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\title{Performance Evaluation of Encrypted Text Message Transmission in 5G Compatible Frequency-domain Subband Superposed Scheme Implemented MIMO OFDM Wireless Communication System}
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\begin{document}

             \author[1]{Mst. Afrin  Naher}

             \author[2]{Md. Omor  Faruk}

             \author[3]{Md. Mahbubur  Rahman}

             \author[4]{Shaikh Enayet  Ullah}

             \affil[1]{  University of Rajshahi}

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\date{\small \em Received: 9 December 2018 Accepted: 2 January 2019 Published: 15 January 2019}

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\begin{abstract}
        


In this paper, an investigative study has been made on the performance evaluation of encrypted text message transmission in 5G compatible multiuser frequency-domainsubband superposed (FDSS) scheme implemented MIMO OFDM wireless communication system. The 2×2 multiantenna configured simulated system under consideration incorporates modern channel coding (LDPC and Repeat and Accumulate (RA)) and signal detection (Cholesky decomposition based ZF detection, Group Detection (GD) approach aided Efficient Zero-Forcing (ZF) and Lanczos method based efficient signal detection) techniques. In the scenario of transmitting encrypted text message over AWGN and Rayleigh fading channels, it is noticeable that implementation of Repeat and Accumulate channel coding and Group Detection (GD) approach aided Efficient Zero- Forcing (ZF) signal detection techniques is very much robust and effective in retrieving transmitted text messages for all users.

