Partitioned Cyclic Code Shift Keying for JTIDS

Hong-Jun Noh and Jae-Sung LimGraduate School of Information Technology,

Ajou University

Suwon, South Korea

{nonoboy, jaslim}@ajou.ac.kr

Abstract—In this paper, we propose partitioned cyclic codeshift keying (PCCSK) for the Joint Tactical Information Distri-bution System (JTIDS) by combining a Hadamard matrix anda modified maximal length sequence (MMLS). The proposedapproach adaptively increases the transmission data rate withina limited transmission range in the battlefield. By exploiting anew code set as a spreading code and by adopting code selection,the system is easily able to achieve higher spectral efficiency. Foradditional performance enhancement, we apply adaptive channelcoding with PCCSK, and we derive the appropriate code pairs.Monte Carlo simulations are conducted to show the transmissionranges of the proposed scheme, and the results show that PCCSKwith adaptive coding can support a higher data rate with areasonable transmission range.

I. INTRODUCTION

In 1997, the concept of network-centric warfare (NCW)

was introduced as an information and intelligence architecture

based on sensors, information, and engagement grids in order

to enable new operational concepts of speed of command

and self-synchronization [1]. Without the mass associated

with conventional styles of warfare, maneuver and information

are critical to NCW. This implies that shooters and decision

makers, who are physically separated, are linked via a ubi-

quitous network. Therefore, tactical data links are playing an

increasingly important role in the modern battlefield, and they

have attracted considerable attention in recent years. Many

investigations into tactical data links have been undertaken

[2]–[4].

Link 16, also known as the Joint Tactical Information Distri-

bution System (JTIDS) and/or the Multifunctional Information

Distribution System (MIDS), was designated as the United

States Department of Defense’s primary tactical data link for

all military service and defense agency command, control, and

intelligence (C2I) systems. As it is used in the battlefield, it

must have sufficient timeliness, high capacity, strict security,

and survivability [3]. The primary drawback of Link-16 is

its limited data rate [4]. The conventional Link-16 system is

unable to support higher data rate applications (video/imagery

and TCP/IP packet switching), and it is necessary to make

better use of Link-16 networks for existing high data rate

applications (e.g., secure voice systems) [4]–[7].

To meet these challenging requirements, transmission tech-

niques must be carefully considered. Therefore, research has

been focused on transmission techniques and their perfor-

mance in Link-16 [3]–[6]. Link performances have been

evaluated by theoretical analysis and simulation, according

to the specifications of the Link-16 system that have been

disclosed [3]. In order to increase transmission performance,

an alternative waveform with variable channel coding was

proposed in [4]. Link-16 Enhanced Throughput (LET) was

developed to obtain enhanced throughput over a Link-16 net-

work by changing to the Link-16 baseband coding [5]. In [5],

the combined Reed Solomon channel coding (RS) and cyclic

code shift keying (CCSK) modulation schemes are replaced

with a RS and convolutional coding scheme. However, the

existing schemes inevitably experience degradation in their

low probability of intercept/detection (LPI/LPD) performance

at the enhanced data rates.

To evaluate the performance of Link-16, we should study the

transmitter and receiver components of JTIDS. In JTIDS, some

well-known transmission techniques have been applied, such

as channel coding, CCSK, interleaving, and frequency hop-

ping. Particularly, CCSK which is a form of M -ary signaling

over a communication channel shows dramatic performance

gains, especially in its LPI/LPD properties. It has also been

shown that CCSK requires significantly fewer computations

than the existing orthogonal signaling schemes and, for codes

that provide LPI, the cyclic shifts are correlated with each

other; that is, the cyclic autocorrelation function has non-zero

side lobes [8].

