1

On the Anti-Jamming Performance of the
NR-DCSK System

arXiv:1711.05417v1 [] 15 Nov 2017

Binh Van Nguyen, Hyoyoung Jung, and Kiseon Kim

Abstract—This paper investigates the anti-jamming performance of the NR-DCSK system. We consider several practical
jamming environments including broad-band jamming (BBJ),
partial-time jamming (PTJ), tone jamming (TJ) consisting of
both single-tone and multi-tone, and sweep jamming (SWJ). We
first analytically derived the bit error rates of the considered
system under the BBJ and the PTJ environments in closed-form
expressions. Our derived results show that the system performances under these two jamming environments are enhanced
as P increases, where P is the parameter of the NR-DCSK
modulation scheme denoting the number of times a chaotic
sample is repeated. In addition, our results demonstrate that
for the PTJ, the optimal value of the jamming factor is close
to zero when the jamming power is small, however, it increases
and approaches one as the jamming power enlarges. We then
investigate the performance of the considered system under the
TJ and the SWJ environments via Monte-Carlo simulations.
Our simulations show that single-tone jamming causes a more
significant performance degradation than that provided by multitone jamming counterparts. Moreover, we point out that the
system performance is significantly degraded when the starting
frequency of the sweep jammer is close to the carrier frequency
of the transmitted chaotic signals, the sweep bandwidth is small,
and the sweep time is half of the transmitted bit duration.
Index Terms—Chaotic communication, noise reduction differential chaotic shift keying, jamming environments, bit-error-rate.

I. I NTRODUCTION
HAOTIC communications (CC) has recently been considered as a promising alternative to the conventional
direct sequence spread-spectrum (DS-SS) systems. The basic
idea of CC is to replace pseudo-noise sequences by chaotic
sequences, which can be directly generated by chaotic maps.
Among various chaotic maps, logistic has been extensively
exploited due to its simplicity and good performance [1].
Chaotic systems are generally categorized as coherent and
non-coherent chaotic systems. In the former systems, chaotic
synchronization plays a vital role in deciding the systems
performance. However, designing an efficient chaotic synchronization scheme still remains as a challenging problem. As
a result, research works on the coherent chaotic systems are
very limited. On the other hand, in the latter systems, data
recovery procedure is much simpler than that of the coherent
counterparts since the chaotic synchronization is not required.
Consequently, a lot of efforts have been devoted to design
effective non-coherent modulation schemes and to find novel
applications of non-chaotic coherent systems in reality [2].
The fundamental and most studied non-coherent modulation
scheme is differential chaotic shift keying (DCSK). In a
chaotic system with the DCSK scheme, referred to as DCSK

C

system, a bit duration is divided into two equal time slots.
The first slot is for transmitting a chaotic signal, namely as
reference signal, which contains β different chaotic samples.
In addition, depending on the bit to be sent, the reference
signal is either repeated or multiplied by a factor of −1 and
transmitted in the second slot. At the receiver, the received
signal is correlated with its ”half a bit”-delayed version to
estimate the transmitted information bit. The performances
of the DCSK system over the additive white Gaussian noise
(AWGN) and the multipath fading channels are extensively
investigated in [3]-[4] and [5], respectively. It is shown that
enlarging the spreading factor beyond a certain value degrades
the performance of the DCSK system. Although the DCSK
system is simple and largely considered, it suffers from
several drawbacks, i.e. low data rate, high energy consumption,
using complex wideband delay, and so on. Motivated by this
fact, several advanced systems have been recently proposed
including reference modulated DCSK [6], high efficiency
DCSK [7], improved DCSK [8], short reference DCSK [9],
and noise reduction DCSK (NR-DCSK) [10], among which
the NR-DCSK system provides the best noisy performance.
The generation of the reference signal in the NR-DCSK
system is totally different from that in the DCSK counterpart.
Particularly, only β/P different chaotic samples are generated
and each sample is repeated P time to make a reference signal
of β samples in total.
Although chaotic systems in general and non-coherent
chaotic systems in particular are partly designed for the antijamming (AJ) purpose, the AJ performance of a non-coherent
chaotic system is only carried out in [11]. Particularly, the
performance of the DCSK system under the single-tone jamming (STJ) environment is studied. The authors derived the
system bit-error-rate (BER) in a closed-form expression and
show that the system performance is significantly degraded
when the jamming frequency is an integer multiple of the bit
frequency. Despite the fact that the fundamental DCSK system
is already investigated, the AJ performances of its recent
advanced variants have not been reported in the literature yet.
To fill this gap, in this paper, we will consider the recent
proposed NR-DCSK system and analyse its AJ performance
under various practical jamming environments such as broadband jamming (BBJ), tone jamming (TJ), partial-time jamming
(PTJ), and sweep jamming (SWJ). We first analytically derived
the BERs of the NR-DCKS system under the BBJ and PTJ
in closed-form expressions. We then investigate the BER
of the considered system under the TJ and the SWJ via
Monte-Carlo simulations. Our analytical and simulation results
reveal several novel insights about the effects of the jamming

