Method for SER approximation for OSTBC in distributed wire communication systems
A method for Symbol Error Rate (SER) approximation of an SER-based transmission power allocation operation for an Orthogonal Space Time Block Code in a DWCS equipped with multiple transmission Distributed Antennas (DA) geographically dispersed at random. The method for SER approximation includes the steps of: setting multiple combinable antenna subsets from the multiple DAs; selecting a quasi-optimal antenna subset A g (1≦g≦2 n −1) having a quasi-optimal power allocation weight w g based on predetermined power allocation, for each of the set multiple antenna subsets; and calculating an SER approximation value of the selected quasi-optimal antenna subset by applying a Probability Density Function (PDF) of a Signal-to-Noise Ratio (SNR) to the OSTBC SER having symbol constellation of a predetermined modulation scheme. The output of the SER approximation value can be output to a transmitter, or to a space-time encoder of a central processor for optimal power transmission.
1. A method for Symbol Error Rate (SER) approximation of an SER-based transmission power allocation operation for an Orthogonal Space Time Block Code (OSTBC) in a Distributed Wireless Communication System (DWCS) equipped with multiple transmission Distributed Antennas (DA) geographically dispersed at random, the method for SER approximation comprising the steps of:
setting a plurality of multiple combinable antenna subsets from dispersed multiple Das;
selecting quasi-optimal antenna subsets, each quasi-optimal antenna subset A g (1≦g≦2 n −1) having a quasi-optimal power allocation weight w g based on a predetermined power allocation, for each one of the plurality of multiple combinable antenna subsets;
calculating a plurality of SER approximation values of the selected quasi-optimal antenna subsets by applying a Probability Density Function (PDF) of a Signal-to-Noise Ratio (SNR) to a OSTBC SER having a symbol constellation of a predetermined modulation scheme;
determining an optimal SER approximation value to be equal to a minimum of the plurality of SER approximation values; and
outputting the optimal SER approximation value to an encoder for optimal power allocation based on the optimal SER approximation value;
wherein the OSTBC SER includes at least one among an OSTBC SER having Multiple Quadrature Amplitude Modulation (MQAM) symbols, an OSTBC SER having M-ary Phase Shift Keying (MPSK) symbols, an OSTBC SER having Binary Phase Shift Keying (BPSK) symbols, and an OSTBC SER having Quadrature Phase Shift Keying (QPSK) symbols; and
wherein the PDF of the SNR is defined by
f
η
(
x
)
≈
∏
j
=
1
g
(
∫
-
∞
+
∞
(
1
-
si
Ω
j
w
j
q
j
ρ
/
m
j
)
-
gm
j
m
ⅇ
-
ⅈ
sx
ⅆ
s
)
1
g
=
x
m
∑
j
=
1
g
m
j
-
1
∏
j
=
1
g
(
Γ
(
gm
j
m
)
)
-
1
g
(
Ω
j
w
j
q
j
ρ
m
j
)
-
m
j
m
ⅇ
-
m
j
x
Ω
j
w
j
q
j
ρ
g
=
x
m
∑
j
=
1
g
m
j
-
1
ⅇ
-
∑
j
=
1
g
m
j
x
Ω
j
w
j
q
j
ρ
g
∏
j
=
1
g
(
Γ
(
gm
j
m
)
)
-
1
g
(
Ω
j
w
j
q
j
ρ
m
j
)
-
m
j
m
=
x
D
-
1
ⅇ
-
x
C
2
C
1
,
wherein
D
=
m
∑
j
=
1
g
m
j
,
C
1
=
∏
j
=
1
g
(
Γ
(
gm
j
m
)
)
-
1
g
(
Ω
j
w
j
q
j
ρ
/
m
j
)
-
m
j
m
,
C
2
=
∑
j
=
1
g
m
j
/
Ω
j
w
j
q
j
ρ
g
,
η
=
SNR
,
f
η
(
x
)
=
of
η
,
w j =corresponding power allocation weight,
ρ=Transmit Power to Receive Noise Ratio (TSNR),
m j =corresponding Nakagami fading parameter,
Ω j =the j th DA for large-scale fading, and
g=combination of optimal DAs.