In this paper, we discuss a CCSK technique for JTIDS in

order to increase transmission performance. The main contri-

bution of this paper is a method for adaptively increasing the

transmission data rate. To this end, we propose a partitioned

CCSK (PCCSK) scheme. More specifically, we construct a

spreading code as a set of partitioned sub-spreading codes

by combining a Hadamard matrix and a modified maximal

length sequence (MMLS). In contrast to the conventional

maximal length sequence (MLS) or MMLS, the new code

set is constructed with multiple sub-codewords. As multiple

sub-spreading codes participate in CCSK, we obtain a higher

resource granularity. Moreover, we also improve the system

capacity with a reasonable transmission range. For an addi-

tional performance enhancement, we apply adaptive channel

coding with PCCSK and derive the appropriate code pairs.

The rest of the paper is organized as follows. In Section

II, the overall system model is described. We introduce the

proposed PCCSK scheme in Section III, and present our sim-

ulation results in Section IV. Finally, we draw our conclusions

in Section V.

978-1-4673-3/12/$31.00 ©2013 IEEE978-1-4673-3/12/$31.00 ©2013 IEEE

Fig. 1. Signal transmission model of JTIDS

II. SYSTEM MODEL DESCRIPTION

A. Joint Tactical Information Distribution System

The typical signal transmission model of JTIDS can be

simplified to that shown in Fig. 1. JTIDS is based on a time

division multiple access (TDMA) protocol, and all communi-

cation takes place in time slots whose size is fixed to 7.8125

milliseconds. Information in each time slot is generally carried

in a number of 75-bit words, which are arranged as 15 symbols

of 5 bits each. These words are subject to forward error

correction (FEC) using a RS code (RS(31, 15)) which adds 16

parity symbols to each 15 information symbols, giving a total

of 31 symbols per word. The RS coded symbols containing

5 bits of information are modulated using CCSK and spread

to a 32-chip sequence known as a CCSK symbol. The CCSK

chips are then further processed by being combined with a 32-

bit pseudo-random noise sequence for transmission security.

After this, the chips are modulated using minimum shift keying

(MSK) to generate analog pulses. In some cases, the start of

the pulse train is jittered pseudo-randomly within a time slot.

The instantaneous noise bandwidth of the signal is approx-

imately 3 MHz, and each pulse is transmitted over a carrier

frequency that is pseudo-randomly selected from a set of 51

between 960 MHz and 1215 MHz [9]. The Link-16 message

data can be sent with either a single- or double-pulse structure

[10]. In a double-pulse structure, each 32-chip symbol is

mapped onto two consecutive pulses that are guaranteed to

be on separate frequencies. This repetition provides robust-

ness against fading and/or jamming as it provides frequency

diversity.

The data rate of JTIDS varies depending on the system con-

figuration. Fig. 2 depicts the JTIDS symbol packing structures.

The data contained in JTIDS messages is always transmitted

as fixed-length, 3-word blocks of 225 bits each. These 3-

word blocks may be packed into a time slot at different

densities. In the standard double-pulse (STDP) mode, one 3-

word block is transmitted in each time slot. It is possible to

send two 3-word blocks in one slot using either the packed-

2 double-pulse (P2DP) mode or the packed-2 single-pulse

(P2SP) mode. For P2SP the information is not repeated on

two separate pulses, so that twice as much as information can

be sent in the same number of pulses as STDP. The trade-

off for this extra throughput is a reduction in jam resistance

and/or fading protection. For P2DP, the increased throughput is

accomplished by increasing the number of pulses per time slot.

In order to accommodate the longer pulse train, the jittering of

the start of the pulse train is eliminated. Finally, the packed-

4 single pulse (P4SP) mode can be used to send four 3-

word blocks per time slot. In this mode, each information

Fig. 2. JTIDS symbol packing structure

symbol packet contains only one pulse and the timing jitter

is eliminated. The theoretical maximum throughput for P4SP

(i.e., using every time slot) is generally calculated as 115,200

bps for a single terminal. For the P2 modes, the throughput is

57,600 bps, and for STDP it is 28,800 bps. If we recall that

the channel bandwidth of JTIDS is 3 MHz, we can see that

the spectral efficiency of JTIDS is too low.