2

Fig. 2. A graphical representation of the transmitted signal of the bit bl .

Fig. 1. A NR-DCSK system in a jamming environment.

parameters on the system performance.
The remainder of this paper is organized as follows. Section
II introduces the system model. Practical jamming signals
are described in the section III. In section IV, we present
mathematical frameworks to derive the system BERs under
the BBJ and the PTJ environments. Thereafter, representative
simulations are provided in section V to verify our analysis
and further demonstrate the effects of the TJ and the SWJ on
the performance of the considered system, followed by our
conclusion in section VI.

The received baseband signal at the receiver can be express
as follows

II. S YSTEM M ODEL
The considered system consists of a pair of sourcedestination and a jammer, as illustrated in Fig. 1. Each node
has a single antenna. In addition, the NR-DCSK scheme is
employed for modulating and demodulating legitimate signals.
Moreover, the logistic map is exploited for generating chaotic
sequences. Here, the logistic map is considered because of its
simplicity and good performance. A mathematical representation of the map is given by [1]
xk+1 = 1 − 2x2k ,
(1)
 2
 2
where E [xk ] = 0, E xk = 1, and var xk = 1/2 for
normalized xk .
For the modulation process, each bit duration is divided
into two equal time slots. The first time slot is allocated
for transmitting a reference chaotic sequence length β, called
spreading factor, while the second one is used for transmitting
either the reference sequence (when the bit being sent is
+1) or its inverted version (when the bit being sent is -1).
The reference sequence is generated as follows. The chaotic
generator first generates β/P samples. Then, each chaotic
sample is replicated P times to obtain the reference sequence
with length β in total. As a result the transmitted signal of the
lth bit, bl , can be expressed as [10]
( l
if 0 < k ≤ β,
x k ,
⌈P ⌉
(2)
slk =
l
bl x k −β , if β < k ≤ 2β,
⌈P ⌉
where ⌈·⌉ denotes the ceiling operator. Graphically,
illustrated as in Fig. 2.

Fig. 3. Receiver’s structure and operation of the NR-DCSK system.

slk

rkl = slk + jkl + nlk ,

(3)

where jkl and nlk are the jamming signal and the AWGN.
Here we consider the AWGN channel so that we can solely
focus on the effect of jamming on the system performance.
The assumption of the AWGN channel has also been adopted
in several related works, i.e. [11]-[12]. The received signal
is first averaged using a block average filter (BAF) with a
block size of P . The averaged signal is then correlated with its
replica that is time delayed by a factor of β/P . Thereafter, the
resultant correlated signal is summed over β/P samples and
passed through a threshold detector to recover the transmitted
information bit. The BAF is used to reduce the power of the
AWGN, from which the noisy performance enhancement of
the NR-DCSK can be achieved. A detailed illustration of the
receiver is given in Fig. 3, in which the output of the BAF
would be given as

r̄kl =

1
P

kP
X

rpl

p=(k−1)P +1

= slk +

1
P

kP
X

p=(k−1)P +1

jpl +

1
P

kP
X

nlp .

