2024年5月16日发(作者：可复制的万能空白昵称)

N

etwork

-

C

onnected

UAV C

ommunications

Distributed Transmit Beamforming for UAV to Base

Communications

Yin Lu*1*, Jun Fang2, Zhong Guo2, J. Andrew Zhang3

1 Jiangsu Provincial Key Laboratory of Wireless Communications, Nanjing University of Posts and Telecommunications,

Nanjing 210023, China

2 Wuxi Longi Intelligent Technology Co. Ltd., Wuxi 214400, China

3 University of Technology Sydney, Ultimo NSW 2007, Australia

* The corresponding author, email: luyin@

Abstract: Distributed transmit beamform­

ing (DTB) is very efficient for extending the

communication distance between a swarm of

UAVs and the base, particularly when con­

sidering the constraints in weight and battery

life for payloads on UAVs. In this paper, we

review major function modules and potential

solutions in realizing DTB in UAV systems,

such as timing and carrier synchronization,

phase drift tracking and compensation, and

beamforming vector generation and updating.

We then focus on beamforming vector genera­

tion and updating, and introduce a concatenat­

ed training scheme, together with a recursive

channel estimation and updating algorithm.

We also propose three approaches for tracking

the variation of channels and updating the vec­

tors. The effectiveness of these approaches is

validated by simulation results.

Keywords: unmanned aerial vehicle; distribut­

ed transmit beamforming; beamforming vector

generation and updating; channel prediction

I. I

ntroduction

We consider a situation where a swarm of

UAVs work collaboratively on a task, in an

area that is relatively far away from the base.

For example, these UAVs are doing formation

China Communications • January 2019

flight, or patrolling an area. These UAVs are

connected to the base via wireless communi­

cation links, and form a communication net-

work including these UAVs and the base. Con­

sidering the constraints in weight and battery

life, we prefer communication systems with

small profile, low weight and low power con­

sumption. When the distances among UAVs

are much smaller than the distance from UAVs

to the base, distributed beamforming can be

an excellent solution for achieving long-range

and low-power communications. Since the

main communication traffic is typically from

UAVs to the base and the base can have much

higher transmission power, we only consider

the realization of distributed transmit beam­

forming (DTB) in this paper.

DTB [1] is a form of cooperative communi­

cation where two or more information sources

simultaneously transmit a common message

and control the phase (and power) of their

transmissions so that the signals are construc­

tively combined at an intended destination.

Ideally, DTB with N nodes/antennas can result

in an N-fold gain in received power, for a giv­

en total transmitted power [2]. Hence using

DTB, UAVs may significantly reduce the total

transmission power, or extend their communi-

F ’

cation distance to the base.

Received: Feb. 14,2018

Revised: Apr. 10,2018

15

In this paper, we re­

view major function

modules and potential

solutions in realizing

DTB in UAV systems,

such as timing and

carrier synchroniza­

tion, phase drift track­

ing and compensation,

and beamforming

vector generation and

updating.

DTB for conventional sensor networks has

been well studied in [2] [3] [4] [5]. There are

some specific problems for applying DTB to

UAV networks, associated with the signal prop­

agation environment, their movement and the

geographical shape of the UAV swarms. There

is very limited work on DTB for UAV networks

that addresses these problems. An earlier work

in this area was published in [6], where the au­

thor only reviewed the challenges and prelimi­

nary solutions, but provided little detail.

In this paper, we investigate the specific real­

ization of DTB in a swarm of UAVs, where the

group of UAVs transmit signals cooperatively

to the base via forming distributed transmit

beamforming. We review the major function

modules and discuss potential solutions to im­

plementing these modules, including timing

and frequency synchronization, tracking phase

drift, and beamforming vector generation and

updating. We show that most of these modules,

apart from beamforming vector generation and

updating, can be efficiently implemented with­

in UAVs, without requiring the involvement

of the base. We then introduce a concatenated

training scheme with scattered training sym­

bols for estimating the channels between the

base and UAVs and obtaining the DTB vector.

