Chaos MIMO-based Downlink Non-orthogonal Multiple ... - IEEE Xplore

2018 15th IEEE Annual Consumer Communications & Networking Conference (CCNC)

Chaos MIMO-based Downlink Non-orthogonal Multiple Access Scheme With Physical Layer Security Naoto Horiike Graduate School of Engineering, Nagoya Institute of Technology Nagoya, Aichi, Japan [email protected]

Hiroki Kitagawa Graduate School of Engineering, Nagoya Institute of Technology Nagoya, Aichi, Japan [email protected]

Abstract—Recently, owing to the rapid increase of wireless  higher-capacity wireless traffic on smartphones and tablets, communication systems have been developed. The non-orthogonal multiple access (NOMA) scheme has been studied as one of the potential solutions. In addition to the need for higher capacity, the demand for secure wireless transmission has also grown. To meet these requirements, we propose a chaos multiple-input multipleoutput (C-MIMO) scheme that realizes both physical layer security and channel coding gain. In this paper, we apply the principle of C-MIMO to the NOMA scheme, and propose a chaos NOMA scheme that achieves higher-capacity, enabling a secure downlink wireless communication system. By performing numerical simulations, we show that compared to conventional power-domain NOMA schemes, we obtain improved performances and the physical layer security effect by introducing the C-MIMO principle into NOMA. In addition, we show that the throughput enhancement is obtained in the proposed scheme compared to previously proposed chaos orthogonal frequencydivision multiple access (C-OFDMA) scheme. Keywords—5G, non-orthogonal multiple access, downlink, chaos MIMO, physical layer security

I. INTRODUCTION In recently times, wireless traffic has rapidly increased with the development of applications and services using mobile terminals. This has resulted in additional demands for an increase in the capacity of wireless communication systems, and there are also greater expectations for the fifth-generation mobile communication systems (5G), which are currently being standardized [1]. In current 3.9th and fourth-generation mobile communication systems, which are called long-term evolution (LTE) and LTE-Advanced, respectively, the orthogonal frequency-division multiple access (OFDMA) scheme has been adopted as a multicarrier multiple-user access scheme for downlink channels. In OFDMA, one user is allocated to one subcarrier in the frequency domain, and a frequency-efficient multiple-user access is realized [2]. However, additional advanced multiple-access schemes are required to accommodate the increased mobile traffic expected in the near

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Eiji Okamoto Graduate School of Engineering, Nagoya Institute of Technology Nagoya, Aichi, Japan [email protected]

Tetsuya Yamamoto Core Element Technology Development Center, Panasonic Corporation, Yokohama, Kanagawa, Japan. yamamoto.tetsuya001@ jp.panasonic.com

future. Hence, a downlink non-orthogonal multiple-access (DL-NOMA) scheme in which more than two users are allocated to one subcarrier is considered as a leading candidate for new multiple-access methods in 5G [3,4]. In DL-NOMA, a power domain is used for user multiplexing in addition to the frequency domain, which has been used in conventional mobile communication systems [5]. On the other hand, it is also important to ensure security in wireless transmission environments where multiple mobile terminals simultaneously access the wireless network. To this end, we have previously proposed a chaos multiple-input multiple-output (C-MIMO) transmission scheme, which is a common-key-encryption scheme aimed at securing wireless communication in the physical layer [6]. In this scheme, the modulated signals following the Gaussian distribution are generated from chaos signals that are correlated to transmit bits. In addition, these signals are transmitted using a MIMO block transmission scheme, and achieve a rate-one channel-coding gain and encryption effect. Previously, we adopted the CMIMO principle for the sparse code multiple access (SCMA) scheme [7], which is a non-orthogonal multiple-access scheme that enables an overloaded transmission of up to about 150%. Then, we have proposed a sparse chaos code multiple-access (SCCMA) scheme, which has physical layer security capabilities [8]. In SCCMA, only pairs that share a common key can decode data bits by utilizing a chaotic codebook of transmit sequences. Using this scheme, it is possible to realize overload and encrypted transmission in the uplink channels of systems such as intelligent transport systems (ITS) or massive Internet of things (IoT) device communications. However, to date, there is no physical layer encrypted multiple-access transmission system that targets downlink wireless transmission systems. Therefore, in this paper, we propose a downlink chaos NOMA (C-NOMA) transmission scheme with physical layer security, in which chaos-modulated signals of multiple users are superimposed into one subcarrier in the power domain and then simultaneously transmitted. The proposed C-NOMA realizes a secure and high-capacity downlink transmission. We