(4)

p=(k−1)P +1

can be
In addition, the decision variable at the input of the threshold

3

detector can be written as


β/P
kP
kP
X
X
X
1
xlk + 1
Bl =
jpl +
nlp 
P
P
k=1
p=(k−1)P +1
p=(k−1)P +1


kP
kP
X
X
1
1
l
jp+β
+
nlp+β  .
· bl xlk +
P
P
p=(k−1)P +1

p=(k−1)P +1

(5)

III. JAMMING M ODELS
In this section, we shall present several jamming types
that are commonly encountered in military systems. These
common jamming types include BBJ, PBJ, TJ, and SWJ.
A. Broad-band Jamming [13]
A broad-band jammer places jamming energy across the
entire frequency bandwidth used by the target communication
system. The BBJ essentially raises the background noise level
at the receiver, creating a higher noise environment, which
makes it more difficult for the target communication system to
operate. At the very least it decreases the range over which the
target communication system is effective. Since BBJ generates
signals that are similar to broadband background noise, it is
commonly modeled as a zero-mean Gaussian random variable
with variance (power) Pj .
B. Partial-time Jamming [14]
A partial time jammer turns on and off periodically acon
, where Ton and
cording to the jamming factor ρ = TonT+T
of f
Tof f denote the periods in which the jammer is on and off,
respectively. In addition, the summation of Ton and Tof f is
called the jamming duty cycle. When the jammer is on, it is
commonly assumed to emits broad-band signals, i.e. Gaussian
noise, with power Pj /ρ, where Pj is the average jamming
power. It means that the jammer turns on and off periodically
to focus more power on degrading the communication of the
target system. It is noteworthy that the BBJ is a special case
of the PTJ when ρ = 1.
C. Tone Jamming [15]
In TJ, one ore more jammer tones are strategically placed
in the target signals’ spectrum. TJ includes STJ and multipletone jamming (MTJ). STJ places a single-tone where it is
needed, while MTJ equally distributes the jamming power
among several tones. Mathematically, the TJ can be expressed
as follows
M r
X
2Pj
sin (2πfm t + θm ),
(6)
Jtj (t) =
M
m=1

where M , Pj , fm , and θm are the number of jamming tones,
total jamming power, and the frequency and the phase of
the mth jamming tone, respectively. In addition, it should
be noticed that fm here is the baseband frequency of the
mth jamming tone, which is different from the passband
counterpart, i.e. fm +fc where fc denotes the carrier frequency
of the transmitted chaotic signals.

D. Sweep Jamming [16]
A sweep jammer rapidly sweeps a narrow band jamming
signal over a wide frequency band. The SWJ can be characterized by its starting frequency fstart , stopping frequency fstop ,
sweep rate ∆f , and sweep time Tsw . In addition, there are
several variants of the SWJ depending on narrow-band signals
being used and sweep methods that specify the evolution of
the instantaneous sweep frequency. Generally, narrow-band
signals used to generate the SWJ include sinusoidal, triangular
pulses, and rectangular pulses. Moreover, sweep methods
contain linear, quadratic, and logarithmic. Among various
aforementioned options, the one based on sinusoidal signals
and linear sweep method is commonly used and modeled as
follows
p

Jsw (t) = 2Pj sin 2πfstart t + π∆f t2 + θsw , (7)
f

where ∆f = stopTswstart and θsw denotes the initial phase
of the sweep jamming signals. Similar to the case of the TJ,
fstart and fstop here are all the baseband frequencies.
−f

IV. A NTI -JAMMING P ERFORMANCE A NALYSIS
In this section, we analytically analyse the BER of the
NR-DCSK system under the PTJ environment. In addition,
since the BBJ is a special case of the PTJ, the system BER
under the BBJ environment can be straightforwardly obtained
from that under the PTJ. The system performances under the
other types of jamming will be evaluated via Monte-Carlo
numerical simulations in the next section due to mathematical
intractability.
The decision variable presented in (5) can be further expanded as follows
β/P

Bl =

X

k=1

|

2
bl xlk

β/P

+

{z

β/P

+

}

U

X xl
k
P
k=1
|

kP
X bl xl
X
k
jpl
P
k=1
p=(k−1)P +1
{z
}
|

kP
X

l
jp+β

p=(k−1)P +1

{z

}

I1

I2

β/P

+

X 1
P2
k=1
|

β/P

X xl
k
+
P
k=1
|
β/P

+

X 1
P2
k=1
|

β/P

+

X 1
P2
k=1
|

kP
X

kP
X

jpl

l
jp+β

p=(k−1)P +1

p=(k−1)P +1

{z

}

I3

kP
X

β/P

nlp+β

p=(k−1)P +1

{z

N1
kP
X

jpl

}

+

kP
X
X bl xl
k
nlp
P
k=1
p=(k−1)P +1
|
{z
}
N2

kP
X

nlp+β

p=(k−1)P +1

p=(k−1)P +1

{z

N3
kP
X

nlp

p=(k−1)P +1

{z

N4

kP
X

}

l
jp+β

p=(k−1)P +1

}

4

β/P

X 1
+
P2
k=1
|

kP
X

nlp

kP
X

nlp+β ,

(8)