In this scheme, UAVs send training sequences

scattered over time, and the base estimates the

channel, generate the DTB vector and feedback

to UAVs. This scheme can efficiently combine

discontinuous training symbols within one

packet or across multiple packets for channel

estimation. Hence training overhead can be

significantly reduced to improve spectrum

efficiency. We consider channel variation due

to both UAV movement and the residual fre­

quency offset, and propose three methods for

updating beamforming in possibly fast varying

channels. These schemes have varying com­

plexity, and demonstrate different performance

in simulation. They can be selectively adopted

depending on channel varying speed.

number of UAVs for technologies discussed

in this paper. To provide concrete results, we

consider an exemplified swarm of 16 UAVs,

flying in formation (in two rows here). The

moving speeds of the UAVs are up to 50 m/s,

and the base is static. We consider a 2D geo­

graphical setup with horizontal distance and

the height to the base only, represented as x-

and y- axis respectively. The base is assumed

to be at (x,y)=(0,0). The initial relative posi­

tions of these UAVs are in two rows, one row

with 8 UAVs at y=200 m, and the other row

also with 8 UAVs at y=250 m. The distance

between two neighbouring UAVs in each row

is 100 m. UAVs are travelling horizontally

away from the base. The initial horizontal dis­

tance between the base and the nearest UAV is

5 km.

The carrier frequency used for wireless

communication between UAVs and the base is

assumed to be 900MHz, with a bandwidth of

5MHz. Thus the maximal Doppler frequency

is 150 Hz. The packet length is assumed to be

200 samples, and hence the packet period is

0.04 ms. So over one packet, the maximum

Doppler frequency can cause a phase shift of

about 7 degrees, which is insignificant.

With DTB, the received baseband signal, in

the absence of noise, at the base can be repre­

sented as

>-(t) = exp( j2nfst) xn (t) hn (t)

,

⑴

=s ^Lnan ) exp (j^n )) Wn )

exp ( j2n( fs - fC n )t)

II. S

ignal

and

S

ystem

F

ormulation

There is no limitations on the formation and

16

where n is the index of the UAVs, f

s

is the

receiver's carrier frequency; Xn(t)=sw„(t)ex-

p(j2n/cnt)) is the signal transmitted from the

n-th UAV, with the transmitted data symbol s,

beamforming weight w

n

(t) and carrier frequen­

cy /

c,n

; and h

n

(t)=a

n

(t)Qxp(j^

n

(t)) is the complex

channel between the n-th UAV and the base

with magnitude a„(t) and phase pjt). Here,

^

n

(t) has incorporated phase shifts caused by

propagation delay, initial phase difference be­

tween transmitters, phase drift, and Doppler

phase shift. Since line-of-sight multipath is

dominating in the UAV-to-base connection,

a

n

(t) mainly depends on the path loss and

China Communications • January 2019

changes slowly. Therefore it can be assumed to

be fixed for each UAV in this formulation, and

the variable t can be dropped. The term ^

n

(t)

contains both fast and slow time-varying com­

ponents, and needs to be treated separately, as

will be detailed later. In the above expression,

we have assumed that the difference between

signal arrival times is small enough so that

no resolvable multipath signal is caused. This

assumption is based on the fact that timing in

DTB for UAVs is a less challenging problem

and can be achieved with well-known tech­

nologies, such as through locking to the GPS

timing.

From the above equation, we can see that

in order to achieve a robust beamforming,

it is necessary to synchronize f

c,n

for any n,

estimate (p

n

(t), and track and compensate for

their variations over time. These are the main

challenges in realizing DTB, in addition to

other challenges such as information sharing

between beamforming nodes. For more infor­

mation on DTB, the readers are referred to [1]

and [2] for overviews and [7] for MAC and

routing design.

