤ 2M2
+1
n=(N+1/2)
|Jn(kR)| (34)
In real-world radar systems, the maximum signal-to-noise
ratio (SNR) is mainly limited by the transmit power and the
receiver noise. Whenever the SNR ≪ a(u) 2
/|1G(N )|2
, the
residual modelling error can be neglected. In other words, if
the error floor caused by W is much smaller than the
variance of the DOA estimates at the highest achievable
SNR, the modelling error W can be neglected.
3.2.4 Computational complexity analysis: For a
monostatic MIMO radar system consisting of M elements,
the computational complexity of the covariance matrix and
the eigendecomposition are O((M2
)
2
L) and O((M2
)
3
),
respectively. The computation of Q samples of the MUSIC
null-spectrum function requires O(QM2
(M2
2 P)). The
complexity to compute the polynomial coefficients and root
finding is given by O(NM2
(M2
2 P) + N 2
(M2
2 P) + N 3
).
When the search interval is 0.018, Q will be 36 000.
Suppose M ¼ 8, N ¼ 25, P ¼ 4, the complexities of the
conventional MUSIC method and the proposed method are
O(108
) and O(105
), respectively.
3.2.5 Summary of the DOA estimation algorithm for
monostatic MIMO radar: In summary, the source DOAs
for the monostatic MIMO radar with arbitrary array
configurations can be estimated via the following procedure:
Step 1: Select the proper number of modes N.
Step 2: Form the calibration matrix Ac
[ CM2
×K
and the
matrix D [ CN×K
. Compute the matrix G using (30) or
using (19).
These two steps above are done offline, and it needs to be
computed only once for a given antenna array.
Step3: Apply matched filters for each transmitted waveform at
each receiver to obtain the data vector X(l) [ CM2
×1
.
Step 4: Estimate the covariance matrix ˆRx and noise-subspace
matrix ˆEn using (8) and (9), respectively.
Step 5: Computer the MUSIC null-spectrum function
f (z′
) = dT
(1/z′
)GH ˆEn
ˆEH
n Gd(z′
).
Step 6: Use root-MUSIC method to estimate the source
DOAs. A fast root-MUSIC method [24] can be used to
further reduce the computational complexity.
4 Simulation results
In this section, the performances of the proposed DOA
estimation algorithm are discussed. Consider a monostatic
MIMO radar with uniform circular array (UCA)
configuration that can be easily extended to other 2D array
configurations. Suppose there are M ¼ 8 sensors and radius
r is 0.6l and there are no array amplitude and phase
mismatch, array mutual coupling, antenna manufacturing
errors, sensor orientation, position errors etc. In the
simulations we have formed a grid of 360 calibration points
which are uniformly distributed over the whole 3608
coverage area.
4.1 Normalised fitting errors analysis
The normalised fitting error is defined as [21]
1 =
1
2p
2p
0
||a(u) − Gd(u)||
||a(u)||
du (35)
Fig. 2 shows the normalised fitting error against the value of N
of the array radar and the monostatic MIMO radar. From
Fig. 2a we can see that the parameter N should be taken
significantly greater than the array dimension M to achieve
an acceptable normalised fitting error. We can also see that
it is unnecessary to select the parameter N to be greater
than steering vector dimension M2
in the monostatic MIMO
radar. Small normalised fitting error can be obtained even
when N , M2
for the monostatic MIMO radar.
4.2 Root mean square error (RMSE) of the DOA
estimations
In the example, we validate the results of asymptotic
performance of DOA estimation using the manifold
separation technique for the monostatic MIMO radar. Two
equally powered signal sources are assumed to impinge on
the array from the directions 20 and 508. The number of
snapshots to estimate the array covariance matrix is 100.
Throughout our simulations, 1000 independent Monte Carlo
runs have been used in this example.
Fig. 3 shows the impact of the SNR on the DOA estimates.
By fixing the parameter N and increasing the SNR, it can be
seen that the RMSEs decrease until it reaches an error floor.
For example, the curve saturates at SNR ¼ 10 dB when
N ¼ 21. From Fig. 3, we can see that the approximation
error dominates the RMSEs of DOA at high SNR. In this
case, the error of the DOA estimate remains constant for a
fixed N.
