642 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 14, 2015
Direction Finding by Time-Modulated Array With
Harmonic Characteristic Analysis
Chong He, Xianling Liang, Member, IEEE, Zhaojin Li, Junping Geng,Member
, IEEE,and
Ronghong Jin, Senior Member, IEEE
Abstract—A novel direction-finding method by the time-modu-
lated array (TMA) is proposed through analyzing the harmonic
characteristic of received signal, which requires only two antenna
elements and a single RF channel. The signal processing of the pro-
posed method is concise, and its calculation amount concentrates
on a two-point discrete Fourier transform (DFT). Numeric simu-
lations are provided to examine the performance of the proposed
method, and a simple S band two-element TMA is constructed and
tested to verify its effectiveness.
Index Terms—Direction finding, discrete Fourier transform
(DFT), time-modulated array (TMA).
I. INTRODUCTION
D
IRECTION finding has a very extensive use in wireless
communication, sensor network, and military appli-
cations. Most existing direction-finding methods, including
the Watson–Watt method [1], interferometer [2], and spatial
spectrum estimation method [3], generally exploit four or more
elements and need a rather complex signal processing. In con-
trast, the direction-finding function of the time-modulated array
(TMA) attracts more and more attention for having simple
structure and requiring low signal processing burden [4].
TMA was first proposed by Shanks and Bickmore in the
1950s [5], which added the periodically controlled switches to
the RF front end. Because of the periodical modulation, the
power of RF signal is distributed along both the fundamental
and harmonic components. Recently, the research about TMAs
mainly focused on ultra-low sidelobe level (SLL) pattern
synthesis [6], the beamforming [7], [8], and the direction
finding [9]. The direction-finding property of TMAs was first
proposed in [4] by analyzing the relationship between the
pattern of the first harmonic component and the mark-to-space
ratio of the modulation signal. In 2010, an experimental result
of direction finding by a two-element TMA was reported [10],
which obtained the direction of an incident plane wave by
Manuscript received May 29, 2014; accepted June 24, 2014. Date of pub-
lication November 24, 2014; date of current version February 27, 2015. This
work was supported by the National Natural Science Foundation under Grants
61201058 and 61471240, the Research and Innovation Project of Shanghai Ed-
ucation Commission under Grant 12Z112030001, and the Scientific Research
Foundation for Returned Overseas Chinese Scholars, State Education Ministry,
and the Project of “SMC Excellent Young Faculty.”
The authors are with the Department of Electronic Engineering, Shanghai
Jiao Tong University, Shanghai 200240, China (e-mail: hechong@sjtu.edu.cn;
liangxl@sjtu.edu.cn).
Color versions of one or more of the figures in this letter are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/LAWP.2014.2373432
Fig. 1. Block diagram for direction finding of time-modulated array with har-
monic characteristic analysis.
inserting a coaxial line stretcher into one channel for the phase
compensation. The principle is that if the phase shift caused
by the stretcher can counteract the phase shift generated in the
space, the first harmonic will completely vanish. However,
the procedure to adjust the stretcher means searching in the
range of
, which is time-consuming and may not suitable
for the real-time direction finding. Actually, the stretcher can
be taken out if we make numerical analysis to the harmonic
characteristic directly. We deduce the mathematical expression
to calculate the incident direction using the fundamental and the
first harmonic components. In the digital domain, they can be
conveniently calculated out by the discrete Fourier transform
(DFT). Then, the proposed method can help to implement
direction-finding systems with simple structure and low cost.
The remainder of the letter is as follows. Section II is de-
voted to the theory of the proposed direction-finding method. In
Section III, numeric simulations are given to examine its per-
formance. In Section IV, a simple S-band two-element TMA
is constructed and tested to verify its effectiveness. Eventually,
some conclusions are drawn in Section V.
II. T
HEORY
The block diagram of the direction finding by the TMA is
schematically shown in Fig. 1. Consider a two-element TMA
working on the receiving state, with the element spacing
.The
RF signals received in the two elements are alternatively se-
lected to enter in the single RF channel by a single-pole double-
throw (SPDT) RF switch. The modulation period of the SPDT
switch is
, and the duty cycle is 50%. Assume that the far-field
sinusoidal plane wave at the frequency
enters in the array,
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