# Performance of OFDM: FSO Communication System with Hybrid Channel Codes during Weak Turbulence

Authors: Ritu Gupta; Tara Singh Kamal; Preeti Singh
Journal: Journal of Computer Networks and Communications
 (2019)

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## Abstract

The performance of orthogonal frequency division multiplexing- (OFDM-) based free-space optics (FSO) depends on various parameters such as number of subcarriers, base band modulation, nature of laser beam, turbulence modelling, and much more. Various diversity techniques have been studied by researchers for the improvement of signal strength due to fading caused by atmospheric turbulence. In this paper, a novel channel coding scheme formed by serially concatenation of irregular low-density parity check (LDPC) and trellis code modulation (TCM) codes linked by interleaver is proposed. The proposed unified coding scheme is simulated and analyzed using the lognormal scintillation model, which is suitable for weak turbulent conditions. The obtained results are the comparative study of various channel coding schemes in terms of bit error rate (BER) vs. signal-to-noise ratio (SNR). Simulation results confirm that newly designed hybrid code outperforms the independently coded and uncoded systems under weak turbulence conditions by reducing the number of errors in the transmitted information that occurs due to fading. It is found that the presented hybrid coded OFDM-FSO system with 16-level quadrature amplitude modulation (QAM) provides significant improvement with less decoding complexity and reasonable delay.


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## Body

## 1. Introduction

In the past, free-space optics (FSO) has received the researcher’s attention due to its numerous advantages over radio-frequency (RF) communication such as less cost, easy deployment, and free of license and subsequently used in high-bandwidth applications [1, 2]. FSO has various knock-on effects in military applications, disaster recovery, backhaul connectivity, and line-of-sight (LOS) link for communication between planes, ships etc. [1] due to varying atmospheric turbulent conditions. Because of atmospheric turbulence conditions, link performance droops due to water particles and aerosols, which causes changes in the refractive index, affecting the propagation of the LASER beam through atmosphere [3, 4]. Atmospheric turbulence provides high hindrance as LOS requirement is not contended. Various diversity techniques have been analyzed in the earlier research for reducing the impact of turbulence on the performance of FSO link [5, 6]. Among various atmospheric aspects such as rain, haze, snow, hail, and fog, the major deterrent that affects the consistency and reliability of the FSO link is fog [7].While data transmission through free space, it is foreseen that channel encoding plays the utmost important role and contributes for better performance of data carriage. The various channel coding schemes also known as forward error correction (FEC) schemes have been used in FSO communication due to their pros such as containing numerous valid code words, transmitting quickly, and detecting or correcting block of errors [8–11]. Convolutional coding (CC) has been considered as powerful error-correcting codes as proved by Fang et al. in [12]. In most cases, it makes a good compromise between performance and decoding complexity, so it becomes a suitable choice for transmission of data through wireless means, whereas, in the presence of intrachannel nonlinear effects, low-density parity-check (LDPC) codes outperform the turbo-product codes in burst error-prone channels such as the optical fiber channel [13, 14]. Simple trellis-coded modulation (TCM) codes itself are a hybrid scheme having a combination of coder and modulator and are appropriate for signal transmission in FSO communication because of its worthier performance or rise in throughput (in bits per second) with sophisticated coding gain. TCM improves the noise immunity of digital communication systems without data-rate reduction or bandwidth expansion [15, 16].Wavelength division multiplexing (WDM) multiplexes the multiple optical carriers into single fiber [17, 18], whereas orthogonal frequency division multiplexing (OFDM) is chosen for multicarrier modulation because of its inherent resilience to frequency selectiveness of the optical communication channel [19]. OFDM is computationally effectual by using inverse fast Fourier transform (IFFT) and fast Fourier transform (FFT) techniques to carry out the modulation and demodulation functions, respectively. For mitigation of short-term loss of signal strength due to fading, other diversity techniques such as time diversity and spatial diversity have also been studied by Lee and Chan in [20]. In this paper, a novel unified coding scheme which is a serial concatenation of LDPC and TCM codes has been proposed. The performance of the hybrid LDPC-TCM-coded FSO-OFDM system with 16-QAM has been analyzed using the lognormal turbulence model during weak turbulence. The key idea is to fully exploit the advantages of both OFDM and channel coding for the FSO communication system.The remainder of the paper is organized as follows. In Section2, the system model and general assumptions are presented. Next, simulation results are discussed in Section 3, and Section 4 has shown the comparative analysis of various channel coding schemes. Finally, Section 5 concludes the paper.


