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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 2, FEBRUARY 2018 1343
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 abovethe clouds," we propose a multiple-antenna aided adaptive codingand modulation (ACM) for aeronautical communications. Theproposed ACM scheme switches its coding and modulationmode according to the distance between the communicatingaircraft, which is readily available with the aid of the airborneradar or the global positioning system. We derive an asymptoticclosed-form expression of the signal-to-interference-plus-noiseratio (SINR) as the number of transmitting antennas tends toinfinity, in the presence of realistic co-channel interference andchannel estimation errors. The achievable transmission rates andthe corresponding 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 four 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-Mb/s data rate when thecommunication distance is less than 25 km.
Index Terms— Aeronautical communication, large-scaleantenna array, Rician channel, adaptive coding and modulation,precoding.
I. INTRODUCTION
THE appealing service of the ‘Internet above theclouds’ [1] motivates researchers to develop high data
rate and high spectral-efficiency (SE) aeronautical communica-tion techniques. Traditionally, satellite-based access has beenthe main solution for aeronautical communication. However,
Manuscript received March 1, 2017; revised September 9, 2017; acceptedNovember 23, 2017. Date of publication December 4, 2017; date of currentversion February 9, 2018. This work was supported in part by the EuropeanResearch Council’s Advanced Fellow Grant, in part by the Royal SocietyWolfson Research Merit Award, in part by the Innovate U.K. throughHarmonised Antennas, Radios, and Networks, and in part by the NationalNatural Science Foundation of China under Grant 61301150. The researchdata for this paper is available at https://doi.org/10.5258/SOTON/D0315. Theassociate editor coordinating the review of this paper and approving it forpublication was Z. Sun. (Corresponding author: Lajos Hanzo.)
J. Zhang is with the School of Electronics and Computer Science,University of Southampton, Southampton SO17 1BJ, U.K., and alsowith the School of Information Engineering, Zhengzhou University,Zhengzhou 450001, China (e-mail: [email protected]).
S. Chen is with the School of Electronics and Computer Science, Universityof Southampton, Southampton SO17 1BJ, U.K., and also with King AbdulazizUniversity, Jeddah 21589, Saudi Arabia (e-mail: [email protected]).
R. G. Maunder, R. Zhang, and L. Hanzo are with the School of Electronicsand Computer Science, University of Southampton, Southampton SO17 1BJ,U.K. (e-mail: [email protected]; [email protected]; [email protected]).
Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TWC.2017.2777985
it suffers from the drawbacks of low throughput and highprocessing delay as well as high charges by the satelliteproviders. The aeronautical ad hoc network (AANET) [2]concept was conceived for supporting direct communicationand data relaying among aircraft for airborne Internet access.However, the current existing transmission techniques areincapable of providing the high throughput and high SE com-munications among aircraft required by this airborne Internetaccess application.
The planed future aeronautical communication systems,specifically, the L-band digital aeronautical communicationssystem (L-DACS) [3], [4] and the aeronautical mobile airportcommunication 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 positioning
1536-1276 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
1344 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 2, FEBRUARY 2018
system (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 powerful tech-nique of increasing data rate and improving SE over wirelessfading channels. It has been extensively investigated also inthe context of IEEE 802.11 [11], LTE-advance 4G mobilesystems [12], [13] and broadband satellite communicationsystems [14]. The optimal ACM relies on the perfect knowl-edge of the instantaneous CSI, but channel estimation errorsare unavoidable in practical communication systems [15].Furthermore, the CSI of frequency division duplexing basedsystems must be obtained through a feedback channel, whichpotentially introduces feedback errors and delays [16]. Thesefactors significantly degrade the ACM performance. In order toreduce the sensitivity to CSI errors, Zhou and Giannakis [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] and [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, on anaircraft [22], especially a large-scale antenna array, the devel-opment 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 andlarge-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 adopted
by 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 switchesits ACM mode based on the distance between thedesired pair of communicating aircraft. This schemeis more practical than the existing ACM schemes thatrely on instantaneous channel-quality metrics, such asthe instantaneous signal-to-noise ratio (SNR). This isbecause in aeronautical communication it is extremelydifficult to acquire an accurate estimate for any instan-taneous channel-quality metric, and an ACM based onsuch a switching metric will frequently fail. By contrast,the accurate distance information between the com-municating aircraft can readily be acquired with theaid airborne radar. Alternatively, the accurate positioninformation can also be acquired with the assistance ofGPS.
2) We explicitly derive a closed-form expression ofthe asymptotic signal-to-interference-plus-noiseratio (SINR) of multiple-antenna aided aeronauticalcommunication in the presence of realistic channelestimation errors and the co-channel interferenceimposed by other aircraft within the communicationrange. This closed-form SINR formula enables us todirectly derive the achievable theoretical transmissionrates and the associated mode-switching distance-thresholds for the proposed ACM scheme. Moreover,as a benefit of large-scale antenna arrays, every pair ofcommunicating aircraft in our system uses the samefrequency resource block, which dramatically enhancesthe 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-formasymptotic 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 withina given communication zone.1 Aircraft a∗ and b∗ are thedesired pair of communicating aircraft, with a∗ transmittingdata to b∗, while aircraft a = 1, 2, · · · , A are interferingaircraft. As the system operates in SHF band, it is feasible todesign compact high-gain antennas [25] and hence to deploya large-scale antenna array on an aircraft. This also enables
1Since Internet access is forbidden at takeoff and landing, it is reasonableto consider only aircraft en-route at cruising altitude.
