Optimal power allocation scheme on generalized ... - IEEE Xplore
Optimal Power Allocation Scheme on Generalized Layered Space-Time Coding Systems Leung Hang Ching Jason, Meixia Tao and Roger S Cheng Department of Electrical and Electronic Engineering The Hong Kong University of Science and Technology Clear Water Bay, Kowloon, Hong Kong Email: tiason, eecheng) @ee.ust.hk Abstract - We consider a generalized layered Space-Time (GLST) architecture with parallel Space-Time (ST) codes and derive an optimal power allocation (PA) scheme over the SpaceTime encoders to minimize the overall frame error rate. We prove that the optimal power allocation scheme will equate the derivatives of the frame error rate functions of all the ST codes. From simulation, we show that the derived optimal power allocation has a 1-2 dB gain over equal power scheme. Also, the proposed scheme has a better performance than the power allocation scheme proposed by [2]. Since various power allocation schemes have the same receiver structure, the gain can be achieved simply using the optimized parameters with no increase in complexity.
allocation scheme can take advantages over this property. Furthermore, in Section IV, we will present simulation results to show the performance gain obtained by power allocation which by itself does not increase the complexity of the system. Then, we will conclude in Section V. 11. SYSTEM MODEL
A . Encoding
-
Y
Coder 1
Input bit
I. INTRODUCTION In recent years, many research have focused on achieving the capacity of multi-antennas system. Many techniques have been proposed and Space-Time (ST) code was introduced in [l]. However, as the number of transmit and receive antennas increases, both the design and the decoding of ST code become much more complex. For example, a maximum likelihood detector on a &transmit antenna system with QPSK symbol requires calculating the Euclidean distances for sixty thousands constellation points per transmitted symbol. Thus, separating the transmit antennas into groups is a natural way to reduce the complexity. Generalized layered Space Time, GLST, code structure, studied by [ 2 ] and [3], takes this approach to reduce the complexity.
However, with the special decoding structure of the GLST system, it was shown in [2] that different subsystems see different system parameters and channel conditions. In this paper, we will exploit these differences with our power allocation (PA) scheme to improve the performance of the GLST structure. We will present the GLST structure in Section 11. Then, in Section 111, we will discuss an interesting property of the GLST structure and explain how our power
*
stream + s/ P
4 Fig. 1
Y Y B
I I
SpaceTime Coder R
-
Y
General layout of a LST system
A GLST system is shown in Figure 1. It has R Space-Time encoders which are by themselves optimum Space-Time encoders according to the criteria stated in [l]. The i-th Encoder occupies a total of ni transmit antennas during the transmission. The number of transmit antennas used by each encoder can be different and the total number used is equal to the total number of transmit antennas. The assignment of the transmit antennas to the Space-Time coder is controlled by a sequence of mappings in time. With the time varying nature of the mapping, the encoder can use different transmit antennas at different time. Different mapping will lead to different GLST systems and two
The research is support in part by the Hong Kong RGC & HKTIIT
0-7803-7097-1/01/$10.00 02001 IEEE
Coder 2
Time varying mapping between coder and antennas
1706
interesting special cases are the Horizontal GLST (HGLST) and the Diagonal GLST (DGLST) system.
random variable with variance N0/2 per dimension. H = (h,, jMxN is the channel matrix where each clement is
In the HGLST system, the mapping is actually not varying in time and the output from each Space-Time encoder is then directly passed to a fixed group of antennas for transmission. Thus, the symbols are “horizontally” passed from the encoder to the antennas. In the DGLST case, mapping performs a grouped cyclic shift. The encoders cycle through all groups of antcnnas periodically. The “diagonal” structure appears when we plot the assignment of the output of each individual encoder to the transmit antennas over time. Examples of these two systems are illustrated in Figure 2 . In these examples, we have assumed that the system has 3 Space-Time coders, each requiring 2 transmit antennas and
independent zero-mean complex Gaussian random variable with variance equal to 1 and is constant over onc frame.