2. The method for SER approximation according to claim 1 , wherein, in a predetermined power allocation by a reception side, transmission power is allocated by using a water pouring algorithm.
3. The method for SER approximation according to claim 1 , wherein in a predetermined power allocation by a reception side, allocating power in proportion to a Nakagami fading parameter of each DA of the multiple DAs.
4. The method for SER approximation according to claim 1 , wherein the OSTBC SER having the at least one among an OSTBC SER having Multiple Quadrature Amplitude Modulation (MQAM) symbols, the OSTBC SER having M-ary Phase Shift Keying (MPSK) symbols, the OSTBC SER having Binary Phase Shift Keying (BPSK) symbols, and the OSTBC SER having Quadrature Phase Shift Keying (QPSK) symbols, is defined by
P
MQAM
=
1
-
(
1
-
∫
0
∞
2
(
1
-
1
M
)
Q
(
3
M
-
1
x
)
f
η
(
x
)
ⅆ
x
)
2
,
P
M
g
PSK
=
∫
0
∞
(
2
Q
(
2
x
sin
π
M
g
)
-
1
π
∫
π
2
π
M
g
π
2
ⅇ
-
x
(
sin
π
M
g
)
/
cos
2
θ
ⅆ
θ
)
f
η
(
x
)
ⅆ
x
,
P
BPSK
≈
∫
0
∞
Q
(
2
x
)
f
η
(
x
)
ⅆ
x
,
and
P
QPSK
≈
1
2
∫
0
∞
Q
(
x
)
f
η
(
x
)
ⅆ
x
,
respectively
,
wherein
η=SNR,
f η (x)=PDF of η, and
M=M-ary level of MQAM and MPSK.
5. The method for SER approximation according to claim 1 , wherein the plurality of SER approximation values obtained by applying the PDF of the SNR to the OSTBC SER having symbols of MQAM, MPSK, BPSK, and QPSK are defined by
P
M
g
-
QAM
A
g
≈
1
-
(
1
-
C
1
Γ
(
D
)
(
C
2
)
-
D
×
(
1
-
1
M
g
)
(
1
-
∑
t
=
0
D
-
1
μ
(
1
-
μ
2
4
)
t
(
2
t
t
)
)
)
2
,
P
M
g
-
PSK
A
g
≈
C
1
Γ
(
D
)
(
C
2
)
-
D
(
1
-
∑
t
=
0
D
-
1
(
1
+
C
2
/
sin
2
(
π
/
M
g
)
)
-
0.5
(
1
-
(
1
+
C
2
/
sin
2
(
π
/
M
g
)
)
-
1
4
)
t
(
2
t
t
)
)
,
P
BPSK
A
g
≈
1
2
C
1
Γ
(
D
)
(
C
2
)
-
D
(
1
-
∑
t
=
0
D
-
1
(
1
+
C
2
)
-
0.5
(
1
-
(
1
+
C
2
)
-
1
4
)
t
(
2
t
t
)
)
,
and
P
QPSK
A
g
≈
1
4
C
1
Γ
(
D
)
(
C
2
)
-
D
(
1
-
∑
t
=
0
D
-
1
(
1
+
2
C
2
)
-
0.5
(
1
-
(
1
+
2
C
2
)
-
1
4
)
t
(
2
t
t
)
)
,
respectively
,
wherein
D
=
m
∑
j
=
1
g
m
j
,
C
2
=
∑
j
=
1
g
m
j
/
Ω
j
w
j
q
j
ρ
g
,
C
1
=
∏
j
=
1
g
(
Γ
(
gm
j
m
)
)
-
1
g
(
Ω
j
w
j
q
j
ρ
/
m
j
)
-
m
j
m
,
μ
=
3
/
(
3
+
2
C
2
(
M
g
-
1
)
)
,
M=M-ary level of MQAM and MPSK,
w j =corresponding power allocation weight,
ρ=Transmit Power to Receive Noise Ratio (TSNR),
m j =corresponding parameter of Nakagami fading,
Ω j =large-scale fading for the j th DA, and
g=combination of optimal DAs.