ZHANG et al.: ACM FOR LARGE-SCALE ANTENNA ARRAY-BASED AERONAUTICAL COMMUNICATIONS 1345
Fig. 1. A TDD based aeronautical communication model with co-channel interference, where aircraft a∗ is transmitting data to aircraft b∗.
every pair 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 , Nt }determine the supportable data streams, and thus the numberof DRAs should be no higher than the number of DTAsin order to make sure that the number of data streamsafter transmit precoding is no higher than min {Nr , Nt }; and2) The remaining (Ntotal − Nr ) or (Ntotal − Nt ) antennas arecapable of transmitting/receiving other information, such asair traffic control or emergency information, at a frequencydifferent from that of the data transmission. The systemadopts orthogonal frequency-division multiplexing (OFDM)for mitigating the multipath effects and for achieving a highSE. We further assume that all the aircraft are jumbo jets, andthey are all equipped with a same large-scale antenna array.We also assume that each aircraft has an airborne radar capableof measuring the distance to nearby aircraft. Alternatively,the distance 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 toreceive data. Therefore, a∗ has to know the multi-input multi-output (MIMO) channel matrix linking its Nt DTAs to theNr DRAs of b∗ in order to carry out transmit precoding. Thechannel estimation is performed by pilot based training beforedata transmission, as shown in Fig. 1 (a). More specifically,aircraft b∗ transmits pilot symbols from its Nr DRAs to aircrafta∗’s Nt DTAs to enable a∗ to perform the training basedchannel estimation. The required MIMO channel matrix canthen be obtained by exploiting the TDD channel’s reciprocity.
A. Pilot Based Training
During the pilot based training stage shown in Fig. 1 (a),aircraft b∗ transmits its pilot symbols via its Nr DRAs to
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 samepilot symbols as aircraft b∗. The frequency domain (FD)MIMO channel between the Nr DRAs of b∗ and the Nt DTAsof a∗, on the nth OFDM subcarrier of the sth symbol, isdefined by the matrix Hb∗
a∗ [s, n] ∈ CNt ×Nr , where 0 ≤ n ≤N −1 with N denoting the length of the OFDM block. Let usassume that the length of the cyclic prefix (CP) Ncp is longerthan the channel impulse response (CIR) P . The FD discretesignal model at the nth subcarrier and sth time interval duringthe pilot training period can be written as
˜Ya∗[s, n] =√
Pb∗r,a∗ Hb∗
a∗ [s, n]˜Xb∗ [s, n]
+A∑
a=1
√
Par,a∗ Ha
a∗ [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, σ 2w INt
)
is the associatedFD additive white Gaussian noise (AWGN) vector, whilethe worst-case co-channel interference is considered with˜Xa[s, n] = ˜Xb∗ [s, n] for 1 ≤ a ≤ A. Here we have used0 to represent the zero vector of an appropriate dimensionand INr to represent the (Nr × Nr )-element identity matrix.Furthermore, in (1), Pb∗
r,a∗ and Par,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] = ν Hb∗
d,a∗[s, n] + ς Hb∗r,a∗[s, n], (2)
1346 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 2, FEBRUARY 2018
vec(
Hb∗a∗)
= vec(
ν Hb∗d,a∗
)
+ ς2 Rrr,t
(
σ 2w
Pb∗r,a∗
INr Nt + ς2 Rrr,t +
A∑
a=1
Par,a∗
Pb∗r,a∗
ς2 Rrr,t
)−1
×⎛
⎝vec(
ς Hb∗r,a∗)
+A∑
a=1
√
Par,a∗
Pb∗r,a∗
vec(
ς Har,a∗)+ 1
√
Pb∗r,a∗
vec(
˜Wa∗(
˜Xb∗)H
)
⎞
⎠. (9)
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 =√
KRiceKRice+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] = R
12a∗ 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] ∈ C
Nt ×Nr has theindependently identically distributed complex-valued entries,each obeying the distribution CN (0, 1). As a benefit of theCP, the OFDM symbols do not overlap in time and theprocessing 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 applied tomatrix A. Clearly, E
{
vec(
Hb∗r,a∗)
}
= 0, where E{ } denotes
the expectation operator, and the covariance matrix Rb∗r,a∗ ∈
CNt Nr ×Nt Nr of vec(
Hb∗r,a∗)
is given by
Rb∗r,a∗ = E
{
vec(
Hb∗r,a∗) (
vec(
Hb∗r,a∗))H
}
= Rb∗ ⊗ Ra∗,
(4)
where ⊗ denotes the matrix Kronecker product. Therefore,vec
(
Hb∗a∗)
∼ CN(
vec(
ν Hb∗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 hold.2 By the same argument,we assume that Rar = Rr ∀ar ∈ A hold.3 Thus, all thechannels’ covariance matrices are assumed to be equal, i.e., wehave
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 channelcovariance matrix Rb∗
r,a∗ = Rb∗ ⊗ Ra∗ = Ra∗ ⊗ Ra∗ = Rr ⊗ Rt .
