Performance Analysis and Design of MIMO-OFDM System Using Concatenated Forward Error Correction Codes

J. Cent. South Univ. (2017) 24: 1322−1343 DOI: 10.1007/s11771-017-3537-2

Performance analysis and design of MIMO-OFDM system using concatenated forward error correction codes

Arun Agarwal1, Saurabh N. Mehta2

1. PhD Scholar, School of Electrical Engineering, Department of Information Technology, AMET University, Tamil Nadu, Chennai 603112, India; 2. Department of Electronics and Telecommunication Engineering, Vidyalankar Institute of Technology, Mumbai-400037, Maharashtra, India

Abstract: This work investigates the performance of various forward error correction codes, by which the MIMO-OFDM system is deployed. To ensure fair investigation, the performance of four modulations, namely, binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), quadrature amplitude modulation (QAM)-16 and QAM-64 with four error correction codes (convolutional code (CC), Reed-Solomon code (RSC)+CC, low density parity check (LDPC)+CC, Turbo+CC) is studied under three channel models (additive white Guassian noise (AWGN), Rayleigh, Rician) and three different antenna configurations(2×2, 2×4, 4×4). The bit error rate (BER) and the peak signal to noise ratio (PSNR) are taken as the measures of performance. The binary data and the color image data are transmitted and the graphs are plotted for various modulations with different channels and error correction codes. Analysis on the performance measures confirm that the Turbo + CC code in 4×4 configurations exhibits better performance.

Key words: bit error rate (BER); convolutional code (CC); forward error correction; peak signal to noise ratio (PSNR); Turbo code

signal reliability as well as the multiple transmissions, 1 Introduction without extra radiation and spectrum bandwidth [6−9]. OFDM is a technique for high-rate wireless transmission In recent years, MIMO (multiple input multiple systems because of its high spectral efficiency, immunity output) has developed and emerged as a very important against inter-symbol interference and robustness against technology in wireless communications [1−9]. MIMO multi-path channel fading. It also provides frequency supports multiple transmission purposes through diversity and thereby, it improves the BER performance exploiting its unique properties, such as the spatial of the frequency selective fading channels [16−22]. The diversity gain and the properties that are related to the combination of MIMO wireless technology with OFDM spatial multiplexing capability [10]. The MIMO system has been recognized as a most promising technique [23]. has the advantages of wide bandwidth, good isolation, The combined MIMO-OFDM technique has advantages enhanced radiation with low correlation [2] and such as, increased spectral efficiency of OFDM [24] and bandwidth efficiency [10]. Orthogonal frequency improved link reliability that enables the support of more division multiplexing (OFDM) is one of the most antennas and larger bandwidths, leading to high data rate powerful modulation techniques that is employed in as well as high performance and it has larger utilization networking [10−15]. Plenty of designs have been in high-speed wireless transmission [25]. The increase in introduced and the generated codes have varied the transmission bandwidth efficiency of the combined multiplexing and diversity gains [4]. The merits of MIMO-OFDM has been studied through estimating the OFDM include high robustness to linear fiber effects, blind channel of the system [26]. The combined MIMO sharp roll-off of OFDM spectrum, multiple access system (Alamouti space-time block coding (STBC) capabilities and tolerance to inter-symbol interference MIMO system within space division multiplexing and inter-carrier interference [13]. MIMO systems (SDM)) has been analyzed and studied through consume less extra spectrum because of the development considering the matrix structure, which is present in the of space–time (ST) coding [10]. In addition, the MIMO equivalent channel matrix H of Ref. [5]. For the reliable technology provides a quality system to enhance the transmission of signals through the MIMO system,

Received date: 2016−02−26; Accepted date: 2016−09−29 Corresponding author: Arun Agarwal, Assistant Professor, PhD; E-mail: [email protected] J. Cent. South Univ. (2017) 24: 1322−1343 1323 STBC has been developed. The STBC transmission correction representation is shown in Fig. 1. Forward using the combined SDM and STBC has been well- error correction (FEC) applies on the communication analyzed and it was found to be useful for the evaluation over wireless and it has been used as a technique for of other MIMO transmissions with quasiorthogonal controlling as well as correcting the errors that are STBC [1]. The XPM-induced degradation in each produced during video distribution. FEC codes include subcarrier of the double sideband-OFDM (DSB-OFDM) the recursive systematic convolution code and the Turbo systems that employ a DD receiver has been analytically code. While using MIMO system, an inter-layer FEC characterized in Ref. [13]. An innovative method has coding technique that is combined with UEP is applied been developed to reduce the complexity and peak to [38]. The concatenated error correction code scheme, average power ratio of T-OFDM systems in Ref. [12]. termed as LDPC with Alamouti code MIMO-OFDM, has The DCP-OQAM-OFDM and the ECP-OQAM-OFDM been analyzed under various fading conditions, such as systems have been analyzed and their power spectral spatially independent, spatially correlated, spatial densities have also been studied in Ref. [11]. Generally, temporal correlated and spatial time frequency correlated the error-correcting codes produce a threshold effect that quasi-static Rayleigh, Rician and Nakagami fading gradually reduces the performance at the low signal to channels. Due to the correlation structure, the loss of noise ratio (SNR) range. So, in order to minimize the diversity and the coding gain emerges. The arrangement threshold effect, two types of error correction codes that of concatenated code has been achieved by considering are related to the chaotic dynamical systems [27] have all the individual blocks [26]. been introduced. One of the error correction codes is This work presents a systematic study on the based on the principles of diversity and the other one is performance of the MIMO-OFDM system with based on the LDPC code. LDPC was introduced by concatenated forward error correction codes. Firstly, an GALLAGER [28] in 1962 and was rediscovered by MIMO-OFDM system is constructed with the Mackay and NEAL [29] in 1996. The LDPC code convolutional codes as the error correction codes and the exhibits a very low threshold effect. Orthogonal space concatenation of the convolutional codes with the time block codes (OSTBC) is used, in the case of the renowned block codes, such as LDPC codes, RSC and transmitting antennas [30]. It exhibits the property of Turbo codes then follows. diversity, but there is no coding gain. Hence, OSTBC Secondly, the systems are tested by transmitting that is concatenated with MIMO-OFDM [31, 32] has one-dimensional binary data and the BER analysis is been used to provide diversity in both space and time. performed. Subsequently, image transmission is also The concatenation scheme includes an inner OSTBC performed on these systems and the PSNR analysis is code and an outer channel code. The BER performance carried out. of the OSTBC code with MIMO-OFDM has been evaluated by not concatenating with the channel codes of 2 Concatenated FEC codes for MIMO- [33−36]. Convolution code is a channel coding technique, OFDM system which is concatenated with Alamouti STBC under various fading conditions that include uncorrelated 2.1 Without concatenation of FEC codes fading and spatial correlated as well as spatial time Prior to the description of the concatenated FEC correlated fading [33]. The efficiency of the convolution codes for the MIMO OFDM system, the MIMO OFDM coded MIMO-OFDM systems has been analyzed without system with convolutional codes alone (i.e., without the correlation channel models [37]. The block diagram concatenating multiple FECs) is presented. BIGDELI of MIMO-OFDM system with the forward error and ABOLHASSANI [39] have proposed a method for

