Target Direction-of-Arrival Estimation Using
Nested Frequency Diverse Array
Chenglong Zhu, Wen-Qin Wang, Hui Chen
∗
, and Huaizong Shao
School of Communication and Information Engineering,
University of Electronic Science and Technology of China.
Email: zhuchenglong01@126.com, wqwang@uestc.edu.cn, huichen0929@uestc.edu.cn, hzshao@uestc.edu.cn
Abstract—This paper proposes a receiving nested frequency
diverse array (FDA) design scheme. The essence of the proposed
technique is to construct a new array structure by systematically
nesting two or more uniform linear FDA. Using second-order
statistics of the received data, it is capable of providing a
significant increasing degrees-of-freedom. The frequency incre-
ment across the array results in a scan angle that varies with
range and provides resistance to range-dependent interference.
The improvement offered by the proposed method as compared
to traditional FDA are demonstrated by extensive simulation
through analyzing the corresponding beampattern and direction-
of-arrival estimation performance.
Index Terms—Frequency diverse array (FDA), FDA radar,
nested array, range-dependent, direction-of-arrival, nested FDA.
I. INTRODUCTION
Array antenna technology has been continuously develop-
ing in recent years. The desire for new more progressive tech-
nologies is driven and dictated by its widespread applicability.
Direction-of-arrival (DOA) estimation is the major application.
However, for traditional uniform linear array (ULA), the
number of interesting sources that can be resolved with a N-
element ULA is N − 1. It is highly desirable to increase the
array degrees-of-freedom (DOFs) to detect more sources for
a given number of physical sensors.
When it comes to detect more sources with less physical
sensors, much attention has been received in recent years [1],
[2], [3]. For the minimum redundancy arrays [3], the closed-
form expression concerning the array geometry and achievable
DOFs has not resolved by now. Moreover, optimal array is
difficult to design in most cases and suitable covariance matrix
often converges only to local optimum. In [3], [4], fourth-
order cumulants were exploited to increase the DOFs. But it is
restricted to non-Gaussian sources. The method mentioned in
[5] required active sensing, and was not applicable for passive
sensing. In order to resolve more interesting sources than the
actual number of physical sensors, [11] proposed the nested
array, which was capable of increasing the DOFs. Nested array
is formulated by combing two or more ULAs. It can provides
O(N
2
) DOFs using only N physical sensors by exploiting
second-order statistics of the received data. The advantages of
The work described in this paper was supported in by the Program for
New Century Excellent Talents in University under grant NCET-12-0095 and
Sichuan Province Science Fund for Distinguished Young Scholars under grant
2013JQ0003.
nested array are obvious, but it is restricted to phased-array
and angle-independent direction. This limits its applicability
in mitigating non-desirable range-dependent interference.
In this paper, we develop a nested frequency diverse
array (FDA), which combines the advantages of nested array
in increasing DOF with the advantages of FDA in range-
dependent beamforming. FDA is different from a phased array
because a linear frequency increment is applied across the
array and consequently the array beampattern is a function
of range, time, and angle [7], [8]. Equivalently, the scan
angle will vary with the range in far-field. This provides
many potential new applications [9]. In doing so, the proposed
approach is capable of providing significant increased DOFs
and range-dependent beam steering for target localization.
This paper is organized as follows. Section II proposes the
receiving nested FDA. The signal model and corresponding
array processing are also studied. Section III is devoted to the
analysis of nested FDA performance in direction of arrival
(DOA) estimation. A spatial smoothing method is used to
resolve the problem of coherent noise caused by the difference
co-array processing. Finally, simulation results are demon-
strated in Section IV and concluding remarks are given in
Section V.
II. R
ECEIVING NESTED FDA
In earlier literatures, most of the FDA concepts are applied
only on transmitter. However, receiving FDA is considered in
this paper. In [10], the authors proposed an useful receiving
FDA based on linearly frequency modulated continuous wave-
form (LFMCW), as illustrated in Figure 1. Without loss of
generality, in this paper, we assume the signal coming to the
receiving FDA is a chirp signal
s(t) = exp
j(2πf
0
t + k
r
t
2
)
(1)
where f
0
and k
r
are the carrier frequency and chirp rate,
respectively.
Then the signal related with the direction θ and range r in
far-field and received by the nth sensor can be modeled as
x
n
(t)=
√
σ
r
n
s(t−τ
n
)exp
−j
2πf
0
+ k
r
(t − τ
n
)
c
0
r
n
+ν
n
(t)
(2)
where r
n
and τ
n
denote the target range to the nth sensor and
corresponding propagation time, respectively, σ is the target
200
2015 International Conference on Estimation, Detection and Information Fusion (ICEDIF 2015)
978-1-4799-6418-5/15/$31.00 ©2015 IEEE
Harbin, CHINA
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