IEEE Microwave Magazine - October 2016 - 30

While all components of the array
simultaneously transmit the entire
spectrum, each frequency range is
directed to a different subresolution
region at the target.

R (v n) =

transmit the entire spectrum, each frequency range
is directed to a different subresolution region at
the target. Return signals received from the target
are detected by a single small-dimension antenna
[12]. The signal received from the antenna is processed so that each frequency range is correlated to
a specific location on the target, yielding a superresolved outcome.

Mathematical Analysis
The radiation source illuminates the object in the far
field with N radiation beams, each at a different frequency. For purposes of simplicity, a mathematical
description for a 1-D system is presented here, although
the same theory applies for a 2-D system.
The transverse dependence of the projected farfield pattern g(x) can be denoted as
g (x) = / a n exp c 2ri $ v n $ x m .
cr $ z
n

(1)

∆f

Multiplexing
Matching

This equation describes the pattern projected onto the
target plane by the antenna: v n is the wave propagation velocity of the illumination beam, c r is the speed
of light, a n is the amplitude of the field for each frequency, z is the distance from the target, and x is the
transverse coordinate of the object's spatial plane. This
projection is multiplied by the reflectance function of
the object T(x) and captured by a monodetector. The
signal detected by a monodetector is represented by
the spatial averaging R (v n), given as

1
2
3
4

∆f 1
1
∆f 2
2
∆f 3 3
∆f 4 4

(a)

(b)

Figure 1. The system configuration: (a) a conventional
radar and (b) a split-spectral spatial transmission beam
radar system. NA: network analyzer.

T (x) $ / a n exp c 2ri $ v n $ x m dx.
cr $ z
n

(2)

The signal received by the detector passes through
a frequency demultiplexer, so that each frequency (of
the illuminating beam) goes through a time-domain
analysis separately. Recall that each of the signals
obtained at a specific frequency is reflected from a
different subresolution area on the target. Thus, the
decoded signal can be expressed by the following:
3

D (t ) =

#
3

u
T (x) $ / a n exp c 2ri $ x $ V m exp (- 2ritVu ) d (Vu )
c
r
n

= / a n $ T (x) $ d ` t + x j .
cr
n

(3)

The variable Vu is the ratio between the velocity v n and
the distance z. Thus, we obtain the spatial characteristics of the target by the signal at a specific frequency,
encoding a specific spatial region of the target.

System Configuration
To confirm our theory, a spatial spectral-encoding
method was developed. An electromagnetic simulation and experimental system was designed to
simulate two types of radar: a normal, conventional
radar system [Figure 1(a)] and a radar system with
a split-spectral spatial transmission beam, which
carries out the spectral spatial encoding process
[Fig ure 1(b)]. In both types of radars, an identical
receiving array was implemented having a smallaperture horn antenna. A scanned frequency range
of 10-14 GHz and identical transmission power were
used in both simulations.
We placed a target in the far field of the radar. The
scanned target structure was assembled from four
metal squares with a boundary between the squares.
To compare the two radars, we examined several
target configurations. These configurations include
the full object structure with all four metal squares
as well as missing-target structures, in which one or
more squares are missing. To obtain a spectral split
beam, we used an array of four matched horn antennas. In each frequency range, the obtained radiation
curve is different, so a different area in the target is
illuminated each time. For example, in the 10-11-GHz
frequency range, the radiation curve is adjusted to
illuminate the metal square marked by the number 1; in the 11-12-GHz frequency range, the radiation curve is adjusted to illuminate the metal square
marked by the number 2 (Figure 1).
In the normal radar simulation, we used the same set
of four horn antennas so that the antenna array matching
was different and the obtained radiation curve was spectrally uniform. The far-field separation ability depends on
the distance between the targets and the source, as well

October 2016

Table of Contents for the Digital Edition of IEEE Microwave Magazine - October 2016