2It is reasonable to assume that all jumbo jets are equipped with identicalantenna array. However, because the geometric shapes of different types ofjumbo jets are slightly different, Rat = Rt ∀at ∈ A only hold approximately.
3Similarly, Rar = Rr ∀ar ∈ A only hold approximately.
It can be seen that Rb∗ = Ra∗is the real assumption required.4
The received power Pb∗r,a∗ at aircraft a∗ is linked to the
transmitted signal power Pb∗t of aircraft b∗ by the following
path loss model [25]
Pb∗r,a∗ = Pb∗
t 10−0.1Lb∗
path loss,a∗ , (6)
where Lb∗path loss,a∗ represents the path loss in dB, which can
be 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 Pa
r,a∗ , we have a similarpath loss model. Each entry of the FD AWGN vector Wa∗obeys the distribution C N(0, σ 2
w) with σ 2w = PN
N , in whichPN is the receiver noise power given by [28]
PN = FkT0 B, (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.
Since every aircraft knows its channel covariancematrix, we can apply the optimal minimum mean squareerror (MMSE) estimator [29] to estimate the channel matrixHb∗
a∗ . The MMSE estimate Hb∗a∗ of Hb∗
a∗ is given in (9), shown
at the top of this page, where ˜Xb∗
∈ CNr ×Nr consists of
the Nr pilot symbols with ˜Xb∗(
˜Xb∗)H = INr , and ˜Wa∗ ∈
CNr ×Nr is the corresponding AWGN vector over the Nr
consecutive OFDM pilot symbols. It is well-known that thedistribution of the MMSE estimator (9) is vec
(
Hb∗a∗)
∼CN
(
vec(
ν Hb∗d,a∗
)
,�b∗a∗)
[29], that is, vec(
Hb∗a∗)
is an unbi-
ased estimate of vec(
Hb∗a∗)
with the estimation accuracy
specified by the covariance matrix �b∗a∗ ∈ CNt Nr ×Nt Nr , which
is given by
�b∗a∗ = ς2 Rr
r,t
(
σ 2w
Pb∗r,a∗
INr Nt + ς2 Rrr,t +
A∑
a=1
Par,a∗
Pb∗r,a∗
ς2 Rrr,t
)−1
× ς2 Rrr,t . (10)
4Alternatively, we can also avoid imposing this assumption. Then, a∗ canask 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.
ZHANG et al.: ACM FOR LARGE-SCALE ANTENNA ARRAY-BASED AERONAUTICAL COMMUNICATIONS 1347
B. Data Transmission
During the data transmission, aircraft a∗ transmits the sym-bols Xa∗ = [
Xa∗1 Xa∗
2 · · · Xa∗Nr
]T ∈ CNr ×1 from its Nt DTAs tothe Nr DRAs of aircraft b∗. Let us denote the MIMO channelmatrix during this data transmission as Ha∗
b∗ ∈ CNr ×Nt . Then,upon exploiting the channel’s reciprocity in TDD 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 matrix V a∗
b∗ ∈CNt ×Nr , including the convex optimization based methodof [30], the minimum variance method of [31], the minimumbit-error rate (MBER) design of [32], the MMSE designof [33] and the zero-forcing (ZF) design as well as the eigen-beamforming or matched filter (MF) design of [34]. For alarge-scale MIMO system, the complexity of the optimizationbased TPC designs of [30]–[32] may become excessive. Addi-tionally, in this case, the performance of the MBER design [32]is indistinguishable from the MMSE one. Basically, for large-scale antenna array based MIMO, the performance of theMMSE, ZF and MF based TPC solutions are sufficiently good.The MF TPC design offers the additional advantage of thelowest complexity and, therefore, it is chosen in 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 the
channel estimate obtained during pilot training.In the presence of the interference imposed by aircraft a for
1 ≤ 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∗ =√
Pa∗r,b∗ Ha∗
b∗ V a∗b∗ Xa∗ +
A∑
a=1
√
Par,b∗ Ha
b∗ V aba Xa + Wb∗,
(12)
where V aba ∈ CNt ×Nr denotes the TPC matrix at aircraft a
transmitting the signal Xa = [
Xa1 Xa
2 · · · XaNr