p=(k−1)P +1

p=(k−1)P +1

{z

}

N5

where U , Ii , and Nj represent the desired, interference, and
noise components. It is noteworthy that U , Ii , and Nj are
independent because the chaotic signal, jamming signal, and
AWGN are independent. In addition, at any given time, the
chaotic signal is independent of its time-delayed version.
Under the PTJ condition, the jamming signal jk is modeled as
a zero-mean Gaussian random variable with variance (power)
Pj /ρ, where Pj is the average jamming power. In addition,
the power of the AWGN nk is assumed to be N0 /2.
Following the central limit theorem, the decision variable
Bl can be assumed to follows the Gaussian distribution, and
thus, the error probability of transmitting the bit bl can be
calculated as follows
1
1
Pr [Bl < 0|bl = +1] + Pr [Bl > 0|bl = −1]
2
2

!−1/2 
2var [Bl ]
1
,
= erf c 
(9)
2
2
(E [Bl ])

BERl =

where erf c (·), var [·], and E [·] are the complementary error
function, the variance, and the mean operations, respectively.
Equation (9) indicates that to obtain BERl , the mean and
variance of Bl are required. Firstly, the mean of Bl can be
readily derived as follows


β/P

E [Bl ] = E [U ] = bl E 

X

k=1



2
xlk  = bl EP .

(10)

To derive the variance of Bl , it is necessary to consider
whether the jammer is on or off during the transmission time
of the bit bl . Let’s first consider the case that the jammer is on.
Under this condition, the bit bl can be assumed to be jammed
with a probability of ρ. With a typical assumption of a high
β/P
P h l 2 i
E xk
spreading factor, the bit energy Eb = 2P
=
k=1

2P EP can be considered to be constant [8]-[10]. In addition,
we can readily show that the average of P independent and
identically distributed (i.i.d.) samples of a zero-mean Gaussian
variable with variance of X is still a zero-mean Gaussian
random variable with a reduced variance of X/P . Based on
this results, we can derive the following results

var [Bl ] =

3
X
i=1

var [Ii ] +

5
X

var [Nj ],

(11)

j=1

where var [Ii ] and var [Nj ] are given by
var [I1 ] =

EP Pj
= var [I2 ] ,
ρP

(12)

βPj2
,
ρ2 P 3
EP N0
= var [N2 ] ,
var [N1 ] =
2P
βPj N0
var [N3 ] =
= var [N4 ] ,
2ρP 3
βN02
var [N5 ] =
.
4P 3
var [I3 ] =

(13)
(14)
(15)
(16)

Plugging all the results given in (10)-(16) into (9), yields the
following error probability of transmitting the bit bl while the
PTJ jammer is on

1
4Pj /ρ + 2N0
BERlon = erf c
2
P EP
!−1/2 
2Pj N0 /ρ + 2Pj2 /ρ2 + N02 /2
.
+β
P 3 EP2

(17)

On the other hand, when the partial-time jammer is off during
the transmission time of the bit bl , we can readily obtain the
corresponding error probability by setting Pj = 0 in (17). That
is,
"
−1/2 #
1
N02 /2
2N0
of f
.
(18)
BERl = erf c
+β 3 2
2
P EP
P EP
Then, a weighted summation of (17) and (18), whose weighting factors are the probabilities that the bit bl is jammed and
un-jammed, produces

ρ
4Pj /ρ + 2N0
BERl = erf c
2
P EP
!−1/2 
2Pj N0 /ρ + 2Pj2 /ρ2 + N02 /2

+β
P 3 EP2
"
−1/2 #
1−ρ
N02 /2
2N0
.
(19)
+
+β 3 2
erf c
2
P EP
P EP
We observe that the above BERl does not depend on the bit
index l, and thus, the system BER under the PTJ environment
can be expressed as follows


2 −1/2 
Pj
N0
Pj
N0

 ρ + 2
ρ + 2
ρ


+ 8β
BERptj = erf c 

8
2


2
Eb
P Eb
1−ρ
+
erf c
2

"

2βN02
4N0
+
Eb
P Eb2

−1/2 #

.