Observed over a period of [

知

/^，（k

0

+K-1)

T

0

] with K samples, the normalized mean DTB

beamforming gain, normalized to the ideal one

with perfectly known channels, is defined as

(2) bellow.

• Get rid of fast varying phase components

in ^n(t

)；

• Generate the beamforming vector based

on the observed signals at the base, and feed­

back it to UAVs;

• Track the changes and repeat the above

steps when necessary.

3.1 Time synchronization between

UAVs

Ideally, the arrival time of signals from dif­

ferent UAVs should be the same. However,

this will require complex interaction between

UAVs and the base. In DTB, we mainly con­

cern large timing difference between UAVs

that will lead to misalignment between the

symbols from different UAVs, and cause large

inter-symbol interference (ISI) at the receiver.

Accumulated timing offset also needs to be

compensated, as it will be translated as large

ones. The beamforming vector can generally

absorb small timing difference, which only

cause some phase shift of the received signal.

The propagation time difference between

UAVs and the base is typically small and

hence is not a concern here. Since the distanc­

es between UAVs are much smaller than the

distance between them and the base, their trav­

el distances to the base only vary insignificant­

ly. For example, when the UAVs are 5 kilome­

tres away from the base, a relative distance of

III. M

ain

F

unction

M

odules

and

S

olutions

Successfully implementing DTB in a swarm

of UAVs relies on the following operations, as

shown in figure 1 in the order of processing:

• Synchronize UAVs’ transmission time

so that their signals arrive at the base receiver

approximately at the same time;

• Synchronize UAVs’ carrier frequen­

cies so that (f

s

- f

c,n

) becomes the same for all

UAVs;

1

A

Channel

Estimation

y

Time sync

Carrier frequency

：

葡

sync

1

1

1

Tracking

Generate

Beamforming Vector

Fig. 1. Major process in forming distributed transmit beamforming. Operations in

square blocks and round-corner blocks are done in UAVs and the base, respectively.

2k0+K-1

X ^

n

a

n

exp (jV„ (

kT0

)) w

n

(

kT0

) exp (j2

n

( f

s

- f

c,n

)

kT0

)

|

(2)r = J

k

d

k

2----------------------------------------------------------------------.

China Communications • January 2019

17

50 metres between UAVs will only lead to a

difference of about 1.25m in the propagation

distance. For a data rate 10Mbps, this corre­

sponds to about 5% of the bit period, which

can be ignored. Hence once UAVs' transmis­

sion time is synchronized, we can assume that

propagation delay causes little degradation to

beamforming performance.

Time synchronization can thus be limited

to be within UAVs, which is required to en­

sure that all of the cooperating UAVs start to

transmit the same symbol at the same time.

Being simplified as a conventional time syn­

chronization problem in a network, various

well-developed methods can be applied [8],

for example, synchronizing to the GPS time is

easy to achieve in UAVs.

3.2 Carrier synchronization between

distributed UAVs

The more critical and challenging problem is

carrier synchronization [9] [10]. The phases

of the signals from different nodes may vary

with time quickly and diversely if their carrier

frequencies are different. We call them

carrier

frequency offset (CFO) here. Thus the beam­

forming gain will vary with time rapidly and

randomly. Large CFO can result in complete

failure of DTB and hence must be compen­

sated. For phase shift caused by smaller CFO,

it is shown in [4] that beamforming gains

are quite robust to moderate errors in phase

alignment. For example, 90 percent of an ide­

al two-antenna beamforming gain is attained

even with phase offsets on the order of 30°

[4]. The phase shift caused by small CFO can

also be compensated by tracking its variation

and updating the beamforming vector, as will

be shown in Section IV Thus practically, car­

rier synchronization will become solved if we

can maintain the carrier frequencies' stability

to several ppm (parts per million) and achieve

similar synchronization accuracy.

