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Adaptive Coding and Modulation for Large-ScaleAntenna Array Based Aeronautical Communications
in the Presence of Co-channel InterferenceJiankang Zhang, Member, IEEE, Sheng Chen, Fellow, IEEE, Robert G. Maunder, Senior Member, IEEE,
Rong Zhang, Senior Member, IEEE, and Lajos Hanzo, Fellow, IEEE
Abstract—In order to meet the demands of ‘Internet above theclouds’, we propose a multiple-antenna aided adaptive codingand modulation (ACM) for aeronautical communications. Theproposed ACM scheme switches its coding and modulation modeaccording to the distance between the communicating aircraft,which is readily available with the aid of the airborne radar or theglobal positioning system. We derive an asymptotic closed-formexpression of the signal-to-interference-plus-noise ratio (SINR)as the number of transmitting antennas tends to infinity, inthe presence of realistic co-channel interference and channelestimation errors. The achievable transmission rates and thecorresponding mode-switching distance-thresholds are readilyobtained based on this closed-form SINR formula. Monte-Carlosimulation results are used to validate our theoretical analysis.For the specific example of 32 transmit antennas and 4 receiveantennas communicating at a 5 GHz carrier frequency and using6 MHz bandwidth, which are reused by multiple other pairsof communicating aircraft, the proposed distance-based ACM iscapable of providing as high as 65.928 Mbps data rate when thecommunication distance is less than 25 km.
Index Terms—Aeronautical communication, large-scale an-tenna array, Rician channel, adaptive coding and modulation,precoding
I. INTRODUCTION
The appealing service of the ‘Internet above the clouds’[1] motivates researchers to develop high data rate and highspectral-efficiency (SE) aeronautical communication tech-niques. Traditionally, satellite-based access has been the mainsolution for aeronautical communication. However, it suffersfrom the drawbacks of low throughput and high processing de-lay as well as high charges by the satellite providers. The aero-nautical ad hoc network (AANET) [2] concept was conceivedfor supporting direct communication and data relaying amongaircraft for airborne Internet access. However, the currentexisting transmission techniques are incapable of providing thehigh throughput and high SE communications among aircraftrequired by this airborne Internet access application.
The planed future aeronautical communication systems,specifically, the L-band digital aeronautical communicationssystem (L-DACS) [3], [4] and the aeronautical mobile airport
The authors are with Electronics and Computer Science, University ofSouthampton, U.K. (E-mails: [email protected], [email protected],[email protected], [email protected], [email protected]). J. Zhang isalso with School of Information Engineering, Zhengzhou University, China.S. Chen is also with King Abdulaziz University, Jeddah, Saudi Arabia.
The financial support of the European Research Council’s Advanced FellowGrant, the Royal Society Wolfson Research Merit Award, and the Innovate UKfunded Harmonised Antennas, Radios, and Networks (HARNet) are gratefullyacknowledged.
communication system (AeroMACS) [5], [6], only provideupto 1.37 Mbps and 9.2 Mbps air-to-ground communicationdate rates, respectively. Moreover, the L-DACS1 air-to-airmode [7] is only capable of providing 273 kbps net userrate for direct aircraft-to-aircraft communication, which cannotmeet the high throughput demand of the Internet above theclouds. Furthermore, these rates are achievable for point-to-point transmissions, but multiple frequency resources arerequired for supporting multiple pairs of aircraft communi-cations. Therefore, these future aeronautical communicationtechniques fail to satisfy the demanding requirements ofairborne Internet access. Additionally, the L-DACS1 air-to-airmode has to collect and distribute the associated channel stateinformation (CSI) to all aircraft within the communicationrange [7], which is challenging in practical implementation.Even if the air-to-air communication capacity of these futureaeronautical communication systems could be made suffi-ciently high, they would still be forbidden for commercialairborne Internet access, because their frequency bands arewithin the bands assigned to the safety-critical air trafficcontrol and management systems.
In order to meet the high throughput and high SE demandsof the future AANET, we propose a large-scale antenna arrayaided adaptive coding and modulation (ACM) based solutionfor aeronautical communication. Before reviewing the familyof ACM and multiple-antenna techniques, we first elaborateon the specific choice of the frequency band suitable for theenvisaged AANET. Existing air traffic systems mainly usethe very high frequency (VHF) band spanning from 118 MHzto 137 MHz [8], and there are no substantial idle frequencybands. The ultra high frequency (UHF) band has almostbeen fully occupied by television broadcasting, cell phonesand satellite communications, including the global positioningsystem (GPS). Thus, no substantial idle frequency bands canbe found in the UHF band either. This motivates us to explorethe super high frequency (SHF) band spanning from 3 GHzto 30 GHz, for example, using 5 GHz carrier frequency forthis aeronautical communication application. Note that evenif there were sufficient unused frequency slots in the VHFand UHF bands, it is advisable not to use them becausethe frequency band of the envisaged airborne Internet accesssystem should be sufficiently far away from the bands assignedto the safety-critical air control and management systems,satellite communication and GPS systems.
ACM [9], [10] has been demonstrated to be a powerfultechnique of increasing data rate and improving SE over
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wireless fading channels. It has been extensively investigatedalso in the context of IEEE 802.11 [11], LTE-advance 4Gmobile systems [12], [13] and broadband satellite communi-cation systems [14]. The optimal ACM relies on the perfectknowledge of the instantaneous CSI, but channel estimationerrors are unavoidable in practical communication systems[15]. Furthermore, the CSI of frequency division duplexingbased systems must be obtained through a feedback channel,which potentially introduces feedback errors and delays [16].These factors significantly degrade the ACM performance. Inorder to reduce the sensitivity to CSI errors, Zhou et al. [15]proposed an adaptive modulation scheme relying on partialCSI, while Taki et al. [17] designed an ACM scheme baseddirectly on imperfect CSI. A whole range of differentiallyencoded and non-coherently detected star-QAM schemes werecharacterized in [18], while the channel coding aspects weredocumented in [10]. Most existing research on ACM focusedon terrestrial wireless communications, where the channelsexhibit Rayleigh fading characteristics. But the research com-munity seldom considered the propagation characteristics ofaeronautical communications in designing ACM schemes.
In aeronautical communication, typically there is line-of-sight (LOS) propagation, in addition to multipath fading,where the LOS component dominates the other multipathcomponents of the channel. The investigations of [19], [20]have revealed that the aeronautical channel can be modeledas a Rician channel for the flight phases of taxiing, landing,takeoff and en-route, while the aeronautical channel duringthe aircraft’s parking phase can be modeled as a Rayleighchannel, which can be viewed as a specific case of the Ricianchannel with a zero Rician K-factor. Furthermore, multiple-antenna aided techniques have been employed in aeronauticalcommunication for increasing the transmission capacity [21].Although it is challenging to deploy multiple antennas, onan aircraft [22], especially a large-scale antenna array, thedevelopment of conformal antenna [23] has paved the way fordeploying large-scale antenna arrays on aircraft. At the timeof writing, however, there is a paucity of information on howmuch capacity can be offered by employing multiple antennasin aeronautical communications.
Against this background, we develop an ACM based and
large-scale antenna array aided physical-layer transmissiontechnique capable of facilitating en-route airborne Internetaccess for the future AANET employing the time divisionduplexing (TDD) protocol, which has already been adoptedby the so-called automatic dependent surveillance-broadcaststandard [24], as well as by the L-DACS and AeroMACSarrangements. Our main contributions are summarized.
1) We propose and analyze a distance-information basedACM scheme for large-scale antenna array aided aero-nautical communication in SHF band, which switches itsACM mode based on the distance between the desiredpair of communicating aircraft. This scheme is morepractical than the existing ACM schemes that rely oninstantaneous channel-quality metrics, such as the in-stantaneous signal-to-noise ratio (SNR). This is becausein aeronautical communication it is extremely difficultto acquire an accurate estimate for any instantaneouschannel-quality metric, and an ACM based on such aswitching metric will frequently fail. By contrast, theaccurate distance information between the communicat-ing aircraft can readily be acquired with the aid airborneradar. Alternatively, the accurate position informationcan also be acquired with the assistance of GPS.
2) We explicitly derive a closed-form expression ofthe asymptotic signal-to-interference-plus-noise ratio(SINR) of multiple-antenna aided aeronautical commu-nication in the presence of realistic channel estima-tion errors and the co-channel interference imposed byother aircraft within the communication range. Thisclosed-form SINR formula enables us to directly de-rive the achievable theoretical transmission rates andthe associated mode-switching distance-thresholds forthe proposed ACM scheme. Moreover, as a benefit oflarge-scale antenna arrays, every pair of communicatingaircraft in our system uses the same frequency resourceblock, which dramatically enhances the system’s SE.
The rest of this paper is organized as follows. Section IIdescribes the multiple-antenna aided aeronautical communi-cation system, with emphasis on the propagation and signalmodels. Section III is devoted to the proposed distance-basedACM scheme, including the derivation of the closed-form
Interference links
(a) Pilot training (( b∗ )
a∗
b∗
A
a∗
1 a∗
b∗
2
b∗
a∗
b∗
2
b∗
a∗
1
A
b∗
a∗
a∗to(b) Data transmission)
Desired link
Interference links
b∗
a∗to
Desired link
2
21
· · ·21· · ·NrNr
1
1 Nr1
Antennas on
2
· · ·21
2 21
· · ·Nr
Antennas on
1Antennas on
2
Antennas onNt NtNtNt
· · ·· · · · · ·· · ·
Fig. 1. A TDD based aeronautical communication model with co-channel interference, where aircraft a∗ is transmitting data to aircraft b∗.
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asymptotic SINR in the presence of imperfect CSI and co-channel interference that leads to our detailed design of theachievable data rates and the associated switching distancethresholds. Section IV presents our simulation results for char-acterizing the impact of the relevant parameters in aeronauticalcommunication. Our conclusions are given in Section V.