\end{abstract}


\keywords{OFDM, FDSS, 5G, Signal to noise ratio (SNR), Bit error rate (BER), LDPC and RA, Lanczos, ZF and Cholesky decomposition.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
n scenario of high out-of-band emission (OOBE) with relatively low spectrum efficiency and little flexibility, Orthogonal frequency division multiplexing (OFDM) cannot meet up the diverse layouts of the future fifth generation (5G) networks.\par
In 2017, Wang and et al., proposed a nonuniform subband superposed OFDM (NSS-OFDM) scheme based on a variable granularity (VG) spectrum allocation technique with the utilization of a multistage poly-phase sub-filtering architecture.\par
In their works, the authors demanded significant reduction of OOBE with enhanced spectral efficiency in terms of spectrum utilization rate and minimization of the frequency guard intervals between subbands \hyperref[b0]{[1]}. At \hyperref[b1]{[2]}, the authors made a comprehensive study on significant performance degradation of the traditional OFDM system in high-speed mobile scenarios. They proposed a subband superposed oversampled OFDM (SS-OOFDM) scheme for accommodating the diverse synopsis with the inclusion of the scenarios with high II. 
\section[{Review of Signal Processing Techniques}]{Review of Signal Processing Techniques}\par
In this sub-section, various channel coding and signal detection techniques are implemented. A brief observation of each technique has been outlined below: 
\section[{a) LDPC Channel Coding}]{a) LDPC Channel Coding}\par
In 1962, Gallager invented low-density paritycheck (LDPC) code. Such LDPC code is a linear block subband superposed (FDSS) scheme implemented MIMO OFDM wireless communication system. The 2×2 multiantenna configured simulated system under consideration incorporates modern channel coding (LDPC and Repeat and Accumulate (RA)) and signal detection (Cholesky decomposition based ZF detection, Group Detection (GD) approach aided Efficient Zero-Forcing (ZF) and Lanczos method based efficient signal detection) techniques. In the scenario of transmitting encrypted text message over AWGN and Rayleigh fading channels, it is noticeable that implementation of Repeat and Accumulate channel coding and Group Detection (GD) approach aided Efficient Zero-Forcing (ZF) signal detection techniques is very much robust and effective in retrieving transmitted text messages for all users.\par
Postgraduate Student, Department of Electrical \& Electronic mobility and development of the time-domain channel estimation method to track the fast-varying mobile channel. In their work, a subband decision feedback and feed forward equalizer for exploiting the Doppler and multipath diversity gains was designed, and the simulation results showed that the SS-OOFDM, especially in high-speed mobile channels outperformed the traditional OFDM receiver in terms of the bit-errorrate (BER) performance.\par
The enhanced multicarrier transmission scheme implemented subband superposed OFDM(SS-OFDM) system achieves narrower guard bands and flexible subband division through subband partitioning and filtering. Allowing for the multiple accesses, the superposition schemes of the signal from the users sharing the transmission channel in both frequency and time domains are considered at \hyperref[b2]{[3]}.\par
In our study, we have considered Frequencydomain subband superposed scheme aided the OFDM system to study its system performance on encrypted text message transmission. ? code and its generated parity-check matrix H o contains only a little 1's with the comparison of 0's (i.e., sparse)] r 1 c ( P / ) r 0 c ( P [ ln ) c ( L i i i i i = = ? ) P / P [ ln ) P ( L 1 ij 0 ij ij ? (1) ) Q / Q [ ln ) Q ( L 1 ij 0 ij ij ? ) Pj / Pj [ ln ) P ( L 1 0 j ?\par
Where in equation(  {\ref 1}), (ln) illustrates the natural logarithm operation. The bit node j is initially set with an edge to check node i:2 i i ij / r 2 ) c ( L ) P ( L ? = = (2)\par
In message passing from the check nodes to the bit nodes for each check node i with an edge to bit node j; L(Q ij) has been updated as:) j j and n ..... .......... 2 , 1 j ( )] ( [ ) Qij ( L j j i j j i ? ? = ? ? ? ? ? = ? ? ? ? ? ? (3) . )] P ( L [ and )] P ( L [ sign , where ij ij ij ij ? ? ? ?\par
The ? function has been defined as:)] 1 e /( ) 1 e ln[( )] 2 / x ln[tanh( ) x ( x x ? + = ? = ? (4)\par
From bit nodes to check nodes for each bit updated as:) i i and m ..... .......... 2 , 1 i ( ) Qij ( L ) c ( L ) Pij ( L i i ? ? = ? + = ? ? (5)\par
Decoding and soft outputs: for j=1,2,3?,n; L(Pj) is updated as:) m ......... 2 , 1 i ( ) Pij ( L ) c ( L ) Pj ( L i i = + = ? (6) ? ? ? < = else 0 0 ) P ( L if 1 c j i (7)\par
If cH o T =0 or the number of iterations reaches the maximum limit \hyperref[b3]{[4]} b) Repeat and Accumulate (RA) Channel Coding\par
The RA is a mighty advance error-correcting channel coding scheme. In this type of channel coding scheme, all the extracted binary bits from the text message are arranged into a one block and the binary bits of such block has been repeated 2 times and reorganized into a single block with contains binary data which is double of the number of input binary data \hyperref[b4]{[5]}. Where, H is a channel matrix with its (j,i) th entry h ???? for the channel gain between the j th receive antenna and the i th transmit antenna, j=1,2,??.N R and i=1,2,??.N T , + = =\textbf{(9)}\par
Where, H H is the Hermitian conjugate of the estimated channel. In the interference limit scheme, the more advanced ZF detector has been required which operates on the MF data byMF 1 H ZF x ) H H ( x ?? =\textbf{(10)}\par
In Cholesky Decomposition (CD) base ZF detection, Equation \hyperref[b9]{(10)} has been written in modified form as:MF 1 H MF 1 H ZF x ) LL ( x ) H H ( x ?? ? = =\textbf{(11)}\par
With forward and backward substitution, the detected signal in CD-based ZF detection would be \hyperref[b5]{[6]}.MF 1 H ZF x L L x ?? ? = (12)\par
d) Group Detection approach aided Efficient Zero-Forcing (GDEZF) Group Detection (GD) approach based Efficient Zero-Forcing (ZF) detectors reduce the computational cost of the conventional linear detectors. In such a technique, Equation (  {\ref 8}) can be rearranged as:[ ] n s H s H n s s H H y 2 2 1 1 2 1 2 1 + + = + ? ? ? ? ? ? = (13) Where, L N 1 R C H × ? and ) L N ( N 2 R C H ? × ? are composed of first L 