2018 15th IEEE Annual Consumer Communications & Networking Conference (CCNC)

show the improved performances of C-NOMA by performing numerical simulations, and the results obtained are compared with conventional unencrypted NOMA transmission and chaos OFDMA (C-OFDMA) transmission [9]. The remainder of this paper is organized as follows. We describe the outline of a downlink NOMA scheme in Section II. Then, in Section III, we describe the system model of the proposed C-NOMA scheme and its chaos-modulation process. In Section IV, we present the numerical results, and we evaluate the transmission characteristics and security capabilities of the proposed scheme. Finally, we conclude the paper in Section V. II. DOWNLINK NOMA TRANSMISSION SCHEME The outline of the downlink NOMA system we utilize is shown in Fig. 1. In this study, the base station (BS) is assumed to transmit signals to each user equipment (UE) in a single-cell environment. In this cell, the BS takes into account the proportional fairness (PF) between users based on the channel state of each UE, and assigns users to each subcarrier. In the NOMA transmission, users are allocated to each subcarrier, while permitting interference because of user superimposition. For example, in Fig. 1, signals for UE1 and UE2 are superimposed in subcarrier 1, and UE2 and UE5 are also superimposed in subcarrier 3. On the other hand, in subcarrier 2, a signal for only UE3 is assigned and transmitted using orthogonal multiple access (OMA). In this paper, we assume a MIMO transmission environment in which the BS and each UE has transmit antennas and receive antennas, respectively. users are randomly placed in the cell, and subcarriers in one orthogonal frequency-division multiplexing (OFDM) frame are allocated to each user. We utilized each of subcarriers to achieve OMA transmission for a single user or NOMA transmission for multi-users, where the user . In the -th subcarrier, the BS multiplexing number is selects a set of users U = (1), (2), ⋯ , ( ) from users, where ( ) indicates the -th (1 ≤ ≤ ) user transmitted in the -th (1 ≤ ≤ ) subcarrier. The NOMA transmit vector in the -th subcarrier generated at the BS is given by =

()

() ,

(1)

( ) is the transmit power allocated to user ( ) , where ( ) is the transmit vector for user ( ) in the -th and subcarrier [10]. The total transmission power of each subcarrier is constrained by

(2)

() =

Moreover, the channel power of user ( ) at the -th subcarrier is given as () =

(3)

() ,

,

= min( , ) , and , ( ) is the -th where eigenvalue of the × -dimensional channel matrix between ( ) . In the NOMA system, a set of user ( ) and BS, users with different channel conditions, such as a near user and a far user, are selected based on the channel gain, and nonorthogonal user allocation is performed. Finally, the transmit vector is transmitted via MIMO antennas after the inverse fast Fourier transform (IFFT) and the addition of a guard interval (GI). ( ) is obtained by At each UE, the receive vector (4) () = () + () , ( ) is the thermal noise vector for user ( ). On where the receiver side, a successive interference cancellation (SIC) [11] is commonly used at the near user to suppress the interference. In SIC, the near user decodes the received signal to obtain his own data after subtracting the far user’s signal because the far-user signal is transmitted with a higher power in SIC-NOMA, and can be correctly decoded by the near user. At the far user, because the superimposed near-user signal is sufficiently decayed, the received signal is just decoded to obtain the far user’s data. In contrast, the maximum-likelihood detection (MLD) scheme, where the MLD for the desired signal is just conducted and the superimposed signal is only used for the log-likelihood ratio (LLR) calculation of the desired signal, has been proposed in [12]. In this scheme, the other UE’s signal is not decoded, and only the modulation scheme of the other UE is needed. However, it is reported that the decoding performance is degraded by a biased power allocation in the MLD scheme. In this paper, because the chaos demodulation is conducted using maximum-likelihood estimation (MLSE), as described in detail later in Section III-A, we adopted the latter decoding scheme and compose a joint MLSE for C-NOMA, where the desired UE signal and the other UE signal are jointly decoded.  In NOMA subcarrier allocation, it is assumed that the channel matrix for user ( ) in the -th subcarrier is perfectly known to the BS. In the conventional NOMA, when SIC is applied, the channel capacity of user ( ) at the -th subcarrier per 1 Hz is given by () ⎛ = log ⎜1 + ⎜ ∑ ⎝