]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, σ 2w INr
)
. Inparticular, 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 nr th row of A ∈ CN×M
and [A][ :nr ] ∈ CN×1 denotes the nr th 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 basedon the channel estimate obtained during the pilot train-ing by exploiting the TDD channel’s reciprocity. However,
the receiving aircraft b∗ does not have this CSI. Thus,the ergodic achievable rate is adopted for analyzing the achiev-able throughput. In order to explicitly derive this capacity,we rewrite the received signal at the antenna n∗
r of aircraft b∗,namely, Y b∗
n∗r
of (13), as shown at the top of the next page,in the form given in (14), as shown at the top of the nextpage. Observe that the first term of (14) is the desired signal,the second term is the interference caused by the channelestimation error, the third term is the interference arriving fromthe other antennas of b∗, and the fourth term is the interferenceimpinging from the interfering aircraft, while the last term isof course the noise. Thus, the SINR at the nr -th antenna ofb∗, denoted by γ a∗
b∗,nr, is given by
γ a∗b∗,nr
=Pa∗
r,b∗
∣
∣
∣
∣
E{
[
Ha∗b∗]
[n∗r : ]
[
V a∗b∗]
[ :n∗r ]
}∣
∣
∣
∣
2
PI&Na∗b∗,nr
, (15)
in which the power of the interference plus noise is
PI&Na∗b∗,nr
= σ 2w + Pa∗
r,b∗Var
{
[
Ha∗b∗]
[n∗r : ]
[
V a∗b∗]
[ :n∗r ]
}
+ Pa∗r,b∗
∑
nr �=n∗r
E
{
∣
∣
∣
∣
[
Ha∗b∗]
[n∗r : ]
[
V a∗b∗]
[ :nr ]
∣
∣
∣
∣
2}
+A∑
a=1
Par,b∗
Nr∑
nr =1
E{
∣
∣
∣
[
Hab∗]
[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 + γ a∗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 4.63 km)when surveillance radars are intensively deployed, such as inan airport’s airspace. Thus, the minimum distance is set toDmin = 5 km in the envisaged AANET. Intuitively, an aircraftalways transmits its signal to an aircraft having the bestpropagation link with it for relying its information in theAANET. Here we simply assume that a pair of aircraft having
1348 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 2, FEBRUARY 2018
Y b∗n∗
r=√
Pa∗r,b∗
[
Ha∗b∗]
[n∗r : ] V a∗
b∗ Xa∗ +A∑
a=1
√
Par,b∗
[
Hab∗]
[n∗r : ] V a
ba Xa + W b∗n∗
r=√
Pa∗r,b∗
[
Ha∗b∗]
[n∗r : ]
[
V a∗b∗]
[ :n∗r ] Xa∗
n∗r
+∑
nr �=n∗r
√
Pa∗r,b∗
[
Ha∗b∗]
[n∗r : ]
[
V a∗b∗]
[ :nr ]Xa∗
nr+
A∑
a=1
Nr∑
nr =1
√
Par,b∗
[
Hab∗]
[n∗r : ][
V aba
]
[ :nr ] Xanr
+ W b∗n∗
r, (13)
Y b∗n∗
r= E
{
√
Pa∗r,b∗
[
Ha∗b∗]
[n∗r : ]
[
V a∗b∗]
[ :n∗r ]
}
Xa∗n∗
r+(
√
Pa∗r,b∗
[
Ha∗b∗]
[n∗r : ]
[
V a∗b∗]
[ :n∗r ] − E
{
√
Pa∗r,b∗
[
Ha∗b∗]
[n∗r : ]
[
V a∗b∗]
[ :n∗r ]
})
Xa∗n∗
r
+∑
nr �=n∗r
√
Pa∗r,b∗
[
Ha∗b∗]
[n∗r : ]
[
V a∗b∗]
[ :nr ]Xa∗
nr+
A∑
a=1
Nr∑
nr =1
√
Par,b∗
[
Hab∗]
[n∗r : ][
V aba
]
[ :nr ] Xanr
+ W b∗n∗
r. (14)
the 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 signalpower for the transmission from aircraft a to aircraft b∗ as
Pr = Par,b∗ = E
{
Par,b∗} = Pa
t1015.406
f 2
1
Dmax Dmin. (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 statis-
tically 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(
ν Ha∗d,b∗)
,�a∗b∗)
, (20)
where the covariance matrix �a∗b∗ of the MMSE estimate
vec(
Ha∗b∗)
is given by.
�a∗b∗ = ς2 Rt
r,r
(
σ 2w
Pa∗r,b∗
INr Nt + ς2 Rtr,r +
A∑
a=1
Par,a∗
Pa∗r,b∗
ς2 Rtr,r
)−1
× ς2 Rtr,r , (21)
in which ς2 Rtr,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 �a∗b∗ . Clearly,
we have
�a∗b∗ = ς2 Rt
r,r − �a∗b∗ ∈ C
Nt Nr ×Nt Nr , (23)
and �a∗b∗ can be explicitly expressed in the following form
�a∗b∗ =
⎡
⎢
⎢
⎢
⎣
[
�a∗b∗]
(1,1)
[
�a∗b∗]
(1,2)· · ·
[
�a∗b∗]
(1,Nr )...