Carrier synchronization can be implement­

ed in either analog circuit or digitally. The

core components of the analog circuit are

phase looped lock (PLL) and a voltage con­

trolled oscillator (VCO) [4] [8]. The unknown

18

carrier frequency is generally accompanied by

an unknown phase shift, which may be caused

by propagation delay and the different phase

response of hardware. The analog implemen­

tation requires phase offset to be known and

compensated before correcting the frequency

offset [4]. Estimation of the phase offset is a

complex process, requiring generally closed-

loop between transmit and receive nodes.

The digital implementation can estimate the

frequency offset and phase shift independently

[8].

The digital implementation, resembling a

digital PLL, is typically based on a maximum

likelihood (ML) or maximum a posterior

probability (MAP) formulation of parameter

estimation [8]. The estimation of frequency

offset is independent of the phase offset in the

digital implementation. Hence we can ignore

the phase offset during frequency offset esti­

mation. Actually, the phase offset, which typi­

cally changes slowly, does not need to be esti­

mated separately here as it can be incorporated

to the channel estimation later. In this case,

we can use a simple algorithm for frequency

offset estimation, based on computing the one-

lag autocorrelation of the baseband signal, as

discussed in Chapter 8 in [8]. Assign any UAV

as a master and let it transmit a beacon/train-

ing signal, other UAVs can implement this

autocorrelation algorithm and work out their

frequency offsets to the master UAV readily.

The estimation can be done without involving

the base.

After getting the carrier offset estimation, it

can be either used to adjust the carrier frequen­

cy of the transmitter or inject a time-varying

digital phase shift term to the beamforming

weight.

3.3 Tracking phase drift during

beamforming

There are three types of phase drifts that may

be of concern, caused by oscillator instability,

residual frequency offset, and the movement of

UAVs (Doppler frequency), respectively. The

oscillator phase drift is random, and may rep­

resent an irreducible phase error if the stability

China Communications • January 2019

period of the oscillator is too short. The last two

generally change slowly, and can be compen­

sated by updating beamforming vector, which

will be considered in detail in Section 4.

Several studies have reported that the oscil­

lator phase drift is generally not a significant

issue for distributed beamforming design. In

[11], using Brownian motion to model the os­

cillator drift, a Cramer-Rao bound is derived

for the performance of estimating phase and

frequency in the presence of the random phase

drift. It is shown that estimation performance

can be improved by increasing the number of

observations, increasing the sampling frequen­

cy, and applying a Kalman filter [11] [12]. In

[4], a statistical model is applied to analyze the

effect of the oscillator phase drift on the beam­

forming gain. The results demonstrate that

beamforming gain is robust to phase errors

under some typical phase noise parameters.

In average beamforming gains of at least 91%

are achievable and 81% of the maximum for

an extraordinary 35o phase drift is obtained.

lobe and has lower chance of large sidelobes.

Figures 2 and 3 present the beam pattern of

the DTB formed by the 16 UAVs at their ini­

tial locations. The figures show clear main and

sub lobes of the beam. The size of the main-

lobe is geographically large in both horizontal

and vertical domains.

1000

vertical span (m)

3.4 Impact of UAV formation on

beamforming

The relative location of UAVs has some im­

pact on the shape of beamforming. Although

the “antenna geometry” of a distributed

beamformer may be random, the beamform-

er pattern may be characterized statistically

based on some statistical approximation of

the geometrical distribution of UAVs. The

probability distribution of the far-field beam

pattern of a distributed beamformer with

node locations uniformly distributed on a

two-dimensional disk of radius R is analyzed

in [13]. It is demonstrated that very narrow

beamwidths can be achieved for a reasonable

number of nodes. For example, a network with

10 randomly placed source nodes on a disk

of radius 25 meters will, on average, achieve

a 3dB beamwidth of less than half a degree if

the sources transmit with 900MHz carriers. In

[3], the beam pattern is analysed based on an

assumption of Gaussian distributed instead of

uniformly distributed nodes, and it is shown

that Gaussian deployment gives wider main-

China Communications • January 2019

-50 -1000

horizontal span (m)

Fig. 2. 3D plot of the beamforming pattern seen around the base. The base locates

at (horizontal span, vertical span) = (0,0).

horizontal span (m)

Vertical span (m)

Fig. 3. Sample 2D-plot of the beam pattern at vertical span=0 (top) and horizontal

span=0 (bottom).