## 2. System Model

While it can be difficult to realize perfect knowledge of the turbulence distribution, it is feasible to find and make use of the statistical moments of the turbulence. The commonly used statistical models for depicting atmospheric turbulence channels are the gamma-gamma model, negative exponential, lognormal distribution model, K-distribution model, and I-K distribution. The lognormal distribution is suitable for weak turbulence and characterizes wireless optical communications links over few hundred meters during the clear weather conditions [15]. The K-distribution model is fit for characterizing strong turbulence. The negative exponential distribution defines the limiting instance of saturated scintillation. The gamma-gamma (ΓΓ) distribution is a general model that can be functional under varied range of turbulence conditions during weak to strong [10]. In this work, weak turbulence condition is considered, and so the lognormal distribution model is highlighted because of its proficiency under such conditions. According to the lognormal distribution channel model, the optical irradiance I is specified by(1)I=expX,where X = Gaussian RV with mean μ and variance σ2.Probability density function (pdf) of the receiving irradiance fluctuation is given as [21, 22](2)pI=12π⋅1σI⋅exp−lnI+μ22σ2,where I = signal intensity assuming mean of I is 1 due to normalized channel effect. σ2 is a Rytov variance or variance of light intensity:(3)σ2=1.23CN2k7/6L11/6,where CN2 = refractive-index structure parameter, k (wave number) = 2π/λ, and L = the distance between transmitter and receiver.The system model discussed in this paper is the single-input-single-output (SISO) OFDM-FSO system with hybrid coding scheme to endure the consequence of weak turbulence conditions such as maritime and light fog on FSO link. The system’s efficiency is estimated from the bit error rate (BER), and comparative analysis of the proposed hybrid channel coded scheme is done with the preexisting channel coding schemes under weak turbulence conditions such as maritime and light fog. The simulations have been done using MATLAB 2016Ra. This section of the paper confers the design deliberations of the systems.


### 2.1. System I: OFDM-FSO System with Single Channel Coding

The system setup side is the same as it is done in wireless networks except it uses optical transmitters such as LASER and optical receivers such as photodetectors for communication. The SISO-based OFDM-FSO system, which has been considered in MATLAB, is shown in Figure1.Figure 1
Block diagram of OFDM-based FSO communication system [10].It consists of a transmitter, a receiver, and a free-space channel between them. The transmitter uses a random bit generator, FEC or channel encoder, interleaver, QAM modulator, IFFT, OFDM multiplexer, and an optical source (LASER) for transmission. The receiver section has OFDM demultiplexer, FFT, demodulator, deinterleaver, and decoder. Use of interleaver upsurges total delay because before the packets can be decoded, the entire interleaved block must be received. Also, the error’s structure has not been exposed by interleavers. The bit error rate (BER) has been analyzed at the receiver end. For channel modelling, the lognormal turbulence model is obliged.The wavelength used is 1550 nm due to its low attenuation characteristics. The system is designed with the use of OFDM network. The number of subcarriers used in the system is 4 because as the number of subcarriers increases, the SNR needed to achieve the required BER also increases [22].In OFDM, the required FFT/IFFT is calculated using 16 points. The simulation parameters considered in the proposed SISO model as depicted in Figures1 and 2 are given in Table 1.Figure 2
Block diagram of SISO OFDM-based FSO hybrid LDPC- and TCM-coded system.Table 1
System parameters used in the proposed model.
Parameter
Value
Coding rate
1/2
Coding scheme
LDPC, TCM, hybrid LDPC, and TCM
Modulation scheme
16-QAM
Encoding sequence
LDPC then TCM
Wavelength (λ)
1550 nm
Range (L)
1000 m
Refractive-index structure
Parameter (CN2)
0.75 ∗ 10−14


### 2.2. Design of the OFDM-FSO System with LDPC Encoder

Low-density parity-check (LDPC) codes are powerful channel (FEC) codes that enhance the constant size redundancy to correct random and burst errors [13]. Due to its various pros such as high code rate and low hardware complexity [11], LDPC codes are currently used in FSO communication and perform decent during strong turbulence. The LDPC code is a special linear group of codes with sparse parity-check matrix with N-K by N. Many methods have already been settled for the construction of parity-check matrix [13, 14]. The LDPC decoder halts when a permissible code word is found and significantly has a potential to reduce the effort. These codes are advantageous when considering long codes due to parallel implementation of decoders. In presented LDPC encoder, the matrix dimensions are 32400 : 64800 and the BER vs. SNR is shown in Figure 3. In the said system, an irregular LDPC code is used with code rate 1/2. From the results, it can be observed that, at 25 dB, the error rate of 10−6 is achieved.Figure 3
BER vs. electrical SNR of OFDM-FSO system with LDPC encoder.