... · · · ...[
�a∗b∗]
(Nr ,1)
[
�a∗b∗]
(Nr ,2)· · ·
[
�a∗b∗]
(Nr ,Nr )
⎤
⎥
⎥
⎥
⎦
,
(24)
where[
�a∗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,[
�a∗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}
= ν2 Ma∗b∗ + �a∗
b∗ , where
Ma∗b∗ = vec
(
Hb∗d,a∗
)
vec(
Hb∗d,a∗
)H ∈ CNt Nr ×Nt Nr . (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 )+[
�a∗b∗]
(n∗r ,n∗
r )
}
, (27)
where Tr{ } denotes the matrix trace operator, and[
�a∗b∗]
(i, j )∈
CNt ×Nt , ∀i, j ∈ {1, 2, · · · , Nr }, is the (i, j)-th sub-matrix of�a∗
b∗ which has a structure similar to (24). Thus, by denoting[
�a∗b∗]
(n∗r ,n∗
r )= ν2
[
Ma∗b∗]
(n∗r ,n∗
r )+[
�a∗b∗]
(n∗r ,n∗
r ), (28)
ZHANG et al.: ACM FOR LARGE-SCALE ANTENNA ARRAY-BASED AERONAUTICAL COMMUNICATIONS 1349
we have∣
∣
∣
∣
E{
[
Ha∗b∗]
[n∗r : ]
[
V a∗b∗]
[ :n∗r ]
}∣
∣
∣
∣
2
=(
Tr
{
[
�a∗b∗]
(n∗r ,n∗
r )
})2
.
(29)
Note that multiplying (29) with Pa∗r,b∗ leads to the desired signal
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
{
[
�a∗b∗]
(n∗r ,n∗
r )
[
�a∗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 )
+( [
�a∗b∗]
(nr ,nr )+ σ 2
w
Pa∗r,b∗
INt +A∑
a=1
Par,a∗
Pa∗r,b∗
ς2 [Rtr,r
]
(nr ,nr )
)
×[
�a∗b∗]
(nr ,nr )
)(
ν2[
Ma∗b∗]
(n∗r ,n∗
r )+ ς2 [Rt
r,r
]
(n∗r ,n∗
r )
)}
,
(31)
asymptotically, where[
�a∗b∗]
(nr ,nr )∈ CNt ×Nt is given by
[
�a∗b∗]
(nr ,nr )= ς2 [Rt
r,r
]
(nr ,nr )
( σ 2w
Pa∗r,b∗
INt + [
Rtr,r
]
(nr ,nr )
+A∑
a=1
Par,a∗
Pa∗r,b∗
ς2 [Rtr,r
]
(nr ,nr )
)−1, (32)
in which[
Rtr,r
]
(i, j )∈ CNt ×Nt , ∀i, j ∈ {1, 2, · · · , Nr },
represents the (i, j)-th sub-matrix of Rtr,r , which has
a structure similar to (24). Similarly, we can express
E{
∣
∣
∣
[
Hab∗]
[n∗r : ][
V aba
]
[ :nr ]∣
∣
∣
2}
asymptotically as
E{
∣
∣
∣
[
Hab∗]
[n∗r : ][
V aba
]
[ :nr ]∣
∣
∣
2}
= Tr
{(
ν2 [Maba
]
(nr ,nr )
+(
[
�aba
]
(nr ,nr )+
A∑
a=1
Par,a∗ς2
Pa∗r,b∗
[
Rtr,r
]
(nr ,nr )+ σ 2
w
Pa∗r,b∗
INt
)
× [
�aba
]
(nr ,nr )
)
(
ν2 [Mab∗]
(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∗,nrgiven in (34) at the top of this page.
Fig. 2. Schematic of the proposed distance-based adaptive coding andmodulation scheme.
Furthermore, substituting (29) into (15) leads to the followingasymptotic SINR expression
γ a∗b∗,nr
=Pa∗
r,b∗
(
Tr
{
[
�a∗b∗]
(n∗r ,n∗
r )
})2
PI&Na∗b∗,nr
. (35)
Remark 1: Both[
Maba
]
(nr ,nr )and
[
Mab∗]
(n∗r ,n∗
r )in (34), as
shown at the bottom of the next page, are unavailable toaircraft a∗, since there is no cooperation between the relatedaircraft. However, both these two terms can be substituted by[
Ma∗b∗]
(n∗r ,n∗
r )as a reasonable approximation. The simulation
results presented in Section IV will demonstrate that thisapproximation 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 Cramér-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 scopeof this paper. Some highly effective robust precoding designscan be found in [36] and [37].
Remark 3: As our derivation does not impose any spe-cific geometric structure on the antenna array, our resultsand therefore our proposed physical-layer transmissionscheme is applicable to systems equipped with uniformlyspaced linear arrays (ULAs), uniformly spaced rectangulararrays (URAs), or any other generic antenna arrays.
B. Distance-Based ACM Scheme
The proposed distance-based ACM scheme is illustratedin Fig. 2. Our scheme explicitly uses the distance da∗
b∗between aircraft a∗ and aircraft b∗ as the switching metricto adapt the modulation mode and code rate. Similar to theconventional ACM scheme, our distance-based ACM alsoconsists of the set of K ACM modes, but its switching
1350 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 2, FEBRUARY 2018
TABLE I
AN EXAMPLE OF ADAPTIVE CODING AND MODULATION SCHEME WITH Nt = 32 AND Nr = 4. THE OTHER SYSTEM PARAMETERSFOR THIS ACM ARE LISTED IN TABLE III
TABLE II
AN 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
thresholds comprise the K distance thresholds {dk}Kk=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 thedata rate per DRA is calculated as: spectral efficiency× Btotal,in which Btotal is the bandwidth available, while the total datarate is given by: data rate per DRA × Nr . The modulationschemes and code rates are adopted from the design ofVersaFEC [38], which covers a family of 12 short-block LDPCcode rates with the matched modulation schemes. VersaFEC isspecifically designed for low latency and ACM applications.The operations of this distance-based ACM are now givenbelow.