19

IV. G

eneration

and

U

pdating

of

B

eamforming

V

ector

Once time and frequency synchronization are

completed, beamforming vector can be deter­

mined through channel estimation at the base,

and then feedback to UAVs. There are sev­

eral known channel estimation and feedback

schemes, such as the 1-bit feedback scheme

[14], and nonfeedback scheme using spa­

tial-temporal extraction [15]. The 1-bit feed­

back scheme is a close-loop implementation

requiring least feedback, but it takes very long

time to converge. The nonfeedback scheme

does not require information feedback, but has

high computational complexity and requires

other information for processing, apart from a

complex training scheme.

In this section, we introduce a concatenated

training scheme for estimating the channels

and obtaining the DTB vector, considering

channel variation due to both UAV movement

and the residual frequency offset.

In [16], we proposed a concatenated train­

ing scheme for channel estimation in DTB

systems, and derived the optimal training sig­

nals, particularly for spatially correlated chan­

nels and for the case when the number of con­

secutive training symbols, N, are less than the

number of distributed nodes, M. The scheme

distributes a block of complete training signals

to multiple sub-blocks, each being applied to

one packet or a fraction of the packet. Training

signals over different packets can be seam­

lessly combined for channel estimation. This

scheme can be effectively applied to the UAV

setup here. Using scattered training signals

are helpful for tracking channel variation, and

training overhead can be reduced to improve

spectrum efficiency.

Figure 4 shows an example of the frame

structure, where the training signals are placed

in the middle and the end of the packet to re­

duce the delay in applying the estimated DTB

vector to the data signal in the next packet.

These training symbols can be flexibly placed

in many different forms, such as being divided

into more and shorter sub-blocks, even as a

single pilot, and uniformly scattered over the

packet. The preamble in the beginning of a

packet may contain additional training signals

for estimating the combined channels that are

weighted by the DTB vector.

Ignoring the correlation between the path-

loss of the UAV channels, we can use an or­

thogonal matrix as the basis of constructing

these training signals. Given an matrix

T, we can generate Pk from T cyclically. For a

NkxM matrix P, mathematically, the q-th row

of Pk, q

e

[1, Nk ] is the (mod(q+p,M))-th row

of T, where p is the index of the next row in T

after obtaining Pk] and mod(x,y) denotes the

operation of x modulo

y.

A recursive algorithm can then be conve­

niently applied to combine signals from these

sub-blocks to get the channel estimation at the

receiver. Typically, at least K>M/N sub-blocks

are combined to get the channel estimates, un­

less channels change too rapidly. Referring to

(35) in [16], the recursive equation is given by

k

= h

k-1

+ P

k

y

k

- P

k-K

y

k-K

, (3)

where is the conjugate transpose of Pk, jk

is the corresponding received signals, K is the

number of subblocks selected for combination,

and h

k

denotes the channel estimate obtained

at the k-th subblock (but with previous signals

combined). The DTB vector is then deter­

mined through /h

k

, ^

k

= conj(h

k

),

where conj (x) denotes the conjugate of x.

Without noted otherwise, we will assume that

K>M/N is used in the following discussion and

Fig. 4. Frame structure and signal flow of DTB vector generation.

20

China Communications • January 2019

simulation.

When both Doppler frequency and residual

CFO are small enough, the recursive equation

(3) works quite reliably. But its performance

will deteriorate significantly when channels

change rapidly. We propose the following

three improved methods to deal with the rapid

channel variation. Their performance will be

compared in Section 5 through simulation.

power and the updated benchmarking value at

k-th block for value K, respectively. If channel

is stable, Pk(K) is expected to be larger than

bk(K-1) and smaller than bk(K+1); if channel

becomes less stable, pk(K) is expected to be

smaller than bk(K) and even bk(K-1). The algo­

rithm is summarized below.