Fig. 1. Outline of downlink NOMA system.

() ∈

,

()

( )

()

( )

() ()

( 2) +

⎞ ⎟, () ⎟ ⎠

(5)

2018 15th IEEE Annual Consumer Communications & Networking Conference (CCNC)

( ) is the average power of the thermal noise

where

vector ( ) . Then, the user selection obtained by the PF scheduling method is conducted using the following metric: ( | , ) , ( , )

( )= ∈

= max

( ),

(6)

init. key Data user #1

Chaos mod.

⋮

⋮ Chaos mod.

Data user #

1

( , − 1) +

1

1

(7)

( , − 1) ,

where is an averaging parameter in the time direction, and is set to 20 in this study. The number of combinations of the candidate user set is given by (8) + + ⋯+ 1 2 User scheduling based on (6) realizes a high-capacity allocation, while considering fairness between users. In the NOMA scheme, the power allocation for each user significantly affects the overall system throughput because signals for users are superimposed in the power domain. When SIC is used, a higher power should be allocated to distant users than near users in order for the SIC to work effectively. One of these allocation methods is the fractional transmit power control (FTPC) method [10]. With this method, the power for user at the -th subcarrier is allocated based on the channel gains of superimposed users. The allocated power is given as follows:

=

()= ∑

∈

S / P S / P

⊗

⋮

Freq. map.

Σ

IFFT

+GI

⊗

,

where ( ) is the scheduling metric of the candidate user set , and is the sum of all users’ metrics in . ( | , ) is the (1 ≤ ≤ ) allocated to the -th capacity of user subcarrier at time , and ( | , ) becomes zero if user is not allocated at the -th subcarrier. ( , ) indicates the average throughput of user at time , and is defined by ( , ) = 1−

Base Station

Scheduler

,

(

)/

(

)

() ()

,

(9)

(0.0 ≤ ≤ 1.0) is a parameter to adjust the where power allocation. When = 0.0 , the transmit power is equally allocated to each user, and as it gets closer to 1.0, the higher transmit power is allocated to the far user, whose channel gain is small. III. PROPOSED DOWNLINK CHAOS NOMA SYSTEM A. System model Fig. 2 shows the proposed C-NOMA system model. We explain the difference between the proposed chaos NOMA system and the conventional NOMA scheme with SIC, as discussed in Section Ⅱ. In the proposed scheme, complex Gaussian symbols are generated for each user from a transmit bit sequence using chaos modulation, which is described in the next subsection. We assumed that the chaos modulation efficiency is 1 bit/symbol/antenna, which is equivalent to binary phase shift keying (BPSK) modulation, and a block transmission with length is used. Each user's transmit bit bits, and -modulated sequence is divided into

User Equipment user #1 P / S

FFT

-GI

Data user #1

Chaos demod. , ,

1≤

≤

,

≠1

Fig. 2. System model of the downlink proposed chaos NOMA.

