Performance Analysis of Hybrid FSO/RF Transmission Assisted Airborne Free-Space

Shiqi Wu,Shaoqian Li ,Yixiang Lin,Haijun Zhou

Abstract—This paper investigates the reliability problem of airborne free-space optical(FSO)communications,and a hybrid FSO/radio frequency(RF)communication system with parallel transmission is proposed,where the data stream is transmitted over both FSO and RF links simultaneously.Further,to combat channel fading,maximal ratio combining is utilized at the receiver for combining received signals from both links.The performances of the proposed system are analytically derived in terms of the outage probability and the average bite-error rate(BER).Numerical results show that the proposed hybrid FSO/RF system with parallel transmission outperforms a single airborne FSO or a single RF link,which provides technical guidance for designing reliable high-speed airborne communication systems.

Keywords—FSO,hybrid FSO/RF,pointing error,outage probability,bit-error rate

I.INTRODUCTION

The application of airborne-assisted free-space optical(FSO)communication such as front hauling in 5G networks,fast transmission of high-resolution and large-volume data,etc.,has recently attracted increasing attention due to its merit of easy deployment,low cost,flexible configuration,and the possibility of a better channel state[1-3].Different from conventional radio frequency(RF)communications,the FSO communication can better exploit the advantage of highbandwidth,license-free,high security,and immunity to jamming and interference.In 2016,a recorded FSO data transmission of 1.72 Tbit/s over a distance of 10.45 km has been demonstrated by the German Aerospace Center in Ref.[4].Also,the FSO communication is investigated and flight-tested for networking aerial platforms since link blockage in terrestrial FSO seldom occurs in airborne FSO communication[5-8].In 2021,the Mynaric in combination with H3 HATS has successfully demonstrated a bidirectional air-to-ground FSO communication at 10 Gbit/s in Ref.[9],which boosts the market of airborne FSO communication.

In airborne FSO communication,the transmission performance suffers from atmospheric turbulence along long transmission distance,atmospheric attenuation by adverse weather conditions,e.g.,fog,snow,and smog,and pointing errors due to misalignment or vibrations[10-14].To enhance the reliability of the airborne FSO link,an RF link based on the millimeter wave(MMW)with comparable data rate is often suggested along with the FSO link.As for the RF link,it is less sensitive to the attenuation by fog or smog,the loss by pointing error,and the fading due to atmospheric turbulence.However,the RF link is more sensitive to rain and small-scale fading,which leads to the RF link performance degradation in rainy environment[15-17].

To exploit the complementary characteristics in each sublink,the hybrid architecture of the FSO link in parallel with the RF link is often applied to improve the overall performance[11-17].In these existing hybrid schemes,the receiver needs to measure the channel state information(CSI)of the FSO link frequently and sends a feedback signal to activate the RF link,which leads to frequent channel switching and reduces communication efficiency[15-18].Further,this could not be easily realized in airborne FSO communication since the CSIs of both the FSO and the RF links change frequently at the high-speed flight,which makes it prohibitively difficult to update CSIs timely.

In this paper,we propose a parallel data transmission scheme over both the FSO and the RF link in the airborne hybrid FSO/RF communication system.In order to maximize the channel spectrum utilization and combat the channel fading,a maximal ratio combing scheme is carried out at the receiver.As for the airborne FSO channel,a generalized Gamma-Gamma distribution is assumed considering that not only the line-of-sight(LOS)component but also non-LOS components exist due to the cloudy channel state in airborne communication.Also,the impact of pointing error is considered as the effect of misalignment and vibration in the airborne platform.For the airborne RF link,the Rician fading channel is considered because the presence of the line-of-sight component is utilized for MMW propagation.Based on the proposed hybrid FSO/RF system,the outage probability and the average bit-error-rate(BER)are analytically derived by the moment generating function in Meijer’s G function.Through numerical simulations,performances of outage and average BER is analyzed,which show that the reliability of the airborne FSO communication can be enhanced by the proposed parallel data transmission scheme.

II.FSO/RF SYSTEM AND CHANNEL MODELS

The hybrid FSO/RF system with a single threshold is considered in this paper,as illustrated in Fig.1.At the transmitter,the information stream is modulated using M-ary Phase Shift Keying(M-PSK)modulation and then fed to both the FSO and RF subsystems.Owing to complimentary transmission characteristics,the RF and the FSO links are simultaneously utilized.At the receiver,the data demodulated from both links are adaptively combined with the MRC.

