Importance of noise models in FSO communications
© Khan; licensee Springer. 2014
Received: 30 January 2014
Accepted: 26 May 2014
Published: 19 June 2014
Free-space optical (FSO) communication is an emerging technology which offers enormous bandwidth, license-free spectrum and highly secure link. Avalanche photodiodes (APD) are normally used for the detection of high-speed FSO signals, where the noise shows signal-dependent Gaussian noise (SDGN) distribution rather than the signal-independent Gaussian noise (SIGN) distribution. We investigate the use of on-off keying (OOK) and low density parity check (LDPC) code on the performance of a FSO communication system. We also provide a good comparison of FSO communication noise models considering a moderate atmospheric turbulence condition. We show that large gains are possible using an LDPC decoder (i.e. at a bit error rate of 10-3, there is a gain of about 6 dB considering the SDGN model in case of no turbulence condition at λ = 10 dB), when the channel state information (CSI) is known at the receiver. We develop an extrinsic information transfer (EXIT) chart to measure the decoder convergence with and without the effect of turbulence noise. It is also shown that the SDGN model should be considered for the optimum detection with significant gain of 2.5 dB at λ = 0 dB and about 1 dB at λ = 10 dB.
Free-space optical (FSO) communication systems are capable of providing high data transmission rates and have received considerable attention during the past few years in many applications - satellite communications, fibre backup, RF-wireless back haul and last mile connectivity. In practice, the FSO communication link availability becomes limited during foggy weather and heavy snow fall[2–5]. The FSO signal intensity undergoes random fluctuation due to the atmospheric turbulence, known as scintillation. Scintillation causes performance degradation and possible loss of connectivity. These drawbacks pose the main challenge for the FSO communication system deployment. The desire to mitigate these drawbacks has generated studies of coding systems in a manner similar to their radio frequency (RF) counterparts that can improve the system performance[6, 7].
Low density parity check (LDPC) code was first introduced by Gallager in 1962, and its performance is nearly close to the Shannon limits. The performance of the LDPC code is better than Turbo codes with iterative decoding algorithms which are easy to implement with lower decoding complexity. The LDPC code of any rate and block length can also be created easily by just changing the shape of the parity check matrix. The rate adaptability in the LDPC code can be obtained easily compared to other codes. The LDPC code has the feature of parallelism for supporting different speeds, performances and memory consumption. It is therefore better to consider the LDPC code for FSO communications because of its capacity approaching performance and comparatively easy implementation.
The detection of weak signals in the FSO communication is dominated by the presence of dark current due to the background noise. This problem can be overcome by using the avalanche photodiode (APD) which amplifies the electrical current due to the internal current gain. The APD gain allows the reduction or elimination of noisy external amplifiers. APDs are easily available for a wide range of wavelengths. These APDs can measure even lower level light signals and are used in a wide variety of applications requiring high sensitivity. APDs are incorporated in many high-performance FSO communication applications because they enable high signal-to-noise ratio (SNR). APDs are preferred over positive-intrinsic-negative (PIN) diodes due to their high internal gain characteristics and improved SNR capability.
In this paper, we study the signal-independent Gaussian noise (SIGN) and signal-dependent Gaussian noise (SDGN) models for the FSO communication and develop a comparison between these noise models. We also develop an error analysis along with the effects of the background noise level in both models. We performed the novel investigations of log-likelihood ratio (LLR) mappings for the SDGN and SIGN model taking into account the effect of scintillation. We are not aware of such existing coded and uncoded error analysis comparison. A decoding convergence behaviour (i.e. extrinsic information transfer (EXIT) chart) for the SDGN and SIGN models is also provided. The proposed conceptual study using the LDPC code and EXIT chart has not been introduced for such noise models.
We incorporate the implementation of APDs (i.e. considering the InGaAs APD) for the FSO communication system and present new results for the uncoded and coded bit error rate (BER) considering SDGN and SIGN models. In this paper, the communication system of interest is the same as that analysed by (see references therein). However, the combined photodetection (PD) shot noise and the thermal noise of the APD has been considered as the SDGN and compared with the SIGN model. We assume both cases (i.e. with and without scintillation), and the transmitter and receiver are perfectly aligned. In our simulation, we assume that the channel state information (CSI) is known at the receiver.
The remainder of this paper is organized as follows. In Section 2, we present the system model, which provides the SDGN/SIGN model for the FSO communication system. Section 3 discusses the structure of the LDPC code used for the performance improvement of the FSO communication system under atmospheric turbulence condition. It also provides the main results of LLR mappings for the SDGN and SIGN models. The EXIT chart analysis is given in Section 4. Simulation results for the uncoded/coded BER and the EXIT chart are presented in Section 5. Section 6 provides the final concluding remarks.
2 System model
2.1 SDGN and SIGN models
where μ lnh and are the mean and variance of the logarithm of h. It is assumed that E[h] = 1 so that the average received optical power remains constant, and from the moments of the LN distribution, it follows that and, where is the scintillation index (SI) defined in. In, we relate physical parameters of the APD with statistical parameters of the SDGN model by saying and. The relationship shows the dependence of statistical parameters (i.e. μ x and) on physical parameters (i.e. G and F) of the APD.
