Airplane-Aided Integrated Next-Generation Networking
Muralikrishnan Srinivasan, Sarath Gopi, Sheetal Kalyani, Xiaojing Huang, Lajos Hanzo
aa r X i v : . [ ee ss . SP ] J a n Airplane-Aided Integrated Next-GenerationNetworking
Muralikrishnan Srinivasan , Sarath Gopi , Sheetal Kalyani , Xiaojing Huang , Lajos Hanzo Abstract —A high-rate yet low-cost air-to-ground (A2G) com-munication backbone is conceived for integrating the space andterrestrial network by harnessing the opportunistic assistanceof the passenger planes or high altitude platforms (HAPs) asmobile base stations (BSs) and millimetre wave communication.The airliners act as the network-provider for the terrestrial userswhile relying on satellite backhaul. A null-steered beamformingtechnique relying on a large-scale planar array is used fortransmission by the airliner/HAP for achieving a high directionalgain, hence minimizing the interference between the users.Furthermore, approximate spectral efficiency (SE) and areaspectral efficiency (ASE) expressions are derived and quantifiedfor diverse system parameters.
I. I
NTRODUCTION
Next-generation wireless standards are expected to copewith increased traffic demands and support emerging appli-cations even in remote locations such as rural hinterlands,mountains, deserts and even for vessels such as cruise-shipsin the oceans [1]. However, the operational 5G standardshave predominantly been designed for terrestrial commu-nications. One of the promising techniques of augmentingcellular communication is through air-based platforms suchas unmanned aerial vehicles (UAV) or high-altitude platforms(HAP). Hence, extensive research has been dedicated to thedesign, channel modelling, and security of UAV-based cellularcommunications [2]–[5], as well as to their performanceanalysis [6]–[15].Integrating the aerial networks with the terrestrial networkshas the potential of increasing both the data rate and thecoverage quality of terrestrial networks [16]–[21]. There havealso been some attempts to integrate the space networks withterrestrial networks or to provide Internet coverage for air-liner [22]–[28]. However, most of these contributions rely onreusing the existing LTE bands, which are already congestedin the sub-6GHz bands [29], [30]. Therefore, the creation ofa high-capacity integrated space terrestrial network (ISTN)is still elusive both due to the bandwidth limitation aerial
1. Muralikrishnan Srinivasan is with ETIS UMR8051, CY Universit´e,ENSEA, CNRS, Cergy, France. (Email:[email protected])2. Sarath Gopi and Sheetal Kalyani are with the Dept. of Electrical Engi-neering, Indian Institute of Technology, Madras, India. (Emails:ee14d007@ee,[email protected]).3. Xiaojing Huang is with the University of Technology Sydney. (Email:[email protected])4. Lajos Hanzo is with the School of Electronics and Computer Science,University of Southampton.(Email: [email protected])Muralikrishnan Srinivasan and Sarath Gopi are co-first authors.This work has been submitted to the IEEE for possible publication.Copyright may be transferred without notice, after which this version mayno longer be accessible. backbones and owing to the limited area spectral efficiency(ASE) of the air-to-ground (A2G) systems given their largefootprint on the ground. Therefore, it is imperative to explorenew architectures integrating the existing terrestrial networkswith space networks.A critical cornerstone of 5G and beyond 5G (B5G) systemsis the potential usage of millimetre wave (mmWave) carrierfrequencies to benefit from their broad unused spectrum.Hence the authors of [31]–[36] have investigated the chal-lenges of mmWave based A2G and air-to-air (A2A) com-munications. The concept of mmWave architecture for A2Anetworks was first explored by Cuvelier and Heath [34] whilemmWave HAP to terrestrial transmissions were studied in [35],[36].As a further development, Huang et al. [1] have proposedthe ISTN concept relying on civil airliner networks andmmWave communication to form a high-capacity yet low-cost A2A and A2G communications backbone employinghigh-gain antenna arrays. In this concept, the airliners actas an efficient network-provider for terrestrial users, sincethe distance from the planes to the ground is much shorterthan that from the satellite. Furthermore, to provide A2Gcellular coverage for small cells that can support high ASE,adaptive beamforming is proposed. In areas where the civil-airliners cannot be used, dedicated HAPs would be used asthe backbone. A similar topology is presented in [37, Fig 1].