1) Aircraft a∗ estimates the channel Ha∗b∗ based on the pilots
transmitted by aircraft b∗, as detailed in Section II-A.2) Aircraft a∗ calculates the TPC matrix V a∗
b∗ accordingto (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’ communication
range. 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 perDRA as a function of distance is calculated using (15). Thedistance thresholds {dk}K
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 bandwidth isBtotal = 6 MHz which is reused by every aircraft in the system.The theoretically achievable rate per DRA as a function ofdistance is depicted as the dot-marked solid curve in Fig. 3(a).By designing the 7 distance thresholds dk for 1 ≤ k ≤ 7 toensure that the SE of mode k is lower than the theoreticallyachievable rate in the distance range [dk, dk−1], we obtain the7 desired distance thresholds for this ACM example, which areindicated in Fig. 3(a) as well as listed in Table I. The designed7 ACM modes are: mode 1 having the SE of 0.459 bps/Hz,mode 2 with the SE 1.000 bps/Hz, mode 3 with the SE1.322 bps/Hz, mode 4 with the SE 1.809 bps/Hz, mode 5with the SE 2.194 bps/Hz, mode 6 with the 2.747 bps/Hz,and mode 7 with the SE 3.197 bps/Hz.
PI&Na∗b∗,nr
= σ 2w + Pa∗
r,b∗Tr
{
[
�a∗b∗]
(n∗r ,n∗
r )
[
�a∗b∗]
(n∗r ,n∗
r )
}
+ Pa∗r,b∗
Nr∑
nr =1nr �=n∗
r
Tr
{(
ν2[
Ma∗b∗]
(nr ,nr )+( [
�a∗b∗]
(nr ,nr )+ σ 2
w
Pa∗r,b∗
INt
+ APr
Pa∗r,b∗
ς2 [Rtr,r
]
(nr ,nr )
) [
�a∗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 [Maba
]
(nr ,nr )
+(
[
�aba
]
(nr ,nr )+ APr
Pa∗r,b∗
ς2 [Rtr,r
]
(nr ,nr )+ σ 2
w
Pa∗r,b∗
INt
)
[
�aba
]
(nr ,nr )
)
(
ν2 [Mab∗]
(n∗r ,n∗
r )+ ς2 [Rt
r,r
]
(n∗r ,n∗
r )
)
}
. (34)
ZHANG et al.: ACM FOR LARGE-SCALE ANTENNA ARRAY-BASED AERONAUTICAL COMMUNICATIONS 1351
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.
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 the same asthe ACM scheme listed in Table I. As shown in Fig. 3(b) andTable II, the five ACM modes have the SEs of 1.322 bps/Hz,1.809 bps/Hz, 2.194 bps/Hz, 2.747 bps/Hz and 3.197 bps/Hz,respectively, while the corresponding switching thresholds are400 km, 250 km, 120 km, 50 km, and 5.56 km, respectively.By comparing Table II to Table I, it can be seen that employinga larger number of transmit antennas enables an ACM modeto operate over a larger range of distances, or it allows thesystem to transmit at a higher SE over a given communicationdistance. This makes sense because a well-known MIMOproperty is that employing more transmit antennas can mitigatethe interference more effectively.
Remark 4: It is worth recapping that the conventionalinstantaneous SNR-based ACM is unsuitable for aeronauticalcommunication applications, because the speed of aircraft isultra high, which results in rapidly changing of large-scalefading and consequently very unreliable estimate of theinstantaneous SNR as well as leads to frequently switchingamong 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, whichis readily available to the transmitting aircraft, since everyjumbo jet has a radar and is equipped with GPS. It can be seenthat this distance-based ACM scheme is particularly suitablefor aeronautical communication applications. Furthermore,it is worth emphasizing that using the distance as theswitching metric is theoretically well justified, because for theaeronautical communication channel the achievable capacityis mainly dependent on the distance, as we have analytically
TABLE III
DEFAULT PARAMETERS USED IN THE SIMULATED AERONAUTICAL
COMMUNICATION SYSTEM
derived 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 enhancingreliable communication among aircraft. Discussing thesehigher-layer techniques is beyond the scope of this paper.