Fig.1 The proposed hybrid FSO/RF system in airborne FSO communication.At the transmitter,the in-formation stream is modulated using M-PSK and then transmitted through the FSO and RF links.Both the FSO and the RF transmission channels are assumed to be slowly changed,and hence the CSIs of both channels can be obtained at the receiver

A.FSO Subsystem

According to reported airborne laser communication tests[19-21],the sub-carrier intensity modulation based M-ary phase-shift-keying(SIM-MPSK)scheme is adopted for the FSO subsystem.At the FSO transmitter,a direct current(DC)bias is added to the original electrical data stream to avoid power clipping while the laser intensity is modulated.Then the modulated laser signal is power amplified and transmitted through the FSO channel.At the FSO receiver,the optical signal is detected in timet,rFSO[t],and then further demodulated to recover the original data stream,given by whereRis the optical-to-electrical responsibility,Iis the irradiance intensity of the FSO subsystem considering the FSO channel effect,x[t]is the transmitted data,andnFSOis the additive white Gaussian noise(AWGN)with a variance ofσ2FSOand zero mean.Accounting for FSO channel effects and system parameters,the equivalent discrete-time baseband signal in thekthbit is given by

wherePFSOis the transmitted laser power,GFSOis the FSO channel gain effect relating to transceiver optical gain and coupling loss effects,hFSOaccounts for the normalized FSO channel fading effects.Even the transmission characteristic of the airborne FSO channel is complicated,it is mainly determined by

wherehlis the atmospheric attenuation due to the atmospheric scattering and absorption,harepresents the optical intensity scintillation due to atmospheric turbulence effect,andhpdenotes the pointing error impairment by platform vibration,misalignment,etc.

1)Atmospheric Attenuation:According to laser transmission experiment[19-21],the atmospheric attenuation is deterministic and changes slowly at a time scale of tens of minutes,and can be normalized to unity for simplification.

2)Atmospheric Turbulence:As for the FSO channel fading in airborne laser communication,not only the atmospheric turbulence but also the optical scattering effect of cloud should be considered[21,22].Considering the co-existence of the LOS component and scattered components in airborne FSO channel within a wide range of atmospheric turbulence from weak to strong,the Gamma-Gamma distribution is selected,and the PDF is given as

whereKv(·),Γ(·)are thevth order modified Bessel function of the second kind and Gamma function,respectively.αandβare the shaping parameters,representing the FSO channel fading due to the large-scale scattering effect and the smallscale scattering effect,respectively.By assuming a spherical wave propagation,the parametersαandβrelating to the FSO transmission characteristics are given by

3)Pointing Error:In the airborne FSO communication,the LOS alignment between the transmitter and receiver is achieved by the pointing,acquisition,and tracking(PAT)system in Ref.[8].However,there always exists pointing error caused by the noise of the PAT system,vibrations of the airborne platform,beam wandering due to atmospheric turbulence.In general,the pointing error impairment is widely modeled as Rayleigh distribution[23,24],with the probability density function(PDF)ofhlexpressed as

whereξ=wZeq/2σsis the ratio of the equivalent beam radius at the receiver to the standard deviation of pointing error displacement at the receiver.A0is the maximum collected power fraction,given byA0=[erf(v)]2,where,ais the radius of receiver aperture,wzis the beam waist radius,and erf(·)is the error function.

4)Composited FSO Channel Model:As the above factors are statistically independent in airborne FSO channel,the joint distribution of the airborne FSO channel is calculated by utilizing

By using the PDFs ofhaandhpfrom(4)to(6),the PDF of the composited FSO channel is then derived as[23-25]

III.RF SUBSYSTEM

At the transmitter of the RF subsystem,the electrical phase shift keying(PSK)-modulated data stream is up-converted to MMW RF carrier frequency(i.e.,5 GHz[11],15 GHz[26],60 GHz[18],80 GHz[27],etc.)before transmission.In this way,a LOS transmission is applied for the RF signal transmission as similar to Ref.[11].At the receiver,the MMW signal is down-converted and demodulated,and the output signalrRFis expressed as

wherehRFaccounts for the RF channel fading and loss factors,x[t]is the transmitted signal,andnRFis the electrical noise.

Furthermore,the discrete-time equivalent baseband signal is given as

wherePTx,RFis the transmitted RF power,GRFis the average power gain,hRFis the RF channel fading gain withE[h2RF]normalized to unity,andnRF[k]is the additive Gaussian noise with varianceσ2n,RF.