\section[{and the remaining (N-L) columns of}]{and the remaining (N-L) columns of} 
\section[{Global Journal of Computer Science and Technology}]{Global Journal of Computer Science and Technology}\par
Volume XIX Issue II Version I matrix). The LDPC codes have been graphically represented by the bilateral Tanner graph, and their nodes have been grouped into first set of n bit nodes (or variable nodes) and another set of m check nodes (or parity nodes). Check node i has been connected to bit node j in case of any elemental value of unity in the parity matrix. The decoding is operated alternatively on the bit nodes and the check nodes to find the most similar codeword c which is satisfy the condition cH o T =0. In the iterative Log Domain Sum-Product LDPC decoding under the consideration of AWGN noise LLR (log-likelihood ratios) instead of probability have been defined as: node j with an edge to check node i; L(Pj) has been channel of variance ? 2 and the received signal vector r, H respectively, where the total number of columns of H is N. Similarly, n W s H W s y W 1 2 2 1 1 1 + + = (14)\par
Or equivalently, we can writen W s H W y W s 1 2 2 1 1 1 ? ? = (15)\par
Substituting equation (15) into equation (  {\ref 13}) and after some small manipulation, we get2 2 2 2 n s H ? + = (16) Where, , 1 N 2 R C y × ? , ) L N ( N 2 R C H \textasciitilde ? × ? and 1 N 2 R C n × ? . The 2 y , 2 H \textasciitilde  and 2\par
n can be rewritten as:y ) W H I ( y 1 1 2 ? = (17) 2 1 1 2 H ) W H I ( H \textasciitilde ? = (18) n ) W H I ( n 1 1 2 ? = (19)\par
another weight matrix 2 W can be defined asH 2 1 2 H 2 2 H ) H H ( W ? = (20)\par
The sub-symbol vector 2 s is estimated using) y W ( Q s ?1 1 2 =\par
, where the symbol Q is indicative of quantization. The effect of 2 s is canceled out from y to[ ] T T 2 T 1 s ? x ?= (21) 
\section[{e) Lanczos method based efficient signal detection}]{e) Lanczos method based efficient signal detection}\par
The signal model is presented in Equation (  {\ref 8}), the Minimum mean square error (MMSE) weight matrix can be represented as:H n H MMSE H I H H W 1 2 ) ( ? + = ? (22)\par
and the detected desired signal from the transmitting antenna is given by \hyperref[b7]{[8]} y W X \textasciitilde MMSE MMSE = x x A x 2 1 ) x ( T T ? ? ? ? ? = ? (25) x ? ?? = x ? 0 + Q k y k\textbf{(26)}\par
Substitute equation ( \hyperref[formula_19]{26}) into the function of the can acquire that ?? ?? is the minimum solution to the equation set:?? ?? ?? ??Q ?? ?? ?? =?? ?? ?? (?? ? ?? x ? 0 )\textbf{(27)}\par
Which lead\par
x ? ?? = x ? 0 + Q ?? ?? ?? as the approximated minimum point of function Equation (25). It is obvious that equation ( \hyperref[formula_20]{27}) is not easy to solve, and the computation of x ?\par
?? would be storage inefficient if [q 1 , q 2 , q 3 , ? , q k ] was used at the last iteration. Here, Lanczos vector was adopted to overcome these two be written as:? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? = = ? ? k 1 k 1 k 2 1 1 1 k T k k 0 . 0 ... .......... AQ Q T (28)\par
Lanczos method is an iteration method to convert symmetric definite positive matrix A into tri- ) y W ( Q s ?1 1 1 =\par
. Here x is transmitted signal vector, which has been approximated as \hyperref[b6]{[7]}:\par
Where A? ? ??×?? is a symmetric positive definite matrix, b? ? ?? is a non-zero vector. Taking partial derivatives of x? , we obtain that ??? ? x ? ? = ?? x ? ? ??. Therefore b A x 1 ? = ?\par
is the unique minimum value of function presented in Equation (25).\par
Assuming Q ?? =[q 1 , q 2 , q 3 , ? , q k ] is a group of a standard orthogonal basis of Krylov subspace ??(A, B, k), we can overwrite solution x ? as:\par
Equation (  {\ref 25}) and take the partial derivative of ?? ?? , we problems instead of q k . The tri-diagonal matrix as ?? ?? can diagonal matrix T as a function (28). At the k th step of the vector and ?? ?? is the unit vector with the k th element ? ? k?1 = ? k?1 /d k?1 d k = ? k ?? k?1 ? k?1\textbf{(29)}\par
Combine equation ( \hyperref[formula_19]{26}), ( \hyperref[formula_20]{27}) and (  {\ref 28}), and assume that?? ?? = ?? ? ?? x ?\par
?? , we can derive Equation (26) asx ? k = x ? 0 + Q k T k ?1 Q k T r 0 = x ? 0 + Q k (L k D k L k T ) ?1 Q k T r 0\textbf{(30)}\par
matrix ?? ?? ? ? ??×?? and vector ?? ?? ? ? ?? which satisfy: The conceptual block diagram of 5G compatible frequency-domain subband superposed (FDSS) scheme implemented MIMO OFDM wireless communication system has been shown in fig. \hyperref[fig_3]{1}. In such a system, it is considered that three users are sending their encrypted text messages. The binary data extracted from each user's text message are encrypted with a secret key of bit length 8 \hyperref[b9]{[10]}. The encrypted binary data are channel encoded and subsequently digitally modulated \hyperref[b10]{[11]}. Before IFFT implementation for each user, the number of complex digitally modulated symbols subbanding for the user\#3, user\#2 and user\#1 are128, 256 and 512 respectively in symbol mapping. The proper designed symbol mapped complex digitally modulated data have been undergone multicarrier modulation, and subsequently cyclic prefixed and digital to analog (D/A) converted. The output for all the three users are sum up and feed into spatial multiuser encoding sections. Each output is sent up in two layers where baseband to RF conversion is made before transmission from each of the two transmitting antennas. In receiving section, each user has been equipped with two receiving antennas where primarily RF to baseband conversion is made with detection of the transmitted signal. The detected signal is feed into a spatial multiplexing decoder to extract the respective signal. The extracted signal is A/D converted with the removal of cyclic prefixing and subsequently undergone OFDM demodulation. The demodulated complex symbols are demapped, digitally demodulated, channel decoded, decrypted and eventually users own text messages is retrieved. ? C ?? ?? ?? ?? = Q k L k D k p k = Q k T (b ? A x ? 0 )\textbf{(31} 
\section[{Results and Discussion}]{Results and Discussion}\par