B. Cyclic Code Shift KeyingIn JTIDS, the spread spectrum technique of CCSK is used

to obtain anti-jamming and LPI/LPD performance. CCSK

provides M -ary baseband modulation before MSK modulation

and is applied to the interleaved symbols of the RS codewords.

Each 5-bit symbol of the RS codewords is represented by a

32-chip. Starting with the base sequence (s0), there are 32

unique sequences that represent the values of the 5-bit symbols

between 0 and 31. Each sequence is derived by cyclically

shifting s0 to the left between 1 and 31 times to obtain a

unique sequence for all possible combinations of 5 bits. This

is illustrated in Table I.

TABLE I32-CHIP CCSK CODEWORDS

5-bit symbol 32-chip CCSK sequence chosen for JTIDS

00000 s0 = 01111100111010010000101011101100

00001 s1 = 11111001110100100001010111011000

00010 s2 = 11110011101001000010101110110001

.

.

....

11111 s31 = 00111110011101001000010101110110

The receiving terminal matches each of the received chip

sequences to entries in a look-up table and, when the percent-

age match exceeds a programmed threshold level, the terminal

decodes the chip sequence as the appropriate RS symbol. The

calculation of percentage match is accomplished by computing

the cross-correlation between the received 32-chip sequence

and all possible 32-chip CCSK codewords. If we denote a

received sequence after MSK demodulation by the row vector

r, then cross-correlation is defined as

κi = snrT (1)

where (·)T denotes the transpose and all zeros in the sequences

are replaced by −1.

III. PROPOSED SCHEME

A. Partitioned Cyclic Code Shift Keying

In this section, we propose a PCCSK scheme for JTIDS.

The proposed scheme consists of two steps: (i) PCCSK code

set construction based on the required data rate, (ii) appropriate

code selection and modulation.

In conventional CCSK, the spreading codewords are gener-

ated by the MMLS [8]. An MMLS is made by inserting −1or +1 in an MLS, which is a sequence of length M = 2γ − 1whose cyclic auto-correlation has a peak of M and side lobes

of 0. Unfortunately, in such MLSs, M is not a power of two, so

the number of bits transmitted is less than γ. To alleviate this

problem, an MMLS is used to extend the length to M = 2γ .

This modification results in the occurrence of non-zero auto-

correlation side lobe values, unlike with the true MLS.

The new spreading code set for PCCSK is constructed by

combining MMLS and Hadamard matrices. Let M = 2γ be

the total length of the transmitted codeword and L = 2α be

the length of the sub-spreading codeword, where α ≤ γ. Let

us define the L× L cyclic shifting matrix SL as

SL =

⎡⎢⎢⎢⎢⎢⎢⎣

0 0 · · · 0 11 0 · · · 0 0

0 1. . .

......

.... . .

. . . 0 00 · · · 0 1 0

⎤⎥⎥⎥⎥⎥⎥⎦. (2)

We extend the MMLS of length L to the base sub-spreading

code set U(L) using SL. We can then construct a new

spreading code set C(M) as

C(M = 2γ) = U(L = 2α)⊗H(2β) (3)

for β = γ − α, where ⊗ denotes the Kronecker product and

H(φ) is the Hadamard matrix of order φ.

Fig. 3 shows the whole PCCSK code set generation process

when β = 2. In this case, one codeword has four partitioned

codewords. If d is the total number of partitioned codewords

in one transmitted codeword, we can easily find that d = 2β .

As shown in Fig. 3, the PCCSK code set looks similar to the

Fig. 3. A spread code set for PCCSK (α = γ − 2, β = 2)

CCSK code set, in that the cyclic shift is applied to all the

codewords. However, the length of the base MMLS of PCCSK

is shorter than in conventional CCSK. Using this code set, we

can send variable sizes of data.

