METHOD FOR SER APPROXIMATION FOR OSTBC IN DISTRIBUTED WIRE COMMUNICATION SYSTEMS

• US 20080205538A1
• Filed: 02/21/2008
• Published: 08/28/2008
• Est. Priority Date: 02/22/2007
• Status: Active Grant

• Current Assignee: Samsung Electronics Co. Ltd.
• Original Assignee: Samsung Electronics Co. Ltd.
• Inventors: HAN, Shuangfeng, Hwang, Seong-Taek, Lee, Han-Lim
• Granted Patent: US 8,571,121 B2
• Time in Patent Office: Days
• US Class Current: 375/267
• CPC Class Codes: H04B 7/0443 utilizing "waterfilling" technique
• CPC Class Codes: H04L 1/0618 Space-time coding
• CPC Class Codes: H04L 1/20 using signal quality detector
• CPC Class Codes: Y02D 30/70 in wireless communication networks

Abstract

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≦2ⁿ−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.

Claims

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 a quasi-optimal antenna subset A_g (1≦

g≦

2ⁿ−

1) having a quasi-optimal power allocation weight w_g based on a predetermined power allocation, for each one of the plurality of 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 a symbol constellation of a predetermined modulation scheme; and

outputting the SER approximation value to an encoder for optimal power allocation based on the SER approximation value.

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 PDF of the SNR is defined by

$f_{\eta }$



( x ) ≈

∏

j = 1 g 



( ∫

- ∞

+ ∞



( 1 - si 



Ω

j 

w j 

q j 

ρ

/ m j ) - gm j 

m 



- 





sx 





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 



- m j 

x Ω

j 

w j 

q j 

ρ





g = x m 

∑

j = 1 g 



m j - 1 



- ∑

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 



- x 



C 2 

C 1 , 

wherein $D=m<br><br>\underset{j=1}{\overset{g}{\sum <br><br>}}<br><br><br><br>m_j,<br><br>C_1=\underset{j=1}{\overset{g}{\prod <br><br>}}<br><br><br><br>{\left(\mathrm{\Gamma <br><br>}<br><br>\left({\mathrm{gm}}_j<br><br>m\right)\right)}^{-\frac{1}{g}}<br><br>{\left({\mathrm{\Omega <br><br>}}_j<br><br>w_j<br><br>q_j<br><br>\mathrm{\rho <br><br>}/m_j\right)}^{-m_j<br><br>m},<br><br>C_2=\underset{j=1}{\overset{g}{\sum <br><br>}}<br><br><br><br>m_j/{\mathrm{\Omega <br><br>}}_j<br><br>w_j<br><br>q_j<br><br>\mathrm{\rho <br><br>}<br><br><br><br>g,<br><br>\mathrm{\eta <br><br>}=\mathrm{SNR},<br><br>f_{\mathrm{\eta <br><br>}}<br><br>\left(x\right)=\mathrm{PDF}<br><br><br><br>\mathrm{of}<br><br><br><br>\mathrm{\eta <br><br>},$

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.

5. The method for SER approximation according to claim 1, wherein the OSTBC SER having the symbol constellation of the predetermined modulation scheme includes 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, which are defined by

$P_{\mathrm{MQAM}}=1-{(1-{\int }_{}^{}}^{}$

0 ∞



2 

( 1 - 1 M ) 

Q ( 3 M - 1 

x ) 



f η



( x ) 



x ) 2 , 

P M g 

PSK = ∫

0 ∞



( 2 

Q ( 2 

x 

sin 

π

M g ) - 1 π



∫

π

2 

π

M g π

2 



- x 

( sin 

π

M g ) / cos 2 

θ







θ

) 

f η



( x ) 



x , 

P BPSK ≈

∫

0 ∞



Q ( 2 

x ) 

f η



( x ) 



x , 

and $P_{\mathrm{QPSK}}\approx <br><br>\frac{1}{2}<br><br>{\int <br><br>}_0^{\mathrm{\infty <br><br>}}<br><br>Q\left(\sqrt{x}\right)<br><br>f_{\mathrm{\eta <br><br>}}<br><br>\left(x\right)<br><br><br><br><br><br>x,\mathrm{respectively},$

wherein

η

=SNR,

f_η

(x)=PDF of η

, and

M=M-ary level of MQAM and MPSK.

6. The method for SER approximation according to claim 1, wherein the 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

$P_{M_g-\mathrm{QAM}}^{A_g}\approx$

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 $P_{\mathrm{QPSK}}^{A_g}\approx <br><br>\frac{1}{4}<br><br>C_1<br><br>\mathrm{\Gamma <br><br>}<br><br>\left(D\right)<br><br>{\left(C_2\right)}^{-D}<br><br>\left(1-\underset{t=0}{\overset{D-1}{\sum <br><br>}}<br><br><br><br>{\left(1+2<br><br>C_2\right)}^{-0.5}<br><br>{\left(\frac{1-{\left(1+2<br><br>C_2\right)}^{-1}}{4}\right)}^t<br><br>\left(\begin{array}{c}2<br><br>t\\ t\end{array}\right)\right),\mathrm{respectively},$

wherein

D=mΣ

_j=1^gm_j,

C₂=Σ

_j=1^gn_j.Ω

_jw_jq_jρ

g,

C₁=Π

_j=1^g(Γ

(gm_jm))<sup>−

1/g</sup>(Ω

_jw_jq_jρ

/m_j)<sup>−

mjm</sup>,

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.

7. The method for SER approximation according to claim 1, wherein, when 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⁻

xC² from the PDF of the SNR in a high TSNR region, as defined by

$P_{M_g-\mathrm{QAM}}^{A_g<br><br>\left(\mathrm{High\_\rho <br><br>}\right)}=1-{\left(1-\frac{\underset{t=1}{\overset{D}{\prod <br><br>}}<br><br><br><br>\left(2<br><br>D-\left(2<br><br>t-1\right)\right)}{D}<br><br>\left(1-\frac{1}{\sqrt{M_g}}\right)<br><br>{\left(\frac{3}{M_g-1}\right)}^{-D}<br><br>C_1\right)}^2,<br><br>\mathrm{and}$ $P_{M_g-\mathrm{PSK}}^{A_g<br><br>\left(\mathrm{High}-\mathrm{\rho <br><br>}\right)}=\frac{\underset{t=1}{\overset{D}{\prod <br><br>}}<br><br><br><br>\left(2<br><br>D-\left(2<br><br>t-1\right)\right)}{D}<br><br>{\left(2<br><br><br><br>{\sin }^2<br><br>\left(\mathrm{\pi <br><br>}/M_g\right)\right)}^{-D}<br><br>C_1,\mathrm{respectively},$

wherein

D=mΣ

_j=1^gm_j,

C₁=Π

_j=1^g(Γ

(gm_jm))<sup>−

1/g</sup>(Ω

_jw_jq_jρ

/m_j)<sup>−

mjm</sup>,

C₂Σ

_j=1^gm_j/Ω

_jw_jq_jρ

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.

8. The method for SER approximation according to claim 1, wherein the SER approximation values are calculated by a transmitter of the DWCS.

9. The method for SER approximation according to claim 1, wherein the SER approximation value is calculated by a receiver of the DWCS and the result of power allocation is fed back to a transmitter.

10. The method for SER approximation according to claim 1, wherein the 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 SER approximation values are calculated by the receiver