II. SYSTEM MODEL
Fig. 1 depicts an aeronautical communication system con-sisting of (A + 2) aircraft at their cruising altitudes within agiven communication zone1. Aircraft a∗ and b∗ are the desiredpair of communicating aircraft, with a∗ transmitting data tob∗, while aircraft a = 1, 2, · · · , A are interfering aircraft.As the system operates in SHF band, it is feasible to designcompact high-gain antennas [25] and hence to deploy a large-scale antenna array on an aircraft. This also enables everypair of communicating aircraft to use the same frequencyand time slot. Specifically, the system is based on the TDDprotocol, and each aircraft has Ntotal antennas, which arecapable of transmitting and receiving on the same frequency.Furthermore, from these Ntotal antennas, Nt antennas areutilized for transmitting data, while Nr antennas are utilizedfor receiving data. We assume that the number of data-receiving antennas (DRAs) is no higher than that of the data-transmitting antennas (DTAs), i.e., Nr ≤ Nt < Ntotal. Thereasons are: 1) The spatial degrees of freedom min Nr, Ntdetermine the supportable data streams, and thus the numberof DRAs should be no higher than the number of DTAs inorder to make sure that the number of data streams aftertransmit precoding is no higher than min Nr, Nt; and 2) Theremaining (Ntotal − Nr) or (Ntotal − Nt) antennas are capableof transmitting/receiving other information, such as air trafficcontrol or emergency information, at a frequency differentfrom that of the data transmission. The system adopts orthog-onal frequency-division multiplexing (OFDM) for mitigatingthe multipath effects and for achieving a high SE. We furtherassume that all the aircraft are jumbo jets, and they are allequipped with a same large-scale antenna array. We alsoassume that each aircraft has an airborne radar capable ofmeasuring the distance to nearby aircraft. Alternatively, thedistance information may be acquired with the aid of GPS.
As illustrated in Fig. 1 (b), aircraft a∗ employs Nt antennasto transmit data and aircraft b∗ employs Nr antennas to receivedata. Therefore, a∗ has to know the multi-input multi-output(MIMO) channel matrix linking its Nt DTAs to the Nr DRAsof b∗ in order to carry out transmit precoding. The channelestimation is performed by pilot based training before datatransmission, as shown in Fig. 1 (a). More specifically, aircraftb∗ transmits pilot symbols from its Nr DRAs to aircraft a∗’sNt DTAs to enable a∗ to perform the training based channelestimation. The required MIMO channel matrix can then beobtained by exploiting the TDD channel’s reciprocity.
A. Pilot based trainingDuring the pilot based training stage shown in Fig. 1 (a),
aircraft b∗ transmits its pilot symbols via its Nr DRAs to
1Since Internet access is forbidden at takeoff and landing, it is reasonableto consider only aircraft en-route at cruising altitude.
the Nt DTAs of aircraft a∗, and this pilot based training isinterfered by all adjacent aircraft within the communicationrange. The most serious interference is imposed when theinterfering aircraft a = 1, 2, · · · , A also transmit the same pilotsymbols as aircraft b∗. The frequency domain (FD) MIMOchannel between the Nr DRAs of b∗ and the Nt DTAs of a∗,on the nth OFDM subcarrier of the sth symbol, is defined bythe matrix Hb∗
a∗ [s, n] ∈ CNt×Nr , where 0 ≤ n ≤ N − 1 withN denoting the length of the OFDM block. Let us assumethat the length of the cyclic prefix (CP) Ncp is longer than thechannel impulse response (CIR) P . The FD discrete signalmodel at the nth subcarrier and sth time interval during thepilot training period can be written as
Ya∗ [s, n] =√
P b∗r,a∗Hb∗
a∗ [s, n]Xb∗ [s, n]
+A∑
a=1
√P a
r,a∗Haa∗ [s, n]Xa[s, n] + Wa∗ [s, n], (1)
where Ya∗ [s, n] =[Y a∗
1 [s, n] Y a∗
2 [s, n] · · · Y a∗
Nt[s, n]
]T∈
CNt×1 represents the signal vector received by the Nt DTAs
of a∗, Xb∗ [s, n] =[Xb∗
1 [s, n] Xb∗
2 [s, n] · · · Xb∗
Nr[s, n]
]T∈
CNr×1 is the transmitted pilot symbol vector, which obeysthe complex white Gaussian distribution with a zero meanvector and the covariance matrix of INr , namely, Xb∗ [s, n] ∼CN (0, INr ), and Wa∗ [s, n] ∼ CN
(0, σ2
wINt
)is the as-
sociated FD additive white Gaussian noise (AWGN) vector,while the worst-case co-channel interference is consideredwith Xa[s, n] = Xb∗ [s, n] for 1 ≤ a ≤ A. Here we have used0 to represent the zero vector of an appropriate dimension andINr to represent the (Nr ×Nr)-element identity matrix. Fur-thermore, in (1), P b∗
r,a∗ and P ar,a∗ denote the received powers
of the desired signal and the interference signal transmittedfrom b∗ and a at a single receive antenna, respectively.
The FD channel transfer function coefficient (FD-CHTFC)matrix Hb∗
a∗ [s, n] is explicitly given by
Hb∗
a∗ [s, n] =νHb∗
d,a∗ [s, n] + ςHb∗
r,a∗ [s, n], (2)
where Hb∗
d,a∗ [s, n] ∈ CNt×Nr and Hb∗
r,a∗ [s, n] ∈ CNt×Nr
denote the deterministic and scattered channel components,respectively, while ν =
√KRice
KRice+1 and ς =√
1KRice+1 , with
KRice being the K-factor of the Rician channel. Furthermore,the scattered channel component is given by [26]
Hb∗
r,a∗ [s, n] =R12a∗Gb∗
a∗ [s, n]Rb∗ 12 , (3)
where Ra∗ ∈ CNt×Nt and Rb∗ ∈ CNr×Nr are the spatialcorrelation matrices for the Nt antennas of a∗ and the Nr
antennas of b∗, respectively, while Gb∗
a∗ [s, n] ∈ CNt×Nr
has the independently identically distributed complex-valuedentries, each obeying the distribution CN (0, 1). As a benefitof the CP, the OFDM symbols do not overlap in time andthe processing can be carried out on a per-carrier basis [27].Hence, to simplify our notations, we will omit the OFDMsymbol index s and the subcarrier index n in the sequel.
Let vec(A) denote the column stacking operation appliedto matrix A. Clearly, E
vec
(Hb∗
r,a∗
)= 0, where E
4
vec(Hb∗
a∗
)=vec
(νHb∗
d,a∗
)+ ς2Rr
r,t
(σ2
w
P b∗r,a∗
INrNt+ ς2Rr
r,t +A∑
a=1
P ar,a∗
P b∗r,a∗
ς2Rrr,t
)−1
×
vec(ςHb∗
r,a∗
)+
A∑a=1
√P a
r,a∗
P b∗r,a∗
vec(ςHa
r,a∗
)+
1√P b∗
r,a∗
vec
(˜W a∗
(˜Xb∗)H) . (9)
denotes the expectation operator, and the covariance matrixRb∗
r,a∗ ∈ CNtNr×NtNr of vec(Hb∗
r,a∗
)is given by
Rb∗
r,a∗ =Evec
(Hb∗
r,a∗
)(vec
(Hb∗
r,a∗
))H
=Rb∗⊗Ra∗, (4)
where ⊗ denotes the matrix Kronecker product. Therefore,vec
(Hb∗
a∗
)∼ CN
(vec
(νHb∗
d,a∗
), Rb∗
r,a∗
). Since all the air-
craft have the same antenna array, we make the assumptionthat all the spatial correlation matrices Rat for at ∈ A =1, 2, · · · , A, a∗, b∗ are approximately equal, i.e., we assumethat Rat = Rt ∀at ∈ A hold2. By the same argument, weassume that Rar = Rr ∀ar ∈ A hold3. Thus, all the channels’covariance matrices are assumed to be equal, i.e., we have
Rarr,at
=Rrr,t = Rr ⊗ Rt, ∀at, ar ∈ A and at = ar. (5)
This implies that every aircraft has the knowledge of itschannel covariance matrix. For example, aircraft a∗ knowsits antenna array’s spatial correlation matrices Ra∗ = Rt andRa∗
= Rr, and since Rb∗ = Ra∗, it knows its channel covari-
ance matrix Rb∗
r,a∗ = Rb∗ ⊗Ra∗ = Ra∗ ⊗Ra∗ = Rr ⊗ Rt. Itcan be seen that Rb∗ = Ra∗
is the real assumption required4.The received power P b∗
r,a∗ at aircraft a∗ is linked to thetransmitted signal power P b∗
t of aircraft b∗ by the followingpath loss model [25]
P b∗
r,a∗ = P b∗
t 10−0.1Lb∗path loss,a∗ , (6)
where Lb∗
path loss,a∗ represents the path loss in dB, which canbe modeled as [25]
Lb∗
path loss,a∗ [dB] = −154.06+20 log10 (f)+20 log10 (d) , (7)
where f [Hz] is the carrier frequency and d [m] is the distancebetween the transmit antenna and the receive antenna. For thereceived interference signal power P a
r,a∗ , we have a similarpath loss model. Each entry of the FD AWGN vector Wa∗
obeys the distribution CN (0, σ2w) with σ2
w = PN
N , in whichPN is the receiver noise power given by [28]
PN = FkT0B, (8)
where F [dB] is the receiver’s noise figure, T0 is the referencetemperature in Kelvin at the receiver, k = 1.3 × 10−23 isBoltzmann’s constant and B [Hz] is the bandwidth.
2It is reasonable to assume that all jumbo jets are equipped with identicalantenna array. However, because the geometric shapes of different typesof jumbo jets are slightly different, Rat = Rt ∀at ∈ A only holdapproximately.
3Similarly, Rar = Rr ∀ar ∈ A only hold approximately.4Alternatively, we can also avoid imposing this assumption. Then, a∗ can
ask b∗ to send its antenna correlation matrix Rb∗ . For example, during theinitial handshake of establishing the link, b∗ can sends Rb∗ to a∗ throughthe signaling at the expense of increasing the signaling overhead.