For higher information granularity, a smaller value of α is

better, but when α = 0, C(M) becomes the conventional

Hadamard matrix. On the other hand, when α = γ, C(M)becomes the conventional CCSK code set. Therefore, the

determination of the length of the smallest sub-spreading code

is important. We will discuss this code selection problem for

JTIDS in the following subsection.

Fig. 4. Sub-code selection for PCCSK (α = γ − 2, β = 2)

Fig. 4 illustrates an example of code selection for PCCSK.

Let us define CP (d,M) as the selected partitioned code set

for data transmission, where d is the number of partitions and

q is the transmitted codeword. So, the length of the partitioned

codeword L is the same as M/d. If d = 1, then CP (1,M)is equal to C(M), so we consider the case d > 1. When the

selected set of partitioned codes is CP (d,M), the proposed

partitioned CCSK scheme transmits

d · log2 L = d · log2(M/d) = d · (log2 M − log2 d)

= d · (γ − β) = d · ibits(4)

in a single codeword transmission. As d > 1, d is larger than

log2 d. Because M > d, the proposed scheme has a higher

data transmission rate than the conventional CCSK scheme.

Thus, the larger the selected value of d, the more data can

be transmitted. The transmitted spread sequence matrix Qγ is

given by

Qγ = {Qγ,1, Qγ,2, . . . , Qγ,d}. (5)

Although PCCSK has a good data rate performance, it

also has some limitations. First, we should select the base

MMLS very carefully because some MMLSs have positive

values of the auto-correlation side lobe, and the concatena-

tion of these sequences results in larger values of the auto-

correlation side lobe. Thus, we should select an MMLS that

has a negative auto-correlation side lobe value. The second

limitation of PCCSK is the degradation in processing gain

because of the partitioning. In JTIDS, this degradation causes

the transmission range to decrease. Thus, we should select

an appropriate code for transmission, not only for the data

rate but also for the range of operation. We demonstrate the

transmission range of PCCSK by simulation in section IV.

B. Code Selection of PCCSK

In this subsection, we show the error performance of

PCCSK and the selection process for an appropriate data

rate. JTIDS uses the RS code with n = 31 and k = 15for FEC. A code rate for RS(31, 15) is almost 1/2, so the

error correction capability is very powerful but the overhead

of data transmission is also large. Therefore, LET varies the

RS code rate to enhance the system throughput. PCCSK can

also increase the capacity and error performance by applying

an adaptive RS code rate.

Before we adopt the variable RS code rate, we derive the

error performance of PCCSK. The equations for evaluating

CCSK performance are given in [7]. They calculate an upper

bound for the probability of symbol error for a given number

N of chip errors. A CCSK symbol error occurs when κi ≥ κ0,

where κi is the ith cross-correlation value from (1) when a

chip error occurs and the 0th codeword is the desired one. In

[7], κi was found to be

κi = hi + 2(N − 2q), 0 ≤ q ≤ N , 1 ≤ i ≤M − 1 (6)

by observation, where hi is the ith cross-correlation value in

the no error case. They also derived the conditional probability

mass function (pmf) for κi as

P{κi = hi + 2(N − 2q)|N = j} =((M+hi)/2

q

)((M−hi)/2

j−q

)(Mj

) .

(7)

Using (7), the conditional probability of symbol error for

CCSK can be derived, and then the probability of CCSK

symbol error is obtained as

PSCCSK=

M∑j=0

P{symbol error|N = j}P{N = j}. (8)

For JTIDS, N is a binomial random variable with a pmf

P{N = j} =(M

j

)P jc (1− Pc)

M−j , j = 0, 1, . . . , 32 (9)

where Pc is the probability of chip error at the output of

the MSK chip demodulator. In this subsection, we assume a

coherent matched filter. Therefore, the probability of channel

chip error is calculated as

Pc = Q

(√2Ec

N0

). (10)