Fig. 1 High-level architecture of MIMO-OFDM system with forward error correction codes

1324 J. Cent. South Univ. (2017) 24: 1322−1343 deriving an exact closed-form transfer function (TF) for model include frequency selectivity, unfading, the convolutional code. LIU et al [40] have developed a interference and nonlinearity. Interference may result two-relay full-duplex asynchronous cooperative network in some cases, so it is not a good model for the terrestrial with the amplify-and-forward (AF) protocol and links [4]. The effect of AWGN on the concatenated error convolutional space-time coding. A three-layer decoding correction codes is investigated here. Simulation results framework for the asynchronous convolutional-coded are plotted for BPSK, QPSK, QAM-16 and QAM-64 PNC systems has been developed by YANG and system, in terms of BER with variation in the SNR ratio, LIEW [41]. as shown in Figs. 2−5, respectively. In Fig. 2, at 10 dB SNR, the BER is monotonically reduced to 0.04, 0.03 2.2 Concatenation of LDPC codes with convolutional and 0.02 for CC code, 0.03, 0.02 and 0.008 for codes RSC+CC, 0.02, 0.008 and 0.004 for LDPC+CC and GROSJEAN et al [42] have developed the 0.02, 0.004 and 10−3 for Turbo code in 2×2, 2×4 and 4×4 non-terminated systemic photograph-based LDPC, which configurations, respectively. The 4×4, 2×4 and 2×2 plot was concatenated with the convolutional code that reach the BER of 10−1 for CC at 7 dB, 8 dB and 9 dB contained high memory for achieving anytime reliability SNR, for RSC+CC at 6 dB, 7 dB and 8 dB SNR, for in an asymptotic way. The bilayer LDPC convolutional LDPC+CC at 5 dB, 6 dB and 6 dB SNR, respectively. In codes have been developed by SI et al [43] for three- CC, the 4×4 slope is smaller than the other slopes and the node relay channels. noise enhancement is found to be nil. When the SNR level changes from 1 to 2 dB, the symbols overlap each 2.3 Concatenation of RSC with convolutional codes other. When RSC is combined with CC, the 4×4 plot CHEN [44] has developed a novel iterative soft reaches 10−2 BER only. When LDPC is combined with decoding algorithm for the RSC concatenated CC, the 2×4 as well as the 4x4 plots reaches the 10−2 convolutional code, aiming to better exploit its error BER at an SNR of 10 dB. When the Turbo code is correction potential. NGO et al [45] have proposed the combined with CC, the 4×4, 2×4 and 2×2 plots reach the non-coherently detected Reed-Solomon coded and slow BER of 10−2 at an SNR of 8 dB, 9 dB and 10 dB, frequency hopping (SFH)-assisted M-array frequency respectively. Only 4×4 plots reach the 10−3 BER. The shift keying for the cooperative wireless networks. noise enhancement is high among these plots. The slope is more for the 4×4 antenna configuration and there is no 2.4 Concatenation of Turbo codes with convolutional symbol overlapping. The 2×2 plot fails to reach 10−3 codes BER. In Fig. 3, at 10 dB SNR, the BER reduces to 0.03, KAYA and OZTURK [46] have proposed a new 10−2 and 0.008 for CC code, 0.01, 0.004 and 10−3 for distributed Turbo coded (DTC) scheme, which used two RSC+CC, 0.004, 0.0003 and 0.0003 for Turbo code in best relays that were selected among multi-relays. The 2×2, 2×4 and 4×4 configurations, respectively. The 4×4, double binary convolutional Turbo code was applied to 2×4 and 2×2 plots reach the BER of 10−1 for CC at 6 dB, the 21451-5 sensor and the actuator networks and a 7 dB and 8 dB SNR, for LDPC+CC at 10−4, 10−3, 10−2 low-complexity decoding solution has been proposed for SNR, respectively. In CC, the 4×4 plot reaches the BER the iterative decoding by ZHAN et al [47]. of 10−2 only. In RSC+CC, the 4×4 plot reaches the BER of 10−3. The noise enhancement level is found to be more 3 Error rate analysis between the 2×4 and the 2×2 plots. The 4×4 as well as the 2×4 plots reaches the BER of 10−2 at an SNR of 8 3.1 Experimental setup dB and 9 dB, in a respective fashion. When LDPC is The MIMO-OFDM system with various concatenated with CC, the BER reduces to 0.002 and concatenations of FEC codes is simulated in MATLAB 0.0002 at an SNR of about 10 dB for the 2×4 and 4×4 and the BER is observed for varying SNR. The systems plots, respectively. The 4×4 plot reaches the BER of 10−4 are separately studied under the AWGN environment, the only. The noise enhancement level is found to be more Rayleigh channel and the Rician channel. The between the 4×4 and the 2×4 plots. In Fig. 4, at 10 dB experimentation is extended by considering the four SNR, the BER reduces to 0.004, 0.004 and 10−3 for CC renowned modulation schemes, namely, BPSK, QPSK, code, 0.004, 0.0003 and 0.00003 for RSC+CC, 10−5, QAM16 and QAM64. 10−6 for LDPC+CC and 10−6, 10−6 and 10−8 for Turbo code in 2×2, 2×4 and 4×4 configurations, respectively. 3.2 Effect of AWGN environment The 4×4, 2×4 and 2×2 plot reaches the BER of 10−2 for AWGN is one of the noise models that often corrupt CC at 8 dB, 9 dB and 10 dB SNR, respectively. In CC, the signal, while it travels in the deep space the 4×4 plot reaches the BER of 10−3. When RSC +CC is communication links. The characteristic features of this used, the 4×4 plot reaches the BER of 10−2. The noise