A. Design challenges:
To actually design such a high-capacity airline-aided inte-grated network, several challenges have to be addressed. Forexample, a cruising airliner maintains an altitude of at least km from the ground, while solar-charged unmanned aircraftare envisioned to circle above km for avoiding civilianplanes. The mmWave channel suffers from substantial pathlossowing to raindrops, high-absorption and other atmosphericeffects, especially at a carrier frequency of . GHz. Anotherchallenge to overcome is the huge channel estimation over-head, which results from the rapidly fluctuating high-Dopplerchannel between the cruising airliner and ground users. Hence,a careful selection of the channel model, antenna dimensions,Rician factor and other system parameters is required forinvestigating a realistic stand-alone model.
B. Contributions
To overcome the above-mentioned challenges, we designa high-performance system having a high data-rate and ASEand provide theoretical performance guarantees with the aid
Our Scheme [38] [39] [40] [41] [42] [43] [44] [45]mmWave
X X X X X X
Airliner/UAV backbone Airliner UAV UAV UAV UAV UAV UAVAdaptive null steering
X X X
Channel unawareprecoding
X X X X
Rician channel
X X
Simulated Metric ASE/SE SE Array SE SE SE SE Beam Beamresponse coverage coverageTheoretical expressions ASE/SE SETABLE IC
OMPARISON OF THE PROPOSED SCHEME WITH EXISTING WORKS of approximate expressions. We consider a planar-array aidedstand-alone airliner/HAP in a macro-cell communicating withthe terrestrial BS/users. To achieve a high directional gainwhile minimizing the users’ interference, we rely on a null-steered beamforming technique for transmission from theairliner/HAP to the ground. Although a strong line-of-sight(LOS) component exists between the airplane and the groundusers, the non-line-of-sight (NLOS) component fluctuatesdrastically over time. Hence, we propose channel-agnostictransmit precoding for avoiding the massive pilot overheadrequired for estimating the channel-state information (CSI)or the NLOS component. Explicitly, our Transmit Precoder(TPC) relies only on the users’ position relative to the airliner.We also derive approximate expressions for the SE/ASEof the users. Furthermore, the proposed scheme is evaluatedthrough extensive simulations, and its performance is com-pared to the analytically obtained values. Additionally, de-pending on the dimensions of the planar array and of the LOSfactor, the ASE achieved by our system becomes several timeshigher than that of conventional terrestrial networks [46]–[49] capable of providing data rates on the order of severalGbps. Although the authors of [38]–[45] have considered 3Dbeamforming in the context of UAV communications, theytend to rely on UAVs at a modest altitude.Against the above backdrop, we boldly contrast our novelcontributions to the prior art in Table I. The theoretical analysisof the proposed system and our extensive simulations indicatethat our design leads to high capacity airplane-aided integratednetworks that are eminently suitable for filling the coverage-holes of next-generation wireless systems.The rest of the paper is structured as follows. In SectionII, the proposed system design is discussed in detail, alongwith null-steered beamforming. In Section III, theoreticalexpressions are derived for the ASE/SE using the popular useand forget bound. In Section IV, our simulation results andinteresting design guidelines are discussed, while in SectionV, some future research directions are provided.II. P
ROPOSED S YSTEM D ESIGN
In this section, we design the ISTN backbone and proposea system model using null-steered adaptive beamforming forsupporting high data-rates and seamless connectivity. Considera circular macro-cell of radius R with an airliner at its centre atan altitude H t . The radius R is chosen to be at least km , soa minimum inter-airliner distance of km is maintained. Inremote locations outside the regular flight path, HAPs can be installed for providing seamless connectivity to satellites. Free-space optical (FSO) links connect them to Low-Earth orbit(LEO)/ medium-Earth orbit (MEO) satellites as their high-speed backhaul.Each airliner/HAP is equipped with a planar antenna having M × M equally spaced elements. Without loss of generality,it can be assumed that the antenna elements are parallel to theground and the centre of the antenna is the origin (0 , , .The macro-cell is further divided into several tightly packedmicro-cells of radius r << R . Each micro-cell supports asingle time-frequency block. The users can either be a cellularuser equipment (CUE) or even an LTE base station, which inturn supports