symbols are obtained, where is also the MIMO block length. These modulated symbols of each user are transmitted by OMA (OFMDA) or the NOMA scheme using MIMO with transmission antennas at each subcarrier after scheduling. Here, in the proposed scheme, the number of subcarriers allocated to each user must be a multiple of . Hence, subcarriers are treated as one subchannel and subcarriers of one OFDM frame are scheduled per subchannel by the PF scheduling of (6). Here, the average value of subcarriers is used in (5) and (6). After scheduling, chaos-modulated symbols are superimposed in the power domain in NOMA based on (1), or they are allocated by OMA into each subchannel, after which they are transmitted. In the proposed scheme, the equal-power superposition of α = 0.0 is used in NOMA allocation in order to optimize the joint MLSE decoding. In the receiver of each user, the MIMO detection and chaos-block demodulation are jointly conducted by MLSE. When OMA is used, the decoded bit sequence on the -th MIMO block is obtained by = argmin

‖

( )−

( )

(10)

( )‖ ,

where is a chaos iteration number described in the next subsection. ( ) , ( ), and ( ) are the -th received vector, the channel matrix at the -th MIMO block, and the transmit candidate vector modulated by , respectively. In NOMA allocation, because the joint MLSE for desired and superimposed users is conducted, the following decoding search is used at each user: = argmin ,

′ ( )−

( )

( )+

,

( )

,

(11)

,

where ′ ( ) is the received NOMA vector, and , ( ) is the transmit candidate vector that is modulated by , for other users, and is superimposed by NOMA. , ( ) is the interference affecting the desired signal. Therefore, to suppress the interference, it is assumed that each UE holds initial chaos keys of all users in the target cell; then, , ( ) can be calculated from , . Thus, in this system we assume that users in the target cell are the trusted users to achieve a secure NOMA transmission in the physical layer. Furthermore, the optimum

2018 15th IEEE Annual Consumer Communications & Networking Conference (CCNC)

channel capacity for (11) is used in the proposed scheme instead of (5), and is given as ()

()

= log

1+

()

(12)

()

B. Chaos modulation The chaos modulation scheme for each user is described in [13]. It is assumed that chaos modulation is conducted for an –bit sequence to user . The -bit sequence is divided into bits, and the -th transmit bit sequence is given by =  , ∈ {0,1}, (13) , ,…, , ) − 1 and 0 ≤ ≤ where 0 ≤ ≤ ⁄( − 1 . The modulated complex Gaussian symbol sequence in the BS is given as follows: = ,

. , ,⋯, , for chaos generation is set as

(14)

(15) 0 < Re < 1,  0 < Im[ , ] < 1 , is a random complex symbol, and is used as the where , initial values of the chaotic system. In the chaos NOMA transmission, , is shared as the common key signal between the transmitter and the receiver for secure transmission based on physical layer security. In this paper, it is assumed that each of the accommodated users has a common key according to (15), and the BS and all users in a cell share their keys’ signals. The chaos modulation is conducted using of , of (15) and (13). The real and imaginary parts of , are shifted by the different bits of , , and the transmit bits are correlated with . the generated chaotic signal in the range of 1 ≤ ≤ In one-bit/symbol/antenna chaos modulation, the modulation process is conducted according to the following rules:

 =

,

=0

  



,

= 1,

> 1⁄2

+ 1⁄2

,

= 1,

≤ 1⁄2

1−

Real part: = Re ( ) Imaginary part: = Im

, (

, ) ,

= ,

−1 =

mod (

=

,

Imaginary part: Im

This is because in the joint MLSE of (11), the signals of the superimposed partner are estimated simultaneously, and the signals of the others in the same NOMA vector are not treated as interference components. Therefore, in (12), the signal component of the superimposed partner is removed from the denominator of (5).