(20)

Under the special case of the BBJ environment, the system
BER can also be readily obtained from (20) by setting ρ = 1.
Particularly,
"
2 !−1/2 
Pj + N20
Pj + N20
1
.
BERbbj = erf c
+8β
8
2
Eb
P Eb2

(21)

5

100

Analysis
Lower bound
Simulation

10-1

EbN0 = 15 dB
0.15
0.1

BER

BER

10-2
10-3
 = 0.2, 0.5, 1 with P = 20

0
35

-4

10

0.05

30

 = 1 with P = 100

25

1
20

-5

0.8
15

10

0.6
10

10-6

Pj (in decimal)
0

5

10

15

0.4
5

0.2
0

0



20

EbN0 (dB)
Fig. 4. The system BERs under the PTJ and the BBJ environments with
P
JSR = Pj = 5 dB.
s

It is observed from (20) and (21) that as P increases, the BERs
are reduced and tend to the lower bound given by
"
−1/2 #

ρ
P
N
8
j
0
lower
BERptj
= erf c
+
2
Eb ρ
2
"
−1/2 #
4N0
1−ρ
.
(22)
erf c
+
2
Eb
Taking a closer look at (20) and (22), we can observe that
when Pj is large enough, the partial-time jammer should select
ρ = 1 to optimally degrade the performance of the target
system. On the other hand, when Pj is small, it is obvious that
ρ should be chosen close to zero to increase the instantaneous
jamming power, and thus, further deteriorates the performance
of the target system.
V. S IMULATION R ESULTS
In this section, we shall provide several representative
simulation results to (i) verify our analysis on the system BERs
under the BBJ and the PTJ environments and (ii) illustrate the
effects of the TJ and the SWJ on the system performance.
In Fig. 4, we simulate the BER of the NR-DCSK system
Eb
versus N
under the PTJ and the BBJ environments with
0
P
JSR = Psj = 5 dB. The figure first shows that the analysis
curves follow the simulated ones closely, which validates our
analysis. Secondly, we observe that with JSR = 5 dB, the
system BER is enhanced as the jamming factor ρ increases.
In other words, from the jammer’s perspective, the jammer
is better to be active with a short duration and transmit with
a higher power to more severely degrade the target system
performance. Lastly, the figure confirms that as P enlarges,
the system BER improves and tends to the lower bound given
in (22).
To further illustrate the effects of the jamming factor ρ of
the PTJ on the system performance, we present the system
BER versus ρ and Pj in Fig. 5. We observe the trend that as

Fig. 5. The system BERs versus ρ and Pj with P = 20 and EbN 0 = 15
dB.

Pj is small, the optimal value of ρ (from the jammer point of
view) is close to zero. In addition, as Pj increases, the optimal
value of ρ also increases and approaches one. This observation
is understandable because when the jamming power is small,
if the jamming is active all the time, the jamming power
density will be very small, and thus, the jamming effect on
the system performance could be negligible. Therefore, it is
optimal for the jammer to turn on for a short period of time and
transmit with a much higher power. On the other hand, when
the jamming power is larger than a certain value, the composite
jamming and AWGN power is comparable with (or even larger
than) that of the targeted signal, and thus, it is unnecessary to
further increase the jamming power. As a result, the jammer
should turn on all the time to optimally degrade the target
system performance. It is noteworthy that given Eb /N0 , β,
P , and Pj , the optimal value of ρ can be easily derived by
numerically solving the optimization problem, whose objective
function is the equation (20), with mathematical programs such
as Matlab or Mathematica, i.e. with Eb /N0 = 15 dB, β = 200,
P = 20, and Pj = 10 dB, the optimal value of ρ is found to
be 0.24576.
We now turn our interest to the effect of the TJ on the
performance of the NR-DCSK system. In the simulation, we
use the following discrete baseband model of the TJ signals
[11]


M r
X
2Pj
Fm
(23)
sin πk
+ θm ,
jk =
M
β
m=1
where Fm = fm Tb is the normalized jamming frequency of
the mth tone and Tb denotes the bit duration. Here, θm is
modeled as an arbitrary constant angle selected from [−π, π].
In addition, we simulate the system BER under single-tone,
3-tone, and 5-tone cases. It is shown in Fig. 6 that the
STJ causes the most significant performance degradation and
increasing the number of jamming tones actually enhances the
performance of the target system. Moreover, for the STJ case,
increasing P can improve the system performance. The reason
is that with a larger value of P , the receiver can further reduces
the composite power of jamming and AWGN (by using the