several UEs. The intended user is at position ( x , y , − H t ) , and the micro-cell containing it is referred toas the micro-cell of interest (MCI).Assume that there are N , N ... N J interfering micro-cellsin the first J tiers using the same time-frequency block. Thecentres of these micro-cells are located at distances D , D , ..., JD from the MCI, where D denotes the reuse distance. Let N I = N + N + ... + N J be the total number of interferingcells and let the coordinates of these interfering users be ( x i , y i , − H t ) i = 1 , ..., N I . All the users are assumed to havea single antenna. Let ( θ zi , θ ai ) represent the zenith and azimuthangle pair for the i th user, which are: θ zi = tan − p x i + y i − H t ! , i = 0 , ..., N I (1)and θ ai = tan − (cid:18) y i x i (cid:19) , i = 0 , ..., N I . (2)Here i = 0 represents the user under consideration, while i = 1 , ..., N I represent the interferers. The entire system isshown in Fig. 1. Null-steered beamforming design
Note that the typical cruising airliner altitudes are in the − km range. At such distances, the mmWave chan-nels’ attenuation, say at . GHz , is significant. Existingcontributions, such as [40]–[42], [44], [45], which deal withaerial mmWave networks, consider only low-flying UAVs orLAPs and hence suffer from relatively low attenuation. Inthe absence of beamforming at the transmitter, the users inthe macro-cell suffer from mutual interference, resulting in areduced data-rate. Therefore, to reduce the mutual interferenceamongst the users and improve spectral efficiency, some form
User
Reuse Distance D Macro-cell centery macro-cell radius R xOrigin θ z zenith angle θ a azimuth anglez Fig. 1. The Airliner/HAP is assumed to be at the origin. The macro-cell centre is the point on the ground directly below the airliner. A circular macro-cell ofradius R is considered around the macro-cell centre. The zenith-azimuth angle pair ( θ z , θ a ) of the ’User’ in a micro-cell of interest (MCI), is marked withrespect to the airliner. Each micro-cell has a radius r . The first tier of N I interfering micro-cells is shown at a reuse distance D . In this figure, N I = 6 . of adaptive beamforming must be used by the airliner’s planararray. We propose using the popular null steering beamformingor zero-forcing precoding at the Airliner/HAP. Null-steeredtransit beamforming relies on signal processing techniquesfor creating transmit nulls and maxima in the undesired anddesired receivers’ directions, respectively, for mitigating theinterference [39], [50], [51]. The design of the beamformingvectors is described in the subsequent paragraphs.For i = 0 , , .., N I , let e i be the M × vector rep-resentation of the i th user’s steering vector with respectto each of the components of the planar array. The three-dimensional Cartesian co-ordinates of the ( m, n ) th componentof the planar array are represented by ( x m , y n , , where x m = (cid:2) − M − + ( m − (cid:3) λ and y n = (cid:2) − M − + ( n − (cid:3) λ , for m = 1 , ..M and n = 1 , ..., M . Note that the inter-elementalspacing is λ/ , where λ is the wavelength of the carrier. Thusthe entry of e i , which corresponds to the position of the userwith respect to the ( m, n ) th element of the planar array, isgiven by exp (cid:2) j πλ ( x m ψ xi + y n ψ yi ) (cid:3) , where we have ψ xi = sin θ zi cos θ ai , (3)and ψ yi = sin θ zi sin θ ai , (4)while θ zi and θ ai are defined in (1) and (2), respectively,which are functions of the user location. Now the null-steeredbeamforming vector ˜ e i used by the airliner is ˜ e i = e i − E i (cid:0) E Hi E i (cid:1) − E Hi e i , ∀ i = 0 , , ..., N I , (5)where E i is the matrix whose columns are the steering vectors,except for e i , which is given by: E i = [ e e ... e i − e i +1 ... e N I ] (6) This can be obtained by solving the following optimization problem [52]: min ˜ e i k ˜ e i − e i k such that ˜ e Hi E i = , The null-steered beam-former may also be interpreted asa zero-forcing precoder, where the precoding vectors only re-quire the knowledge of the user location. The system’s efficacyis determined by a pair of popular metrics, namely the ASEand the SE, which are functions of various system parameters,like the Rician factor K , the array dimensions M × M , orthe micro-cell radius, etc. In the next section, we derive theapproximate expressions of the performance metrics, followedby extensive simulation results for characterizing the system.III. T HEORETICAL APPROXIMATIONS FOR
