paper, we assumed that both of the transmitter and receiver have the same RF chains
which is limited due to the constraints of the system cost and power consumption.
The mmWave channel between UAVs can be modeled as [13]
H ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
M MS M BS K
1 þ K
r
a 0 a MS ðh h ; h v Þa
H
BS ðw h ; w v Þ
ð 2Þ
where M MS and M BS denote the antenna numbers of receiver and transmitter, respectively. K is the Ricean factor, and a 0 is the complex channel gain. Moreover,
a BS ðw h ; w v Þ is the array response vector of transmitter, which can be described as
a BS ðw h ; w v Þ ¼ a BSM h ðw h Þ a BSM v ðw v Þ
ð 3Þ
where a BSM h ðw h Þ and a BSM v ðw v Þ can be given by
a BSM h ðw h Þ ¼
1
ffiffiffiffiffiffi
M h
p
1; e
jkd h sin w h cos w v ; . . .; e
jkðM h À1Þd h sin w h cos w v
h
i T
a BSM v ðw v Þ ¼
1
ffiffiffiffiffiffi
M v
p
1; e
jkd v sin w v ; . . .; e
jkðM v À1Þd v sin w v
h
i T
ð4Þ
where k ¼ 2p/k, k is the signal wavelength, d h and d v are both set as k/2, w hðvÞ is the
angle of departure (AoD). h and v denote horizontal and vertical domains, respectively.
a MS ðh h ; h v Þ is the array response vectors of receiver and it can be written in a similar
form with (4).
3 Improved Beam Design
3.1 Equivalent Spectral Efficiency
In order to evaluate the performance of beam, we need to derive the expression of
equivalent spectral efficiency. Based on the mmWave system model, the spectral
efficiency achieved can be expressed by [14]
R ¼ log 2 I + qR
À1
n w
H
BB W
H
RF HF RF v BB v
H
BB F
H
RF H
H W RF w BB
Á
À
ð5Þ
where R n ¼ r
2
w
H
w is the noise covariance matrix. We focus on the design of
precoder/combiner to improve spectral efficiency. However, it is difficult to obtain
global optimal value. To simplify this problem, we design the precoding vector c ¼
F RF v BB by using singular value decomposition (SVD) of channel as H ¼ URV
H . Then,
(5) can be simplified as
R ¼ log 2 ð1 þ q h
H
c
2 Þ
ð 6Þ
where h ¼R 1 V 1 is the equivalent channel state coefficient.
Millimeter-Wave Beamforming of UAV Communications for Small …
283
which is limited due to the constraints of the system cost and power consumption.
The mmWave channel between UAVs can be modeled as [13]
H ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
M MS M BS K
1 þ K
r
a 0 a MS ðh h ; h v Þa
H
BS ðw h ; w v Þ
ð 2Þ
where M MS and M BS denote the antenna numbers of receiver and transmitter, respectively. K is the Ricean factor, and a 0 is the complex channel gain. Moreover,
a BS ðw h ; w v Þ is the array response vector of transmitter, which can be described as
a BS ðw h ; w v Þ ¼ a BSM h ðw h Þ a BSM v ðw v Þ
ð 3Þ
where a BSM h ðw h Þ and a BSM v ðw v Þ can be given by
a BSM h ðw h Þ ¼
1
ffiffiffiffiffiffi
M h
p
1; e
jkd h sin w h cos w v ; . . .; e
jkðM h À1Þd h sin w h cos w v
h
i T
a BSM v ðw v Þ ¼
1
ffiffiffiffiffiffi
M v
p
1; e
jkd v sin w v ; . . .; e
jkðM v À1Þd v sin w v
h
i T
ð4Þ
where k ¼ 2p/k, k is the signal wavelength, d h and d v are both set as k/2, w hðvÞ is the
angle of departure (AoD). h and v denote horizontal and vertical domains, respectively.
a MS ðh h ; h v Þ is the array response vectors of receiver and it can be written in a similar
form with (4).
3 Improved Beam Design
3.1 Equivalent Spectral Efficiency
In order to evaluate the performance of beam, we need to derive the expression of
equivalent spectral efficiency. Based on the mmWave system model, the spectral
efficiency achieved can be expressed by [14]
R ¼ log 2 I + qR
À1
n w
H
BB W
H
RF HF RF v BB v
H
BB F
H
RF H
H W RF w BB
Á
À
ð5Þ
where R n ¼ r
2
w
H
w is the noise covariance matrix. We focus on the design of
precoder/combiner to improve spectral efficiency. However, it is difficult to obtain
global optimal value. To simplify this problem, we design the precoding vector c ¼
F RF v BB by using singular value decomposition (SVD) of channel as H ¼ URV
H . Then,
(5) can be simplified as
R ¼ log 2 ð1 þ q h
H
c
2 Þ
ð 6Þ
where h ¼R 1 V 1 is the equivalent channel state coefficient.
Millimeter-Wave Beamforming of UAV Communications for Small …
283