Since every aircraft knows its channel covariance matrix, wecan apply the optimal minimum mean square error (MMSE)estimator [29] to estimate the channel matrix Hb∗
a∗ . The MMSEestimate Hb∗
a∗ of Hb∗
a∗ is given in (9) at the top of this page,
where ˜Xb∗
∈CNr×Nr consists of the Nr pilot symbols with˜Xb∗(˜Xb∗)H =INr , and ˜W a∗ ∈CNr×Nr is the correspondingAWGN vector over the Nr consecutive OFDM pilot symbols.It is well-known that the distribution of the MMSE estimator(9) is vec
(Hb∗
a∗
)∼ CN
(vec
(νHb∗
d,a∗
),Φb∗
a∗
)[29], that is,
vec(Hb∗
a∗
)is an unbiased estimate of vec
(Hb∗
a∗
)with the
estimation accuracy specified by the covariance matrix Φb∗
a∗ ∈CNtNr×NtNr , which is given by
Φb∗
a∗ =ς2Rrr,t
(σ2
w
P b∗r,a∗
INrNt +ς2Rrr,t+
A∑a=1
P ar,a∗
P b∗r,a∗
ς2Rrr,t
)−1
× ς2Rrr,t. (10)
B. Data transmission
During the data transmission, aircraft a∗ transmits thesymbols Xa∗
=[Xa∗
1 Xa∗2 · · ·Xa∗
Nr
]T ∈ CNr×1 from itsNt DTAs to the Nr DRAs of aircraft b∗. Let us denote theMIMO channel matrix during this data transmission as Ha∗
b∗ ∈CNr×Nt . Then, upon exploiting the channel’s reciprocity inTDD systems, we have Ha∗
b∗ =(Hb∗
a∗
)H.
To mitigate the interference between multiple antennas,transmit precoding (TPC) is adopted for data transmission.There are various methods of designing the TPC matrixV a∗
b∗ ∈ CNt×Nr , including the convex optimization basedmethod of [30], the minimum variance method of [31], theminimum bit-error rate (MBER) design of [32], the MMSEdesign of [33] and the zero-forcing (ZF) design as wellas the eigen-beamforming or matched filter (MF) design of[34]. For a large-scale MIMO system, the complexity of theoptimization based TPC designs of [30]–[32] may becomeexcessive. Additionally, in this case, the performance of theMBER design [32] is indistinguishable from the MMSE one.Basically, for large-scale antenna array based MIMO, theperformance of the MMSE, ZF and MF based TPC solutionsare sufficiently good. The MF TPC design offers the additionaladvantage of the lowest complexity and, therefore, it is chosenin this work. Specifically, the MF TPC matrix is given by
V a∗
b∗ =(Ha∗
b∗
)H
= Hb∗
a∗ , (11)
where Ha∗
b∗ denotes the estimate of Ha∗
b∗ , and Hb∗
a∗ is thechannel estimate obtained during pilot training.
5
Y b∗
n∗r
=√
P a∗r,b∗
[Ha∗
b∗
][n∗
r : ]V a∗
b∗ Xa∗+
A∑a=1
√P a
r,b∗ [Hab∗ ][n∗
r : ] Va
baXa + W b∗
n∗r
=√
P a∗r,b∗
[Ha∗
b∗
][n∗
r : ]
[V a∗
b∗
][ :n∗
r ]Xa∗
n∗r
+∑
nr =n∗r
√P a∗
r,b∗
[Ha∗
b∗
][n∗
r : ]
[V a∗
b∗
][ :nr ]
Xa∗
nr+
A∑a=1
Nr∑nr=1
√P a
r,b∗ [Hab∗ ][n∗
r : ] [Va
ba ][ :nr] Xanr
+ W b∗
n∗r, (13)
Y b∗
n∗r=E√
P a∗r,b∗
[Ha∗
b∗
][n∗
r : ]
[V a∗
b∗
][ :n∗
r ]
Xa∗
n∗r+(√
P a∗r,b∗
[Ha∗
b∗
][n∗
r : ]
[V a∗
b∗
][ :n∗
r ]−E√
P a∗r,b∗
[Ha∗
b∗
][n∗
r : ]
[V a∗
b∗
][ :n∗
r ]
)Xa∗
n∗r
+∑
nr =n∗r
√P a∗
r,b∗
[Ha∗
b∗
][n∗
r : ]
[V a∗
b∗
][ :nr]
Xa∗
nr+
A∑a=1
Nr∑nr=1
√P a
r,b∗ [Hab∗ ][n∗
r : ] [Va
ba ][ :nr ] Xanr
+W b∗
n∗r. (14)
In the presence of the interference imposed by aircraft a for1 ≤ a ≤ A, the received signal vector at aircraft b∗, Yb∗ =[Y b∗
1 Y b∗
2 · · ·Y b∗
Nr
]T ∈ CNr×1, can be written as
Yb∗ =√
P a∗r,b∗H
a∗
b∗ V a∗
b∗ Xa∗+
A∑a=1
√P a
r,b∗Hab∗V
abaXa+Wb∗ ,
(12)
where V aba ∈ CNt×Nr denotes the TPC matrix at aircraft a
transmitting the signal Xa =[Xa
1 Xa2 · · ·Xa
Nr
]T to its desiredreceiving aircraft ba for ba = b∗, and the channel’s AWGNvector is Wb∗ =
[W b∗
1 W b∗
2 · · ·W b∗
Nr
]T ∼ CN(0, σ2
wINr
). In
particular, the signal received at the antenna n∗r of aircraft b∗,
for 1 ≤ n∗r ≤ Nr, is given by (13) at the top of this page,
where [A][nr: ] ∈ C1×M denotes the nrth row of A ∈ CN×M
and [A][ :nr ] ∈ CN×1 denotes the nrth column of A.
III. PROPOSED ADAPTIVE CODING AND MODULATION
In order to attain the required high-throughput transmissionfor our large-scale antenna assisted aeronautical communi-cation system, we propose a distance-based ACM scheme.We begin by analyzing the system’s achievable throughput,followed by the detailed design of this distance-based ACM.
A. Achievable throughput analysis
The transmitting aircraft a∗ pre-codes its signals based onthe channel estimate obtained during the pilot training by ex-ploiting the TDD channel’s reciprocity. However, the receivingaircraft b∗ does not have this CSI. Thus, the ergodic achievablerate is adopted for analyzing the achievable throughput. Inorder to explicitly derive this capacity, we rewrite the receivedsignal at the antenna n∗
r of aircraft b∗, namely, Y b∗
n∗r
of (13), inthe form given in (14). Observe that the first term of (14) is thedesired signal, the second term is the interference caused bythe channel estimation error, the third term is the interferencearriving from the other antennas of b∗, and the fourth term isthe interference impinging from the interfering aircraft, whilethe last term is of course the noise. Thus, the SINR at thenr-th antenna of b∗, denoted by γa∗
b∗,nr, is given by
γa∗
b∗,nr=
P a∗
r,b∗
∣∣∣E [Ha∗
b∗
][n∗
r : ]
[V a∗
b∗
][ :n∗
r ]
∣∣∣2PI&Na∗
b∗,nr
, (15)
in which the power of the interference plus noise is
PI&Na∗b∗,nr
= σ2w + P a∗
r,b∗Var[
Ha∗
b∗
][n∗
r : ]
[V a∗
b∗
][ :n∗
r ]
+ P a∗
r,b∗
∑nr =n∗
r
E
∣∣∣∣[Ha∗
b∗
][n∗
r : ]
[V a∗
b∗
][ :nr ]
∣∣∣∣2
+A∑
a=1
P ar,b∗
Nr∑nr=1
E∣∣∣[Ha
b∗ ][n∗r : ] [V
aba ][ :nr ]
∣∣∣2 , (16)
where Var denoting the variance. The achievable transmis-sion rate per antenna between the transmitting aircraft a∗ anddestination aircraft b∗ can readily be obtained as
Ca∗
b∗ =1
Nr
Nr∑nr=1
log2
(1 + γa∗
b∗,nr
). (17)
As mentioned previously, the distance between the trans-mitting aircraft and the receiving aircraft is available withthe aid of airborne radar or GPS. But we do not requirethat the distances between the interfering aircraft and thedesired destination aircraft are known to the transmittingaircraft. Realistically, the distance between two aircraft canbe assumed to follow the uniform distribution within therange of [Dmin, Dmax], where Dmin is the minimum sepa-ration distance required by safety and Dmax is the maximumcommunication range [35]. For example, we have Dmax =400 nautical miles, which is approximately 740.8 km, for atypical cruising altitude of 10.68 km. Normally, the Inter-national Civil Aviation Organization prescribes the minimumseparation as 5 nautical miles (approximately 9.26 km) whensurveillance systems are in use. But the minimum separationdistance could be reduced to 2.5 nautical miles (about 4.63km) when surveillance radars are intensively deployed, suchas in an airport’s airspace. Thus, the minimum distance isset to Dmin = 5 km in the envisaged AANET. Intuitively, anaircraft always transmits its signal to an aircraft having thebest propagation link with it for relying its information in theAANET. Here we simply assume that a pair of aircraft havingthe shortest communication distance have the best propagationlink, since large-scale fading dominates the quality of propaga-tion in aeronautical communication. Being in mind (6) and (7)as well as the fact that the distance d is uniformly distributedin [Dmin, Dmax], we can express the average received signal
6
power for the transmission from aircraft a to aircraft b∗ as
Pr =P ar,b∗ = E
P a
r,b∗
= P at
1015.406
f2
1DmaxDmin
. (18)
The relationship between the MMSE estimate[Ha∗
b∗
][nr: ]
and the true MIMO channel[Ha∗
b∗
][nr: ]
can be expressed as[Ha∗
b∗
][nr : ]
=[Ha∗
b∗
][nr: ]
+[Ha∗
b∗
][nr: ]
, (19)
where[Ha∗
b∗
][nr : ]
denotes the estimation error, which is
statistically independent of both[Ha∗
b∗
][nr : ]
and[Ha∗
b∗
][nr: ]
[29]. Similar to the distribution of vec(Hb∗
a∗
), we have
vec(Ha∗
b∗
)∼ CN
(vec
(νHa∗
d,b∗
),Φa∗
b∗
), (20)
where the covariance matrix Φa∗
b∗ of the MMSE estimatevec
(Ha∗
b∗
)is given by.