C. Decoding The decoding of a GLST code is basically a group interference suppression and cancellation scheme undertaken on a code level. In decoding, wc assume that the transmit side knows nothing about the channel and the receive side have perfect knowledge about it. First of all, a particular order of decoding is selected. This order can affect the system performance significantly and two approaches to determine the decoding order had been proposed.
p ,V ,a,are the symbol vectors transmitted by the three coders respectively at time t.
DGLST
HGLST
Transmit Ant. No. Fig. 2
Time
Transmit symbol arrangements of HGLST and DGLST system
B. Channel Model
We consider the above system over an independent and slow fade environment. Let c ,=(c
1, ...,cy)T
denote the
denote the symbol transmitted at time t and rt =(ri ,...,r y corresponding symbol received at time t where N is the number of transmit antennas and M is the number of receive antennas. Then, we have
r, = H c , + n ,
(1)
:,
where the noise n t =(n ...,nf.1 at time t is modeled as independent samples of a zero-mean complex Gaussian
0-7803-7097-1 /Ol/$lO.OO02001 IEEE
1707
An optimal ordering determined by the receiver based on the channel information for HGLST system with no coding was proposed in [4] and the overall structure is known as VBLAST. This result has also been generalized recently to HGLST with ST code in [ 5 ] . The other approach was proposed in [2] where it was shown that the orders of antenna diversity gain for code to be decoded first is less than those being decoded later. Hence, different power levels are allocated to different codes according to their positions in the decoding order. As this power allocation has to be done at the transmitter which has no knowledge of the instantaneous channel information, the transmitter can select an arbitrary decoding order and then allocate power according to that order. In this paper, we adopt the latter approach and derive the optimal power allocation scheme. Without loss of generality, we select an arbitrary order and perform the decoding from encoder 1 to R.
At time t, assuming the first encoder uses the first n, antennas and the second encoder uses the next n2 antennas and so on. At the decoding of the i-th decoder, 1 to i-1 coder should all be decoded. An interference cancellation is performed here with the signal component transmitted from the first i-1 coders subtracted from the received signal, i.e. the received signal for the i-th decoder is j=l
where k i = n l + n 2 +...+ni-l and h j is the j-th column for channel matrix H. Moreover,
H. =
hl(k,+l)
hl(k,+2)
'.'
hIN
h2(k,+l)
h2(k,+2)
"'
h2N
hM(k,+l)
hh4(k,+2)
'.'
hMN
For i = 1,. . .,R, we first denote C, to be the event that the i-th subsystem is decode correctly. Then, G , = P ( C , IC,;..,C,-,) is the probability that the i-th subsystem is decoded correctly given that the interference cancellation is perfect. As the decorrelater is a linear filter that will suppress all the interference of the sub-systems that are decoded after i, this conditional probability has the form of a Q function or the Error function (Erf). Note that G, is a random variable induced by the implicit dependence on the channel gains. Moreover, we denote s, to be the signal power that is assigned to the i-th subsystem and a i to be the random variable that represents the post detection, or effective, channel gain of the i-th subsystem. For a system with given parameter and channel condition, G, is only a function of s, and ~1 , . The probability of a correct frame,
is the channel matrix of the remaining antennas. We compute the null space of the matrix HI and a matrix U, consists of the orthonormal basis for that null space is obtained. We then left multiply r: with U: to obtain an interference suppressed version of the received signal, ii = U I r: . There is no need to suppress the interference from coder 1 to i-1 as they are removed by the interference cancellation scheme. For different time instance, the suppression is done on different set of transmit antennas according to the periodic sequence of mappings. Afterwards, decoding is performed and the same process continues for encoder i+l. The iteration goes until all the R codewords are decoded. The last codeword will not need to go through the decorrelation process at all as there is no interference left. 111. THEOPTLMUM POWERALLOCATION SCHEME
R
As the transmit side do not have the channel information, we need to consider the average probability of error. Taking the expectation over the probability of correct frame, we have
The objective is to maximize the above terms under the constraint of a given amount of total power. To solve this problem, we apply the Lagrange Multiplier method and set
We define {nl,n2,...,n R ) as the number of transmit antennas used by encoder 1,2,...R. With the above encoding and decoding structure, for encoder r l R , we have a
(5)
R
subsystem with n, transmit antennas and M -
n receive i=r+I
where S is the total transmitted power. Differentiated C with respect to si, wc have
antennas. Thus, as shown in [2], we can easily see that the encoder which is decoded later has a larger received signal power and diversity as the number of actual receive antennas is larger. Thus, allocating different power levels to different encoders allow the transmitter to take advantage of this situation. In this section, we will propose a power allocation scheme that minimizes the overall frame error rate.