IV. SIMULATION STUDY
The default values of the parameters used for our sim-ulated aeronautical communication system are summarizedin Table III. Unless otherwise specified, these default valuesare used. 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 at
1352 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 2, FEBRUARY 2018
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
[
da∗b∗ , Dmax
]
. The rest of the parameters are specified in Table III.
the receiver. The deterministic part of the Rician channel,which satisfies Tr
{
Had,b Ha,H
d,b
}
= Nt Nr , is generated in everyMonte-Carlo simulation. The scattering component of theRician channel Ha
r,b ∈ CNr ×Nt is generated according to
Har,b = Rb G Ra, (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 ∼ C N(0, 1)is the magnitude of the correlation coefficient, which is deter-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[
Maba
]
(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. Results
Fig. 4(a) investigates the achievable throughput per DRA asa 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 approximation of
both the unknown[
Maba
]
(nr ,nr )and
[
Mab∗]
(n∗r ,n∗
r ). As expected,
the achievable throughput degrades as the number of inter-fering aircraft increases. Also the theoretical throughput is
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 asa 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 toNt ≥ 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 increase
ZHANG et al.: ACM FOR LARGE-SCALE ANTENNA ARRAY-BASED AERONAUTICAL COMMUNICATIONS 1353
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 of[
da∗b∗ , Dmax
]
. The rest of the parameters are specified in Table III.
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 throughputs perDRA for different numbers of DTAs Nt . The distances between the interfering aircraft and the desired receiving aircraft are uniformly distributed within therange of
[
da∗b∗ , Dmax
]
. The rest of the parameters are specified in Table III.
in the sum rate is not proportional to the increase of Nr . In fact,it is clearly seen from Fig. 7(a) that the achievable throughputper DRA is reduced with the increase of Nr . The reason forthis trend is because the inter-antenna interference increaseswith the increase of Nr , as seen in the third and fourth termsof (34). The CCDFs of the simulated throughputs per DRA areillustrated in Fig. 7(b) for different Nr , which agree with thecurve of the simulated capacity per DRA shown in Fig. 7(a),namely the achievable throughput per DRA is lower for largernumber 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 achiev-able throughput is shown in Fig. 9. Specifically, Fig. 9(a)depicts the achievable throughputs per DRA as a functions
1354 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 2, FEBRUARY 2018
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
[
da∗b∗ , Dmax
]
. Therest of the parameters are specified in Table III.
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 of[
da∗b∗ , Dmax
]
. The rest of the parameters are specified in Table III.
of the Rician factor KRice, while the CCDFs of the simulatedthroughput per DRA recorded for different values of KRice aregiven in Fig. 9(b). The results of Fig. 9 clearly show that ahigher 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 care-fully investigated how the number of interfering aircraft A,the number of DTAs Nt , the number of DRAs Nr , thedistance da∗
b∗ between the desired pair of communicating
aircraft, the correlation factor ρ between antennas, and theRician factor KRice of the aeronautical communication channelimpact on the achievable system performance of our distance-based ACM and large-scale antenna array aided AANET.Based on the simulation results, we can draw the followingobservations.
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 increases
ZHANG et al.: ACM FOR LARGE-SCALE ANTENNA ARRAY-BASED AERONAUTICAL COMMUNICATIONS 1355
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 of[
da∗b∗ , Dmax
]
. The rest of the parameters are specified in Table III.
the 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-based ACM scheme has been proposed for aeronautical com-munications. Unlike the terrestrial instantaneous-SNR basedACM design, which is unsuitable for aeronautical communi-cation applications, the proposed distance-based ACM schemeswitches its coding and modulation mode according to thedistance between the desired communicating aircraft. Basedon our asymptotic closed-form theoretical analysis, we haveexplicitly derived the set of distance-thresholds for the pro-posed ACM design and have provided a theoretical upperbound of the achievable spectral efficiency and throughput,which has considered the impact of realistic channel estimationerror and of co-channel interference. Our extensive simulationresults have validated our design and theoretical analysis.This study therefore has provided a practical high-data-rateand high-spectral-efficiency solution for supporting the futureInternet above 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 1
N 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→∞ xH Ax = Tr
{(
1
NM + 1
Nϒ
)
A}
, (39)
where M = mmH.Proof: Let y = √
N x − m. As x ∼ CN(
1√N
m, 1N ϒ
)
,we have y ∼ CN (0,ϒ). Furthermore, we have
xH Ax =(
1√N
m + 1√N
y)H
A(
1√N
m + 1√N
y)
= 1
NmH Am + 1
NyH Ay + 1
NmH Ay + 1
NyH Am.
(40)
Since y ∼ CN (0,ϒ) and y does not depend on m, accordingto Lemma 1 of [43], we have
limN→∞
mH AyN
= 0, (41)
limN→∞
yH AmN
= 0. (42)
Furthermore, according to the trace lemma of [44], we have
limN→∞
(
1√N
yH)
A(
1√N
y)
= Tr
{
1
Nϒ A
}
. (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 : ]
}
=[
�a∗b∗]
(n∗r ,n∗
r ). (44)
1356 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 2, FEBRUARY 2018
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
{
[
�a∗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 : ]
[
�a∗b∗]
(n∗r ,n∗
r )
[
˜Ha∗b∗]H
[n∗r : ]
}
= Tr
{
[
�a∗b∗]
(n∗r ,n∗
r )
[
�a∗b∗]
(n∗r ,n∗
r )
}
. (48)
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
{
[
�a∗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
{
[
�a∗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 : ]
}
=[
�a∗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.