Φa∗
b∗ =ς2Rtr,r
(σ2
w
P a∗r,b∗
INrNt +ς2Rtr,r+
A∑a=1
P ar,a∗
P a∗r,b∗
ς2Rtr,r
)−1
× ς2Rtr,r, (21)
in which ς2Rtr,r is the channel’s covariance matrix and the
channel’s spatial correlation matrix Rtr,r is given by
Rtr,r =Rt ⊗ Rr. (22)
Denote the covariance matrix of the channel estimation errorvec
(Ha∗
b∗
)= vec
(Ha∗
b∗
)− vec
(Ha∗
b∗
)by Ξa∗
b∗ . Clearly,we have
Ξa∗
b∗ =ς2Rtr,r − Φa∗
b∗ ∈ CNtNr×NtNr , (23)
and Ξa∗
b∗ can be explicitly expressed in the following form
Ξa∗
b∗ =
[Ξa∗
b∗
](1,1)
[Ξa∗
b∗
](1,2)
· · ·[Ξa∗
b∗
](1,Nr)
...... · · ·
...[Ξa∗
b∗
](Nr,1)
[Ξa∗
b∗
](Nr,2)
· · ·[Ξa∗
b∗
](Nr,Nr)
,
(24)
where[Ξa∗
b∗
](i,j)
= E[
Ha∗
b∗
]H[i: ]
[Ha∗
b∗
][j: ]
∈ CNt×Nt ,
∀i, j ∈ 1, 2, · · · , Nr. This indicates that the distribution of[Ha∗
b∗
][nr: ]
is given by[Ha∗
b∗
]T[nr: ]
∼CN(0Nt×1,
[Ξa∗
b∗
](nr,nr)
), (25)
where 0Nt×1 is the Nt-dimensional zero vector.Noting the distribution (20), the correlation matrix obeys
E
vec(Hb∗
a∗
)vec
(Hb∗
a∗
)H
= ν2Ma∗
b∗ + Φa∗
b∗ , where
Ma∗
b∗ =vec(Hb∗
d,a∗
)vec
(Hb∗
d,a∗
)H
∈ CNtNr×NtNr . (26)
Furthermore, Ma∗
b∗ can be expressed in a form simi-lar to (24) having the (i, j)-th sub-matrix
[Ma∗
b∗
](i,j)
=[Hb∗
d,a∗
]H[i: ]
[Hb∗
d,a∗
][j: ]
∈ CNt×Nt , ∀i, j ∈ 1, 2, · · · , Nr.
Hence, upon recalling (11) and (19), we have
E[
Ha∗
b∗
][n∗
r : ]
[V a∗
b∗
][ :n∗
r ]
= E
[Ha∗
b∗
][n∗
r : ]
[Ha∗
b∗
]H[n∗
r : ]
= E
([Ha∗
b∗
][n∗
r : ]+[Ha∗
b∗
][n∗
r : ]
)[Ha∗
b∗
]H[n∗
r : ]
= E
Tr[
Ha∗
b∗
]H[n∗
r : ]
[Ha∗
b∗
][n∗
r : ]
= Tr
ν2[Ma∗
b∗
](n∗
r ,n∗r)
+[Φa∗
b∗
](n∗
r ,n∗r)
, (27)
where Tr denotes the matrix trace operator, and[Φa∗
b∗
](i,j)
∈ CNt×Nt , ∀i, j ∈ 1, 2, · · · , Nr, is the (i, j)-th sub-matrix of Φa∗
b∗ which has a structure similar to (24).Thus, by denoting[
Θa∗
b∗
](n∗
r ,n∗r)
=ν2[Ma∗
b∗
](n∗
r ,n∗r)
+[Φa∗
b∗
](n∗
r ,n∗r)
, (28)
we have∣∣∣∣E [Ha∗
b∗
][n∗
r : ]
[V a∗
b∗
][ :n∗
r ]
∣∣∣∣2 =(
Tr[
Θa∗
b∗
](n∗
r ,n∗r)
)2
.
(29)
Note that multiplying (29) with P a∗
r,b∗ leads to the desiredsignal power, i.e. the numerator of the SINR expression (15).
As shown in the Appendix, as Nt → ∞, we have
Var[
Ha∗
b∗
][n∗
r : ]
[V a∗
b∗
][ :n∗
r ]
= Tr
[Ξa∗
b∗
](n∗
r ,n∗r)
[Θa∗
b∗
](n∗
r ,n∗r)
. (30)
Additionally, recalling (9) and after some simplifications, we
can express E ∣∣∣[Ha∗
b∗
][n∗
r : ]
[V a∗
b∗
][ :nr]
∣∣∣2 as
E
∣∣∣∣[Ha∗
b∗
][n∗
r : ]
[V a∗
b∗
][ :nr]
∣∣∣∣2
= Tr
(ν2[Ma∗
b∗
](nr,nr)
+( [
Φa∗
b∗
](nr,nr)
+σ2
w
P a∗r,b∗
INt +A∑
a=1
P ar,a∗
P a∗r,b∗
ς2[Rt
r,r
](nr,nr)
)×[Ωa∗
b∗
](nr,nr)
)(ν2[Ma∗
b∗
](n∗
r ,n∗r)
+ ς2[Rt
r,r
](n∗
r ,n∗r)
),
(31)
asymptotically, where[Ωa∗
b∗
](nr,nr)
∈ CNt×Nt is given by
[Ωa∗
b∗
](nr,nr)
=ς2[Rt
r,r
](nr,nr)
( σ2w
P a∗r,b∗
INt +[Rt
r,r
](nr,nr)
+A∑
a=1
P ar,a∗
P a∗r,b∗
ς2[Rt
r,r
](nr,nr)
)−1
, (32)
in which[Rt
r,r
](i,j)
∈ CNt×Nt , ∀i, j ∈ 1, 2, · · · , Nr,represents the (i, j)-th sub-matrix of Rt
r,r, which hasa structure similar to (24). Similarly, we can express
7
PI&Na∗b∗,nr
= σ2w + P a∗
r,b∗Tr[
Ξa∗
b∗
](n∗
r ,n∗r)
[Θa∗
b∗
](n∗
r ,n∗r)
+ P a∗
r,b∗
Nr∑nr=1nr =n∗
r
Tr
(ν2[Ma∗
b∗
](nr,nr)
+([
Φa∗
b∗
](nr,nr)
+σ2
w
P a∗r,b∗
INt
+APr
P a∗r,b∗
ς2[Rt
r,r
](nr,nr)
)[Ωa∗
b∗
](nr,nr)
)(ν2[Ma∗
b∗
](n∗
r ,n∗r)
+ς2[Rt
r,r
](n∗
r ,n∗r)
)+Pr
A∑a=1
Nr∑nr=1
Tr
(ν2 [Ma
ba ](nr,nr)
+(
[Φaba ](nr,nr)+
APr
P a∗r,b∗
ς2[Rt
r,r
](nr,nr)
+σ2
w
P a∗r,b∗
INt
)[Ωa
ba ](nr,nr)
)(ν2 [Ma
b∗ ](n∗r ,n∗
r) + ς2[Rt
r,r
](n∗
r ,n∗r)
). (34)
E∣∣∣[Ha
b∗ ][n∗r : ] [V
aba ][ :nr]
∣∣∣2 asymptotically as
E∣∣∣[Ha
b∗ ][n∗r : ] [V
aba ][ :nr]
∣∣∣2 = Tr
(ν2 [Ma
ba ](nr,nr)
+
([Φa
ba ](nr,nr) +A∑
a=1
P ar,a∗ς2
P a∗r,b∗
[Rt
r,r
](nr,nr)
+σ2
w
P a∗r,b∗
INt
)
× [Ωaba ](nr,nr)
)(ν2 [Ma
b∗ ](n∗r ,n∗
r)+ς2[Rt
r,r
](n∗
r ,n∗r)
).
(33)
Upon substituting (30), (31) and (33) into (16), therefore,we arrive asymptotically at the power of the interferenceplus noise PI&Na∗
b∗,nr
given in (34) at the top of this page.Furthermore, substituting (29) into (15) leads to the followingasymptotic SINR expression
γa∗
b∗,nr=
P a∗
r,b∗
(Tr[
Θa∗
b∗
](n∗
r ,n∗r)
)2
PI&Na∗b∗,nr
. (35)
Remark 1: Both [Maba ](nr,nr) and [Ma
b∗ ](n∗r ,n∗
r) in (34)are unavailable to aircraft a∗, since there is no cooperationbetween the related aircraft. However, both these two termscan be substituted by
[Ma∗
b∗
](n∗
r ,n∗r)
as a reasonable approx-imation. The simulation results presented in Section IV willdemonstrate that this approximation is sufficiently accurate.
Remark 2: The high velocity of aircraft results in rapidlyfluctuating fading. The channel estimator (9) is the mostefficient, since its mean square error matches the Cramer-Rao lower bound. However, by the time the transmittertransmits the precoded signal based on this channel estimate,the real channel has changed. This mobility-induced channelestimation ‘error’ will degrade the achievable performance. Aneffective approach to mitigate this performance degradationowing to channel estimation errors is to adopt robust transmitprecoding. The design of robust precoding is beyond the scope
of this paper. Some highly effective robust precoding designscan be found in [36], [37].
Remark 3: As our derivation does not impose any specificgeometric structure on the antenna array, our results andtherefore our proposed physical-layer transmission scheme isapplicable to systems equipped with uniformly spaced lineararrays (ULAs), uniformly spaced rectangular arrays (URAs),or any other generic antenna arrays.
sign
al p
roce
ssin
g
TimeTime
Data transmission
Rec
eive
d
DistanceChannel estimation
ACM mode
SwitchGenerate theprecoding matrix
Pilot training
da∗
b∗
Va∗
b∗
b∗
a∗
· · ·21 Nr
Data-transmitting antennasData-receiving antennas
21 Nt· · ·
Fig. 2. Schematic of the proposed distance-based adaptive coding andmodulation scheme.
B. Distance-based ACM scheme
The proposed distance-based ACM scheme is illustrated inFig. 2. Our scheme explicitly uses the distance da∗
b∗ betweenaircraft a∗ and aircraft b∗ as the switching metric to adapt themodulation mode and code rate. Similar to the conventionalACM scheme, our distance-based ACM also consists of the setof K ACM modes, but its switching thresholds comprise theK distance thresholds dkK
k=1. An example of this distance-based ACM scheme using K = 7 is given in Table I,where the SE is calculated as: log2(modulation order) ×code rate × [(N − Ncp)/N ], and the data rate per DRA is
TABLE IAN EXAMPLE OF ADAPTIVE CODING AND MODULATION SCHEME WITH Nt = 32 AND Nr = 4. THE OTHER SYSTEM PARAMETERS FOR THIS ACM ARE
LISTED IN TABLE III.