0-7803-7097-1/01/$10.00 02001 IEEE
dC as;
1708
- BE[G] as;
-1
Then, we should consider the following fact. With a certain degree of diversity in each subsystem, each a should have a rather small variance. Also, s, should be set such that Gi is rather close to 1 within the range that a i has high probability in order to have a meaningful overall probability of correct frame. As Gi is a function that will saturate at I, dG slope of Gi will be flatten off and therefore, should ds i ~
dG’ is closed to 0 in the above range. converge to 0. Thus, 2 ds i dG i Consequently, the ratio of the variance to the mean of ds i is much larger than Gi . Under these condition,
n
G can be
jci
approximated by 1.
=
I(2)
By setting E
f(a Ida I -h
dC
-=
ds i
0,
LEi1
= h ,foralli=l,...,R
[E;]
Thus, we should equate E - for all i and then determine h based on the total transmitted power S. -
I:]
-
Moreover, assuming that E - = -E[G i:
3 , we can also
d optimize the PA scheme by equalizing -E[G,] for all i. ds , Since F, = 1 - GI, equalizing the derivative of Fi can also optimize the power allocation. IV. SIMULATION In this paper, we present simulation result in order to compare the performance for different power allocation schemes. We perform the simulation on a 4x 4 and a 8x8
0-7803-7097-1/01/$10.00 02001 IEEE
1709
systems under a quasi-static independent fading cnvironment. Jn both systems, we have 2 transmit antennas per group and thus have 2 and 4 coders on the two systems, respectively. The Space-Time encoder used in the simulation is a 16-states trellis Space-Time code with 2-bit/s/Rz proposed in [ 11. For each system, we have four simulations. The equal power allocation scheme assigns equal power to different coders. Thc power allocation proposed by Tarokh in [ 2 ] assigned the power for different subsystems with a 3dB difference. Thus, under the decoding order, the i-th subsystem will have double the amount of power whcn compared to the i+l-th subsystem. Both of these two schemes run on a HGLST system. For the next two simulations, we use our proposed power allocation scheme. One of them is on HGLST system and the other is on DGLST system. We have also applied Tarokh’s power allocation scheme to DGLST for comparison purpose. In the first two cases, the power ratio between different encoders is fixed for different SNR. However, for our proposed scheme, the power ratio is individually optimized for each SNR. In the calculation of the optimal power allocation scheme, we need to have the individual frame error rate, FER, as a function of the SNR. We obtain that by simulation with the assumption that interference cancellation is perfect. Afterwards, a curve fitting technique is done on the FER curve and thus a function is obtained. Then, differentiation is taken on thc FER function. The curve fitting function we have used is f ( s , ) = e x p ( p , ( s , ) ) where p , ( s i ) is a polynomial function of signal power, s, with degree q. In the simulation, q is equal to 3. With any change of system parameter such as the number of antennas or the realization of mapping, we will have to update the FER function and recalculate the power ratio between different encoders. The simulation results are shown in Figures 3 and 4. We found that for the 4x4 system, our proposal optimized scheme has on average an 1 dB gain over the equal power case. For 8x8 system, the gain is even larger and is around 2.5 dB. This has shown that the gain due to power allocation increases as the number of transmission groups increases. Moreover, our proposed scheme has a performance gain over the Tarokh’s scheme in all cases. This demonstrates that our proposed power allocation scheme can work well for any GLST structure independent of the realization of the mapping. The gain is nearly I dB in 8x8 system. In addition, from the simulation results, we can also see that DGLST have a better performance than the HGLST case as it allows a higher transmit antenna diversity. However, DGLST requires additional computation for finding the decorrelator weight
V. CONCLUSIONS
vcctors used in different decoding orders. The HGLST only requires one decorelater for a whole fkame.
