Precise Performance Analysis of Dual-Hop Mixed RF/Unified-FSO DF Relaying With Heterodyne Detection and Two IM-DD Channel Models

Abstract

This paper provides precise performance analysis of the dual-hop mixed radio frequency (RF)/unified free space optical (FSO) decode-and-forward (DF) relaying system, in which the heterodyne detection and the intensity modulation-direct detection (IM-DD) are taken into account for FSO detection. To this end, we derive closed-form expressions for the outage probability, average bit error rate (BER), and the ergodic channel capacity of this system. In this analysis, we utilize, for the first time as per our knowledge, a precise channel capacity result for the IM-DD channel. Moreover, this is the first time that not only the (IM-DD input-independent) but also the (IM-DD cost-dependent) additive white Gaussian noise (AWGN) channel is considered in such system analyses. Additionally in this study, we assume that the first hop (RF link) follows Nakagami-m fading, and the second hop (FSO link) follows Málaga (M) turbulence with pointing errors. These fading and turbulence models contain other models (such as Rayleigh and Gamma-Gamma) as special cases, thus, our analyses can be seen as a generalized one from the RF and FSO fading models point of view. Also, in BER derivation, we assume that the modulation schemes in the two hops can be different, since not all modulation schemes are suitable for IM-DD FSO links. In addition, the system performance is investigated asymptotically at high signal to noise ratios. This investigation leads to new nonreported coding gain and diversity order analyses of such system. Interestingly, we find that in the FSO hop, at high transmitted powers, all the considered FSO detectors result in the same diversity order. Furthermore, we provide simulation results that verify the accuracy of the obtained analytical and asymptotic expressions.

Performance Analysis of Mixed Interference Aligned MIMO RF/Unified FSO DF Relaying With Heterodyne Detection and Two IMDD Models

“…This fading is a result of the atmospheric turbulence and pointing error in the relaydestination channel. In (14), n HD ∼ CN (0, N HD ) is a complex AWGN. Whilst in (15), n IMDD is a real AWGN where n IMDD ∼ N (0, N IMDD ) for the IMDD input-independent AWGN model, and n IMDD ∼ N (0, 2P r I FSO N HD E{x IMDD }) for the IMDD cost-dependent AWGN channel under the assumption of relatively high P r in comparison with the thermal and/or background noises power.…”

“…In the development of the M fading channel [30], the received signal is assumed to be consisted of a LOS component (U L ), a component coupled to the LOS and scattered by eddies on the propagation axis (U C S ), and a component scattered by off-axis eddies (U G S ) that is statistically independent from U L and U C S . Thus by assuming the M fading with pointing mismatch in the FSO channel, the probability density functions (pdfs) of the prior mentioned SNRs in (16) is given in the following unified formula [14]…”

“…, (17) where γ FSO represents the unified SNR of the FSO channel, A and b m are as in [14,Eq. (6)], α is positive parameter and it is related to the effective number of the large-scale cells of the scattering (fading) process, β is a natural number and it is related to the effective number of the small-scale cells of the fading process, 2…”

“…} is the average power of all scattered components, g = E{|U G S | 2 } = 2b 0 (1 − ρ), the parameter 0 ≤ ρ ≤ 1 denotes the part of the scattered power coupled to the LOS, ζ is the ratio between the equivalent beam radius and the standard deviation of the pointing error displacement at the receiver (i.e. ζ → ∞, indicates the nonpointing error case) [32], A 0 is a parameter that represents the pointing losses (or typically the FSO link losses), s and w are the parameters which determine the sort of the FSO detections, i.e., (s, w)=(1, 1), (2, 1) or (1, 2) for the HD, IMDD input-independent, and IMDD cost-dependent respectively, and where µ 1 3 and for normalization purposes µ 2 P 2 r E 2 {I FSO }/N IMDD as defined previously in [14] and the references therein. This definition leads to µ…”

“…Nevertheless, a main problem noticed in the AF mixed RF/FSO relaying systems, as in [4]- [13], is that they do not fulfill the nonnegativity constraint in the FSO IMDD transmitted signal, even when the subcarrier intensity modulation (SIM) is adopted in them. Namely, in those AF systems the relay receives a bipolar unbounded signal, which can not become positive, for the purpose of IMDD transmission, by mere amplification and/or deploying a DC bias [14]. As a result, the mathematical model and the findings of the above AF researches do not provide the real performance of these AF mixed RF/FSO relayings in which IMDD is implemented.…”