ASE/SEIt is essential for us to characterize the signal-to-interferenceand noise ratio (SINR) and then derive theoretical expressionsfor our metrics, such as the ASE and SE. To begin with, let α i i = 0 , , ..., N I represent the symbol intended for the i th user.Without loss of generality, let i = 0 denote the user underconsideration and i = 1 , .., N I denote the interferers in theother micro-cells. The symbol received by the user is y = p P r h H ,Ric ˜ e α + p P r N I X i =1 h H ,Ric ˜ e i α i + n, (7)where n represents the complex Gaussian noise having thepower of σ = kT BN F , with k = 1 . × − beingBoltzmann’s constant, T the temperature in Kelvins, B thebandwidth, and N F the noise figure of the receiver. Thereceived power is given by: P r = P t G t G r ˜ νν , (8)where P t is the power transmitted from the Airliner/HAP, G t and G r are the transmitter and receiver antenna gains,while ˜ ν includes the frequency-dependent atmospheric lossalso including the back-off loss of the modulation scheme aswell as other transmitter and receiver losses. Finally, the term ν represents the path-loss given by [53], ν = 20 log (cid:18) πd f c c (cid:19) dB = (cid:18) πd f c,GHz (cid:19) , (9) where c = 3 × m/s is the speed of the light, d isthe distance from the airliner/HAP to the user in meters and f c,GHz is the carrier-frequency in GHz . The Rician fadingchannel between the Airliner/HAP and the user is representedby: h i,Ric = r K K e i + r
11 +
K h i , (10)where K is the Rician factor and h i is the NLOS component,while is the vector of ones. Furthermore, the NLOS com-ponent h i is a complex Gaussian random variable with zeromean and unit variance. The instantaneous SINR is now givenby the following theorem. Theorem 1.
The instantaneous SINR γ SINR , of the desireduser is given by: γ SINR = P r | X s | P N I i =1 P r | X i | + σ , (11) where X s ∼ CN ( µ, σ s ) , with µ = r K K (cid:16) M − e H E (cid:0) E H E (cid:1) − E H e (cid:17) , (12) and σ s = 11 + K (cid:13)(cid:13)(cid:13) H (cid:16) − E (cid:0) E H E (cid:1) − E H (cid:17) e (cid:13)(cid:13)(cid:13) . (13) Furthermore, still referring to (11), we have X i ∼ CN (0 , σ i ) ,where σ i = 11 + K (cid:13)(cid:13)(cid:13) H (cid:16) − E i (cid:0) E Hi E i (cid:1) − E Hi (cid:17) e i (cid:13)(cid:13)(cid:13) . (14) Proof.
For the proof, please see Appendix A.Assuming that the users in a cell are allocated identicalbandwidths, the Area Spectral Efficiency (ASE) is defined asthe sum of the maximum bit rate/Hz/unit area supported bythe cell’s Airliner/HAP [46]:
ASE = Cπ ( D/ , (15)where C is the capacity of the intended user in Bps/Hz. Given γ SINR , the average channel capacity is formulated as: ¯ C SINR = E [ log (1 + γ SINR )]= Z ∞ log (1 + γ SINR ) f ( γ SINR ) d γ SINR , (16)where E [ . ] represents the expectation and f ( γ SINR ) denotesthe pdf of γ SINR . By applying the popular use-and-forgetbound of [54], the approximate average channel capacity isgiven by ¯ C appSINR = E [ log (1 + γ SINR )] ≈ log P r E [ | X s | ] P N I i =1 P r E [ | X i | ] + σ ! , (17)where we have E [ | X s | ] = σ s + µ and E [ | X i | ] = σ i . Thus,the average ASE in bps/Hz/m is formulated as: ASE appSINR = 4 ¯ C appSINR πD . (18) Similarly, the average SE of the user is given by SE appSINR = ¯ C appSINR . (19)Note that the average capacity is a function of µ , σ s and σ i , i = 1 , ..., N I , which are parameterized by θ zi and θ ai for i = 0 , ..., N I , the zenith and azimuth angles of all theusers. Furthermore, the angles themselves are functions ofthe relative locations of the desired user and the interferersthrough (1) and (2), respectively. Therefore, the total averagecapacity is obtained by averaging the expressions over the userlocations.Recall that the beamforming vectors are only dependent onthe user positions, but not on the channel-gains. IV. S
IMULATION R ESULTSParameter ValueMacro-cell radius R − km Micro-cell radius r m , m , m Vertical airliner/HAP distance H t km , km Carrier frequency f c . GHz
Total Bandwidth B GHz
Reuse factor 7Dimensions of the planar array M , , , Rician factor K , , dB Transmit power dBm Back-Off dBm Transmitter loss . dB Transmitter antenna gain
10 log( M ) Atmospheric and cloud loss . dB Receiver antenna gain . dB Receiver noise figure dB Other receiver loss . dB TABLE IIS
IMULATION PARAMETERS
Distance of MCI from macrocell centre (km) A v e r age ASE ( bp s / H z / k m ) SimulationApproximation r=50m, K=10dBr=100m, K=10dBr=100m, K=30dBr=50m, K=30dB
Fig. 2. Average ASE vs. distance of MCI from the macro-cell centre for M = 500 and H t = 10 km . The theoretical result is based on (18). By exploring the knowledge of channel gain vector, one can improvethe SE. However, this would require accurate channel information at thetransmitter of the high-velocity airliner and is beyond the scope of this work.