In this paper, we have presented an optimal power allocation scheme on the GLST system. As each Space-Timc encoder faces different channel conditions with increasing total receive signal power and antenna diversity according to the decoding order, assigning different power levels to different subsystems, i.e. the power allocation, allows us to optimize the FER performance in a GLST system. We proved that by equalizing the derivative of the individual FER, we can attain the optimum performance of GLST system. As the scheme does not depend on the channel information, this optimization can be done off timc for a targeted operational signal-to-noise ratio. Hence this does not increase the complexity of the system. Through simulations, we showed that power allocation can lead to a significant performance gain, around 1 to 2.5 dB depending on the system configuration, without increasing the complexity of the system.
1 OD
10.’
[r
U w
1o.2
i
8
3
10
I?
1;
1;
114
Reference
1L
EslNo dB (per receive antenna)
Vahid Tarokh, Nambi Seshadri and A. R. Calderbank, “Space -Time Codes for High Data Rate Wireless Communication: Performance Criterion and Code Construction,” IEEE Trans. Inform. neoty, vol. 44, no. 2, pp. 744-765, March 1998,
Fig. 3 GLST system with 4 transmit and 4 receive antennas
Vahid Tarokh, Ayman Naguib, Nambi Seshadri and A. Robert Calderbank, “Combined Array Processing and Space -Time Coding,” IEEE Trans. In/ortn. Theory, vol. 45, no. 4, pp. 1121 - 1 128, May 1999, Da-shan Shiu 62 Joseph M. Kahn, “Layered Space-Time Codes for Wireless Communications Using Multiple Transmit Antennas,” ICC’99, vol.1, pp.436-440, 1999,
P. W. Wolniansky, G. J. Foschini, G. D. Golden, and R. A. Valenzuela. “V-BLAST: An Architecture for Realizing Very High Data Rates Over the Rich -Scattering Wireless Channel,” invitedpuper, Proc. ISSSE-98, Pisa, Italy, Sept. 29, 1998,
(L
LL Lu
1o-?
M. Tao, R. S. Cheng, “LOW complexity post-ordered iterative decoding for generalized layered space-time coding systems,” ICC 2001,Finland, June 200 I , 10.3
8
9
10
11 12 13 14 EslNo dB (per receive antenna)
15
16
17
G . J. Foschini, “Layered Space-Time Architecture For Wireless Communication in a Fading Environment When Using Multi -Element Antennas,” Bell Lalis TechnicalJoournal, Autumn 1996,
Fig. 4 GLST system with 8 transmit and 8 receive antennas
0-7803-7097-1/01/$l0.00 02001 IEEE
N. Sharma, Hsuan-Jung Su, E. Geraniotis, “A Novel Approach For Multi-Antenna Systems,” ICC 2000, vo1.3, pp.1264 - 1269, 2000.