For an APD detector, parameters used are the APD internal current gain G, keff and quantum efficiency η. We relate physical parameters of the APD with our signal model for the Gaussian approximation: μ0 ≈ λ G, μ1 ≈ (λ + P h)G,,. In, we simulate density functions for the Webb and SDGN model considering the InGaAs APD with G = 10, keff = 0.45 and F = 5.5. Simulation results in show the agreement between the Webb and SDGN model near peaks of distributions. These results illustrate the simulation results of the effect of varying background level for the SDGN and SIGN models which are referred to in Section 5.
2.2 Channel model
where. The LLR mappings are analysed so that we can use the LLR mappings for the calculation of the uncoded and coded BER.
3 Low density parity check code
3.1 Uncoded BER
Considering a typical FSO communication system, the information signal from the laser is directed towards the optical receiver along the line-of-sight path. At the receiver, we perform soft demodulation of the received signal, which is to be considered in the form of LLR mappings. We consider the signal presence or absence according to the detection threshold, which we derived in for the SDGN model. For the SIGN model, we consider the decision threshold midway between the mean of the two signal distributions.
To begin, we derive the LLR expression for the SDGN and SIGN models using the OOK modulation scheme. In order to calculate the uncoded BER of the FSO communication system shown in Figure1, we need to make some assumptions for the SDGN modelb. In, we assume a simplistic Poisson approximation in the derivation of LLR mappings for the optimum detector. On the basis of our defined model, we define the maximum likelihood decision (MLD) rule which maximizes the probability of a given sequence of observations corresponding to some threshold value for OOK.
3.1.1 SDGN LLR mapping
3.1.2 SIGN LLR mapping
3.2 Coded BER
Once we derived the soft values, i.e. LLR mappings for the SDGN and SIGN model in subsections 3.1.1 and 3.1.2, we pass those values to the decoder to decode the message and evaluate the probability of bit error. For the decoding purpose, we use the same SPA algorithm proposed in[7, 8].
4 SDGN/SIGN EXIT curves
In the FSO communication system, an information sequence is encoded into a bit stream considering the FSO channel symbol. Then, the received signals are demapped as shown in Figure3. Demapping is an important step before soft decision decoding. The FSO demapper needs to be designed to demap the received signals. The LLR demapping algorithm proposed in works well in traditional uniform modulations, but they result in channel capacity loss. Therefore, the iterative demapping algorithm derived by ten Brink in with a priori knowledge of other bits corresponding to the same bits was employed in many systems.
where L v denotes the channel LLR (i.e. either the ΛSDGN and/or ΛSIGN). The main components of the EXIT chart curves are the EXIT functions of the component decoder, which relates the a priori MI (I AV ,I AC ) at the input and the extrinsic MI (I EV ,I EC ) at the output of component decoder as we described in. We can measure the extrinsic MI (I EC ) of the check node decoder using (6) in.
5 Simulation results
To analyse the BER performance of the SDGN and SIGN models for the OOK, we conduct a number of Monte Carlo simulations. For the SDGN and SIGN detection, each trial involved generating a block of random OOK symbols. We are computing the respective LLRs for the OOK, making soft decisions and finally counting the number of bit errors. These results are performed with and without considering the effect of scintillation. The signal-to-noise ratio (SNR) is calculated on the basis of.
We present simulation results for the background level of 0 and 10 dB because we want to compare the performance of the APD detector for a very low to moderate background level. We developed such sort of analysis for various values of background level in considering the PIN photodiode. We measure the effect of background level on the system performance and provide a good insight for the evaluation of SDGN and SIGN models. After looking into the simulation results for low and moderate background levels, we can see that the SDGN model can be approximated by SIGN at high background levels (i.e. the difference in performance in terms of BER between the SIGN and SDGN models is decreasing by increasing the background level, which is 1 dB at BER = 10-3 for λ = 10 dB). It is also noted that the SDGN model performs better compared to the SIGN model in terms of improving SNR under low background levels, which is 2.5 dB at BER = 10-3 for λ = 0 dB.
Comparison of SDGN/SIGN models at a BER of 10 -3 for the uncoded system
Without atmospheric turbulence effect (SI = 0)
SIGN model SNR (dB)
SDGN model SNR (dB)
With atmospheric turbulence effect (SI = 1)
SIGN model SNR (dB)
SDGN model SNR (dB)
We analyse the uncoded and coded BER for the proposed SDGN and SIGN models and investigate the performance of the LDPC code considering the OOK modulation scheme. New results for LLR mappings have been derived for both the SDGN and SIGN models. It is seen from the simulation results that we can get better performance for the SDGN than the SIGN model under low background levels. The performance of the SDGN model can further be increased by coding gains using the LDPC decoder. We can conclude that for a large number of background levels, the SDGN model can be approximated by the SIGN model, but at low background levels, the SDGN model should be used. The proposed research work can be extended for the hybrid FSO/RF communication under the consideration of different channel models.
aWe say the optimum detection when the noise variance is dependent on the input bits, and sub-optimum when the noise variance is independent of the input bits.
bVariance in the signal slot is greater than the variance in the non-signal slot.
The author would like to thank Prof. Bill Cowley and Dr. Khoa D. Nguyen from the Institute for Telecommunication Research, South Australia for the thorough discussion and help in fulfilling this task and Dr. N. Letzepis from DSTO for providing helpful support and useful suggestions during the course of investigation.
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