Distance of MCI from macrocell centre (km) A v e r age ASE ( bp s / H z / k m ) SimulationApproximationK=30dB, H t =10km, M=500K=15dB, H t =10km, M=500K=15dB, H t =21km, M=500K=15dB, H t =21km, M=200 Fig. 3. Average ASE vs. distance of MCI from the macro-cell centre for r = 75 m . The theoretical result is based on (18). Extensive Monte-Carlo simulations have been carried outfor evaluating the ASE and SE of the system, assuming thatthe Airliner/HAP is located at (0 , , . The desired UE ispositioned uniformly in the MCI of radius r with its centrelocated at ( x, y, − H t ) . For a frequency reuse factor of , thereuse distance is fixed at approximately D = 4 r . We considerthe five tiers of interfering micro-cells with their centres set to kr, ∀ k = 1 , .., from the MCI . The interfering UEs are alsouniformly placed in the interfering micro-cell of radius r . Theinterferences imposed by the more distant tiers of micro-cellsand macro-cells are assumed to be negligible. To represent astrong LOS component, we consider the Rician factors K tobe , and dB. All the other transmission parameterswere proposed initially in [1] and are summarized in Table IIfor completeness.In Fig. 2, the simulated and approximate ASE are plottedvs. the horizontal distance of the MCI from the airliners, forseveral Rician factors K and micro-cell radii r . Naturally,upon increasing K , the ASE/SE increases. Since the ASEis inversely proportional to the cell-radius, it decreases uponincreasing the micro-cell radius r . However, the ASE fialsto reach its maximum, when the MCI is directly below theairliner, namely when the MCI is at the macro-cell centre.The ASE is a function of both the MCI distance from theairliners as well as of K and of the micro-cell radius r . Forexample, for r = 50 m and K = 30 dB, an ASE as high as bps/Hz/km is achieved when the user is at a distanceof km from the macro-cell centre. At the macro-cell centre,the ASE is reduced to bps/Hz/km .When the desired user is at the macro-cell centre, the inter- The number of interfering tiers to be chosen is based on an engineeringtrade-off that varies with the distance from the macro-cell centre. For example,for MCI at the centre of macro-cell (directly below the airliner), consideringthree tiers of interferers is sufficient. In the case of the macro-cell edge, 5tiers of interferers are needed for r = 50 m . The signal and interference powers are approximately of the order of and − respectively. At a reuse distance D = 200 m , the SE and ASEare bps/Hz and bps/Hz/km approximately. ferers are distributed in all the quadrants; hence their azimuthangles are uniformly distributed in [0 , degrees. Now, asthe desired user moves away from the macro-cell centre, thereare two effects. Firstly, the range of azimuth angles of theinterferers decreases because the first five tiers of interfererswe consider are concentrated in a single quadrant. Secondly,the absolute value of the zenith angles ( θ z ) of the interferenceincreases from as we move away from the macro-cellcentre. Both these effects increase the correlation between thedesired and interfering users’ steering vectors, hence reducingthe power of the null-steering vectors. Therefore, both thesignal and interference powers are reduced as the micro-cell centre moves away from the macro-cell centre. Near themacro-cell centre the reductions of both the signal and inter-ference powers become similar and hence the ASE fluctuates.However, as the micro-cell centre moves further away, theinterference power reduction is more substantial than the signalpower reduction and hence the ASE increases. Further away,the desired power reduction becomes substantial and hence theASE decreases. The SE variations vs. the distance can alsobe explained using similar reasoning. Furthermore, for higheraltitudes of the airliner, the SINR of the users decreases owingto their higher path-loss. Therefore, the ASE decreases, asobserved in Fig. 3. Note that the ASE achieved by the massiveMIMO scheme of [47] is on the order of bps/Hz/km ,while that of our scheme is comparable to the ASE achievedby the HetNet and DenseNet of [48] and [49], respectively.