In this section, simulation results using MATLAB R2017a have been presented to illustrate the significant impact of various types of channel coding, signal detection and higher order digital modulation techniques on performance investigation of encrypted text message transmission in 5G compatible frequency-domain subband superposed (FDSS) scheme implemented a MIMO OFDM wireless communication system in terms of bit error rate (BER). It is also considered that the channel state information (CSI) of the cmWave MIMO Rayleigh fading channel is available at the receiver and the fading channel coefficients are constant during simulation. The proposed model is simulated to evaluate the system performance under consideration of parameters presented in Table \hyperref[tab_2]{1}. In analyzing estimated BER values from graphical illustrations presented in Figure \hyperref[fig_6]{2} through Figure 7 for evaluating the performance of the simulated system, an SNR value of 2 dB is assumed typically. On critical observation, it is also noticeable that in all cases, the simulated system shows better performance in case of user\#3 with 16-QAM digital modulation as the efficient transmission bandwidth for user\#3 is lower as modulations which ratifies system performance improvement of 4.69 dB in case of user\#1. For user\#2, the estimated BER values are 0.0743 and 0.1905 which confirms that the system shows system performance improvement of 4.09 dB.\par
In case of user\#3, the estimated BER values are 0.0281 and 0.1194 which is indicative of system performance improvement of 6.28 dB. At 5\% BER, a SNR gain of 5.6 dB is achieved in 16-QAM as compared In Figure \hyperref[fig_7]{5} for user\#1, the estimated BER values are 0.2083 and 0.3350 with 16-QAM and 16-PSK digital modulations which ratifies system performance improvement of 2.06 dB. In the case of user\#2, the estimated BER values are 0.1806 and 0.3067 for For user\#2, the estimated BER values are 0.0674 and 0.2044 for identical consideration 0f 16-QAM and 16-PSK digital modulations; the system shows the system performance improvement of 4.82 dB. For user\#3, the estimated BER values are 0.0398 and 0.1171 with 16-QAM and 16-PSK digital modulations which is indicative of system performance improvement of 4.69 dB. At 5\% BER, an SNR gain of 6.2 dB is achieved in 16-QAM as compared to 16-PSK for user\#3. From Figure  {\ref 3}, the estimated BER values are 0.0757 and 0.223 with 16-QAM and 16-PSK digital to 16-PSK for user\#2. In Figure  {\ref 4} in case of user\#1, the estimated BER values are 0.0977 and 0.2242 with 16-QAM and 16-PSK digital modulations which ratifies system performance improvement of 3.61 dB.\par
In case of user\#2, the estimated BER values are 0.0662 and 0.2102 for identical consideration 0f 16-QAM and 16-PSK digital modulations, the system shows the system performance improvement of 5.02 dB For user\#3, the estimated BER values are 0.0211 and 0.1054 with 16-QAM and 16-PSK digital modulations which is indicative of system performance improvement of 6.98 dB. At 10\% BER, an SNR gain of 6.1 dB has been achieved in 16-QAM as compared to 16-PSK for user\#1. identical consideration 0f 16-QAM and 16-PSK digital modulations, the system shows the system performance improvement of 2.29 dB. In the case of user\#3, the estimated BER values are 0.0764 and 0.1991 with 16-QAM and 16-PSK digital modulations which is indicative of system performance improvement of  Fig.  {\ref 3}: BER performance of subband superposed scheme implemented multi-user 5G compatible MIMO OFDM system with the utilization of Repeat and Accumulate Channel Coding, Group Detection (GD) approach aided Efficient Zero-Forcing (ZF) signal detection and higher order digital modulation schemes Fig.  {\ref 4}: BER performance of subband superposed scheme implemented multi-user 5G compatible MIMO OFDM system with the utilization of Repeat and Accumulate Channel Coding, Lanczos method based efficient signal detection and higher order digital modulation schemes    Original transmitted text message for user \#2: Pattern division multiple access(PDMA) was proposed in 2014.\par
It is a type of non-orthogonal multiple access technology.\par
Retrieved text message for user \#2: Pattern division multiple access(PDMA) was proposed in 2014.\par
It is a type of non -orthogonal multiple access technology.\par
Original transmitted text message for user \#3: D2D technology allows direct communications between devices.\par
Retrieved text message for user \#3: D2D technology allows direct communications between devices.  
\section[{Conclusions}]{Conclusions}\par
In this paper, we have depicted our simulation implemented a MIMO OFDM wireless communication system in encrypted text message transmission. In our proposed desirable design implemented MIMO simulated system, we have tried to show system performance in terms of its BER and OOB reduction. From the simulative work, it is seen that the system shows better performance in retrieving transmitted text message with the implementation of Repeat and Accumulate Channel Coding with Group Detection (GD)\begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_1}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_2}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-4.png}
\caption{\label{fig_3}equals 1 .D}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-5.png}
\caption{\label{fig_4}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-6.png}
\caption{\label{fig_5}Fig. 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-7.png}
\caption{\label{fig_6}Fig. 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5}\includegraphics[]{image-8.png}
\caption{\label{fig_7}Fig. 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6}\includegraphics[]{image-9.png}
\caption{\label{fig_8}Fig. 6 :}\end{figure}
    \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.6611111111111111\textwidth}P{0.18888888888888888\textwidth}}
Performance Evaluation of Encrypted Text Message Transmission in 5G Compatible Frequency-domain\tabcellsep \\
Subband Superposed Scheme Implemented MIMO OFDM Wireless Communication System\tabcellsep \\
\tabcellsep Year 2019\\
\tabcellsep 19\\
\tabcellsep Volume XIX Issue II Version I\\
\tabcellsep ( ) E\\
Where I is the identity matrix. By estimated 2 H \textasciitilde , 2 2 s ? y ? . The sub-symbol vector 1 s is estimated using get 1 y =\tabcellsep Global Journal of Computer Science and Technology\\
© 2019 Global Journals\tabcellsep \end{longtable} \par
 
