Performance of generalized frequency division multiplexing over gamma gamma free space optical link
Introduction
Free space optical (FSO) communications is undergoing through intense study due to its advantages including larger bandwidth, lower power consumption, higher transmission rates, and better security over radio frequency (RF) communications [1], [2]. FSO links are recognized as a fundamental part of the development of future wireless networks since it can improve the system capacity [3]. On the other hand, atmospheric attenuation and turbulence due to changes in refractivity are disadvantages of FSO which may lead to the severe signal distortions [4].
In the literature, there are several channel models proposed to represent the random behavior of FSO links [5] to analyze the performance of the wireless systems. For example, log-normal distribution [6] can be used for weak turbulence levels, while K-distribution [7] and negative exponential [8] can characterize the strong turbulence conditions. Similarly, Malaga channel [9], [10] is another statistical model which results in mathematically intractable analysis in many scenarios. Gamma–Gamma (GG) distribution [11] is a product of two random variables for large scale and small scale optical wave fluctuations which can model moderate to strong turbulence levels. Since it is a generalized model including the K-distribution and negative exponential, it is widely used in the literature. Recently, the performance of coherent OFDM over GG channel model is studied in [12] where Reed–Solomon (RS) code is used to increase reliability. Feng et al. [12] investigates the performance of on–off keying over GG channel. Similarly, Torabi et al. [13] analyzes the outage and error probabilities for hybrid RF-FSO systems over GG link with pointing errors. Lately in [14], approximate and asymptotic expressions of the outage probability and BER in GG fading channel are derived.
OFDM transmission over FSO links is one of the special cases of multiple subcarrier modulation (MSM) as discussed in [15] in order to obtain high speed transmission. Firstly, the bit stream can be mapped into OFDM symbols and then modulated over independent subcarriers at different frequencies with the use of intensity modulation direct detection (IM/DD) technique. One of the advantages of MSM is that it does not require equalization, since the use of subcarriers allow to have narrowband signals carrying lower symbol rates [16]. OFDM is shown to be practically feasible to provide high throughput by using RGB-LED-based FSO communication system as presented by Krishnan et al. in [17]. Recently, the transmission performance of the OFDM over GG channel is investigated by considering nonlinearity of the laser diodes in [16]. An optical coherent OFDM-GG system is studied by [18] in which the phase error caused by the atmospheric turbulence is taken into account. In [19], the performance of the OFDM over GG channel with clipping noise is investigated. The performance of OFDM system is also investigated in exponential weibull fading channels with pointing errors [20]. The main drawback of the IM/DD MSM schemes is the optical power inefficiency which becomes a critical limiting factor for OFDM where a large number of subcarriers creates unfavorable high peak-to-average power ratio (PAPR) [21] even if some input data is left unmodulated. Frequency synchronization is another critical issue for OFDM system to preserve the orthogonality [22] especially when Doppler shift increases. In order to overcome these limitations of OFDM, generalized frequency division multiplexing (GFDM) has been proposed [23].
GFDM is a flexible multicarrier modulation scheme [24] with some advantages over OFDM. GFDM has single cyclic prefix (CP) part for the entire block which makes it spectrally more efficient than OFDM as CP has to be inserted after every OFDM symbol. Each block is processed by a digital filters which preserves the circular properties of the signals over time and frequency domains [25]. This process reduces OOB emissions and PAPR compared to OFDM [24] which lowers the adjacent channel interference and the constraints on power amplifiers [26], [27]. GFDM block structure can be shaped as desired to match the limitations of real-time applications by reducing the signal length [26] which makes it an attractive option for communication and radar applications [28]. Algorithms developed for OFDM and MIMO techniques can be easily adopted to GFDM as discussed in [26] and [29]. GFDM performance under synchronization errors has also been investigated to demonstrate its practicality by [30]. Receiver design for GFDM discussed in [31] has been tested for small values of subcarriers to increase the performance. Recently GFDM is studied over optical wireless communication (OWC) and wireless powered communication in [32] and [33] respectively. However, there is no previous work investigating the GFDM transmission over any FSO links.
The main contributions of this paper can be listed as follows:
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The closed form SEP expression of GFDM over GG turbulence channel is derived.
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The impact of pointing errors on SEP is explored.
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The outage probability performance with and without pointing errors are analyzed after obtaining the PDF of the instantaneous received SNR.
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The impact of non-zero boresight is also investigated.
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The theoretical results are verified with the Monte-Carlo simulations.
The remainder of this paper is organized as follows: Section 2 presents the GFDM system model over the GG channel. Closed form expressions for both of the symbol error and outage probabilities of the GFDM-FSO system are derived in Section 3. Section 4 discusses the numerical results and concluding remarks are given in Section 5.
Section snippets
System model
In GFDM transmission schemes, data is transmitted simultaneously over several narrowband subcarriers as illustrated in Fig. 1. The GFDM block consists of K subcarriers and M subsymbols. The total number of symbols in one block is given by N KM. In the system model, as shown in Fig. 1, data source provide binary data to a QAM symbol mapper which maps the bits into symbols by using valued complex constellation where is the modulation order. After mapping, a vector is obtained which
Performance of the GFDM-FSO system
The SEP and OP performances of GFDM-FSO system over GG channel are analyzed in this section.
Numerical results and discussion
In this section, theoretical SEP and OP expressions for GFDM over GG turbulence channel are compared with the Monte-Carlo simulation results. The GG channel parameters are similar to [18] that are ( and ) for moderate and ( and ) for strong turbulences levels by considering the link distance as km. Wavelength and aperture diameter is selected as 5 cm. Rytov variance and 1.35 are used to model moderate and strong turbulence. In order to simulate GFDM
Conclusion
The performance of GFDM over FSO links are investigated over the gamma gamma fading channel which can have weak to strong turbulence levels. The closed form expressions of the SEP with and without pointing errors are derived. Furthermore, the closed form expression of outage probability with and without pointing errors also investigated. Impact of turbulences on the outage probability as a function of received optical power and average SNR are illustrated with numerical examples. The results
CRediT authorship contribution statement
Muhammad Sameer Ahmed: Formal analysis, Investigation, Software, Data curation, Writing - original draft. Tansal Gucluoglu: Methodology, Conceptualization, Validation, Writing - review & editing, Supervision.
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