The Ambiguity Function Analysis of Complete
Complementary Sequence in MIMO System
Li Shufeng
School of Information Engineering Communication University of China, Beijing
Email: lishufeng@cuc.edu.cn
Abstract-The novelty of Multiple-Input Multiple-Output
(MIMO) radar can effectively improve radar system
performance by utilizing the multi-antennas and orthogonal
signals. While the traditional single sequence can’t keep the
complete orthogonality (the sidelobes of the auto-correlation
and cross-correlation function equal to zero at all delays).
The expression of ambiguity function of complete
complementary sequence (CC-S) is deduced in this paper.
The simulation results show the validity of the proposed
ambiguity function of CC-S. The application of CC-S in
MIMO radar is studied and the MIMO radar transmitter
model based on CC-S is established. It is demonstrated that
the CC-S has the potential to significantly improve the
performance of MIMO radar system and the validity of the
CC-S applied in MIMO radar is verified.
Keywords- complete complementary sequence (CC-S), MIMO
radar, ambiguity function
I. INTRODUCTION
The transmitted signal waveform research of MIMO
radar has been a hot research direction [1-2]. In MIMO
radar system, different transmitting arrays usually emit
mutually orthogonal signals in transmitting end, while the
receiving arrays distinguish the echoes of different
directions through the orthogonality of transmitted
signals in order to improve the detection performance.
That is very important to choose the orthogonal signal to
improve the performance the system performance of
MIMO radar[3-5].
The correlation of signal has an important impact on
matched filter of receiver end directly[6-7]. In order to
separate the noise and extract the beneficial signal from
echo signal, the perfect correlation function of
transmitted signal is also needed for enhancing the
resolution ratio in the detection of multiple targets [8-12].
There is no perfect correlation function in single code
domain, so we extend the code domain to double code
domain. The complementary sequence belongs to the
double code domain, and the complete complementary
sequence (CC-S) is composed of complementary
sequence, which has the complete orthogonality. The
polyphase signal opens a new direction for the two-phase
signal. The polyphase signal has better performance than
the two-phase signal in the condition of equal length.
Based on the optimized simulated annealing algorithm,
the excellent polyphase signal is constructed, which has
low sidelobe in correlation function and is not satisfied
the perfect correlation function character. Based on the
recursion algorithm, a class of four-phase CC-S is
produced and the correlation of CC-S is analyzed [13].
The ambiguity function is a valid method to analyze the
signal of radar, which shows the resolution and the
measure precision under the matched filter. The
ambiguity function of CC-S is derived in this paper. The
MIMO radar signal model based on Complementary
Sequence is established and the feasibility of CC-S in
MIMO radar is proved. The CC-S offers a new choice for
the MIMO radar.
II. T
HE CONCEPT OF CC-S
Supposing that
,
mm
B consists of M pairs of
complementary sequence, the length of
m
and
m
is L.
,
mm
B is called CC-S if both the following correlation
function conditions are satisfied:
i) For every
1, 2, ,mM , it holds that
2 0
() ()
0 1, 2, , ( -1)
mm mm
AA BB
L
RR
L
(1)
ii) For every
1, , mn M m n , it holds that
( ) ( ) 0 0, 1, 2, , ( -1)
mn mn
AA BB
RR L
(2)
Where
()
mn
AA
R
and ()
mn
BB
R
denote the aperiodic
correlation functions between
m
and
n
,
m
B and
n
B
respectively. (1) and (2) shows the ACF and CCF of the
CC-S respectively.
III. A
MBUIGUITY FUNCTION OF CC-S
The CC-S is composed by complementary sequence. In
order to applying the CC-S in MIMO radar, the different
complementary sequence pairs are transmitted in
different antennas.
The MIMO radar transmitter model
based on CC-S is shown in Fig.1. From Fig.1, we can see
that
m
and
m
(1 )mM constitute a complementary
pair, T denotes the delay time. The definition of M pairs
of complementary sequence
,
mm
B is given as:
01 1
01 1
(,,, )
(,,, )
L
mmm m
L
mmm m
Aaa a
Bbb b
(3)
Take
00
A ,B and
11
A ,B for example,
0
A and
1
A are
transmitted by antenna1 and antenna2 respectively in
time t, while
0
B and
1
B are transmitted in time t+T.
ICSPCC2015
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