### 2.3. Design of the OFDM-FSO System with TCM Encoder

TCM has lesser computational complexity because of combination of encoder and modulator in a single block and reasonable BER performance without dropping bandwidth utilization rate. The 1/2 rate trellis structure and 16-QAM modulation have been considered for the analysis. The BER vs. SNR plot is shown in Figure4, and it is found that, at 27 dB, the error rate is 10−6.Figure 4
BER vs. electrical SNR of OFDM-FSO system with TCM encoder.


### 2.4. System II: OFDM-FSO System with Hybrid Channel Codes

The system designed with the combination of two channel codes is shown in Figure2. As shown in figure, the other system arrangements are the same as given in Figure 1 except two channel codes are cascaded to make a hybrid system as the other codes are concatenated in [23, 24].The concatenation of error correcting codes is constructed to achieve copacetic performance with reasonable complexity. LDPC is opted because of better data compression capability, and TCM increases the bit rate by doubling the constellation points of the signal. The other system specifications are the same as the OFDM-FSO system discussed in Section2.1. The SNR vs. BER plot is shown in Figure 5. As predicted from the figure at 30 dB, the error rate is 10−8.Figure 5
BER vs. electrical SNR of OFDM-FSO system with hybrid LDPC-TCM encoder.


## 2.1. System I: OFDM-FSO System with Single Channel Coding

The system setup side is the same as it is done in wireless networks except it uses optical transmitters such as LASER and optical receivers such as photodetectors for communication. The SISO-based OFDM-FSO system, which has been considered in MATLAB, is shown in Figure1.Figure 1
Block diagram of OFDM-based FSO communication system [10].It consists of a transmitter, a receiver, and a free-space channel between them. The transmitter uses a random bit generator, FEC or channel encoder, interleaver, QAM modulator, IFFT, OFDM multiplexer, and an optical source (LASER) for transmission. The receiver section has OFDM demultiplexer, FFT, demodulator, deinterleaver, and decoder. Use of interleaver upsurges total delay because before the packets can be decoded, the entire interleaved block must be received. Also, the error’s structure has not been exposed by interleavers. The bit error rate (BER) has been analyzed at the receiver end. For channel modelling, the lognormal turbulence model is obliged.The wavelength used is 1550 nm due to its low attenuation characteristics. The system is designed with the use of OFDM network. The number of subcarriers used in the system is 4 because as the number of subcarriers increases, the SNR needed to achieve the required BER also increases [22].In OFDM, the required FFT/IFFT is calculated using 16 points. The simulation parameters considered in the proposed SISO model as depicted in Figures1 and 2 are given in Table 1.Figure 2
Block diagram of SISO OFDM-based FSO hybrid LDPC- and TCM-coded system.Table 1
System parameters used in the proposed model.
Parameter
Value
Coding rate
1/2
Coding scheme
LDPC, TCM, hybrid LDPC, and TCM
Modulation scheme
16-QAM
Encoding sequence
LDPC then TCM
Wavelength (λ)
1550 nm
Range (L)
1000 m
Refractive-index structure
Parameter (CN2)
0.75 ∗ 10−14


## 2.2. Design of the OFDM-FSO System with LDPC Encoder

Low-density parity-check (LDPC) codes are powerful channel (FEC) codes that enhance the constant size redundancy to correct random and burst errors [13]. Due to its various pros such as high code rate and low hardware complexity [11], LDPC codes are currently used in FSO communication and perform decent during strong turbulence. The LDPC code is a special linear group of codes with sparse parity-check matrix with N-K by N. Many methods have already been settled for the construction of parity-check matrix [13, 14]. The LDPC decoder halts when a permissible code word is found and significantly has a potential to reduce the effort. These codes are advantageous when considering long codes due to parallel implementation of decoders. In presented LDPC encoder, the matrix dimensions are 32400 : 64800 and the BER vs. SNR is shown in Figure 3. In the said system, an irregular LDPC code is used with code rate 1/2. From the results, it can be observed that, at 25 dB, the error rate of 10−6 is achieved.Figure 3
BER vs. electrical SNR of OFDM-FSO system with LDPC encoder.


## 2.3. Design of the OFDM-FSO System with TCM Encoder

TCM has lesser computational complexity because of combination of encoder and modulator in a single block and reasonable BER performance without dropping bandwidth utilization rate. The 1/2 rate trellis structure and 16-QAM modulation have been considered for the analysis. The BER vs. SNR plot is shown in Figure4, and it is found that, at 27 dB, the error rate is 10−6.Figure 4
BER vs. electrical SNR of OFDM-FSO system with TCM encoder.