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Fig. 2 BER analysis of MIMO-OFDM system with BPSK modulation and FEC schemes in AWGN environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSL+CC; (d) Turbo codes concatenated with convolutional coding

Fig. 3 BER analysis of MIMO-OFDM system with QPSK modulation and FEC schemes in AWGN environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

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Fig. 4 BER analysis of MIMO-OFDM system with QAM-16 modulation and FEC schemes in AWGN environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

Fig. 5 BER analysis of MIMO-OFDM system with QAM-64 modulation and FEC schemes in AWGN environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

J. Cent. South Univ. (2017) 24: 1322−1343 1327 enhancement level is more between the 4×4 and the 2×4 channel are plotted, in terms of BER with variation in plots. In LDPC+CC, the 4×4 plot reaches the BER of SNR ratio, as portrayed in Figs. 6−9, respectively. In 10−2. The noise enhancement level is found to be more Fig. 6, at 10 dB SNR, the BER reduces to 0.03, 0.04 and between the 2×2 and the 2×4 plots. In Turbo code, the 0.04 for RSC+CC, 0.04, 0.04 and 0.03 for LDPC+CC in noise enhancement level is found to be more between the 2×2, 2×4 and 4×4 configurations, respectively. The 4×4, 2×2 and the 2×4 plots. The Turbo concatenated with CC 2×4 and 2×2 plots reach the BER of 10−1 for Turbo+CC offers better performance in reducing the noise level of at 8 dB, 9 dB and 9 dB, respectively. For CC, all plots an AWGN environment with all modulation system. In show reduction in BER to about 0.04 at an SNR of about Fig. 5, at 10 dB SNR, the BER is monotonically reduced 10 dB. The same BER performance results are obtained to 10−2, 0.004 and 10−3 for CC code, 0.004, 0.0003 and because they have the same structures with difference in 0.00003 for RSC+CC, 10−3, 10−5 and 10−6 for LDPC+CC the input data symbols or the truncation of the and 10−4, 10−6 and 10−8 for Turbo code in 2×2, 2×4 and transmitting signal. The symbols seem to overlap and so, 4×4 configurations, respectively. The 4×4, 2×4 and 2×2 the Rayleigh fading-based channel in CC code can plots reach the BER of 10−1 for CC at 8 dB, 9 dB and achieve more multipath diversity gain. When comparing 10 dB SNR, respectively. the three plots in RSC+CC, the error rate variation among them is found to be very less. In LDPC+CC, the 3.3 Effect of Rayleigh channel symbols are noted to overlap each other until 3 dB, Rayleigh fading channel is a channel model for which indicate that there is a lot of interference. At an signal propagation in troposphere and ionosphere. It SNR of about 9 dB, the three plots reach 10−1 BER. often occurs when there is no line of sight between the When the Turbo code is combined with CC, the BER transmitter and the receiver. It is caused by multipath reduces to 0.03 and 0.04 at an SNR of about 10 dB in reception [6]. The BER and the error intensity of the time 2×4 and 4×4 plots, respectively. In Fig. 7, at 10 dB SNR, varying Rayleigh fading channels are analyzed by the the BER reduces to 0.04, 0.03 and 0.03 for RSC+CC, selection combining method of the received signals, 0.04, 0.03 and 0.02 for LDPC+CC and 0.04, 0.03 and which are at the destination of a D-AF relay network that 0.02 for Turbo code in 2×2, 2×4 and 4×4 configurations, employs DBPSK [40]. Simulation results for the BPSK, respectively. The 4×4, 2×4 and 2×2 plots reach the BER QPSK, QAM-16 and QAM-64 systems under Rayleigh of 10− 1 for CC at 7 dB, 8 dB and 9 dB SNR, for