Accounting for the propagation of MMW,the attenuation by oxygen and rain should not be omitted.The average power gainGRFis then defined as

whereGTandGRdenote the transmitter and receiver antenna gain,respectively,λRFrepresents the MMW wavelength,L(km)is the transmission distance,andαoxy[dB|km]andαrain[dB|km]are the RF signal power loss coefficient caused by oxygen absorption and rain,respectively.

As the LOS component is utilized for MMW propagation,it is preferred to model the RF channel fading[25,28],hRF,to be Rician distribution,and its PDF is given by

whereI0(·)is the zeroth-order modified Bessel function of the first kind,Kis the Rician parameter representing the relative strength of the LOS component of the MMW fading coefficient.In general,the lower the Rician parameter is,the more severer the MMW fading becomes.

IV.PERFORMANCE OF THE HYBRID FSO/RF SYSTEM

A.Statistical Properties

The hybrid FSO/RF channel can be treated as a pair of parallel channels since both the FSO and the RF links operate at vastly different carrier frequencies and behave independently.To extend the analysis of statistical properties,the PDFs of signal-to-noise ratio(SNR)and the cumulative distribution functions(CDFs)of SNR are analyzed in the next.

1)SNR Statistics:According to the intensity detection,the instantaneous received SNR of the FSO subsystem is expressed asγFSO=[RPTGFSOhFSO]2/σ2n,FSO,and the average electrical SNR is given by.Taking the impacts of FSO channel,the expectation of the FSO channel fading is calculated asE[h2]=A20h2l ξ4/(1+ξ2)2.By applying power transformation ofas in Ref.[28],the PDF of the instantaneous SNR is

Similarly,the instantaneous received SNR of the RF subsystem is obtained asγRF=γ0,RFh2RF,with its average SNR to beγ0,RF=PTx,RFGRF/σ2n,RF.According to Refs.[10-13],the PDF ofγRFis then expressed as

2)CDF Statistics:The CDF of instantaneous SNR is given by

wherefγ(γ)is the channel PDF,andγthis the threshold of instantaneous SNR.

For the FSO subsystem,the CDF is derived by substituting(13)into(15)and using algebraic manipulations[28-30],leading to

To be similar to Ref.[29],the CDF of the RF subsystem can be expressed as

whereQ1(·)represents the first-order Marcum-Q function.

B.Outage Probability

At a given transmission rate,Pout=Pr(C(γ)＜Rb),the reliability of the transmission can be evaluated by the outage probability as in Ref.[23],whereC(Rb)is the instantaneous capacity of the fading channel,Rbis the transmission rate.In this way,the outage probability can be obtained as

whereγth=C-1(Rb)is the threshold of the SNR required at the data rate ofRb.Hence,the outage probability of both the FSO and the RF links can be evaluated with its CDF.

As for the hybrid FSO/RF system,an outage occurs only if the SNRs of both links are below their respective threshold.Owing to the parallel transmission property,the outage probability of the hybrid FSO/RF system,PHybridout,is calculated by

wherePoFuStO(·)andPoRuFt(·)stands for the outage of the individual FSO and RF links,which are given by(16)and(17),respectively.

C.BER Performance

At the receiver end,the output signals from both links can be combined to be more resilient against transmission impairments.The average BER is computed by averaging the conditional probability of bit error,Pb(e|γ),over the SNRγ.Therefore,the average BER denoted asPb(e)is expressed as

1)BER for Single FSO Link:The average BER for the FSO link is derived by

whereis the conditional BER of M-PSK modulation is defined in Ref.[29].Specifically,A=1,B=1 for SIM-BPSK modulation andA=2/lbM,B=sin(π/M)for SIM-MPSK modulation.By substituting(13)into(21)[29,30],the average BER in analytical form for SIM-BPSK is derived as

2)BER for Single RF Link:In similar,by substituting(14)into(20)and utilizing power series of Bessel function from Ref.[31],the exact BER of the RF link with MPSK can be derived as

3)BER for Hybrid FSO/RF Link:To utilize the diversity gain of the two subsystems effectively,the received signals of each subsystem are combined by the maximal ratio combing(MRC)scheme as in Ref.[29].As a consequence,the output SNR of the MRC is obtained as

The average BER of the MRC combing is then given by

However,the above integral is difficult to be given in closed-form even only two-dimensional integration is involved.Alternatively,we select the moment generating function(MGF)method for performance analysis with the MRC,given by

whereΘ=π(M-1)/M,cMPSK=sin2(π/M),andMγMRC(s)is the MGF defined byAs the two subsystems behave statistically independent,the MGF of the MRC output can be given byMγMRC(s)=MγFSO(s)MγRF(s),within whichMγFSO(s)andMγRF(s)stand for the MGF of the FSO and the RF subsystem,respectively.