6. The method for SER approximation according to claim 1 , wherein, when the plurality of SER approximation values are calculated by applying the PDF of the SNR to the OSTBC SER having symbols of MQAM and MPSK, the SER approximation values are obtained by omitting e −xC 2 from the PDF of the SNR in a high TSNR region, as defined by
P
M
g
-
QAM
A
g
(
High_ρ
)
=
1
-
(
1
-
∏
t
=
1
D
(
2
D
-
(
2
t
-
1
)
)
D
(
1
-
1
M
g
)
(
3
M
g
-
1
)
-
D
C
1
)
2
,
and
P
M
g
-
PSK
A
g
(
High
-
ρ
)
=
∏
t
=
1
D
(
2
D
-
(
2
t
-
1
)
)
D
(
2
sin
2
(
π
/
M
g
)
)
-
D
C
1
,
respectively
,
wherein
D
=
m
∑
j
=
1
g
m
j
,
C
1
=
∏
j
=
1
g
(
Γ
(
gm
j
m
)
)
-
1
g
(
Ω
j
w
j
q
j
ρ
/
m
j
)
-
m
j
m
,
C
2
=
∑
j
=
1
g
m
j
/
Ω
j
w
j
q
j
ρ
g
,
w j =corresponding power allocation weight,
ρ=Transmit Power to Receive Noise Ratio (TSNR),
m j =corresponding parameter of Nakagami fading,
Ω j =large-scale fading for the j th DA, and
g=combination of optimal DAs.
7. The method for SER approximation according to claim 1 , wherein the optimal SER approximation value is calculated by a transmitter of the DWCS.
8. The method for SER approximation according to claim 1 , wherein the optimal SER approximation value is calculated by a receiver of the DWCS and the result of power allocation is fed back to a transmitter.
9. The method for SER approximation according to claim 1 , wherein the optimal SER approximation value is calculated by a receiver of the DWCS, and parameters of large-scale fading and Nakagami fading are fed back to the transmitter from the receiver when the optimal SER approximation value is calculated by the receiver.
10. A method for Symbol Error Rate (SER) approximation of an SER-based transmission power allocation operation for an Orthogonal Space Time Block Code (OSTBC) in a Distributed Wireless Communication System (DWCS) equipped with multiple transmission Distributed Antennas (DA) geographically dispersed at random, the method for SER approximation comprising the steps of:
setting a plurality of multiple combinable antenna subsets from dispersed multiple DAs;
selecting quasi-optimal antenna subsets, each quasi-optimal antenna subset A g ( 1 ≦g≦ 2 n −1) having a quasi-optimal power allocation weight w g based on a predetermined power allocation, for each one of the plurality of multiple combinable antenna subsets;
calculating a plurality of SER approximation values of the selected quasi-optimal antenna subsets by applying a Probability Density Function (PDF) of a Signal-to-Noise Ratio (SNR) to a OSTBC SER having a symbol constellation of a predetermined modulation scheme;
determining an optimal SER approximation value to be equal to a minimum of the plurality of SER approximation values; and
outputting the optimal SER approximation value to an encoder for optimal power allocation based on the optimal SER approximation value;
wherein the OSTBC SER includes at least one among an OSTBC SER having Multiple Quadrature Amplitude Modulation (MQAM) symbols, an OSTBC SER having M-ary Phase Shift Keying (MPSK) symbols, an OSTBC SER having Binary Phase Shift Keying (BPSK) symbols, and an OSTBC SER having Quadrature Phase Shift Keying (QPSK) symbols; and