If « * bk (K -1)< Pk (K )< b“: + 1),

doK = K + l,and4 = 4—i

Elseif pk (K )<

>k;

4.1 Method 1: improved recursion

with

K

adapting to channel variation

A simple way for improving the recursive

algorithm above is to make K adaptive to the

channel variation. When channel is stable, a

larger K can lead to higher SNR and hence bet­

ter channel estimation. However, if it changes

rapidly, larger K introduces more mismatch and

degrades the estimation performance. There­

fore, we want to find a right K that adapts to the

channel variation. Our approach to achieving

this goal is computing the mean signal power

over the data payload period, and comparing

it to some thresholds. The selection of these

thresholds, however, is not straightforward.

UAV channels vary slowly in terms of the

pathloss or channel magnitude due to the dom­

inating line-of-sight propagation. This implies

that the variation of the computed signal pow­

er from DTB will vary consistently with the

variation of the channel phase. Therefore, we

can ignore the magnitude variation, and focus

on the varying channel phase. One approach

is then comparing the received signal power

obtained at the current sub-block to those at the

previous (averaged) ones. If the signal power

decreases, it could be an indicator that K shall

be decreased. However, this cannot tell us when

we should increase K.

Our proposed novel approach is to compute

and update the signal power for each value

of K, and use them as benchmarking values

for comparison with the signal power. More

specifically we compare the signal power ob­

tained at K to the benchmarking values for K-1

and K+1, as they can tell us clearly what we

can expect for different channel variations. Let

Pk(K) and bk(K) denote the measured signal

China Communications • January 2019

~^ ,do K = K — 1, and

hlk = hlk—1 + Pk yk — Pk—Kyk—K — Pk—K —1 yk—K —1;

〇

therwise hk = hk—i + PkHyk - pH

k

yk—

k

.

(4)

In the above algorithm, a is a scalar and

we have found through simulation that a=1.1

is a good choice. The benchmark bk(K)

is updated through a recursive equation

bk(K)=^*bk(K)+(1-^)*pk(K), with the forget­

ting factor p =0.4.

4.2 Method 2: Estimation of Phase

Variation

The second method intends to estimate the

phase variation for each UAV channel at the

base receiver, and then feedback both the

beamforming vector and phase variations to

UAVs. Let hik be the channel estimates obtained

M

with K = . The channel phase variations

N

can be estimated as

么

=Z(hk Oconj(hk—

1

)),

where O denotes element-wise multiplication.

Different sub-blocks see different phase shifts,

hence there is no a constant phase difference

between any two channel estimates for any

UAV. When the phase shift is relatively small,

the estimation performance is acceptable as

will be seen from the simulation results in

Section 5. Once

外

is estimated, each UAV can

generate a phase shifting sequence, multiplied

to its signals to be transmitted, to compensate

for its phase variation due to its movement and

residual CFO.

21

4.3 Method 3: tracking through

channel prediction

A theoretically more rigorous approach is to

apply a channel prediction algorithm to pre­

dict what the channel, or DTB vector, should

be in the next packet period, using the current

and past received signals at the base. We use

a linear prediction [17] for the problem here.

Given the estimates hk

人

—i

，

…,hk—L+i , we can

derive a linear estimator for either the vector

or for each element in the vector individually.

It would be more accurate to predict for the

vector if there are high correlation between the

elements, but the computational complexity

is also much higher. When the sources that

cause channel variation are mainly the residu­

al CFOs, there are generally little correlation

between them. Hence we use element-wise

prediction here. Let fik denote any element in

hk . The linear predictor is given by

hk+1 =ahk +a2 hk—1 +…+aLhk—1,

⑶

where a

；

are the coefficients to be determined.