\caption{\label{tab_1}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.48646477132262056\textwidth}P{0.3635352286773795\textwidth}}
Text messages with number\tabcellsep 1776, 864 and 432\\
of binary bits for user\#1, user\#2 and user\#3\tabcellsep \\
Bandwidth for subband 1, subband 2 and\tabcellsep 6.66, 6.48 and 6.48\\
subband 3\tabcellsep \\
(MHz)\tabcellsep \\
FFT\textunderscore size for user\#1, user\#2 and user\#3\tabcellsep 512, 256 and 128\\
Subcarrier\textunderscore spacing for user\#1, user\#2 and\tabcellsep 15, 30 and 60\\
user\#3\tabcellsep \\
(KHz)\tabcellsep \\
CP length for user\#1 user\#2 and user\#3\tabcellsep 64, 32, 16 samples\\
Signal detection techniques\tabcellsep Cholesky Decomposition (CD) based ZF\\
\tabcellsep detection, Group Detection (GD) approach\\
\tabcellsep aided Efficient Zero-Forcing (ZF), Lanczos\\
\tabcellsep method based efficient signal detection\\
Channel coding\tabcellsep LDPC and Repeat and\\
\tabcellsep accumulate (RA)\\
Symbol mapping\tabcellsep 16-QAM and 16-PSK\\
Pulse shaping filter with Rolloff factor\tabcellsep Raised cosine with 0.25\\
Number of Transmitting or Receiving\tabcellsep 2/2\\
antennas\tabcellsep \\
Channel\tabcellsep MIMO fading channel\\
Signal to noise ratio (SNR)\tabcellsep 0 to 10 dB\end{longtable} \par
 