200 250 300 350 400 450 500 A v e r age ASE ( bp s / H z / k m ) SimulationApproximation
K=30dB, MCI at 5 kmK=30dB, MCI at 3 kmK=10dB, MCI at 3 kmK=30dB, MCI at 0 kmK=10dB, MCI at 0 km
Fig. 4. Average ASE vs. M for H t = 10 km and r = 50 m . The theoreticalresult is based on (18). The ASE and SE variations vs. M are portrayed in Fig. 4and 5. An array dimension of × provides the highestASE. For an antenna element spacing of λ/ , where λ =4 mm is the career wavelength, the array dimensions will notexceed m . The increase in ASE vs. M remains marginalcompared to that vs. the Rician factor K . For example, foran increase in M from to , the ASE improves fromapproximately to bps/Hz/km respectively. On theother hand, for an increase in K from dB to dB, the ASEimproves from to bps/Hz/km , respectively. With
200 250 300 350 400 450 500 A v e r age SE ( bp s / H z ) SimulationApproximation
K=15dB, H t =21km, r=100mK=15dB, H t =21km, r=75mK=15dB, H t =10km, r=75mK=30dB, H t =10km, r=75m Fig. 5. Average SE vs. M for MCI at km from the macro-cell center. Thetheoretical result is based on (19). an increase in micro-cell radius, we observe a SE reduction inFig. 5. However, the reduction is only marginal compared tothe ASE reduction seen in Fig.2.Both the theory and simulations indicate substantial ASEgains for our proposed airplane-aided integrated network.However, our work only represents the first step towards real-izing a high-capacity ISTN; hence it relies on some idealizedsimplifying assumptions to be eliminated by future research.V. C ONCLUSIONS AND D IRECTIONS FOR F UTURE R ESEARCH
In this treatise, we considered a planar-array aided stand-alone airliner/HAP in a macro-cell communicating with theterrestrial BS/users. To achieve a high directional gain andto minimize the interference among the users, we invokeda null-steered beamforming technique for transmission fromthe airliner/HAP and provided approximate SE and ASEexpressions.We considered a simple system, where the airliner is thenetwork provider for the terrestrial users. The routing proto-cols, traffic-offloading and optimizing the tele-traffic resourcesin conjunction with the existing terrestrial and space networksrequire careful further study. Another critical topic that canbe explored is the impact of mobility and real flight scheduleon the handovers between the different macro-cells and theexisting networks. Finally, the optimal radius of micro-cellsused at different distances from the macro-cell centre isanother exciting future research direction.A
PPENDIX AP ROOF FOR T HEOREM X s = h H ,Ric ˜ e and thatof the i th interferer is X i = h H ,Ric ˜ e i . In order to determine thedistribution of the SINR, we have to determine the distribution of the components in the numerator and the denominator.Upon expanding X s , we arrive at, X s = h H ,Ric ˜ e = r K K (cid:16) e H e − e H E (cid:0) E H E (cid:1) − E H e (cid:17) + r
11 +
K h H (cid:16) − E (cid:0) E H E (cid:1) − E H (cid:17) e . (20)Observe that by construction, we have: e Hj e i = M ; i = j sin ( M ( ψ xj − ψ xi ))( sin ( ψ xj − ψ xi )) sin ( M ( ψ yj − ψ yi ))( sin ( ψ yj − ψ yi )) ; i = j, (21)where ψ x and ψ y are defined in (3) and (4), respectively. Since, h is a zero-mean Gaussian RV with unit variance, it can bereadily seen that X s is a Gaussian RV with a mean given by(12) and variance by (13). Now the i th interference componentis formulated as: X i = h H ,Ric ˜ e i , = r K K e H + r
11 +
K h H ! ˜ e i = r K K e H + r
11 +
K h H ! × (cid:16) − E i (cid:0) E Hi E i (cid:1) − E Hi (cid:17) e i , (22)where the null-steering beamforming vectors ˜ e j are designedin such a way that e Hi ˜ e j ≈ , ∀ i = j . Hence, the RV X i has a negligible mean component. On the other hand, X i hasa variance given by (14).R EFERENCES[1] X. Huang, J. A. Zhang, R. P. Liu, Y. J. Guo, and L. Hanzo, “Airplane-aided integrated networking for 6G wireless: Will it work?,”
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