Mode k Modulation Code rate Spectral efficiency(bps/Hz)
Switching thresholddk (km)
Data rate per receiveantenna (Mbps)
Total data rate(Mbps)
1 BPSK 0.488 0.459 500 2.754 11.0162 QPSK 0.533 1.000 350 6.000 24.0003 QPSK 0.706 1.322 200 7.932 31.7284 8-QAM 0.642 1.809 110 10.854 43.4165 8-QAM 0.780 2.194 40 13.164 52.6566 16-QAM 0.731 2.747 25 16.482 65.9287 16-QAM 0.853 3.197 5.56 19.182 76.728
8
0
1
2
3
4Capacity/Spectraleffi
ciency
(bps/Hz)
5 104 2 5 105 2 5
Distance (m)
Theoretical result
Mode 1: SE = 0.459 Mode 2: SE = 1.000Mode 3: SE = 1.322 Mode 4: SE = 1.809Mode 5: SE = 2.194 Mode 6: SE = 2.747Mode 7: SE = 3.197
d1d2d5 d3d4d6d7
(a) Nt = 32, Nr = 4
0
1
2
3
4
Capacity/Spectraleffi
ciency
(bps/Hz)
5 104 2 5 105 2 5
Distance (m)
Theoretical result
Mode 1: SE = 1.322 Mode 2: SE = 1.809Mode 3: SE = 2.194 Mode 4: SE = 2.747Mode 5: SE = 3.197
d1d4 d2d3d5
(b) Nt = 64, Nr = 4
Fig. 3. Illustration of how to obtain the desired distance thresholds for the proposed distance-based ACM scheme, using the examples of Tables I and II.
calculated as: spectral efficiency × Btotal, in which Btotal isthe bandwidth available, while the total data rate is given by:data rate per DRA × Nr. The modulation schemes and coderates are adopted from the design of VersaFEC [38], whichcovers a family of 12 short-block LDPC code rates with thematched modulation schemes. VersaFEC is specifically de-signed for low latency and ACM applications. The operationsof this distance-based ACM are now given below.
1) Aircraft a∗ estimates the channel Ha∗
b∗ based on the pilotstransmitted by aircraft b∗, as detailed in Section II-A.
2) Aircraft a∗ calculates the TPC matrix V a∗
b∗ according to(11).
3) Aircraft a∗ selects an ACM mode to transmit the dataaccording to
If dk ≤ da∗
b∗ < dk−1 : choose mode k, (36)
where k ∈ 1, 2, · · · ,K, and we assume d0 = Dmax. Whenda∗
b∗ ≥ Dmax, there exists no available communication link,since the two aircraft are beyond each others’ communicationrange. Since the minimum flight-safety separation must beobeyed, we do not consider the senario of da∗
b∗ ≤ Dmin.The switching distance threshold for each ACM mode is
determined based on the achievable rate per DRA as a functionof distance. Specifically, the theoretically achievable rate per
DRA as a function of distance is calculated using (15). Thedistance thresholds dkK
k=1 are chosen so that the SE ofmode k is lower than the theoretically achievable rate perDRA in the distance range of [dk, dk−1] to ensure successfultransmission. Fig. 3(a) illustrates how the 7 distance thresholdsare designed for the example provided in Table I. For thisexample, Nt = 32, Nr = 4, and the total system bandwidthis Btotal = 6 MHz which is reused by every aircraft inthe system. The theoretically achievable rate per DRA as afunction of distance is depicted as the dot-marked solid curvein Fig. 3(a). By designing the 7 distance thresholds dk for1 ≤ k ≤ 7 to ensure that the SE of mode k is lower than thetheoretically achievable rate in the distance range [dk, dk−1],we obtain the 7 desired distance thresholds for this ACMexample, which are indicated in Fig. 3(a) as well as listedin Table I. The designed 7 ACM modes are: mode 1 havingthe SE of 0.459 bps/Hz, mode 2 with the SE 1.000 bps/Hz,mode 3 with the SE 1.322 bps/Hz, mode 4 with the SE 1.809bps/Hz, mode 5 with the SE 2.194 bps/Hz, mode 6 with the2.747 bps/Hz, and mode 7 with the SE 3.197 bps/Hz.
We also provide another design example of the ACMscheme for K = 5 modes. For this example, we have Nt = 64and Nr = 4, while the other system parameters are thesame as the ACM scheme listed in Table I. As shown inFig. 3(b) and Table II, the five ACM modes have the SEs
TABLE IIAN EXAMPLE OF ADAPTIVE CODING AND MODULATION SCHEME WITH Nt = 64 AND Nr = 4. THE OTHER SYSTEM PARAMETERS FOR THIS ACM ARE
LISTED IN TABLE III.
Mode k Modulation Code rate Spectral efficiency(bps/Hz)
Switching thresholddk (km)
Data rate per receiveantenna (Mbps)
Total data rate(Mbps)
1 QPSK 0.706 1.322 400 7.932 31.7282 8-QAM 0.642 1.809 250 10.854 43.4163 8-QAM 0.780 2.194 120 13.164 52.6564 16-QAM 0.731 2.747 50 16.482 65.9285 16-QAM 0.853 3.197 5.56 19.182 76.728
9
of 1.322 bps/Hz, 1.809 bps/Hz, 2.194 bps/Hz, 2.747 bps/Hz and3.197 bps/Hz, respectively, while the corresponding switchingthresholds are 400 km, 250 km, 120 km, 50 km, and 5.56 km,respectively. By comparing Table II to Table I, it can be seenthat employing a larger number of transmit antennas enablesan ACM mode to operate over a larger range of distances,or it allows the system to transmit at a higher SE over agiven communication distance. This makes sense because awell-known MIMO property is that employing more transmitantennas can mitigate the interference more effectively.
Remark 4: It is worth recapping that the conventional in-stantaneous SNR-based ACM is unsuitable for aeronauticalcommunication applications, because the speed of aircraftis ultra high, which results in rapidly changing of large-scale fading and consequently very unreliable estimate of theinstantaneous SNR as well as leads to frequently switch-ing among the modes. Using erroneous instantaneous SNRestimates to frequently switch modes will cause frequentunsuccessful transmissions. By contrast, the proposed ACMscheme switches its mode based on the distance, which isreadily available to the transmitting aircraft, since every jumbojet has a radar and is equipped with GPS. It can be seen thatthis distance-based ACM scheme is particularly suitable foraeronautical communication applications. Furthermore, it isworth emphasizing that using the distance as the switchingmetric is theoretically well justified, because for the aero-nautical communication channel the achievable capacity ismainly dependent on the distance, as we have analyticallyderived in Subsection III-A. Note that owing to the highvelocity of the aircraft, no physical layer transmission schemecan guarantee successful transmission for every transmissionslot. Other higher-layer measures, such as Automatic-Repeat-reQuest (ARQ) [39], [40], can be employed for enhancing re-liable communication among aircraft. Discussing these higher-layer techniques is beyond the scope of this paper.
TABLE IIIDEFAULT PARAMETERS USED IN THE SIMULATED AERONAUTICAL
COMMUNICATION SYSTEM.
System parameters for ACMNumber of interference aircraft A 4Number of DRAs Nr 4Number of DTAs Nt 32Transmit power per antennas Pt 1 wattNumber of total subcarriers N 512Number of CPs Ncp 32Rician factor KRice 5Bandwidth Btotal 6 MHzFrequency of centre subcarrier 5 GHzOther system parametersCorrelation factor between antennas ρ 0.1Noise figure at receiver F 4 dBDistance between communicating aircraft a∗ and b∗ da∗
b∗ 10 kmMaximum communication distance Dmax 740 km
IV. SIMULATION STUDY
The default values of the parameters used for our simu-lated aeronautical communication system are summarized inTable III. Unless otherwise specified, these default values areused. The number of DRAs is much lower than the numberof DTAs in order to ensure that the DRAs’ signals remainuncorrelated to avoid the interference among the antennas atthe receiver. The deterministic part of the Rician channel,which satisfies Tr
Ha
d,bHa,Hd,b
= NtNr, is generated in
every Monte-Carlo simulation. The scattering component ofthe Rician channel Ha
r,b ∈ CNr×Nt is generated according to
Har,b =RbGRa, (37)
where Rb = INr , since the DRAs are uncorrelated, but themth-row and nth-column element of the correlation matrix ofRa, denoted by [Ra][m,n], is generated according to [41], [42]
[Ra][m,n] =([Ra][n,m[
)‡ = (tρ)|m−n|, (38)
in which ( )‡ denotes conjugate operation, and t ∼ CN (0, 1)is the magnitude of the correlation coefficient, which is deter-
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
Capacity/Spectraleffi
ciency
(bps/Hz)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Number of interference aircraft A
Theoretical resultsApproximate resultsSimulation results
(a) Throughput
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pr(C
>c)
2.5 2.75 3.0 3.25 3.5 3.75 4.0 4.25 4.5 4.75 5.0
Capacity c (bps/Hz)
A = 1A = 4A = 7A = 10A = 13
(b) CCDF
Fig. 4. (a) The achievable throughput per DRA as a function of the number of interfering aircraft A, and (b) The CCDFs of the simulated throughputs perDRA for different numbers of interfering aircraft. The distances between the interfering aircraft and the desired receiving aircraft are uniformly distributedwithin the range of
ˆ
da∗b∗ , Dmax
˜
. The rest of the parameters are specified in Table III.
10
mined by the antenna element spacing [42]. The antenna arraycorrelation matrix model (38) is derived based on the ULA,and this implies that we adopt the ULA in our simulationstudy. However, it is worth recalling Remark 3 stating thatour scheme is not restricted to the ULA. In the investigationof the achievable throughput, ‘Theoretical’ is the throughputcalculated using (17) relying on the perfect knowledge of[Ma
ba ](nr,nr) and [Mab∗ ](n∗
r ,n∗r) in (34), and ‘Approximate’ is
the throughput calculated using (15) with both [Maba ](nr,nr)
and [Mab∗ ](n∗
r ,n∗r) substituted by
[Ma∗
b∗
](n∗
r ,n∗r)
in (34), while‘Simulation’ is the Monte-Carlo simulation result.
