SER performance analysis of MPPM FSO system with three decision thresholds over exponentiated Weibull fading channels
Introduction
In these years, free-space optical (FSO) communication has received increasing attentions for its applications in high speed wireless links as a cost-effective, license-free, high security and high bandwidth access technology compared with traditional radio frequency (RF) communication [1], [2]. However, the performance of FSO system will be severely affected by the scintillation due to the intensity fluctuations at the received signal by atmospheric turbulence [3], [4]. In order to improve the system performance in the presence of turbulence, a variety of techniques were proposed, among which spatial diversity and aperture averaging have been extensively investigated [5], [6], [7], [8]. For spatial diversity, multiple transmitters and receivers are normally required although it is an attractive method to mitigate fading of the received signals [5], [6]. Aperture averaging technique, however, is another effective approach to enhance the FSO system performance for its simplicity and low cost. As known, when the aperture diameter of an optical receiver is larger than the spatial scale of the optical scintillations induced by atmospheric turbulence, the fluctuations of the received waveform over the aperture area will be averaged by the receiver and the signal fluctuations will be further reduced compared with a point receiver [7], [8]. For the turbulence-induced fading, a lot of statistical distributions have been reported to analyze the fading process in the FSO system. The Lognormal (LN) and the Gamma–Gamma (GG) distributions are the most widely accepted fading models [9], [10], [11]. Particularly, both of them have been used to study the effects of aperture averaging [7], [12]. Recently, one novel fading model named exponentiated Weibull (EW) distribution was proposed by Ricardo Barrios and Federico Dios [13], [14]. Their studies show that EW distribution fits more accurately with the actual PDF data than GG and LN distributions under all aperture averaging conditions and weak-to-strong turbulence regime [14]. After that, the error performance of OOK and BPSK modulated FSO systems over EW fading channels has been further investigated by [15], [16], [17] with the effect of aperture averaging taken into account. OOK and BPSK are two important modulation schemes extensively used in many existing works while both of them actually have lower power efficiency for practical FSO applications compared to pulse position modulation (PPM). PPM is an orthogonal modulation scheme that offers a decrease in average-power requirement at the expense of an increased bandwidth [18]. Multipulse PPM (MPPM) can significantly improve the band-utilization efficiency of optical PPM and it could be a compromise between OOK and PPM [19]. The closed-form expression for the average BER of variable weight MPPM FSO system over GG fading channels has been proposed by [20]. This study was based on hyperexponential fitting and Monte Carlo simulations. Furthermore, the performance of FSO communication system with MPPM technique was investigated under GG distribution considering receiver noise. The analysis of shot noise was based on the method of photon counting [21]. However, there are no published works on the error performance of MPPM based FSO systems over the EW fading channels up to now, to the best of our knowledge.
Motivated by the above analysis, the SER performance of MPPM based FSO signals transmission over EW turbulence channels has been studied in this paper with three decision thresholds employed. With the aperture averaging effect considered, the system performances of fixed, optimized and dynamic decision thresholds are compared analytically and numerically.
Section snippets
System model and SER analysis
Fig. 1 shows the block diagram of the studied FSO system. In it, the binary data stream is fed into an electrical digital modulator. The modulated electrical signal is then used to modulate a laser. The modulated laser beam will propagate through the atmospheric channel and be interfered by the turbulence. After transmitting through the optical lens of the optical receiver, the laser beam impinges on the surface of the photodetector, in which the light intensity is changed into electrical
Results and discussion
In this section, under different receiver apertures and turbulence conditions, the SER performance of three kinds of decision thresholds have been investigated both analytically and numerically. It is believed that the shape parameter α for the EW distribution is somehow affected by the ratio and/or the Rytov variance [9]. Here, D is the receiver aperture size and is the atmospheric coherence radius. is defined as . and are the refractive-index
Conclusion
In summary, the SER performance of MPPM based FSO system with three decision thresholds under EW distribution is discussed. The closed-form expressions of the average SERs for three decision thresholds were derived with the help of the generalized Gauss–Laguerre quadrature rule and the analytical results fit well with Monte Carlo simulations. The studies show that the FDT scheme will result in error floor under all receiver apertures, the error floor can be reduced by reducing the fixed
Acknowledgments
This work has been supported by the National Natural Science Foundation of China (Grant no. 61474090), the Nature Science Basic Research Plan in Shaanxi Province of China (Grant no. 2014JM8340), and the Fundamental Research Funds for the Central Universities (Grant no. NSIY041404) and this work is also partly supported by 111 Project of China (B08038).
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