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6. In Fig. 4, the DOA estimation RMSEs of the monostatic
MIMO radar are plotted against the value of N. It can be
seen that the RMSEs decrease with fixing the SNR and
increasing the value of N until it reaches an error floor. It is
no use to improve continually the value of N when the
SNR is fixed. For example, we can choose N ¼ 25 when
SNR ¼ 30 dB for the monostatic MIMO radar with eight
sensor UCA configuration. Increasing N does not always
improve the DOA estimate performance, but renders this
method computationally expensive.
4.3 Monostatic MIMO radar DOAs estimation
using polynomial rooting and MUSIC spectrum
research
Next, we compare the DOA estimation performance of
MUSIC spectrum with the searching step 0.018 and
polynomial rooting method with N ¼ 25. From Fig. 5, we
observe that, with the increase of SNR, the performance of
the MUSIC spectral search and polynomial rooting method
is improved. The figure demonstrates that the proposed
Fig. 2 Normalised fitting error as a function of the parameter N
a Array radar
b MIMO radar
Fig. 3 DOA estimation RMSEs of the proposed method against SNR for monostatic MIMO radar
a Source at 208
b Source at 508
Fig. 4 DOA estimation RMSEs of the proposed method against the number of N
a Source at 208
b Source at 508
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7. polynomial rooting algorithm provides a similar DOA
estimation performance to the MUSIC spectral search
method, which is computationally expensive for a fine grid
search over the whole angle range. However, the proposed
polynomial rooting method alleviates the computation
complexity of DOA estimation for the monostatic MIMO
radar with arbitrary array configurations.
Suppose two equally powered sources are located at 35 and
408 and we are trying to estimate their angles. Fig. 6 shows the
DOA estimation results of the MUSIC spectrum and the
proposed polynomial rooting method. The vertical lines
indicate the angle estimations of the polynomial rooting
method and the curve is the MUSIC spectrum. It can be seen
that there is only one peak associated with the closely spaced
sources, yet the roots show their proper locations. The
simulation demonstrates that the root-MUSIC method for the
monostatic MIMO radar has better resolution performance
than the traditional version of the MUSIC spectral.
5 Conclusion
In this paper, the problem of polynomial rooting DOA
estimation for monostatic MIMO radar with arbitrary array
configuration has been addressed. We derived monostatic
MIMO radar manifold and put the usual array and the
MIMO model to unite. The proposed polynomial rooting
DOA estimation method avoids the MUSIC spectral search
and reduces the computational complexity for monostatic
MIMO radar with arbitrary array configuration. Simulation
results demonstrate that the proposed method has a good
DOA estimation performance even if the number of modes
is smaller than (1/2)M2
for monostatic MIMO radar.
Moreover, the proposed algorithm is superior to the
conventional full-dimensional MUSIC spectral search
method in resolving capability.
6 Acknowledgment
This work was supported by National Natural Science
Foundation of China under Grant no. 60901068 and
61172137, and by the Fundamental Research Funds for the
Central Universities.
7 References
1 Fishler, E., Haimovich, A., Blum, R.S., Cimini, L.J., Chizhik, D.,
Valenzuela, R.A.: ‘Spatial diversity in radars-models and
detection performance’, IEEE Trans. Signal Process., 2006, 54, (3),
pp. 823–838
2 Bekkerman, I., Tabrikian, J.: ‘Target detection and localization using
MIMO radars and sonars’, IEEE Trans. Signal Process., 2006, 54,
(10), pp. 3873–3883