## 2.4. System II: OFDM-FSO System with Hybrid Channel Codes

The system designed with the combination of two channel codes is shown in Figure2. As shown in figure, the other system arrangements are the same as given in Figure 1 except two channel codes are cascaded to make a hybrid system as the other codes are concatenated in [23, 24].The concatenation of error correcting codes is constructed to achieve copacetic performance with reasonable complexity. LDPC is opted because of better data compression capability, and TCM increases the bit rate by doubling the constellation points of the signal. The other system specifications are the same as the OFDM-FSO system discussed in Section2.1. The SNR vs. BER plot is shown in Figure 5. As predicted from the figure at 30 dB, the error rate is 10−8.Figure 5
BER vs. electrical SNR of OFDM-FSO system with hybrid LDPC-TCM encoder.


## 3. Results and Discussion

The results attained from various channel codes for weak turbulence conditions have been validated using MATLAB, and the scintillation has been modelled using the lognormal turbulence model. In the simulation, the Monte Carlo method has been adopted for the verification of results by random attempts.In the proposed hybrid coded system, the pair of single inner-outer encoders and decoders has been used for minimum component cost computational complexity, and synchronization issues. Using proposed hybrid coding scheme, the system’s reliability is increased having acceptable BER with reasonable computational complexity or delay latency. The various channel coding schemes under weak turbulent conditions are analyzed in the following section. The results of system model 1 and 2 are compared in Figure6.Figure 6
BER vs. electrical SNR of OFDM-FSO system with various channel codes using lognormal distribution.As expected, the system with proposed hybrid codes performs well as compared to individually coded system. In Figure6, the hybrid coded 16-QAM modulated system requires an SNR of 20 dB to attain a BER of 10−6, while the system with LDPC and TCM coded individually requires SNR of 25 dB and 27 dB, respectively. To offset the difficulty of applying systems, the performance difference can come out with the ensuing hybrid coded FSO system design.


## 4. Comparative Analysis under Different Turbulence Conditions

In this section, the performance estimation of various channel codes for OFDM-based FSO systems over weak turbulence conditions has been tabulated in Table2 in a compressed format. The table is representing the required SNR for achieving the BER of 10−6 with various coding schemes.Table 2
Comparative analysis of various coding schemes (required SNR for achieving BER of 10−6).
Coding scheme
SNR
TCM
27 dB
LDPC
25 dB
Hybrid
20 dB
Uncoded
30 dBForm Table2, it has been revealed that the proposed hybrid coding scheme gives the best performance among other considered coding schemes during weak turbulence. The different turbulence conditions affect the visibility, and hence, signal is attenuated which further causes the BER. Through simulations, significant improvement in performance has been obtained by concatenating LDPC codes with interleaved schemes of TCM codes over fading channels. The proposed hybrid coding has been compared with the LDPC and TCM coding with same trellis complexity and the uncoded systems with single antenna fading channels. As shown in Figure 6, with the proposed hybrid scheme, the BER of 10−9 is achieved at 30 dB of the SNR value during weak turbulence conditions, whereas BER of 10−8 and 10−7 has been achieved at 30 dB by using LDPC and TCM codes, respectively. The system has been simulated with MATLAB codes under various channel conditions using the lognormal distribution turbulence model.


## 5. Conclusion

Atmospheric turbulence comes out to be the major bottleneck in free-space optical communication systems and limiting its use in extended applications. Consistent research is being carried out for reducing these effects, and channel coding plays the most important role. This paper presented a unified channel coding scheme constituted by concatenation of irregular LDPC and TCM codes of 1/2 rate. They applied the advantages of LDPC and TCM codes to form less complex, reliable, and high-performance concatenated codes. For OFDM-based FSO system, different conventional channel coding schemes have been examined and compared with a new hybrid channel coding scheme. The OFDM-FSO system using the proposed scheme has been compared with the conventionally used coding schemes under weak turbulent conditions. The presented analysis of results indicates that, for attaining BER of 10−6, the required SNR for LDPC, TCM, and hybrid LDPC-TCM scheme is 25 dB, 27 dB, and 20 dB, respectively. The OFDM-FSO system designed with novel hybrid channel coding shows an improvement of 5 dB as compared to solo LDPC and 7 dB as compared to TCM alone. The comparison of results is done by simulating the system model using MATLAB codes.



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