A. ResultsFig. 4(a) investigates the achievable throughput per DRA as
a function of the number of interfering aircraft A, where the
‘Approximate results’ match closely the ‘Theoretical results’,confirming that
[Ma∗
b∗
](n∗
r ,n∗r)
is an accurate approximationof both the unknown [Ma
ba ](nr,nr) and [Mab∗ ](n∗
r ,n∗r). As
expected, the achievable throughput degrades as the number ofinterfering aircraft increases. Also the theoretical throughputis about 0.2 bps/Hz higher than the simulated throughput. Thisis because the theoretical throughput is obtained by usingthe asymptotic interference plus noise power as Nt → ∞and, therefore, it represents the asymptotic upper bound ofthe achievable throughput. The complementary cumulativedistribution functions (CCDFs) of the simulated throughputrecorded for different numbers of interfering aircraft A areshown in Fig. 4(b), which characterizes the probability of theachievable throughput above a given value.
Fig. 5(a) portrays the achievable throughput per DRA as
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Capacity/Spectraleffi
ciency
(bps/Hz)
5 104 2 5 105 2 5
Distance da∗
b∗ (m)
Theoretical resultsApproximate resultsSimulation results
(a) Throughput
0.0
0.2
0.4
0.6
0.8
1.0
Pr(C
>c)
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
Capacity c (bps/Hz)
da∗
b∗ = 5 km
da∗
b∗ = 10 km
da∗
b∗ = 100 km
da∗
b∗ = 300 km
da∗
b∗ = 500 km
(b) CCDF
Fig. 5. (a) The achievable throughput per DRA as a function of the distance da∗b∗ between the desired communicating aircraft a∗ and b∗, and (b) The
CCDFs of the simulated throughputs per DRA for different da∗b∗ . The distances between the interfering aircraft and the desired receiving aircraft are uniformly
distributed within the range ofˆ
da∗b∗ , Dmax
˜
. The rest of the parameters are specified in Table III.
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
Capacity/Spectraleffi
ciency
(bps/Hz)
20 40 60 80 100 120 140 160 180 200
Number of transmitting antennas Nt
Theoretical resultsApproximate resultsSimulation results
(a) Throughput
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pr(C
>c)
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5
Capacity c (bps/Hz)
Nt = 20Nt = 60Nt = 100Nt = 140Nt = 180
(b) CCDF
Fig. 6. (a) The achievable throughput performance per DRA as a function of the number of DTAs Nt, and (b) The CCDFs of the simulated throughputsper DRA for different numbers of DTAs Nt. The distances between the interfering aircraft and the desired receiving aircraft are uniformly distributed withinthe range of
ˆ
da∗b∗ , Dmax
˜
. The rest of the parameters are specified in Table III.
11
a function of the distance da∗
b∗ between the desired pair ofcommunicating aircraft, while the CCDFs of the simulatedthroughput recorded for different values of da∗
b∗ are depictedin Fig. 5(b). As expected, the achievable throughput degradesupon increasing the communication distance. Observe thatthe performance gap between the theoretical curve and thesimulation curve at the point of da∗
b∗ = 10 km is also around0.2 bps/Hz, which agrees with the results of Fig. 4(a).
The impact of the number of DTAs on the achievablethroughput is investigated in Fig. 6. Specifically, Fig. 6(a)shows the throughput per DRA as a function of the numberof DTAs Nt, while Fig. 6(b) depicts the CCDFs of thesimulated throughputs per DRA for different numbers of DTAsNt. Observe that the achievable throughput increases as Nt
increases. Moreover, when the number of DTAs increase to
Nt ≥ 120, the achievable throughput saturates, as seen fromFig. 6(a). Similarly, the CCDFs recorded for Nt = 140 andNt = 180 are indistinguishable, as clearly seen from Fig. 6(b).The implication is that the asymptotic performance is reachedfor Nt ≥ 120.
Next the impact of the number of DRAs on the achievablethroughput is studied in Fig. 7. In particular, Fig. 7(a) portraysthe achievable throughputs as a functions of Nr, where the lefty-axis labels the achievable throughput per DRA and the righty-axis indicates the sum rate of the Nr DRAs. As expected, theachievable sum rate increases with Nr. However, the increasein the sum rate is not proportional to the increase of Nr.In fact, it is clearly seen from Fig. 7(a) that the achievablethroughput per DRA is reduced with the increase of Nr. Thereason for this trend is because the inter-antenna interference
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Capacity/Spectraleffi
ciency
(bps/Hz)
0
5
10
15
20
25
30
Sum
capacity(bps/Hz)
2 4 6 8 10 12 14 16 18 20
Number of receiving antennas Nr
Theoretical resultsApproximate resultsSimulation results
Sum capacity of Nr antennasCapacity per antenna
(a) Throughput
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pr(C
>c)
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
Capacity c (bps/Hz)
Nr = 2Nr = 4Nr = 6Nr = 8Nr = 10
(b) CCDF
Fig. 7. (a) The achievable throughput as a function of the number of DRAs Nr , and (b) The CCDFs of the simulated throughputs per DRA for different numbersof DRAs Nr . The distances between the interfering aircraft and the desired receiving aircraft are uniformly distributed within the range of
ˆ
da∗b∗ , Dmax
˜
. Therest of the parameters are specified in Table III.
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Capacity/Spectraleffi
ciency
(bps/Hz)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Correlation factor ρ
Theoretical resultsApproximate resultsSimulation results
(a) Throughput
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pr(C
>c)
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Capacity c (bps/Hz)
ρ = 0.1ρ = 0.3ρ = 0.5ρ = 0.7ρ = 0.9
(b) CCDF
Fig. 8. (a) The achievable throughput per DRA as a function of the correlation factor of DTAs ρ, and (b) The CCDFs of the simulated throughputs perDRA for different values of ρ. The distances between the interfering aircraft and the desired receiving aircraft are uniformly distributed within the range ofˆ
da∗b∗ , Dmax
˜
. The rest of the parameters are specified in Table III.
12
2.0
2.5
3.0
3.5
4.0
4.5
5.0Capacity/Spectraleffi
ciency
(bps/Hz)
2 4 6 8 10 12 14 16
Rician factor KRice
Theoretical resultsApproximate resultsSimulation results
(a) Throughput
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pr(C
>c)
2.0 2.25 2.5 2.75 3.0 3.25 3.5 3.75 4.0 4.25 4.5
Capacity c (bps/Hz)
KRice = 1KRice = 4KRice = 7KRice = 10KRice = 13
(b) CCDF
Fig. 9. (a) The achievable throughput per DRA as a function of the Rician factor KRice, and (b) The CCDFs of the simulated throughputs per DRAfor different values of KRice. The distances between the interfering aircraft and the desired receiving aircraft are uniformly distributed within the range ofˆ
da∗b∗ , Dmax
˜
. The rest of the parameters are specified in Table III.
increases with the increase of Nr, as seen in the third andfourth terms of (34). The CCDFs of the simulated throughputsper DRA are illustrated in Fig. 7(b) for different Nr, whichagree with the curve of the simulated capacity per DRA shownin Fig. 7(a), namely the achievable throughput per DRA islower for larger number of DRAs.
Fig. 8 depicts the impact of the correlation factor ρ ofDTAs on the achievable throughput per DRA. It can beseen from Fig. 8(a) that strong signal correlation betweenDTAs will reduce the achievable throughput, as expected.This degradation is particularly serious in the Monte-Carlosimulation results, i.e. in practice, but less notable for theasymptotic theoretical upper bound. Note that there is a largegap between the theoretical upper bound and the Monte-Carlosimulation results when ρ ≥ 0.4, indicating that the asymptoticinterference plus noise power, which is a lower bound of thetrue interference plus noise power, is no longer sufficientlytight. The CCDFs of the simulated throughputs per DRA fordifferent values of ρ are shown in Fig. 8(b), which statisticallyvalidates the curve of the simulated throughput per DRA givenin Fig. 8(a).
The impact of the Rician factor KRice on the achievablethroughput is shown in Fig. 9. Specifically, Fig. 9(a) de-picts the achievable throughputs per DRA as a functions ofthe Rician factor KRice, while the CCDFs of the simulatedthroughput per DRA recorded for different values of KRice
are given in Fig. 9(b). The results of Fig. 9 clearly show thata higher Rician factor leads to a higher throughput. Observingthe channel model (2), we can see that a higher KRice results ina larger deterministic or LOS component, which is beneficialfor the achievable performance.
B. Discussions
In the above extensive simulation study, we have carefullyinvestigated how the number of interfering aircraft A, thenumber of DTAs Nt, the number of DRAs Nr, the distance
da∗
b∗ between the desired pair of communicating aircraft, thecorrelation factor ρ between antennas, and the Rician factorKRice of the aeronautical communication channel impact onthe achievable system performance of our distance-based ACMand large-scale antenna array aided AANET. Based on thesimulation results, we can draw the following observations.
The distance between the desired pair of communicatingaircraft and the correlation factor of DTAs have adverse effectson the achievable system performance. Increasing da∗
b∗ and/orρ reduces the achievable transmission rate. On the otherhand, increasing the number of DTAs, the number of DRAs,and/or the Rician factor is beneficial for the achievable systemperformance. Specicially, increasing Nt and/or KRice lead tohigher transmission rate, while increasing Nr also increasesthe total transmission rate, although the achieved throughputper DRA is reduced with the increase of Nr.
Most importantly, our extensive simulation results havevalidated the design presented in Section III and provide theevidence that our design is capable of supporting the futureInternet above the clouds. For example, let us consider theAANET for airborne commercial Internet access having a5 GHz carrier frequency and a 6 MHz bandwidth, which isspatially shared by A = 14 other aircraft within the effectivecommunication zone covered by the AANET. When the dis-tance between the desired pair of communicating aircraft isda∗
b∗ = 10 km, our design is capable of offering a total datarate of 79 Mbps, as seen from Fig. 4. In the senario of A = 4and da∗
b∗ = 70 km, our design is capable of providing a totaldata rate of 60 Mbps, as observed from Fig. 5.