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Jiankang Zhang (S’08–M’12) received the B.Sc.degree in mathematics and applied mathemat-ics from the Beijing University of Posts andTelecommunications in 2006, and the Ph.D. degreein communication and information systems fromZhengzhou University in 2012. Since then, he hasbeen a Lecturer with the School of InformationEngineering, Zhengzhou University. From 2009 to2011, he was a Visiting Researcher with the Schoolof Electronics and Computer Science, University ofSouthampton, U.K. From 2013 to 2014, he was a
Post-Doctoral Researcher with McGill University, Montreal, QC, Canada.Since 2014, he has been a Research Fellow with the University of Southamp-ton. His research interests are in the areas of wireless communications andsignal processing, aircraft communication, and wirelines communication.
Sheng Chen (M’90–SM’97–F’08) received theB.Eng. degree in control engineering from theEast China Petroleum Institute, Dongying, China,in 1982, the Ph.D. degree in control engineeringfrom the City University, London, U.K., in 1986, andthe D.Sc. degree from the University of Southamp-ton, Southampton, U.K., in 2005. From 1986 to1999, he held research and academic appointmentsat the Universities of Sheffield, Edinburgh, andPortsmouth, U.K. Since 1999, he has been withthe School of Electronics and Computer Science,
University of Southampton, where he holds the post of Professor in intelligentsystems and signal processing. His research interests include adaptive signalprocessing, wireless communications, the modeling and identification ofnonlinear systems, neural network and machine learning, intelligent controlsystem design, evolutionary computation methods, and optimization. He hasauthored or co-authored over 550 research papers. He is a fellow of the UnitedKingdom Royal Academy of Engineering and IET, a Distinguished AdjunctProfessor at King Abdulaziz University, Jeddah, Saudi Arabia, and an ISIhighly cited researcher in engineering (2004).
Robert G. Maunder (SM’12) received the B.Eng.degree (Hons.) in electronic engineering and thePh.D. degree in telecommunications from the Uni-versity of Southampton, U.K., in 2003 and 2007,respectively. He began a lectureship in 2007 with theSchool of Electronics and Computer Science, Uni-versity of Southampton, and was promoted to Asso-ciate Professor in 2013 and to Professor in 2017.His research interests include joint source/channelcoding and the holistic design of algorithms andhardware implementations for wireless communica-
tions. He has authored a number of IEEE papers in these areas. He is theFounder and the CTO of AccelerComm Ltd., which is commercializing hisresearch as soft-IP. He is a chartered engineer and a fellow of the IET.
Rong Zhang (M’09–SM’16) received the Ph.D.degree in wireless communications from the Uni-versity of Southampton (UoS), U.K., in 2009.He was a Research Assistant with the Mobile VirtualCentre of Excellence, UoS, one of UK’s largestindustrial-academic partnership in ICT. During hispost-doctoral period with the School of Electronicsand Computer Science, UoS, he contributed, as aUoS Lead Researcher, to a number of internationalprojects. After that, he took his industrial consultingleave for Huawei EU Research and Development as
a System Algorithms Expert. He is currently an Assistant Professor with theSouthampton Wireless Group, UoS. He has a over 80 IEEE/OSA publications,including over 55 journals (over 20 of which as the first author). He is aRAEng industrial fellow and a member of the OSA. Owing to his outstandingacademic achievements, he is a recipient of the prestigious Dean’s PublicationAward, Faculty of Physical Sciences and Engineering, UoS. He is also arecipient of the prestigious RAEng Industrial Fellowship. He regularly servesas a reviewer for IEEE/OSA journals and funding bodies and has served asa TPC member/invited session chair of major conferences several times.
Lajos Hanzo (M’91–SM’92–F’04) received theD.Sc. and Ph.D. degrees in electronics in 1976 and1983, respectively. 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, Germany,and the U.K. Since 1986, he has been with theSchool of Electronics and Computer Science, Uni-versity of Southampton, U.K., where he holds theChair in telecommunications. He has successfullysupervised 111 Ph.D. students, co-authored 18 John
Wiley/IEEE Press books on mobile radio communications totaling in excessof 10 000 pages, authored 1701 research contributions at IEEE Xplore, actedas the TPC and the general chair of the IEEE conferences, presented keynotelectures, and received a number of distinctions. He is currently directing anacademic research team, involved in a range of research projects in the fieldof wireless multimedia communications sponsored by industry, the Engineer-ing and Physical Sciences Research Council, U.K., the European ResearchCouncil’s Advanced Fellow Grant, and the Royal Society’s Wolfson ResearchMerit Award. He is an enthusiastic supporter of industrial and academicliaison, and he offers a range of industrial courses. He is a fellow of REng,IET, and EURASIP. In 2009, he was awarded the honorary doctorate DoctorHonoris Causa from the Technical University of Budapest and in 2015 bythe University of Edinburgh. He is also a Governor of the IEEE VTS. From2008 to 2012, he was an Editor-in-Chief of the IEEE Press and a ChairedProfessor at Tsinghua University, Beijing, China. He has over 30 000 GoogleScholar citations and an H-index of 70.