By substituting M with L and calculating hi for a parti-

tioned code set, we obtain the results for PCCSK with M = 32shown in Fig. 5. In Fig. 5, the results of a Monte Carlo

simulation are also denoted. The transmission power is fixed

in a JTIDS terminal, so the graph depicts the same chip

energy environment. As can be seen, the analytic results for

PCCSK are similar to those of the simulation. We can also

Fig. 5. Probability of symbol error for PCCSK in AWGN: analytic upperbound versus Monte Carlo simulation

recognize the performance degradation caused by a decrease

in processing gain. At PS = 10−5, one partition brings out

a 3 dB increase in Ec/N0, which means that the transmitter

should double its transmission power.

If we select an appropriate RS code for PCCSK, we can

alleviate the performance degradation due to processing gain.

First, we select a larger n for a higher data rate, because the

RS code performs better with a longer codeword. Second, we

set the larger RS code to PCCSK, which has a larger value

of d. The message length in the conventional JTIDS is very

short, and therefore the bigger n is not suitable for low data

rate transmissions.

Table II shows the selected RS and PCCSK pairs. Case 0is identical to the conventional JTIDS waveform, and the data

rate is normalized by the data rate of case 0. Cases 1 to 3relate to each other when only PCCSK is applied to JTIDS;

PCCSK with variable RS code rates are illustrated by cases

4 to 6. For an exact comparison of performance, whether or

not adaptive coding is applied, both cases have the same code

rates.

TABLE IIPCCSK WITH ADAPTIVE CODING

Case RS(n, k) PCCSK Data rate

0 RS(31, 15) CP (1, 32) ×11 RS(31, 15) CP (2, 32) ×1.62 RS(31, 15) CP (4, 32) ×2.43 RS(31, 15) CP (8, 32) ×3.24 RS(63, 49) CP (1, 32) ×1.65 RS(127, 93) CP (2, 32) ×2.46 RS(255, 165) CP (4, 32) ×3.2

The performance of the RS code is well defined in [11] as

PSRS≈ 1

n

n∑e=t+1

e

(n

e

)P eS(1− PS)

n−e (11)

Fig. 6. Probability of symbol error for PCCSK with adaptive coding inAWGN: analytic upper bound

where e denotes the channel symbol errors per word and t =(n−k)/2. In JTIDS, CCSK and RS have the same number of

information bits in a symbol, so (8) is directly applied to (11).

In PCCSK, the following equation (12) has to be multiplied

by (8) to adjust the scale of information bits for RS where

m = log2(n+ 1).

2α−1

2α − 1· 2

m − 1

2m−1(12)

Fig. 6 shows the performance of the RS and PCCSK pairs.

We can observe a performance enhancement when the adaptive

coding is applied to PCCSK. In non-adaptive coding cases, the

required Ec/N0s differ by 3 dB between adjacent partitions

at PS = 10−5. In the adaptive coding cases, however, the

difference between the Ec/N0s is less than 2 dB. Thus, we

can conclude that adaptive coding alleviates the performance

degradation caused by the decrease in processing gain in

PCCSK. In the following section, we use cases 4 to 6 to derive

simulation results.

IV. SIMULATION RESULTS

We evaluated the performance of the proposed algorithm

in JTIDS. The major simulation parameters are described in

Table III. The number of transmission channels is 51, and 3

MHz bandwidth is allocated to each channel. The propagation

channel is characterized by a two-ray model.

First, we compare the proposed scheme with LET-type

waveforms. LET uses the concatenated code of RS and convol-

utional code for a higher data rate. The bit error rate for both

PCCSK and LET is shown in Fig. 7. Code rates of 1/3 and

1/2 are selected for convolutional codes whose constrained

lengths are l = 8 and l = 9, respectively. These convolutional

codes are decoded by Viterbis algorithm with hard decisions.