1710
allocation scheme can take advantages over this property. Furthermore, in Section IV, we will present simulation results to show the performance gain obtained by power allocation which by itself does not increase the complexity of the system. Then, we will conclude in Section V. 11. SYSTEM MODEL
A . Encoding
-
Y
Coder 1
Input bit
I. INTRODUCTION In recent years, many research have focused on achieving the capacity of multi-antennas system. Many techniques have been proposed and Space-Time (ST) code was introduced in [l]. However, as the number of transmit and receive antennas increases, both the design and the decoding of ST code become much more complex. For example, a maximum likelihood detector on a &transmit antenna system with QPSK symbol requires calculating the Euclidean distances for sixty thousands constellation points per transmitted symbol. Thus, separating the transmit antennas into groups is a natural way to reduce the complexity. Generalized layered Space Time, GLST, code structure, studied by [ 2 ] and [3], takes this approach to reduce the complexity.
However, with the special decoding structure of the GLST system, it was shown in [2] that different subsystems see different system parameters and channel conditions. In this paper, we will exploit these differences with our power allocation (PA) scheme to improve the performance of the GLST structure. We will present the GLST structure in Section 11. Then, in Section 111, we will discuss an interesting property of the GLST structure and explain how our power
*
stream + s/ P
4 Fig. 1
Y Y B
I I
SpaceTime Coder R
-
Y
General layout of a LST system
A GLST system is shown in Figure 1. It has R Space-Time encoders which are by themselves optimum Space-Time encoders according to the criteria stated in [l]. The i-th Encoder occupies a total of ni transmit antennas during the transmission. The number of transmit antennas used by each encoder can be different and the total number used is equal to the total number of transmit antennas. The assignment of the transmit antennas to the Space-Time coder is controlled by a sequence of mappings in time. With the time varying nature of the mapping, the encoder can use different transmit antennas at different time. Different mapping will lead to different GLST systems and two
The research is support in part by the Hong Kong RGC & HKTIIT
0-7803-7097-1/01/$10.00 02001 IEEE
Coder 2
Time varying mapping between coder and antennas
1706
interesting special cases are the Horizontal GLST (HGLST) and the Diagonal GLST (DGLST) system.
random variable with variance N0/2 per dimension. H = (h,, jMxN is the channel matrix where each clement is
In the HGLST system, the mapping is actually not varying in time and the output from each Space-Time encoder is then directly passed to a fixed group of antennas for transmission. Thus, the symbols are “horizontally” passed from the encoder to the antennas. In the DGLST case, mapping performs a grouped cyclic shift. The encoders cycle through all groups of antcnnas periodically. The “diagonal” structure appears when we plot the assignment of the output of each individual encoder to the transmit antennas over time. Examples of these two systems are illustrated in Figure 2 . In these examples, we have assumed that the system has 3 Space-Time coders, each requiring 2 transmit antennas and
independent zero-mean complex Gaussian random variable with variance equal to 1 and is constant over onc frame.
C. Decoding The decoding of a GLST code is basically a group interference suppression and cancellation scheme undertaken on a code level. In decoding, wc assume that the transmit side knows nothing about the channel and the receive side have perfect knowledge about it. First of all, a particular order of decoding is selected. This order can affect the system performance significantly and two approaches to determine the decoding order had been proposed.
p ,V ,a,are the symbol vectors transmitted by the three coders respectively at time t.
DGLST
HGLST
Transmit Ant. No. Fig. 2
Time
Transmit symbol arrangements of HGLST and DGLST system
B. Channel Model
We consider the above system over an independent and slow fade environment. Let c ,=(c
1, ...,cy)T
denote the
denote the symbol transmitted at time t and rt =(ri ,...,r y corresponding symbol received at time t where N is the number of transmit antennas and M is the number of receive antennas. Then, we have
r, = H c , + n ,
(1)
:,
where the noise n t =(n ...,nf.1 at time t is modeled as independent samples of a zero-mean complex Gaussian
0-7803-7097-1 /Ol/$lO.OO02001 IEEE
1707
An optimal ordering determined by the receiver based on the channel information for HGLST system with no coding was proposed in [4] and the overall structure is known as VBLAST. This result has also been generalized recently to HGLST with ST code in [ 5 ] . The other approach was proposed in [2] where it was shown that the orders of antenna diversity gain for code to be decoded first is less than those being decoded later. Hence, different power levels are allocated to different codes according to their positions in the decoding order. As this power allocation has to be done at the transmitter which has no knowledge of the instantaneous channel information, the transmitter can select an arbitrary decoding order and then allocate power according to that order. In this paper, we adopt the latter approach and derive the optimal power allocation scheme. Without loss of generality, we select an arbitrary order and perform the decoding from encoder 1 to R.