Accordingly,the MGF of the FSO link is now given by

By substituting(13),the MGF of the FSO link is then derived as

Similarly,the MGF of the RF subsystem is derived as

Therefore,the average BER of the hybrid FSO/RF system can be numerically analyzed with(28)and(29)as in the following

It should be noted that the average BER of the MRC output is now reduced to a single integral form,which is convenient to use a standard numerical approach,e.g.,Gauss-Chebyshev quadrature(GCQ)formula as in Ref.[29].

V.NUMERICAL RESULTS

In this section,numerical calculations on the outage probability and the average BER are illustrated for performance analysis.In the airborne FSO subsystem,the laser wavelength of 1 550 nm and the output power of less than 33 dBm are selected for eye safety.As for the FSO channel,the refraction structure parameter of atmospheric turbulence is set asC2n=1.9×10-17for a typical link distance ofL=100 km.Aided by the Rytov variance[19-22],the effects of atmospheric turbulence are related to parametersαandβ,which are set toα=3.64,β=1.94.For the RF subsystem,the Rician factor isK=6 dB for a typical airborne RF link.

The performances of the outage probability are shown in Fig.2,where three different scenarios are incorporated including FSO link only,RF link only,and hybrid FSO/RF.In Fig.2(a),the outage probabilities for the FSO link only with different levels of pointing error are given with respect to the outage SNR threshold.At first sight,it shows that the outage probability of the FSO link is gradually deteriorated by the impact of pointing errors(pe).Even when the effect of pointing error is negligible,i.e.,ξ=6.7,the FSO link tends to be outage due to the atmospheric turbulence.On the contrary,the hybrid FSO/RF system gives much better outage performance than using either a single FSO or a single RF subsystem,as shown in Fig.2(b).Due to the less probability of being outage for the RF link when the FSO link is becoming unstable,the reliability of the hybrid system is improved with the decrease of SNR thresholdγth.

Fig.2 The outage probability of the hybrid FSO/RF system vs.SNR threshold:(a)The outage probability for the FSO subsystem with the impact of pointing error;(b)The outage probabilities for the FSO link only,the RF link only and the hybrid FSO/RF link with parallel transmission

In Fig.3(a),the impact of pointing error on the BER probability of the FSO subsystem is demonstrated.When the value ofξ=wZeq/2σsincreases,the effect of pointing error is weakened and the BER performance is thus improved.Thus,it requires thatwZeq≈15σsfor negligible effect of the pointing error(ξ=6.7).For a typical airborne FSO link with pointing error,ξ=1.5 is utilized for performance analysis.

Fig.3 Average BER of the hybrid FSO/RF system vs.SNR:(a)The impact of pointing error on the FSO link is considered;(b)The case of the FSO link only,the RF link only and the hybrid FSO/RF link are considered.To ease performance comparison,the BPSK modulation is applied.It can be easily updated to QPSK or M-PSK modulation,but it is beyond the scope of the discussion

In this way,the BER performance of the hybrid FSO/RF is carried out in Fig.3(b).When only the FSO link is applied for high-speed transmission,the average BER is larger than 10-2even at the SNR higher than 30 dB,which would be highly vulnerable in presence of atmospheric turbulence and pointing errors.When only the RF link is applied for low-speed transmission,the average BER value is below 10-2when the SNR is roughly above 8 dB.For the parallel transmission of both FSO and RF signal along with the MRC at the receiver,the BER performance can be enhanced by the reliable RF link when the FSO link is becoming unreliable.Therefore,the hybrid FSO/RF system efficiently exploits the complementary nature of RF and FSO links and gives a more reliable performance for data transmission.

VI.CONCLUSIONS

In this paper,a hybrid FSO/RF communication system with parallel transmission is proposed,and the corresponding performances are analyzed in terms of the outage probability and average BER.Specifically,to model the airborne communication channel state,the FSO link is modeled as Gamma-Gamma turbulence distribution with pointing errors and the RF link experiences the Rician fading.In order to exploit the complementary properties of the FSO and RF channels,the MRC scheme is applied at the receiver.Based on the diversity reception,the outage probability,and average BER probability in analytical form are derived.Numerical results show that the hybrid FSO/RF communication system outperforms a single FSO link or RF only link,which improves the reliability of the airborne FSO communications.