The initial signal

Real part: Re

(16)

)

When = 1, the initial chaos key signal is modulated. Then, the variable of (16) is processed by the Bernoulli shift map, which is one of the chaos generation equations with iteration number given as (17) = 2 mod 1 Here, it is reported that the chaos signal converges to zero with finite resolution [14, 15]. To avoid this zero convergence, (17) is modified slightly from mod 1 to mod (1 − 10 ) to calculate the double floating point. Then, after iterating (17), the processed chaos-modulated signal , is extracted by

⁄ )

,(

,

=

,(

(

⁄

)

)

(

)

,

(18)

where the subscript of indicates the chaos iteration number, and this parameter is shifted by another transmit bit , . This operation leads to an increased randomness of the generated signals. Next, we generated Gaussian symbols from the chaos signals of (18) using the Box-Muller transform [16]. First, we ( ) generated the uniformly distributed random signals and ( ) using the real and imaginary parts of the processed chaos signal , as follows: ( )

=

1

cos [cos{37 (Re[

] + Im[

])}]

(19) 1 2 Then, the -th Gaussian distributed symbol with average transmit power 1 is generated by the Box–Muller transform as follows: ( )

,

=

=

1

sin [sin{43 (Re[

−ln

( )

cos 2

] − Im[

( )

+ sin 2

])}] +

( )

(20)

Using the randomization based on the Box–Muller transform, we obtained a Gaussian-distributed signal with a flatter phase characteristic using a single chaos signal [16]. The generated s , for each user is used as a component for the generation of () . the transmission signal vector IV. NUMERICAL RESULTS We evaluated the transmission performance of the proposed scheme by performing numerical simulations. Table Ⅰ shows the basic simulation conditions. We used a nonsectorized hexagonal single cell model, and eight users were randomly distributed in the cell. The number of maximum users multiplexed in NOMA = 2 (two users are superimposed at a maximum). was set to in one OFDM frame and the size The number of subcarriers of the fast Fourier transform (FFT) are both set to 256. There are 2™2 MIMO antennas for the BS and each user, and its channel state information is known to the BS and each UE. The chaos demodulation is conducted by performing MLSE, as described in Section III-A. With respect to the initial chaos signal of (15) and the iteration number, BS and all of the users perfectly share all initial signals and the iteration number allocated to each user for secure communication. For a fair comparison, we show the characteristics of the conventional BPSK-NOMA transmission as an unencrypted transmission scheme, and those of the C-OFDMA-MLSE transmission as the same encrypted transmission scheme. In the BPSK-NOMA transmission, the joint MLD that considers other superimposed signals is used as well as the proposed scheme. In addition, (5) is used for scheduling in BPSK-NOMA. The other simulation conditions are the same as in Table I, except for modulation. The subchannel-based PF scheduling with MIMO block length is also applied for BPSK-NOMA.

2018 15th IEEE Annual Consumer Communications & Networking Conference (CCNC)

BASIC SIMULATION PARAMETERS.

Cell layout No. of antennas No. of user [/cell] Max. user multiplexing Power decay factor No. of subcarrier FFT size Channel Path loss exponent Standard deviation of shadowing loss [dB] Channel estimation Scheduling algorithm MIMO block length Chaos mod. [bit/sym./ant.] Chaos generation No. of chaos processing Chaos demodulation Outer channel coding

Proposed C-NOMA Hexagonal single-cell model = =2 8 2 0.0 : equal power allocation, ( 0.4 (BPSK-NOMA) ) 256 256 16 pass 1dB decay,quasi-static Rayleigh fading + AWGN 3.5 7.0 Ideal Proportional fairness 2 1 Bernoulli shift map 100 MLSE None

1.E+00

1.E-01

Average bit error rate

TABLE I.

1.E-02

unencrypted

encrypted 1.E-03

[prop.] C-NOMA [prop.] C-NOMA, unsync.