Fig. 6 BER analysis of MIMO-OFDM system with BPSK modulation and FEC schemes in Rayleigh environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

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Fig. 7 BER analysis of MIMO-OFDM system with QPSK modulation and FEC schemes in Rayleigh environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

Fig. 8 BER analysis of MIMO-OFDM system with QAM-16 modulation and FEC schemes in Rayleigh environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

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Fig. 9 BER analysis of MIMO-OFDM system with QAM-64 modulation and FEC schemes in Rayleigh environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

RSC+CC at 8 dB, 9 dB and 9 dB SNR, for LDPC+CC at 10−2. In Turbo concatenation, the noise enhancement 8 dB, 8 dB and 9 dB SNR, for Turbo at 7 dB, 8 dB and 9 level is found to be the same. In Fig. 9, at 10 dB SNR, dB SNR, respectively. When CC is used, the BER the BER is reduced to 0.03, 0.03 and 0.03 for CC code, reduces to 0.03 and 0.04 at an SNR of about 10 dB in 0.03, 0.02 and 0.02 for RSC+CC, 0.03, 0.02 and 10−2 for 2×4 and 4×4 plots, respectively. The noise enhancement LDPC+CC and 0.02, 10−2 and 0.07 for Turbo code in level is found to be the same for all the codes. 2×2, 2×4 and 4×4 configurations, respectively. The 4×4, The three sub plots are found to overlap at 2 dB and 2×4 and 2×2 plot has reached the BER of 10−1 for CC at 3 dB. The noise enhancement level is found to be more 8 dB, 8 dB and 8 dB SNR, for RSC+CC at 7 dB, 8 dB or less same between the plots in RSC+CC and and 8 dB SNR, for LDPC+CC at 6 dB, 7 dB and 8 dB LDPC+CC. SNR for Turbo at 5 dB, 6 dB and 8 dB SNR, respectively. For the Turbo code, the 4×4 plot is more adjacent to In CC, the estimated errors of all the cases decrease with the BER of 10−2 and there is less noise interference in the increase in SNR and the noise enhancement level is 4×4 configurations. found to be the same between the configurations. While In Fig. 8, at 10 dB SNR, the BER reduces to 0.04, comparing the four channel codes, the turbo 0.04 and 0.03 for CC code, 0.04, 0.03 and 0.02 for concatenated with CC exhibits the better performance in RSC+CC, 0.03, 0.02 and 10−2 for LDPC+CC and 0.03, reducing the noise level of the Rayleigh environment 0.02 and 10−2 for Turbo code in 2×2, 2×4 and 4×4 with all types of modulation systems. configurations, respectively. The 4×4, 2×4 and 2×2 plots reach the BER of 10−1 for CC at 7 dB, 8 dB and 9 dB 3.4 Effect of Rician channel SNR, for RSC+CC at 8 dB, 8 dB and 9 dB SNR, for Rician fading model is a type of channel model for LDPC+CC at 7 dB, 8 dB and 8 dB SNR, for Turbo+CC signal propagation with a strong dominant component. at 6 dB, 7 dB and 8 dB SNR, respectively. The 4×4 plot The stationary component is a non fading channel, called reaches the BER of 10−2 only. The symbols tend to as the line of sight component [6]. Simulation results overlap in this case. All the plots are very close to each are plotted, in terms of BER with variation in SNR other and very little noise variation is found between the ratio, for BPSK, QPSK, QAM-16 and QAM-64 systems plots. In LDPC+CC, the 4×4 plot reaches the BER of under the Rician environment as shown in Figs.10−13,

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Fig. 10 BER analysis of MIMO-OFDM system with BPSK modulation and FEC schemes in Rician environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

Fig. 11 BER analysis of MIMO-OFDM system with QPSK modulation and FEC schemes in Rician environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

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Fig. 12 BER analysis of MIMO-OFDM system with QAM-16 modulation and FEC schemes in Rician environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

Fig. 13 BER analysis of MIMO-OFDM system with QAM-64 modulation and FEC schemes in Rician environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