wherein the OSTBC SER having the at least one among an OSTBC SER having Multiple Quadrature Amplitude Modulation (MQAM) symbols, the OSTBC SER having M-ary Phase Shift Keying (MPSK) symbols, the OSTBC SER having Binary Phase Shift Keying (BPSK) symbols, and the OSTBC SER having Quadrature Phase Shift Keying (QPSK) symbols, is defined by
P
MQAM
=
1
-
(
1
-
∫
0
∞
2
(
1
-
1
M
)
Q
(
3
M
-
1
x
)
f
η
(
x
)
ⅆ
x
)
2
,
P
M
g
PSK
=
∫
0
∞
(
2
Q
(
2
x
sin
π
M
g
)
-
1
π
∫
π
2
-
π
M
g
π
2
ⅇ
-
x
(
sin
π
M
g
)
/
cos
2
θ
ⅆ
θ
)
f
η
(
x
)
ⅆ
x
,
P
BPSK
≈
∫
0
∞
Q
(
2
x
)
f
η
(
x
)
ⅆ
x
,
and
P
QPSK
≈
1
2
∫
0
∞
Q
(
x
)
f
η
(
x
)
ⅆ
x
,
respectively
,
wherein
η=SNR,
f η (x)=PDF of η, and
M=M-ary level of MQAM and MPSK.
11. A method for Symbol Error Rate (SER) approximation of an SER-based transmission power allocation operation for an Orthogonal Space Time Block Code (OSTBC) in a Distributed Wireless Communication System (DWCS) equipped with multiple transmission Distributed Antennas (DA) geographically dispersed at random, the method for SER approximation comprising the steps of:
setting a plurality of multiple combinable antenna subsets from dispersed multiple DAs;
selecting quasi-optimal antenna subsets, each quasi-optimal antenna subset A g ( 1 ≦g≦ 2 n= 1) having a quasi-optimal power allocation weight w g based on a predetermined power allocation, for each one of the plurality of multiple combinable antenna subsets;
calculating a plurality of SER approximation values of the selected quasi-optimal antenna subsets by applying a Probability Density Function (PDF) of a Signal-to-Noise Ratio (SNR) to a OSTBC SER having a symbol constellation of a predetermined modulation scheme;
determining an optimal SER approximation value to be equal to a minimum of the plurality of SER approximation values; and
outputting the optimal SER approximation value to an encoder for optimal power allocation based on the optimal SER approximation value;
wherein the OSTBC SER includes at least one among an OSTBC SER having Multiple Quadrature Amplitude Modulation (MQAM) symbols, an OSTBC SER having M-ary Phase Shift Keying (MPSK) symbols, an OSTBC SER having Binary Phase Shift Keying (BPSK) symbols, and an OSTBC SER having Quadrature Phase Shift Keying (QPSK) symbols; and
wherein the plurality of SER approximation values obtained by applying the PDF of the SNR to the OSTBC SER having symbols of MQAM, MPSK, BPSK, and QPSK are defined by
P
M
g
-
QAM
A
g
≈
1
-
(
1
-
C
1
Γ
(
D
)
(
C
2
)
-
D
×
(
1
-
1
M
g
)
(
1
-
∑
t
=
0
D
-
1
μ
(
1
-
μ
2
4
)
t
(
2
t
t
)
)
)
2
,
P
M
g
-
PSK
A
g
≈
C
1
Γ
(
D
)
(
C
2
)
-
D
(
1
-
∑
t
=
0
D
-
1
(
1
+
C
2
/
sin
2
(
π
/
M
g
)
)
-
0.5
(
1
-
(
1
+
C
2
/
sin
2
(
π
/
M
g
)
)
-
1
4
)
t
(
2
t
t
)
)
,
P
BPSK
A
g
≈
1
2
C
1
Γ
(
D
)
(
C
2
)
-
D
(
1
-
∑
t
=
0
D
-
1
(
1
+
C
2
)
-
0.5
(
1
-
(
1
+
C
2
)
-
1
4
)
t
(
2
t
t
)
)
,
and
P
QPSK
A
g
≈
1
4
C
1
Γ
(
D
)
(
C
2
)
-
D
(
1
-
∑
t
=
0
D
-
1
(
1
+
2
C
2
)
-
0.5
(
1
-
(
1
+
2
C
2
)
-
1
4
)
t
(
2
t
t
)
)
,
respectively
,
wherein
D
=
m
∑
j
=
1
g
m
j
,
C
2
=
∑
j
=
1
g
m
j
/
Ω
j
w
j
q
j
ρ
g
,
C
1
=
∏
j
=
1
g
(
Γ
(
gm
j
m
)
)
-
1
g
(
Ω
j
w
j
q
j
ρ
/
m
j
)
-
m
j
m
,
μ=√{square root over (3/(3+2C 2 (M g −1)))},
M=M-ary level of MQAM and MPSK,
w j =corresponding power allocation weight,
ρ=Transmit Power to Receive Noise Ratio (TSNR),
m j =corresponding parameter of Nakagami fading,
Ω j =large-scale fading for the j th DA, and
g=combination of optimal DAs.