V. CONCLUSIONS
A large-scale antenna array aided and novel distance-basedACM scheme has been proposed for aeronautical communica-tions. Unlike the terrestrial instantaneous-SNR based ACM de-sign, which is unsuitable for aeronautical communication ap-plications, the proposed distance-based ACM scheme switches
13
Var[
Ha∗
b∗
][n∗
r : ]
[V a∗
b∗
][ :n∗
r ]
= E
∣∣∣∣∣([
Ha∗
b∗
][n∗
r : ]+[Ha∗
b∗
][n∗
r : ]
)[Ha∗
b∗
]H[n∗
r : ]− Tr
[Θa∗
b∗
](n∗
r ,n∗r)
∣∣∣∣∣2
≈ E
∣∣∣∣∣ [Ha∗
b∗
][n∗
r : ]
[Ha∗
b∗
]H[n∗
r : ]
∣∣∣∣∣2
= E
[Ha∗
b∗
][n∗
r : ]
[Ha∗
b∗
]H[n∗
r : ]
[Ha∗
b∗
][n∗
r : ]
[Ha∗
b∗
]H[n∗
r : ]
= E
[Ha∗
b∗
][n∗
r : ]E[
Ha∗
b∗
]H[n∗
r : ]
[Ha∗
b∗
][n∗
r : ]
[Ha∗
b∗
]H[n∗
r : ]
= E
[Ha∗
b∗
][n∗
r : ]
[Θa∗
b∗
](n∗
r ,n∗r)
[Ha∗
b∗
]H[n∗
r : ]
= Tr
[Ξa∗
b∗
](n∗
r ,n∗r)
[Θa∗
b∗
](n∗
r ,n∗r)
. (48)
its coding and modulation mode according to the distancebetween the desired communicating aircraft. Based on ourasymptotic closed-form theoretical analysis, we have explicitlyderived the set of distance-thresholds for the proposed ACMdesign and have provided a theoretical upper bound of theachievable spectral efficiency and throughput, which has con-sidered the impact of realistic channel estimation error andof co-channel interference. Our extensive simulation resultshave validated our design and theoretical analysis. This studytherefore has provided a practical high-data-rate and high-spectral-efficiency solution for supporting the future Internetabove the clouds.
APPENDIX
First, we have the following lemma.Lemma 1: Let A ∈ CN×N and x ∼ CN
(1√N
m, 1N Υ
),
where 1√N
m ∈ CN×1 and 1N Υ ∈ CN×N are the mean vector
and the covariance matrix of x, respectively. Assume that Ahas a uniformly bounded spectral norm with respect to N andx is independent of A. Then we have
limN→∞
xHAx =Tr(
1N
M +1N
Υ)
A
, (39)
where M = mmH.Proof: Let y =
√Nx−m. As x ∼ CN
(1√N
m, 1N Υ
),
we have y ∼ CN (0,Υ). Furthermore, we have
xHAx =(
1√N
m +1√N
y
)H
A
(1√N
m +1√N
y
)=
1N
mHAm +1N
yHAy +1N
mHAy +1N
yHAm.
(40)
Since y ∼ CN (0,Υ) and y does not depend on m, accordingto Lemma 1 of [43], we have
limN→∞
mHAy
N=0, (41)
limN→∞
yHAm
N=0. (42)
Furthermore, according to the trace lemma of [44], we have
limN→∞
(1√N
yH
)A
(1√N
y
)= Tr
1N
ΥA
. (43)
Substituting (41) to (43) into (40) leads to (39).
Recalling the distribution (20), we have
E[
Ha∗
b∗
]H[n∗
r : ]
[Ha∗
b∗
][n∗
r : ]
=[Θa∗
b∗
](n∗
r ,n∗r)
. (44)
Upon setting x =[Ha∗
b∗
][n∗
r : ]in conjunction with A = INt
in Lemma 1, we have
limNt→∞
[Ha∗
b∗
][n∗
r : ]
[Ha∗
b∗
]H[n∗
r : ]=Tr
[Θa∗
b∗
](n∗
r ,n∗r)
. (45)
Hence, for a large Nt, which is the case considered in thispaper, we have[
Ha∗
b∗
][n∗
r : ]
[Ha∗
b∗
]H[n∗
r : ]≈Tr
[Θa∗
b∗
](n∗
r ,n∗r)
. (46)
In addition, according to the distribution of[Ha∗
b∗
][n∗
r : ]given
in (25), we have
E[
Ha∗
b∗
]H[n∗
r : ]
[Ha∗
b∗
][n∗
r : ]
=[Ξa∗
b∗
](n∗
r ,n∗r)
. (47)
With the aid of (44) and (46) as well as (47), we can readilyderive (30), as shown in (48) at the top of this page.
REFERENCES
[1] A. Jahn, et al., “Evolution of aeronautical communications for personaland multimedia services,” IEEE Commun. Mag., vol. 41, no. 7, pp. 36–43, Jul. 2003.
[2] Q. Vey, A. Pirovano, J. Radzik, and F. Garcia, “Aeronauticalad hoc network for civil aviation,” in Proc. 6th Int. Workshop,Nets4Cars/Nets4Trains/Nets4Aircraft 2014 (Offenburg, Germany), May6-7, 2014, pp. 81–93.
[3] M. Schnell, U. Epple, D. Shutin, and N. Schneckenburger, “LDACS:future aeronautical communications for air-traffic management,” IEEECommun. Mag., vol. 52, no. 5, pp. 104–110, May 2014.
[4] R. Jain, F. Templin, and K.-S. Yin, “Analysis of L-band digital aeronau-tical communication systems: L-DACS1 and L-DACS2,” in Proc. 2011IEEE Aerospace Conf. (Big Sky, Montana), Mar. 5-12, 2011, pp. 1–10.
[5] J. M. Budinger and E. Hall, “Aeronautical mobile airport communi-cations system (AeroMACS),” NASA/TM–2011-217236, NASA GlennResearch Center, Oct. 2011.
[6] G. Bartoli, R. Fantacci, and D. Marabissi, “AeroMACS: a new perspec-tive for mobile airport communications and services,” IEEE WirelessCommun., vol. 20, no. 6, pp. 44–50, Dec. 2013.
[7] T. Graupl, M. Ehammer, and S. Zwettler, “L-DACS1 air-to-air data-linkprotocol design and performance,” in Proc. ICNS 2011 (Herndon, VA),May 10-12, 2011, pp. 1–10.
[8] B. Haind, “An independent technology assessment for a future aeronau-tical communication system based on potential systems like B-VHF,” inProc. DASC 2007 (Dallas, TX), Oct. 21-25, 2007, pp. 4.D.6-1–4.D.6-12.
[9] A. J. Goldsmith and S.-G. Chua, “Adaptive coded modulation for fadingchannels,” IEEE Trans. Commun., vol. 46, no. 5, pp. 595–602, May1998.
14
[10] L. Hanzo, C. H. Wong, and M. S. Yee, Adaptive Wireless Transceivers:Turbo-Coded, Turbo-Equalised and Space-Time Coded TDMA, CDMA,MC-CDMA and OFDM Systems. John Wiley: New York, USA, 2002.
[11] P. H. Tan, Y. Wu, and S. Sun, “Link adaptation based on adaptivemodulation and coding for multiple-antenna OFDM system,” IEEE J.Sel. Areas Commun., vol. 26, no. 8, pp. 1599–1606, Oct. 2008.
[12] E. Dahlman, S. Parkvall, and J. Skold, 4G: LTE/LTE-advanced forMobile Broadband. Academic Press, 2013.
[13] J. Meng and E.-H. Yang, “Constellation and rate selection in adaptivemodulation and coding based on finite blocklength analysis and itsapplication to LTE,” IEEE Trans. Wireless Commun., vol. 13, no. 10,pp. 5496–5508, Oct. 2014.
[14] E. Alberty, S. Defever, C. Moreau, R. De Gaudenzi, A. Ginesi, R. Ri-naldo, G. Gallinaro, and A. Vernucci, “Adaptive coding and modulationfor the DVB-S2 standard interactive applications: capacity assessmentand key system issues,” IEEE Wireless Commun., vol. 14, no. 4, pp. 61–69, Aug. 2007.
[15] S. Zhou and G. B. Giannakis, “Adaptive modulation for multiantennatransmissions with channel mean feedback,” IEEE Trans. WirelessCommun., vol. 3, no. 5, pp. 1626–1636, Sep. 2004.
[16] S. Zhou and G. B. Giannakis, “How accurate channel prediction needsto be for transmit-beamforming with adaptive modulation over RayleighMIMO channels?” IEEE Trans. Wireless Commun., vol. 3, no. 4,pp. 1285–1294, Jul. 2004.
[17] M. Taki, M. Rezaee, and M. Guillaud, “Adaptive modulation and codingfor interference alignment with imperfect CSIT,” IEEE Trans. WirelessCommun., vol. 13, no. 9, pp. 5264–5273, Sep. 2014.
[18] L. Hanzo, S. X. Ng, T. Keller, W. Webb, Quadrature AmplitudeModulation: From Basics to Adaptive Trellis-Coded, Turbo-Equalisedand Space-Time Coded OFDM, CDMA and MC-CDMA Systems (SecondEdition). Wiley-IEEE Press: New York, NY, USA, 2004.
[19] E. Haas, “Aeronautical channel modeling,” IEEE Trans. Vehicular Tech-nology, vol. 51, no. 2, pp. 254–264, Mar. 2002.
[20] S. Gligorevic, “Airport surface propagation channel in the C-Band:measurements and modeling,” IEEE Trans. Antennas and Propagation,vol. 61, no. 9, pp. 4792–4802, Sep. 2013.
[21] C. Zhang, K. Pang, and L. Ma, “Interpolated airborne MIMO antennaarray,” IEEE Antennas and Wireless Propagation Let., vol. 14, pp. 72–75, 2015.
[22] J. Zhang, T. Chen, S. Zhong, W. Zhang, X. Zuo, J. Darlington, R. G.Maunder, and L. Hanzo, “A survey of aeronautical ad-hoc networking,”submitted to IEEE Commun. Surveys & Tutorials, 2017.