3 Li, J., Stoica, P., Xu, L., Roberts, W.: ‘On parameter identifiability
of MIMO radar’, IEEE Signal Process. Lett., 2007, 14, (12),
pp. 968–971
4 Li, J., Stoica, P.: ‘MIMO radar with colocated antennas’, IEEE Signal
Process. Mag., 2007, 24, (5), pp. 106–114
5 Stoica, P., Li, J., Xie, Y.: ‘On probing signal design for MIMO radar’,
IEEE Trans. Signal Process., 2007, 55, (8), pp. 4151–4161
6 Schmidt, R.O.: ‘Multiple emitter location and signal parameter
estimation’. Proc. RADC Spectral Estimation Workshop, Rome, NY,
1979, pp. 243–258
7 Roy, R., Kailath, T.: ‘ESPRIT-estimation of signal parameters via
rotational invariance techniques’, IEEE Trans. Acoust. Speech Signal
Process., 1989, 37, (7), pp. 984–995
8 Duofang, C., Baixiao, C., Guodong, Q.: ‘Angle estimation using
ESPRIT in MIMO radar’, Electron. Lett., 2008, 44, (12), pp. 770–771
9 Yunhe, C.: ‘Joint estimation of angle and Doppler frequency for bistatic
MIMO radar’, Electron. Lett., 2010, 46, (2), pp. 170–172
10 Jinli, C., Hong, G., Weimin, S.: ‘Angle estimation using ESPRIT
without pairing in MIMO radar’, Electron. Lett., 2008, 44, (24),
pp. 1422–1423
11 Jinli, C., Hong, G., Weimin, S.: ‘A new method for joint DOD and DOA
estimation in bistatic MIMO radar’, Signal Process., 2010, 90,
pp. 714–718
Fig. 5 DOA estimation RMSEs against the SNR
a Source at 208
b Source at 508
Fig. 6 Resolution performance of MUSIC spectrum and proposed
method
IET Radar Sonar Navig., 2012, Vol. 6, Iss. 7, pp. 679–686 685
doi: 10.1049/iet-rsn.2011.0362 & The Institution of Engineering and Technology 2012
www.ietdl.org

8. 12 Nan, L., Linrang, Z., Juan, Z.: ‘Direction finding of MIMO radar through
ESPRIT and Kalman filter’, Electron. Lett., 2009, 45, (17), pp. 908–910
13 Barabell, A.: ‘Improving the resolution performance of eigenstructure-
based direction-finding algorithms’. Proc. ICASSP, Boston, MA,
USA, April 1983, pp. 336–339
14 Rao, B.D., Hari, K.V.S.: ‘Performance analysis of root-MUSIC’, IEEE
Trans. Acoust. Speech Signal Process., 1989, 37, (12), pp. 1939–1949
15 Xie, R., Liu, Z., Zhang, Z.: ‘DOA estimation for monostatic MIMO
radar using polynomial rooting’, Signal Process., 2010, 90,
pp. 3284–3288
16 Bencheikh, M.L., Wang, Y., He, H.: ‘Polynomial root finding technique
for joint DOA DOD estimation in bistatic MIMO radar’, Signal
Process., 2010, 90, pp. 2723–2730
17 Friedlander, B.: ‘The root-MUSIC algorithm for direction finding with
interpolated arrays’, Signal Process., 1993, 30, pp. 15–29
18 Hyberg, P., Jansson, M., Ottersten, B.: ‘Array interpolation and DOA
MSE reduction’, IEEE Trans. Signal Process., 2005, 53, (12),
pp. 4464–4471
19 Belloni, F., Koivunen, V.: ‘Beamspace transform for UCA: error
analysis and bias reduction’, IEEE Trans. Signal Process., 2006, 54,
(8), pp. 3078–3089
20 Belloni, F., Richter, A., Koivunen, V.: ‘DOA estimation via manifold
separation for arbitrary array structures’, IEEE Trans. Signal Process.,
2007, 55, (10), pp. 4800–4810
21 Belloni, F., Richter, A., Koivunen, V.: ‘Extension of root-MUSIC to
non-ULA array configurations’. Proc. ICASSP, Toulous, France,
2006, pp. 897–900
22 Ru¨bsamen, M., Gershman, A.B.: ‘Direction-of-arrival estimation for
nonuniform sensor arrays: from manifold separation to Fourier domain
MUSIC methods’, IEEE Trans. Signal Process., 2009, 57, (2),
pp. 588–599
23 Doron, M.A., Doron, E.: ‘Wavefield modeling and array processing, Part
I – spatial sampling’, IEEE Trans. Signal Process., 1994, 42, (10),
pp. 2549–2559
24 Zhuang, J., Li, W., Manikas, A.: ‘Fast root-MUSIC for arbitrary arrays’,
Electronics Lett., 2010, 46, (2), pp. 174–176
686 IET Radar Sonar Navig., 2012, Vol. 6, Iss. 7, pp. 679–686
& The Institution of Engineering and Technology 2012 doi: 10.1049/iet-rsn.2011.0362
www.ietdl.org