The performance of the LET-type waveforms is dominated by

the convolutional code rate. In this simulation environment, we

can see that the PCCSK outperforms LET-type waveforms.

Fig. 7. Bit error rate for PCCSK and LET-type waveforms withNakagami(μ = 2) fading channel

Second, we derived the transmission range of JTIDS with

and without jamming to identify the limitation of PCCSK. In

contrast to the numerical results with additive white Gaussian

noise (AWGN) of III-B, we made an effort to reflect a practical

environment in our simulation. We assume that the altitude of

aircraft using JTIDS is 7 km. For the multi-path model, we

consider line-of-sight (LOS) signal and the reflected signal

from the ground. The second ray to arrive via reflection

experiences more attenuation and delay, and both rays undergo

path loss with Nakagami fading (μ = 2) where μ is the

fading figure. In addition, the double-pulse was applied to

the non-jamming and jamming environments using equal gain

combining (EGC) and selection combining (SC), respectively.

In JTIDS, the message error rate is a standard for evaluating

the communication performance, and an error rate of less

than 1 % is necessary to guarantee the communication. Under

this environment, Fig. 8 shows the transmission range of

the proposed PCCSK waveforms without jamming. We can

see that the error performance curve differs from the Ec/N0

graph because the scale of the horizontal axis is different.

Over the distance scale, the received signal power degraded

TABLE IIISIMULATION PARAMETERS

Parameters Values

Center frequency 969-1206MHz

Bandwidth 3MHz

No. of channels 51

Transmission power 200W

Diversity combining EGC and SC

Spreading code MMLS and CP

Total spreading code length (M ) 32

Channel model Two-ray model

Fading Nakagami fading (μ = 2)

Detection Non coherent detection

Fig. 8. Message error rate for PCCSK with adaptive coding

by the square of the distance. From the graph, we see that

the conventional JTIDS waveform outperforms PCCSK with

regard to transmission range, but if we consider the practical

LOS communication range, other waveforms can perform well

in some limited circumstances. Using the results from Fig. 8,

we can anticipate the transmission range of each waveform.

JTIDS terminals exchange positioning reports with each other,

so we can choose appropriate waveforms.

Fig. 9 shows the anti-jamming performance of the proposed

scheme. In this graph, the jammer position is set to be 500 km

from the receiving node. We can see that the error performance

is slightly degraded by the jammer, and when the position

of the transmitter node is farther from the receiver than the

jammer, the degree of attenuation is greater. However, when

the jammer is farther from the receiver than the transmitter,

the received jamming signal is lower than the received trans-

mission signal, so the performance degradation is very small.

By default, JTIDS has a large number of frequency hopping

channels to secure communication, so even if the waveform

changes, a certain level of anti-jamming performance will be

maintained.

V. CONCLUSION

In this paper, we have described an anti-jamming and

LPI/LPD communication technique known as CCSK, which

uses cyclic shifts of a base sequence to modulate a carrier. This

exhibits excellent anti-jamming and LPI/LPD performance, but

has a limited spectral efficiency. Therefore, we proposed an

approach that increases the transmission data rate adaptively,

within a limited transmission range, in the battlefield. In the

proposed scheme, we constructed a spreading code as a set of

partitioned sub-spreading codes. These were applied to CCSK

modulation and spread data symbols based on user require-

ments. By exploiting a new code set as a spreading code, the

system was easily able to achieve a higher spectral efficiency.

We also compared the error rate performance between variable

RS and PCCSK pairs, and derived the appropriate code pairs

and their transmission ranges.

Fig. 9. Message error rate for PCCSK with adaptive coding under jam-mer(1000W, 500km, 20 jamming channels)

ACKNOWLEDGMENT

“This research was supported by the MKE(The Ministry

of Knowledge Economy), Korea, under the ITRC(Information

Technology Research Center) support program supervised by

the NIPA(National IT Industry Promotion Agency” (NIPA-

2012-(H0301-12-2003))

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