[23] X. Gao, Z. Shen, and C. Hua, “Conformal VHF log-periodic balloonantenna,” IEEE Trans. Antennas and Propagation, vol. 63, no. 6,pp. 2756–2761, Jun. 2015.
[24] DO-242A, “Minimum aviation system performance standards for au-tomatic dependent surveillance-broadcast (ADS-B),” RTCA, Jun. 25,2002.
[25] J. D. Parsons, The Mobile Radio Propagation Channel (2nd Edition).Wiley, 2000.
[26] K. Kim, J. Lee, and H. Liu, “Spatial-correlation-based antenna groupingfor MIMO systems,” IEEE Trans. Vehicular Technology, vol. 59, no. 6,pp. 2898–2905, Jul. 2010.
[27] J. Zhang, S. Chen, X. Mu, and L. Hanzo, “Joint channel estimation andmultiuser detection for SDMA/OFDM based on dual repeated weightedboosting search,” IEEE Trans. Vehicular Technology, vol. 60, no. 7,pp. 3265–3275, Sep. 2011.
[28] R. E. Sheriff and Y. F. Hu, Mobile Satellite Communication Networks.John Wiley & Sons, 2003.
[29] S. M. Kay, Fundamentals of Statistical Signal Processing: EstimationTheory. Prentice-Hall: Upper Saddle River, 2003.
[30] A. B. Gershman, N. D. Sidiropoulos, S. Shahbazpanahi, M. Bengts-son, and B. Ottersten, “Convex optimization-based beamforming: Fromreceive to transmit and network designs,” IEEE Signal Process. Mag.,vol. 27, no. 3, pp. 62–75, May 2010.
[31] R. G. Lorenz and S. P. Boyd, “Robust minimum variance beamforming,”IEEE Trans. Signal Process., vol. 53, no. 5, pp. 1684–1696, May 2005.
[32] W. Yao, S. Chen, S. Tan, and L. Hanzo, “Minimum bit error ratemultiuser transmission designs using particle swarm optimisation,” IEEETrans. Wireless Commun., vol. 8, no. 10, pp. 5012–5017, Oct. 2009.
[33] B. R. Vojcic and W. M. Jang, “Transmitter precoding in synchronousmultiuser communications,” IEEE Trans. Commun., vol. 46, no. 10,pp. 1346–1355, Oct. 1998.
[34] J. Hoydis, S. Ten Brink, and M. Debbah, “Massive MIMO in the UL/DLof cellular networks: How many antennas do we need?” IEEE J. Sel.Areas Commun., vol. 31, no. 2, pp. 160–171, Feb. 2013.
[35] E. Sakhaee and A. Jamalipour, “The global in-flight Internet,” IEEE J.Sel. Areas Commun., vol. 24, no. 9, pp. 1748–1757, Sep. 2006.
[36] S. Gong, C. Xing, S. Chen, and Z. Fei, “Secure communications fordual-polarized MIMO systems,” IEEE Trans. Signal Process., vol. 65,no. 16, pp. 4177–4192, Aug. 2017.
[37] S. Gong, C. Xing, S. Chen, N. Yang, and Y. Zhou, “Robust energy-efficient precoding optimization for dual-polarized multiuser MIMOdownlink,” to be presented at Proc. ICCC 2017 (Chengdu, China), Dec.13-16, 2017, pp. 1–5.
[38] Comtech EF Data, “VersaFEC,” http://www.comtechefdata.com/technologies/fec/versafec, Accessed on February 3rd, 2016, [[Online].Available].
[39] H. A. Ngo and L. Hanzo, “Hybrid automatic-repeat-request systemsfor cooperative wireless communications,” IEEE Commun. Surveys &Tutorials, vol. 16, no. 1, pp. 25–45, 2014.
[40] H. Chen, R. G. Maunder, and L. Hanzo, “A survey and tutorial on low-complexity turbo coding techniques and a holistic hybrid ARQ designexample,” IEEE Commun. Surveys & Tutorials, vol. 15, no. 4, pp. 1546–1566, 2013.
[41] C. Martin and B. Ottersten, “Asymptotic eigenvalue distributions andcapacity for MIMO channels under correlated fading,” IEEE Trans.Wireless Commun., vol. 3, no. 4, pp. 1350–1359, Jul. 2004.
[42] B. Lee, J. Choi, J.-Y. Seol, D. J. Love, and B. Shim, “Antenna groupingbased feedback compression for FDD-based massive MIMO systems,”IEEE Trans. Commun., vol. 63, no. 9, pp. 3261–3274, Sep. 2015.
[43] F. Fernandes, A. Ashikhmin, and T. L. Marzetta, “Inter-cell interferencein noncooperative TDD large scale antenna systems,” IEEE J. Sel. AreasCommun., vol. 31, no. 2, pp. 192–201, Feb. 2013.
[44] J. Hoydis, “Random matrix theory for advanced communication sys-tems,” Ph.D. dissertation, Supelec, 2012.
Jiankang Zhang (S’08-M’12) received the B.Sc.degree in Mathematics and Applied Mathematicsfrom Beijing University of Posts and Telecommu-nications in 2006, and the Ph.D. degree in Commu-nication and Information Systems from ZhengzhouUniversity in 2012. Since then, he has been a lecturerin School of Information Engineering, ZhengzhouUniversity. From 2009 to 2011, Dr Zhang was avisiting researcher in the School of Electronics andComputer Science, the University of Southampton,UK. From 2013 to 2014, Dr Zhang was a postdoc-
toral researcher in the McGill University, Canada. From 2014, he has been aresearch fellow in the University of Southampton, UK. His research interestsare in the areas of wireless communications and signal processing, aircraftcommunication and wirelines communication.
Sheng Chen (M’90-SM’97-F’08) received his BEngdegree from the East China Petroleum Institute,Dongying, China, in 1982, and his PhD degree fromthe City University, London, in 1986, both in controlengineering. In 2005, he was awarded the higherdoctoral degree, Doctor of Sciences (DSc), fromthe University of Southampton, Southampton, UK.From 1986 to 1999, He held research and academicappointments at the Universities of Sheffield, Edin-burgh and Portsmouth, all in UK. Since 1999, he hasbeen with the School of Electronics and Computer
Science, the University of Southampton, UK, where he holds the post ofProfessor in Intelligent Systems and Signal Processing. Dr Chen’s researchinterests include adaptive signal processing, wireless communications, mod-elling and identification of nonlinear systems, neural network and machinelearning, intelligent control system design, evolutionary computation methodsand optimisation. He has published over 550 research papers. Dr. Chen is aFellow of the United Kingdom Royal Academy of Engineering, a Fellow ofIET, a Distinguished Adjunct Professor at King Abdulaziz University, Jeddah,Saudi Arabia, and an ISI highly cited researcher in engineering (March 2004).
15
Robert Maunder (SM’12) received a first classhonours BEng degree in Electronic Engineering inJuly 2003 and the PhD degree in Telecommuni-cations in December 2007, from the University ofSouthampton. He began a lectureship in November2007 with the School of Electronics and ComputerScience, the University of Southampton, UK, andwas promoted to Associate Professor in March 2013and to Professor in August 2017. Professor Maun-der’s research interests include joint source/channelcoding and the holistic design of algorithms and
hardware implementations for wireless communications. He has publisheda number of IEEE papers in these areas. He is the founder and CTO ofAccelerComm Ltd, which is commercialising his research as soft-IP. DrMaunder is a Chartered Engineer and a Fellow of the IET.
Rong Zhang (M’09-SM’16) received his PhD inwireless communications from the University ofSouthampton (UoS) in 2009, where he was a re-search assistant during that period with the MobileVirtual Centre of Excellence, one of UK’s largestindustrial-academic partnership in ICT. During hispost-doctoral period with the School of Electronicsand Computer Science, the UoS, he contributed, asa UoS lead researcher, to a number of internationalprojects. After that, he took his industrial consultingleave for Huawei EU R&D as a System Algorithms
Expert. Currently, he is an assistant professor in Southampton Wireless Group,the UoS. Dr Zhang has a total of 80+ IEEE/OSA publications, including 55+journals (20+ of which as the first author). Owing to his outstanding academicachievements, he is the recipient of the prestigious Dean’s Publication Award,Faculty of Physical Sciences and Engineering, the UoS. He is also the recipientof the prestigious RAEng industrial fellowship. He regularly serves as reviewerfor IEEE/OSA journals and funding bodies and has been several times as TPCmember/invited session chair of major conferences. He is a RAEng industrialfellow and a member of the OSA.
Lajos Hanzo FREng, FIEEE, FIET, Fellow ofEURASIP, DSc, received his degree in electronicsin 1976 and his doctorate in 1983. In 2009 he wasawarded an honorary doctorate by the TechnicalUniversity of Budapest and in 2015 by the Univer-sity of Edinburgh. In 2016 he was admitted to theHungarian Academy of Science. During his 40-yearcareer in telecommunications he has held variousresearch and academic posts in Hungary, Germanyand the UK. Since 1986 he has been with the Schoolof Electronics and Computer Science, University of
Southampton, UK, where he holds the chair in telecommunications. He hassuccessfully supervised 111 PhD students, co-authored 18 John Wiley/IEEEPress books on mobile radio communications totalling in excess of 10,000pages, published 1701 research contributions at IEEE Xplore, acted bothas TPC and General Chair of IEEE conferences, presented keynote lecturesand has been awarded a number of distinctions. Currently he is directing anacademic research team, working on a range of research projects in the field ofwireless multimedia communications sponsored by industry, the Engineeringand Physical Sciences Research Council (EPSRC) UK, the European ResearchCouncil’s Advanced Fellow Grant and the Royal Society’s Wolfson ResearchMerit Award. He is an enthusiastic supporter of industrial and academic liaisonand he offers a range of industrial courses. He is also a Governor of the IEEEVTS. During 2008-2012 he was the Editor-in-Chief of the IEEE Press and aChaired Professor also at Tsinghua University, Beijing. For further informationon research in progress and associated publications please refer to http://www-mobile.ecs.soton.ac.uk. Professor Hanzo has 30,000+ Google Scholar citationsand an H-index of 70.