There are various ways to determine a；. Here

we propose a minimum mean square error

criterion, which can be efficiently solved by

the Levinson Recursive algorithm [17]. In the

simulation, we use L=4 and a correlation ma­

trix of size 4x4 to compute the coefficients a；.

V. S

imulation

R

esults

We present simulation results for the three

proposed beamforming vector generation and

updating schemes, together with one using

M

fixed value of K = . The system setup is

as described in Section II. In the following

presentation, the SNR is defined as the mean

SNR of the received signal from each UAV,

and the DTB gain is normalized to the maxi­

mum ideal value when the channel is perfectly

known. We will compare DTB gains under

the conditions with and without residual CFO,

in line-of-sight multipath only channels or

more general multipath channels simulated

using the well-known Jakes model. For the

residual CFO, we use ppm (parts per million)

to represent its value, e.g., 1ppm for a carrier

frequency 900MHz means a residual CFO of

900Hz. The residual CFO value for each UAV

is generated following a uniform distribution

between 0 and a specified maximum value.

We first consider channels with only line-

of-sight multipath between UAVs and the

base. In this case, Doppler frequency causes

minor variations of the channel. Figs. 5 and 6

plot the normalized beamforming gain in the

absence and presence of residual CFO, respec-

Fig. 5. DTB gain with CFO=0, SNR=-5dB. LOS channels.

u

j

e

o

p

e

z

j

l

e

E

J

O

z

u

ra

c

p

e

N

l

ra

E

J

O

N

0 0.5

Time (s)

1 1.5

X10

-3

Fig. 6. DTB gain with CFO up to 4ppm, SNR=-5dB.

22

China Communications • January 2019

tively, where N=M. From the two figures we

can have the following three observations. (1)

The adaptive method (Method 1) performs

very well when CFO is very small because it

can combine many subblocks to improve the

SNR in channel estimation. It adapts to chan­

nel variation and achieves performance close

to the one with fixed K when CFO is large;

(2) The method calculating the phase shift

(Method 2) performs much better than Method

1 when CFO is large, as expected; and (3) The

prediction method (Method 3) performs well

in both cases thanks to its capability of both

channel prediction and improving SNR. In fig­

ure 6, Method 3 outperforms Method 2 when

more samples become available because its

prediction accuracy improves over time.

We then consider channels generated from

the Jakes model, which combines multiple

multipath signals with randomly generated

Doppler frequencies for each UAV. The num­

ber of multipath used in the model is 7. Figure

7 shows two sample channels generated using

this model, with N=M. For these channels,

Figs. 8 and 9 present the results for the cases

without CFO and with CFO=4ppm, respec­

tively. From these figures, we can get observa­

tions similar to those from Figs. 5 and 6.

Finally, in figure 10, we show the results

with N=M/2, and the other setup is similar to

those used in figure 8. In this case, the single

complete training block is split into two sub­

blocks, and one is put in the middle and the

other is put in the end of the packet. The basic

channel estimates, that are subsequently used

as inputs to Method 2 and 3, are obtained

by combing received signals over K=2 sub­

blocks. The figure indicates that Method 2

performs relatively well due to its phase track­

ing capability. The performance of Method 3

degrades notably as its prediction accuracy is

sensitive to the deteriorated inputs for predic­

tion.

Based on these simulation results, together

with the underlying principle of these three

methods, we can have the following summary

for the physical meaning of these methods,

and their respective advantages and disad­

China Communications • January 2019

vantages. (1) Method 1 intends to achieve

a good balance between collecting more

training signals and avoiding introducing too

large channel variations. It hence works great

when channel changes slowly and has a low

complexity. But it becomes inferior for fast

varying channels. (2) Method 2 tries to esti­

mate the phase difference between varying

channels to update the BF vector. It is simple

Fig. 7. The phase (subFig. a) and magnitude (subFig. b) of sample channels be­

tween two UAVs and the base, generated using the Jakes model.