1332 J. Cent. South Univ. (2017) 24: 1322−1343 respectively. In Fig. 10, at 10 dB SNR, the BER is received image and the results are illustrated. reduced to 0.04, 0.04 and 0.03 for CC code, 0.04, 0.03 and 0.02 for RSC+CC, 0.04, 0.03 and 0.02 for LDPC+ 4.2 Effect of AWGN environment CC and 0.03, 0.02 and 10−2 for Turbo code in 2×2, 2×4 AWGN is a widely used channel model in wireless and 4×4 configurations, respectively. The 4×4, 2×4 and communications. In the MIMO-OFDM system, the 2×2 plots reach the BER of 10−1 for LDPC+CC at 7 dB, communication under AWGN environment is done by 8 dB and 9 dB SNR, respectively. The symbols overlap developing many algorithms and the performance is at 2 dB and the noise enhancement level variation is measured using the PSNR. Simulation results are plotted, found to be very less for the three configurations of the in terms of PSNR with variation in SNR ratio, for BPSK, CC code. The 4×4 plot shows more slopes and its noise QPSK, QAM-16, QAM-64 modulations in the AWGN enhancement level is found to be the same, when channel mode for various error correction codes with compared with the other two plots of RSC+CC. When three antenna configurations as shown in Figs. 14−17, Turbo code is combined with CC, the noise enhancement respectively. In Fig. 14, at an SNR of 10 dB, the level is found to be more between the 4×4 and the 2×4 deviation difference between 2×2, 2×4 and 2×4, 4×4 plots. In Fig. 11, at 10 dB SNR, the BER reduces to 0.04, curves are found to be 80% and 31% for RSC+CC, 38% 0.03 and 0.02 for CC code, 0.03, 0.02 and 10−2 for at 8 dB and 37% at 10 dB for LDPC+CC. When using RSC+CC, 0.03, 10−2 and 0.006 for LDPC+CC and 0.02, CC, the 4×4 curve shows increased PSNR for an SNR of about 10 dB. The 2×4 curve has tilted when it reached a 0.008 and 0.003 for Turbo code in 2×2, 2×4 and 4×4 SNR of about 9 dB. In RSC+CC, the 2×4 curve seems to configurations, respectively. The 4×4, 2×4 and 2×2 plots be linear in nature. In the case of the 4×4 curves, the reach the BER of 10−1 for CC at 8 dB, 8 dB and 9 dB deviation has become more at an SNR of 10 dB. The SNR, for RSC+CC at 6 dB, 7 dB and 8 dB SNR, deviation is found to be more at 8−10 dB in 2×2 curves. respectively. When LDPC is combined with CC, the When LDPC+CC is used, the 4×4 curve reaches the SNR noise enhancement level is found to be more between the of 8 dB. The 2×4 curve has a steep slope in the SNR 2×2 and 2×4 plots, when compared with the 4×4 and 2×4 range of 9−10 dB. More deviational difference is seen plots, and the slope is more for the 4×4 configured plots. between the 2×4 and the 2×2 curves, when the SNR In Fig. 12, at 10 dB SNR, the BER reduces to 0.03, 0.02 assumed values between 7 db and 9 dB. When Turbo+ and 10−2 for CC code, 10−2, 10−2 and 0.007 for RSC+CC, −2 CC is used, the 4×4 curve shows a steep slope up to a 0.02, 0.006 and 0.002 for LDPC+CC and 10 , 0.003 and PSNR of 25. However, for the 2×4 curves at a PSNR of 2, 0.0009 for Turbo code in 2×2, 2×4 and 4×4 the curve bends and causes the PSNR value to get configurations, respectively. The 4×4, 2×4 and 2×2 plots reduced. The 2×2 curve shows a linear form. The peak −1 reach the BER of 10 for CC at 7 dB, 8 dB and 8 dB deviation becomes more at 8 dB for the 2×4 curves. The SNR, respectively. In Fig. 13, at 10 dB SNR, the BER deviation between the 2×2 curve and the 2×4 curve is −2 reduces to 0.03, 0.02 and 10 for CC code, 0.02, 0.008 found to be 110% at 8 dB. In Fig. 15, the deviation −2 and 0.003 for RSC+CC, 10 , 0.03 and 0.0009 for between 2×2, 2×4 and 2×4, 4×4 curves is found to be −3 LDPC+CC and 0.008, 10 and 0.0002 for Turbo code in 44% and 75% at 10 dB for CC, 100% and 280% at 9 dB 2×2, 2×4 and 4×4 configurations, respectively. The 4×4, for RSC+CC, 40% and 400% at 5 dB for LDPC+CC. In −1 2×4 and 2×2 plots reach the BER of 10 for CC at 8 dB, CC code, the 2×2 curve exhibits a linear nature. 7 dB and 6 dB SNR, respectively. In Turbo concatenated In the case of the 4×4 curve, a steep increase from with CC, the noise enhancement level is found to be 9−10 dB that reaches the PSNR of −1 is experienced. more between the 4×4 and 2×4 plots. The 4×4, 2×4 and When the RSC +CC code is used, the 4×4 curve shows a −4, −3 −2 2×2 plots reach the BER of 10 10 , 10 , respectively, steep increase at 6−7 dB. The 2×2 curve reaches the SNR at an SNR of 10 dB. The turbo concatenated with CC level of 10 dB. For the LDPC+CC code, a steep increase shows better performance in reducing the noise level of in the 4×4 curve is seen at an SNR of 4−5 dB, 6−7 dB, the Rician environment with all modulation systems. 8−9 dB and then, a dwindling occurs. While using Turbo +CC code, the 4×4 plot shows a straight line. 4 PSNR analysis on image transmission The 2×4 curve tends to curve slightly with a little increase in the slope. The deviation between the 2×4 4.1 Procedure curve and the 2×2 curve is found to be 150% at an SNR With the similar experimental setup, a color image of 5 dB. is transmitted through the MIMO-OFDM system. Since In Fig. 16, the deviation difference between 2×2 as the color image is a three-dimensional matrix, one- well as 2×4 curves and 2×4 as well as 4×4 curves is dimensional data are constructed from the color image, found to be 36% and 42% at 8 dB, 48% and 38% at 5 dB prior to transmission. The PSNR is determined for the for RSC+CC, 48% and 330% at 7 dB for LDPC+CC.