6




-1

10

%(5

BER







F







7RQH-65
7RQH-65
7RQH-65
7RQH-65
7RQH-65

G%3
G%3
G%3
G%3
G%3







F







start
start

= 3, F
= 1, F

stop
stop

=7
=2

Fstart = 1, Fstop = 4
-2

10



(E1 G%







0

2

4

6

8

10

Tsw / Tb
Fig. 8. The system BERs versus Tsw under the SWJ environment with
P = 20 and JSR = 0 dB.

Fig. 6. The system BERs versus EbN 0 under the TJ environment.
100
P = 20 and JSR = 0 dB
-1

BER

10

10-2
F

start

= 1, F

stop

=2

Fstart = 3, Fstop = 7

P = 100
JSR = 0 dB

Fstart = 3, Fstop = 11

-3

10

Fstart = 7, Fstop = 11

P = 20
JSR = -5 dB

Fstart = 7, Fstop = 11
10-4

Fstart = 7, Fstop = 11
0

5

10

15

20

25

30

performance is degraded. In addition, as expected, with a
larger P or with a smaller JSR, the system performance is
enhanced.
In Fig. 8, we present the system BER versus the ratio of the
sweep time and the bit duration with P = 20 and JSR = 0
dB. It can be seen that the most effective sweep time is half
of the bit duration. The reason is that when Tsw = Tb /2,
the reference and the information bearing sequences of any
bit suffer from the same SWJ signals, which increases the
correlation between the two sequences regardless of the bit
value. Consequently, the decoding performance is degraded.
In addition, the figure shows that when the sweep time is
much larger than the bit duration, its effect on the system
performance is negligible.

EbN0 (dB)
Fig. 7. The system BERs versus EbN 0 under the SWJ environment.

BAF), and thus, the SINR at the receiver is improved, from
which the system BER is enhanced. Finally, it is observed that
as JSR is reduced, the system BER decreases, as expected.
The effects of the SWJ on the performance of the NR-DCSK
system will now be presented. According [17], we can use the
following discrete baseband model of the SWJ signals in our
simulation


p
k 2 ∆F
kFstart
+ θsw , (24)
+π
j (k) = 2Pj sin π
β
4β 2

where Fstart = fstart Tb and ∆F = ∆f Tb2 . In Fig. 7, we
simulate the system BER versus EbN 0 with the condition
that the sweep time equals to the bit time, from which
∆F = Fstop − Fstart , where Fstop = fstop Tb . The figure
shows that the sweep frequencies and the sweep bandwidth
have a great impact on the system performance. Particularly,
the closer to the carrier frequency of the chaotic signals the
starting frequency of the sweep jammer is and the smaller
the sweep bandwidth is, the more significant the system

VI. C ONCLUSION
In this work, we considered the NR-DCSK system under
the BBJ, PTJ, TJ, and the SWJ environments. We analytically
derived closed-form expressions of the system BERs under the
BBJ and the PTJ environments, from which we revealed that
in general increasing P can enhance the system anti-jamming
performance. In addition, we showed that the optimal value of
the jamming factor of the PTJ tends to zero when the jamming
power is small, however, it increases and approaches one as
the jamming power increases. Moreover, via simulations, we
demonstrated that the STJ is more efficient than the MTJ
counterparts, from the tone jammers’ point of view. Furthermore, we illustrated that under the SWJ environment, the
system performance is more significantly degraded when the
starting frequency of the sweep jammer is closer to the carrier
frequency of the chaotic signals and the sweep bandwidth
is small. Finally, we revealed that the most effective sweep
time is half of the bit duration. Our results could be use as a
guideline for systems’ designers in turning existing systems’
parameters to satisfy a certain quality-of-service or designing
novel and effective AJ communication systems.

7

ACKNOWLEDGMENT
The authors gratefully acknowledge the support from Electronic Warfare Research Center at Gwangju Institute of Science and Technology (GIST), originally funded by Defense
Acquisition Program Administration (DAPA) and Agency for
Defense Development (ADD).
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