\caption{\label{tab_2}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.85\textwidth}}
( ) E\\
© 2019 Global Journals\end{longtable} \par
 
\caption{\label{tab_4}}\end{figure}
 		 		\backmatter  			 \par
BER, an SNR gain of dB has been achieved in 16-QAM as compared to 16-PSK for user\#2. In Figure  {\ref 6} in case of user\#1, the estimated BER values are 0.2218 and 0.3238 with16-QAM and 16-PSK digital modulations which ratifies system performance improvement of 1.64 dB. In the case of user\#2, the estimated BER values are 0.1447 and 0.2743 for identical consideration of 16-QAM and 16-PSK digital modulations; the system shows the system performance improvement of 2.78 dB. In the case of user\#3, the estimated BER values are 0.0602 and 0.2384 with 16-QAM and 16-PSK digital modulations which is indicative of system performance improvement of 5.98 dB. At 5\% BER, an SNR gain of 4.2 dB has been achieved in 16-QAM as compared to 16-PSK for user\#3. In Figure  {\ref 7} for user\#1, the estimated BER values are 0.2224 and 0.3378 with 16-QAM and 16-PSK digital modulations which makes confirmation of the system performance improvement of 1.81 dB. In the case of user\#2, the estimated BER values are 0.1725 and 0.3264 for identical consideration 0f 16-QAM and 16-PSK digital modulations, the system shows the system performance improvement of 2.77 dB. In the case of user\#3, the estimated BER values are 0.0764 and 0.2338 with 16-QAM and 16-PSK digital modulations which implies a system performance improvement of 4.86 dB. At 5\% BER, an SNR gain of 6.1 dB is achieved in 16-QAM as compared to 16-PSK for user\#3.			 			  				\begin{bibitemlist}{1}
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