(

u

e

!

p

e

j)

i

q

d

CD

p

e

N

le

L

U

J

O

N

u

je

0.5 1

time (s)

1.5

2

2.5

、

-3

(a) Phase of sample channels

9

3

C

6

I

0.5 1

time (s)

1.5

2

2.5

、

-3

(b) Magnitude of sample channels

n

0.92

0.9

0.88

0.86

0.84

0.82

00.5

Time (s)

11.

V10 "3

Fig. 8. DTB gain with CFO=0, SNR=-5dB. Channels generated from the Jakes

model.

23

and efficient when channels have one domi­

nating multipath and CFO is large. However,

it is inefficient in combining training signals.

(3) Method 3 is a statistically optimal solution

in a determined problem (when N equals to or

larger than M), and it can achieve both good

prediction for phase changes and combination

of training signals for improved SNR. Howev­

er, its performance can degrade significantly

when N

VI. C

onclusion

Distributed transmit beamforming (DTB) is an

efficient solution for extending the communi­

cation distance between a warm of UAVs and

the base. We reviewed major function modules

for realizing DTB, including timing and carrier

synchronization, phase drift tracking and com­

pensation, and beamforming vector generation

and updating. We also discussed potential solu­

tions to implementing these modules. In par­

ticular, we introduce the concatenated training

scheme and a recursive channel estimation and

updating algorithm for generating and updating

beamforming vectors. We also proposed three

approaches for tracking channel variation and

updating the vector: Adaptive-K, phase estima­

tion, and channel prediction. The adaptive-K

method is simple and can achieve great perfor­

mance when channel variation is slow. The pre­

diction method achieves the best performance

but also has the highest complexity. The phase

estimation method is simple for implementa­

tion and performs well when channels change

rapidly. Our future work includes developing a

new method that is robust to channel variations

by combining the Adaptive-K and the phase

estimation methods.

Fig. 9. DTB gain with CFO=4ppm and SNR= -5dB. Channels generated from the

Jakes model.

Fig. 10. DTB gain with CFO=4ppm, SNR= -5dB, and N=M/2. Channels generat-

ed from the Jakes model.

u

!

e

G

p

9

z

!

IB

E

J

O

N

0 0.5

Time (s)

1 1.5

X10

"3

A

cknowledgements

This work was supported by National Natural

Science Foundation of China (No. 61271236),

Major Projects of Natural Science Research

of Jiangsu Provincial Universities (No.

17KJA510004), and Postgraduate Research &

Practice Innovation Program of Jiangsu Prov­

ince (No. KYCX17_0763).

u!eop9z=BLUJOz

0 0.2 0.4 0.6

Time (s)

0.8 1 1.2 1.4

X10

-3

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Biographies

Yin Lu, is an Associate Re­

search Fellow in Jiangsu Pro­

vincial Key Laboratory of Wire­

less Communications, Nanjing

University of Posts and Tele­

communications. He received

his Ph. D. degree in Electro­

magnetic Field and Microwave

Technology from Nanjing University of Posts and

Telecommunications in 2010. His research interests

include wireless communication and electromagnetic

compatibility, spectrum management, and technolo­

gy and application of Internet of Things. Email: lu-

yin@

Jun Fang, is the Industry Pro­

fessor of Jiangsu Province, and

President of Wuxi Longi Intelli­

gent Technology Co. Ltd. His

research interests include data

communication and autono­

mous vehicular networks.

Email: James@

Zhong Guo, is the Chief Tech­

nology Officer of Wuxi Longi

Intelligent Technology Co. Ltd.

His research interests include

wireless communication and

control algorithm of unmanned

aerial vehicle. Email: Michael@

J. Andrew Zhang, is an associ­

ate Professor in School of Elec­

trical and Data Engineering,

University of Technology Syd­

ney, Australia. His research in­

terests are in the area of signal

processing for wireless com­

munications and sensing, and

autonomous vehicular networks. Email: Andrew.

Zhang@

China Communications • January 2019

25