At time t, assuming the first encoder uses the first n, antennas and the second encoder uses the next n2 antennas and so on. At the decoding of the i-th decoder, 1 to i-1 coder should all be decoded. An interference cancellation is performed here with the signal component transmitted from the first i-1 coders subtracted from the received signal, i.e. the received signal for the i-th decoder is j=l
where k i = n l + n 2 +...+ni-l and h j is the j-th column for channel matrix H. Moreover,
H. =
hl(k,+l)
hl(k,+2)
'.'
hIN
h2(k,+l)
h2(k,+2)
"'
h2N
hM(k,+l)
hh4(k,+2)
'.'
hMN
For i = 1,. . .,R, we first denote C, to be the event that the i-th subsystem is decode correctly. Then, G , = P ( C , IC,;..,C,-,) is the probability that the i-th subsystem is decoded correctly given that the interference cancellation is perfect. As the decorrelater is a linear filter that will suppress all the interference of the sub-systems that are decoded after i, this conditional probability has the form of a Q function or the Error function (Erf). Note that G, is a random variable induced by the implicit dependence on the channel gains. Moreover, we denote s, to be the signal power that is assigned to the i-th subsystem and a i to be the random variable that represents the post detection, or effective, channel gain of the i-th subsystem. For a system with given parameter and channel condition, G, is only a function of s, and ~1 , . The probability of a correct frame,
is the channel matrix of the remaining antennas. We compute the null space of the matrix HI and a matrix U, consists of the orthonormal basis for that null space is obtained. We then left multiply r: with U: to obtain an interference suppressed version of the received signal, ii = U I r: . There is no need to suppress the interference from coder 1 to i-1 as they are removed by the interference cancellation scheme. For different time instance, the suppression is done on different set of transmit antennas according to the periodic sequence of mappings. Afterwards, decoding is performed and the same process continues for encoder i+l. The iteration goes until all the R codewords are decoded. The last codeword will not need to go through the decorrelation process at all as there is no interference left. 111. THEOPTLMUM POWERALLOCATION SCHEME
R
As the transmit side do not have the channel information, we need to consider the average probability of error. Taking the expectation over the probability of correct frame, we have
The objective is to maximize the above terms under the constraint of a given amount of total power. To solve this problem, we apply the Lagrange Multiplier method and set
We define {nl,n2,...,n R ) as the number of transmit antennas used by encoder 1,2,...R. With the above encoding and decoding structure, for encoder r l R , we have a
(5)
R
subsystem with n, transmit antennas and M -
n receive i=r+I
where S is the total transmitted power. Differentiated C with respect to si, wc have
antennas. Thus, as shown in [2], we can easily see that the encoder which is decoded later has a larger received signal power and diversity as the number of actual receive antennas is larger. Thus, allocating different power levels to different encoders allow the transmitter to take advantage of this situation. In this section, we will propose a power allocation scheme that minimizes the overall frame error rate.
0-7803-7097-1/01/$10.00 02001 IEEE
dC as;
1708
- BE[G] as;
-1
Then, we should consider the following fact. With a certain degree of diversity in each subsystem, each a should have a rather small variance. Also, s, should be set such that Gi is rather close to 1 within the range that a i has high probability in order to have a meaningful overall probability of correct frame. As Gi is a function that will saturate at I, dG slope of Gi will be flatten off and therefore, should ds i ~
dG’ is closed to 0 in the above range. converge to 0. Thus, 2 ds i dG i Consequently, the ratio of the variance to the mean of ds i is much larger than Gi . Under these condition,
n
G can be
jci
approximated by 1.