12. A method for Symbol Error Rate (SER) approximation of an SER-based transmission power allocation operation for an Orthogonal Space Time Block Code (OSTBC) in a Distributed Wireless Communication System (DWCS) equipped with multiple transmission Distributed Antennas (DA) geographically dispersed at random, the method for SER approximation comprising the steps of:
setting a plurality of multiple combinable antenna subsets from dispersed multiple DAs;
selecting quasi-optimal antenna subsets, each quasi-optimal antenna subset A g ( 1 ≦g≦ 2 n −1) having a quasi-optimal power allocation weight w g based on a predetermined power allocation, for each one of the plurality of multiple combinable antenna subsets;
calculating a plurality of SER approximation values of the selected quasi-optimal antenna subsets by applying a Probability Density Function (PDF) of a Signal-to-Noise Ratio (SNR) to a OSTBC SER having a symbol constellation of a predetermined modulation scheme;
determining an optimal SER approximation value to be equal to a minimum of the plurality of SER approximation values; and
outputting the optimal SER approximation value to an encoder for optimal power allocation based on the optimal SER approximation value;
wherein the OSTBC SER includes at least one among an OSTBC SER having Multiple Quadrature Amplitude Modulation (MQAM) symbols, an OSTBC SER having M-ary Phase Shift Keying (MPSK) symbols, an OSTBC SER having Binary Phase Shift Keying (BPSK) symbols, and an OSTBC SER having Quadrature Phase Shift Keying (QPSK) symbols;
wherein, when the plurality of SER approximation values are calculated by applying the PDF of the SNR to the OSTBC SER having symbols of MQAM and MPSK, the SER approximation values are obtained by omitting e −xC 2 from the PDF of the SNR in a high TSNR region, as defined by
P
M
g
-
QAM
A
g
(
High
_ρ
)
=
1
-
(
1
-
∏
t
=
1
D
(
2
D
-
(
2
t
-
1
)
)
D
(
1
-
1
M
g
)
(
3
M
g
-
1
)
-
D
C
1
)
2
,
and
P
M
g
-
PSK
A
g
(
High
_ρ
)
=
∏
t
=
1
D
(
2
D
-
(
2
t
-
1
)
)
D
(
2
sin
2
(
π
/
M
g
)
)
-
D
C
1
,
respectively
,
wherein
D
=
m
∑
j
=
1
g
m
j
,
C
1
=
∏
j
=
1
g
(
Γ
(
gm
j
m
)
)
-
1
g
(
Ω
j
w
j
q
j
ρ
/
m
j
)
-
m
j
m
,
C
2
=
∑
j
=
1
g
m
j
/
Ω
j
w
j
q
j
ρ
g
,
w j =corresponding power allocation weight,
ρ=Transmit Power to Receive Noise Ratio (TSNR),
m j =corresponding parameter of Nakagami fading,
Ω j =larg-scale fading for the j th DA, and
g=combination of optimal DAs.