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Fig. 14 PSNR analysis of MIMO-OFDM system with BPSK modulation and FEC schemes in AWGN environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

Fig. 15 PSNR analysis of MIMO-OFDM system with QPSK modulation and FEC schemes in AWGN environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

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Fig. 16 PSNR analysis of MIMO-OFDM system with QAM-16 modulation and FEC schemes in AWGN environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

Fig. 17 PSNR analysis of MIMO-OFDM system with QAM-64 modulation and FEC schemes in AWGN environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

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When CC code is used, the 4×4 curve shows rejection. Simulation results are plotted, in terms of increased PSNR value. The three curves differ from each PSNR with variation in SNR ratio, for BPSK, QPSK, other. The 4×4 curve bends slightly after reaching 7 dB QAM-16 and QAM-64 systems as shown in Figs. 18−21, and deviation between 2×2 and 2×4 is more from 8−10 respectively. In Fig. 14, at an SNR of 10 dB, the dB. In RSC+CC, the 2×2 curve shows fewer slopes. The deviation difference between the 2×2 as well as the 2×4 2×4 curve shows a steep rise from 6−7 dB. curve and the 2×4 as well as the 4×4 curves is found to In Fig. 17, when CC code is used, the 2×2 curve be 10% and 4% for CC, 14% and 25% for RSC+CC, shows an increase from 9−10 dB SNR and the 2×4 curve 38% and 15% and 18% at 10 dB for LDPC+CC and 24% increases at 8−9 dB. The 4×4 curve shows a sharp rise and 47% for Turbo code. In CC code, the symbols tend from 6−7 dB SNR. In RSC+CC code, the 4×4 curve to overlap each other at an SNR of 1 dB and 2 dB with a shows a straight line. The 2×2 curve reaches a peak at PSNR of −39 and −38. When using the RSC+CC code, 7 dB and bends to 8 and has a sharp peak at 9 dB SNR at an SNR of about 1 dB with a PSNR of −38, the 2×2 with PSNR of 18. The deviation between 2×2, 2×4 curve and the 2×4 curve overlap each other. So, there is curves is found to be 125% at an SNR of 5 dB. When no deviation between them. Deviation is more between LDPC is combined with CC code, the three plots 4×4, the 2×2 and 2×4 curves at 7−10 dB. In LDPC+CC code, 2×4, 2×2 show a straight line reaching at 2, 3 and 6 dB the 2×2 curves show more slope. The deviation is more respectively. at an SNR of about 10 dB. At an SNR of 1 dB with a But in Turbo+CC code, the 4×4 seems to be a small PSNR of −38, the deviation is less and the symbols are point at 1 dB SNR with −18 PSNR. The 2×4 is a straight found to overlap each other in the Turbo concatenated line at 2 dB SNR with −16 PSNR. The 2×2 is a normal code. The 4×4 curve reaches the PSNR of −9 at an SNR curve at 5 dB SNR with 0 PSNR. of about 10 dB. The turbo concatenated with CC is found to have a In Fig. 19, the deviation difference between the 2×2 better performance in reducing the noise level of the as well as the 2×4 curve and the 2×4 as well as the 4×4 AWGN environment using four types of modulations. curve is found to be 3% and 15% at 10 dB for CC, 16% and 33% at 10 dB for RSC+CC, 28% and 44% for 4.3 Effect of Rayleigh channel LDPC+CC at 9 dB SNR, 56% and 61% at 9 dB for Rayleigh channel is mostly caused by multiple path Turbo code. In Turbo +CC code, the three curves show

Fig. 18 PSNR analysis of MIMO-OFDM system with BPSK modulation and FEC schemes in Rayleigh environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

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Fig. 19 PSNR analysis of MIMO-OFDM system with QPSK modulation and FEC schemes in Rayleigh environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

Fig. 20 PSNR analysis of MIMO-OFDM system with QAM-16 modulation and FEC schemes in Rayleigh environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

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Fig. 21 PSNR analysis of MIMO-OFDM system with QAM-64 modulation and FEC schemes in Rayleigh environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding high deviation differences. The 2×2 curve and 2×4 curve and the 2×4 curve as well as the 2×4 curve and the 4×4 have high deviation than the other two comparisons. The curve is found to be 25% and 27% at 10 dB for CC, 45% 4×4 curve shows a sharp increase from 6−7 dB. When and 84% at 10 dB for RSC+CC, 34% and 46% for using CC code, the three curves show similarity with LDPC+CC at 8 dB SNR, 37% and 100% at 7 dB for small deviational changes. When combining RSC+CC Turbo code. In CC code, the 4×4 curve has increased code, the 4×4 curve shows more deviation at an SNR of PSNR, when compared to 2×4 and 2×2 curves at an SNR 8 dB. In LDPC+CC code, the 2×2, 2×4 and 4×4 curves of about 10 dB. The three curves are found to be similar show less deviation between them and all those curves with small deviation and in RSC+CC code, the 4×4 are similar in nature. In Fig. 20, the deviation difference curve increases at 8−9 dB and slowly bends later on. The between the 2×2 curve and the 2×4 curve as well as the 2×4 curve increases at an SNR of 9−10 dB. When using 2×4 curve and the 4×4 curve is found to be 36% and LDPC+CC code, the 4×4 curve shows increased PSNR, 31% at 10 dB for CC, 55% and 100% at 10 dB for when compared to 2×4 and 2×2 curves at an SNR of RSC+CC, 280% and 100% at 7 dB for LDPC+CC, 60% about 10 dB. The three curves show high deviation and 80% at 10 dB SNR for Turbo-concatenated code. between them. When using Turbo+CC code, the 4×4 In CC code, the three plots show similarity with less curve is a sloped straight line curve. Among the four deviation differences. But in RSC+CC code, the three channel codes considered, the Turbo concatenated with curves show similarity with medium deviation CC has a better performance in reducing the noise level differences and in LDPC+CC code, the three curves of the Rayleigh environment with all four types of show similarity with high deviation differences between modulations. the 4×4 curve and the 2×4 curve. For the Turbo+CC code, the 4×4 curve shows a straight line. The 2×4 curve and 4.4 Effect of Rician channel the 2×2 curve show more deviations. At an SNR of Rician fading model is used for signal transmission 9−10 dB, the 2×2 curve shows a sharp increase in PSNR. with a strong dominant component. Simulation results The three plots are similar with high deviation are plotted, in terms of PSNR with variation in SNR ratio, differences between the 4×4 curve and the 2×4 curve. In for BPSK system, QPSK system, QAM-16 and QAM-64 Fig. 21, the deviation difference between the 2×2 curve as shown in Figs. 22−25, respectively. In Fig. 22, with