1.E-04

[conv. 1] BPSK-NOMA [conv. 2] C-OFDMA (C-NOMA, α_FTPC=0.4)

1.E-05 MIMO block length:B=2 16 path fading channel 8users in single cell

1.E-06 0

5

(BPSK-NOMA, α_FTPC=0.0)

10 15 20 25 30 Avg.SNR per receive antenna at cell edge [dB]

35

(a) Average user bit error rate. 4.5

encrypted

A. Evaluation of transmission performance Then, we calculated the average bit error rate (BER) and the user average throughput versus the average receive SNR per antenna at the cell edge. Figs. 3(a) and (b) show the BER performance and the throughput performance, respectively. In Fig. 3(a), for reference, the performances of the proposed CNOMA and the conventional BPSK-NOMA with different are also plotted. In the conventional BSPK-NOMA-MLD, when the equivalent power allocation of = 0.0 is used, the superimposed signal sometimes converges to zero, and the BER performance is significantly deteriorated. With BPSK modulation, this zero convergence often occurs. On the other hand, in the proposed C-NOMA, the equivalent power = allocation has a superior performance compared with 0.4. This is because in the joint MLSE including interference signal estimation, the optimum estimation is obtained when the receive SNR is equal in overall receive sequence, and the posteriori probability of correct decoding becomes a maximum. Therefore, we selected the best settings for C-NOMA and BPSK-NOMA, and plotted them as the solid lines in Fig. 3(a). As a result, it is shown that the performance of the proposed C-NOMA is greatly improved after the average SNR of the cell edge becomes 2 dB, compared with BPSK-NOMA. Hence, we can realize high-quality transmission compared to the unencrypted transmission with the same transmission efficiency. The decoding complexity per receive subchannel at the UE = 32 for BPSK-NOMA, and (2 ) = becomes (2 ) = 2, = 2, and 256 for the proposed C-NOMA when = 2 . Thus, the complexity of the proposed scheme increases as a trade-off for the BER improvement. The decoding complexity reduction of C-NOMA using different algorithms will be considered in future studies. In Fig. 3(a), “unsync.” shown with the yellow line indicates the decoding performance of a third party who does not have a legitimate initial key. In this case, the BER becomes 0.5 and the correct information is not obtained, showing that the physical

Average throughput [bit/sec/Hz]

4.0 3.5 3.0 2.5

unencrypted

2.0 1.5 1.0 MIMO block length:B=2 16 path fading channel 8users in single cell

0.5

[prop.] C-NOMA [prop.] C-NOMA, unsync. [conv. 1] BPSK-NOMA [conv. 2] C-OFDMA

0.0 0

5

10 15 20 25 Avg.SNR per receive antenna at cell edge [dB]

30

35

(b) Average user throughput. Fig. 3. Comparision of transmission performances for average receive SNR per antenna at cell edge in fading channel.

layer security is ensured. Fig. 3(b) shows the average throughput performance. The proposed C-NOMA is superior to BPSKNOMA as well as Fig. 3(a). In addition, compared to the encrypted conventional C-OFDMA, we obtained the enhanced maximum throughput because of the capacity increase realized by introducing the NOMA scheme. Consequently, compared with the conventional two schemes with the same transmission efficiency, the BER and the throughput performances were improved in the proposed CNOMA, and the decoding complexity increased. B. Evaluation on security ability In the previous subsection, we showed that the physical layer security was obtained for a third party because of the BER deterioration. In this subsection, we evaluate the strength of the chaos initial key using the BER as the evaluation index.

2018 15th IEEE Annual Consumer Communications & Networking Conference (CCNC)

a) Tolerability for proximity of initial keys among users

1.E+00

1.E+00

Average bit error rate

1.E-01

1.E-02 C-NOMA

MIMO block length:B=2 16 path fading channel 8users in single cell Avg.SNR at cell edge =16dB