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Fig. 22 PSNR analysis of MIMO-OFDM system with BPSK modulation and FEC schemes in Rician environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

Fig. 23 PSNR analysis of MIMO-OFDM system with QPSK modulation and FEC schemes in Rician environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

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Fig. 24 PSNR analysis of MIMO-OFDM system with QAM-16 modulation and FEC schemes in Rician environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

Fig. 25 PSNR analysis of MIMO-OFDM system with QAM-64 modulation and FEC schemes in Rician environment: (a) Only convolutional coding, CC; (b) LDPC concatenated with convolutional coding, LDPC+CC; (c) RSC concatenated with convolutional coding, RSC+CC; (d) Turbo codes concatenated with convolutional coding

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CC code at an SNR of about 1 dB, the 2×4 curve and the difference is more between 2×2 and 2×4 at an SNR of 4×4 curve overlap each other and so, the deviation is nil. 8 dB. In Turbo combined with CC code, the 2×2 curve is At about 8 dB, the deviation tends to increase between a normal curve. The 2×4 curve increases at 6−7 dB. The the curves. The three curves move in the same manner. 2×2 curve increases at 4−5 dB SNR. In Fig. 25, the At an SNR of 10 dB, the deviation between the 2×2 deviation between the 2×2 curve and the 2×4 curve as curve and the 2×4 curve as well as the 2×4 curve and the well as the 2×4 curve and the 4x4 curve is found to be 4×4 curve is found to be 10% and 7% for CC, 11% and 40% and 161% at 10 dB for CC, 127% and 28% at 6 dB 21% for RSC+CC, 25% and 22% for LDPC+CC, 45% SNR for RSC+CC, 250% and −26% for LDPC+CC at and 141% for Turbo code. When using RSC+CC code, 7 dB SNR. When CC code is used, the deviation the 4×4 curves’ deviation is high at an SNR of 8 dB. The difference is high among the three plots. In the case of deviation is found to be more at 8 dB (about 14%) the RSC+CC code, high deviation is found among the between the 4×4 and the 2×4 curves. In LDPC+CC code, three sub plots. The 2×4 curve increases from 8−9 dB the symbols do not overlap. The three curves are distinct SNR. The 4×4 curve bends at an SNR of 6−7 dB. When with unique features. The 4×4 curve shows a steep rise at LDPC is combined with CC code, the three plots show an SNR of 6dB and gradually moves to 10 dB. The 2×2 strong deviation differences between them. The 4×4 curve is linear in nature. With Turbo +CC code, the 4×4 shows a steep increase at an SNR of 5 dB, until a PSNR of 38. The 2×4 curve shows a sharp increase in the SNR curve shows a slow linearity up to 8 dB, straightens up to value. The 2×2 curve is a normal slope type. In Turbo 9 dB and steeps at 10 dB finally. The 2×2 curve and the concatenated code, the 4×4 curve is a straight line. The 2×4 curve seem to be a normal curve. 2×4 curve is also a straight line and it bends with an In Fig. 23, at an SNR of 10 dB, the deviation increasing SNR rate. The deviation between the 2×2 between the 2×2 curve and the 2×4 curve as well as the curve and the 2×4 curve is found to be 140% at an SNR 2×4 curve and the 4×4 curve is found to be 14% and of 4 dB. Among the four channel codes considered, the 21% for CC, 50% and 250% for RSC+CC, 60% and 45% Turbo concatenated with CC exhibits better performance for Turbo code and 40% and 220% for LDPC+CC at 8 in reducing the noise level of the Rician environment dB SNR. When using CC code, the 4×4 curve has with all modulation systems. increased PSNR, when compared to 2×4 and 2×2 curves at an SNR of about 10 dB. The three curves show similar 5 Comparative analysis nature with minimal deviation. The deviation is found to be more between the 4×4 and 2×4 curves for CC and With the similar experimental setup, a color image RSC+CC at 6−8 dB. With RSC+CC code, the 4×4 curve is transmitted through the MIMO-OFDM system. Since tends to increase from 8 dB to 10 dB. The 2×2 curve is a the color image is a three-dimensional matrix, one- linear straight curve. The 4×4 curve has increased PSNR, dimensional data are constructed from the color image when compared to 2×4 and 2×2 curves at an SNR of and it is transmitted. The PSNR is determined for the about 10 dB. When using LDPC+CC code, the three received image and the results are illustrated. Table 1 plots differ from each other. The 2×2 curve is a linear shows the simulation results for various modulations curve. The 2×4 curve increases at an SNR of 8−9 dB and under various channels with 3 antenna configurations of bends at 9−10 dB. The 4×4 curve shows a sharp narrow the error correction codes. The performance of Turbo increase from 6 dB to 8 dB SNR. When combined Turbo concatenated with CC is better (shown in bold) in all the +CC code is used, the 2×2 curve slopes in some places. channel modulation systems. About 50% reduction of The 2×4 curve increases and then, straightens from 8 dB error is seen in Turbo +CC, when compared with the to 9 dB. In the case of the 4×4 curves, at 6−7 dB SNR, other codes. It is more effective in the QAM-16 and the the curve seems to increase. In Fig. 24, the deviation QAM-64 modulations. In Rayleigh channel, no between the 2×2 curve and the 2×4 curve as well as the difference is seen in BPSK modulation for the 2×2 2×4 curve and the 4×4 curve is found to be 29% and configuration. In Rician channel, LDPC code shows 17% for CC at 10 dB and 57% and 200% for RSC+CC, better performance for the 2×2 configuration. On the 140% and 100% for LDPC+CC at 8 dB and 290% and whole, the 4×4 configuration shows better performance 166% for Turbo code at 7 dB SNR. In CC code, the three in all the channel modes. Table 2 shows the simulation plots are more or less similar in nature. But, when RSC is results for various modulations under various channels combined with CC code, the 4×4 curve shows a steep with 3 antenna configurations of the error correction rise at 7−8 dB. The 2×2 and 2×4 curves are similar in codes. The performance of the turbo concatenated with nature. When LDPC is combined with CC code, the three CC is better (shown in bold) in all the channel plots show high variation between them. The deviation modulation systems. About 50% reduction of error is

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Table 1 Comparison between concatenated FEC codes under varying channel environments and modulation schemes, while transmitting data BER for 2×2/10−2 BER for 2×4/10−2 BER for 4×4/10−2 Channel Modulation RSC+ LDPC+ Turbo+ RSC+ LDPC+ Turbo+ RSC+ LDPC+ Turbo+ model scheme CC CC CC CC CC CC CC CC CC CC CC CC BPSK 4 3 2 1 3 1 0.8 0.4 2 0.8 0.3 0.1 QPSK 3 2 0.8 0.4 2 0.4 0.1 0.03 0.8 0.1 0.02 0.003 AWGN QAM-16 2 0.8 0.3 0.06 0.8 0.1 0.02 0.0006 0.3 0.02 0.001 0.0001 QAM-64 2 0.4 0.1 0.05 0.4 0.04 0.005 0.0004 0.1 0.003 0.00010.000004 BPSK 5 5 4 4 5 4 4 4 4 4 3 3 Rayleigh QPSK 5 4 4 4 4 4 3 3 4 3 2 2 channel QAM-16 5 4 3 3 4 3 2 2 3 2 2 1 QAM-64 4 4 3 3 4 3 2 1 3 2 1 0.7 BPSK 5 4 4 3 4 3 3 2 4 3 2 1 Rician QPSK 4 3 3 2 3 2 1 0.8 3 1 0.7 0.3 channel QAM-16 4 3 2 1 3 1 0.7 0.4 2 0.7 0.2 0.09 QAM-64 3 2 1 8 2 0.8 0.3 0.1 1 0.3 0.09 0.02

Table 2 Comparison between concatenated FEC codes under varying channel environments and modulation schemes, while transmitting image BER for 2×2/10−2 BER for 2×4/10−2 BER for 4×4/10−2 Channel Modulation LDPC+ Turbo+ RSC+ LDPC+ Turbo+ RSC+ LDPC+ Turbo+ model scheme CC RSC+CC CC CC CC CC CC) CC CC CC CC CC BPSK 3 2 2 1 2 1 0.5 0.02 2 0.5 0.2 0.06 QPSK 2 1 0.5 0.2 1 0.2 0.06 0.0001 0.5 0.06 0.006 0.00007 AWGN QAM-16 2 0.5 0.2 0.01 0.5 0.05 0.005 0.001 0.2 0.006 0.0002 0.0001 0.00000 QAM-64 1 0.2 0.1 0.01 0.2 0.01 0.001 0.00005 0.0006 0.007 0.00001 01 BPSK 4 4 4 4 4 4 3 3 4 3 3 3 Rayleigh QPSK 4 4 3 3 4 3 3 2 3 3 2 1 channel QAM-16 4 3 3 2 3 3 2 1 3 2 1 0.8 QAM-64 4 3 3 2 3 2 1 1 3 1 0.8 0.4 BPSK 4 4 3 3 4 3 2 2 3 2 1 0.9 Rician QPSK 4 3 2 2 3 2 0.9 0.5 2 0.9 0.4 0.2 channel QAM-16 3 2 1 0.1 2 0.9 0.4 0.2 1 0.4 0.1 0.04 QAM-64 3 2 0.9 0.5 2 0.5 0.2 0.06 0.9 0.2 0.04 0.007 seen in Turbo+CC, when compared with the other codes. error correction codes. The MIMO-OFDM system with It is more effective in the QAM-16 and the QAM-64 the convolutional code has been studied and then, the modulations. In Rayleigh channel, no difference is seen concatenated error correction codes of the MIMO- in BPSK modulation for the 2×2 configuration. In Rician OFDM system with different modulations have been channel, the Turbo code and LDPC show better analyzed. The graphs have been plotted (BER vs. SNR performance. On the whole, the 4×4 configuration shows and PSNR vs. SNR) for all the error correction codes better performance in all the channel modes. with concatenation (RSC+CC, LDPC+CC, Turbo+CC) and without concatenation (CC). The results of all the 6 Conclusion and future work error correction codes have been compared, under three different antenna configurations. It has been found that This work has discussed the performance of the Turbo code concatenated with convolutional code MIMO-OFDM system with the concatenated forward exhibits the better performance.

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Cite this article as: Arun Agarwal, Saurabh N. Mehta. Performance analysis and design of MIMO OFDM system using concatenated forward error correction codes [J]. Journal of Central South University, 2017, 24(6): 1322−1343. DOI: 10.1007/s11771-017-3537-2.