1.E-03

1.E-04

1.E-01

Average bit error rate

Here, we assumed that the different chaos initial key , and the same chaos iteration number are assigned to each user, and they are shared among all users and BS. Thus, secure transmission is realized. In this case, we investigate how close the initial keys can be for normal and secure transmission. In other words, we evaluated the BER performance when the difference between the real part and imaginary part of the initial key between each user becomes 10 . For example, when eight users are accommodated in a cell, it is assumed that Re c , − , = Re c , − , = ⋯ = Re c , − = 10 , and the same for the imaginary part. Fig. 4 , shows the BER performance versus the proximity when the average SNR = 20 dB using the simulation condition of Table I. When becomes larger, it means that the initial keys among users become closer. In Fig. 4, it can be seen that when both the real part and the , the BER is imaginary part of the initial keys are at least 10 the same as that for SNR = 20 dB in Fig. 3(a). This means that when each of the initial keys is at least 10 different from others, the proposed C-NOMA has a normal and secure transmission in the physical layer. Meanwhile, when each of the keys is less than 10 , the BER deteriorates, and it becomes constant at BER = 0.2 after = 19. This means that after = 16 , the chaos modulation generates the same modulated symbols for all users, and when they are superimposed in the NOMA allocation, a single inverse mapping often cannot be obtained from the superimposed receive signal. It should be noted that even in this case, the BER of C-NOMA becomes 0.5, but the received symbols of C-OFDMA can be normally decoded, and the BER becomes 0.2, and not 0.5 as shown in Fig. 4. Consequently, we can conclude that when there is a in the initial keys for both real and difference of 10 imaginary parts, the normal and secure transmission can be realized in the physical layer. Thereby, there are many initial

scenario [a]

1.E-02

scenario [b] 1.E-03

MIMO block length:B=2 16 path fading channel 8users in single cell Avg.SNR at cell edge =16dB

1.E-04

1.E-05 4

8

12

16

20

24

28

The difference from the correct initial key in real part and imaginary part: 10^(-x)

Fig. 5. Evaluation of security versus proximity of eavesdropper key in the proposed C-NOMA.

key patterns, and many users can be accommodated in the proposed C-NOMA. b) Security against proximity of initial keys at eavesdroppers In this subsection, we assumed that the initial keys at UEs are slightly different from the correct keys at the BS, and the BER is then calculated. It should be noted that in this case, the security capability is the same in C-NOMA and C-OFDMA. Fig. 5 shows the BER performance versus the proximity in which the real and imaginary parts of initial keys at UE are 10 different from those of the BS under the simulation conditions of Table I. Here, we considered two scenarios: [a] the case when an eavesdropper has the correct key of a superimposed user and a slightly different key of the target user at 10 in NOMA allocation, and [b] the case when an eavesdropper has the correct key of the target user and a slightly different key of superimposed user. From Fig. 5, it can be seen that regardless of the scenario, signals can be normally demodulated by a third person when there is a difference in the key of less than 10 . Meanwhile, if the difference is greater than 10 , correct decoding cannot be obtained. In particular, in scenario [a], in both C-NOMA and C-OFDMA, data cannot be decoded and the BER becomes 0.5. Therefore, in the proposed scheme, even if an eavesdropper obtain one user’s key, correct decoding cannot be achieved unless he obtains all users’ keys with an accuracy having a difference of less than 10 . This confirms the powerful physical-layer security effect of the proposed C-NOMA scheme. V. CONCLUSIONS

1.E-05 4

8

12

16

20

24

28

The difference of the initial key in real part and imaginary part between each user : 10^(-x)

Fig. 4. Evaluation of security versus proximity of user keys in the proposed C-NOMA.

In this paper, we proposed a downlink chaos NOMA transmission scheme that achieved both higher-capacity and physical layer security that is robust to eavesdroppers and other users who do not possess initial keys. To do this, we applied the principle of the chaos MIMO scheme into NOMA. Numerical results showed that the proposed C-NOMA significantly

2018 15th IEEE Annual Consumer Communications & Networking Conference (CCNC)

improved the BER performances compared to the conventional unencrypted BPSK-NOMA scheme, which had the same transmission efficiency. Furthermore, compared to the conventional chaos OFDMA scheme, the system capacity increases in C-NOMA. As a result, we constructed a downlink transmission system with a higher capacity and high security. The tradeoff is the increase in the decoding complexity required at each UE. The complexity of C-NOMA exponentially increases with respect to the maximum superimposed users when the joint MLSE is used. In future studies, we will reduce the decoding complexity using simple algorithms, as well as the application of higherrate chaos modulation equivalent to QPSK.

[7]

[8]

[9]

[10]

[11]

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