=
I(2)
By setting E
f(a Ida I -h
dC
-=
ds i
0,
LEi1
= h ,foralli=l,...,R
[E;]
Thus, we should equate E - for all i and then determine h based on the total transmitted power S. -
I:]
-
Moreover, assuming that E - = -E[G i:
3 , we can also
d optimize the PA scheme by equalizing -E[G,] for all i. ds , Since F, = 1 - GI, equalizing the derivative of Fi can also optimize the power allocation. IV. SIMULATION In this paper, we present simulation result in order to compare the performance for different power allocation schemes. We perform the simulation on a 4x 4 and a 8x8
0-7803-7097-1/01/$10.00 02001 IEEE
1709
systems under a quasi-static independent fading cnvironment. Jn both systems, we have 2 transmit antennas per group and thus have 2 and 4 coders on the two systems, respectively. The Space-Time encoder used in the simulation is a 16-states trellis Space-Time code with 2-bit/s/Rz proposed in [ 11. For each system, we have four simulations. The equal power allocation scheme assigns equal power to different coders. Thc power allocation proposed by Tarokh in [ 2 ] assigned the power for different subsystems with a 3dB difference. Thus, under the decoding order, the i-th subsystem will have double the amount of power whcn compared to the i+l-th subsystem. Both of these two schemes run on a HGLST system. For the next two simulations, we use our proposed power allocation scheme. One of them is on HGLST system and the other is on DGLST system. We have also applied Tarokh’s power allocation scheme to DGLST for comparison purpose. In the first two cases, the power ratio between different encoders is fixed for different SNR. However, for our proposed scheme, the power ratio is individually optimized for each SNR. In the calculation of the optimal power allocation scheme, we need to have the individual frame error rate, FER, as a function of the SNR. We obtain that by simulation with the assumption that interference cancellation is perfect. Afterwards, a curve fitting technique is done on the FER curve and thus a function is obtained. Then, differentiation is taken on thc FER function. The curve fitting function we have used is f ( s , ) = e x p ( p , ( s , ) ) where p , ( s i ) is a polynomial function of signal power, s, with degree q. In the simulation, q is equal to 3. With any change of system parameter such as the number of antennas or the realization of mapping, we will have to update the FER function and recalculate the power ratio between different encoders. The simulation results are shown in Figures 3 and 4. We found that for the 4x4 system, our proposal optimized scheme has on average an 1 dB gain over the equal power case. For 8x8 system, the gain is even larger and is around 2.5 dB. This has shown that the gain due to power allocation increases as the number of transmission groups increases. Moreover, our proposed scheme has a performance gain over the Tarokh’s scheme in all cases. This demonstrates that our proposed power allocation scheme can work well for any GLST structure independent of the realization of the mapping. The gain is nearly I dB in 8x8 system. In addition, from the simulation results, we can also see that DGLST have a better performance than the HGLST case as it allows a higher transmit antenna diversity. However, DGLST requires additional computation for finding the decorrelator weight
V. CONCLUSIONS
vcctors used in different decoding orders. The HGLST only requires one decorelater for a whole fkame.
In this paper, we have presented an optimal power allocation scheme on the GLST system. As each Space-Timc encoder faces different channel conditions with increasing total receive signal power and antenna diversity according to the decoding order, assigning different power levels to different subsystems, i.e. the power allocation, allows us to optimize the FER performance in a GLST system. We proved that by equalizing the derivative of the individual FER, we can attain the optimum performance of GLST system. As the scheme does not depend on the channel information, this optimization can be done off timc for a targeted operational signal-to-noise ratio. Hence this does not increase the complexity of the system. Through simulations, we showed that power allocation can lead to a significant performance gain, around 1 to 2.5 dB depending on the system configuration, without increasing the complexity of the system.
1 OD
10.’
[r
U w
1o.2
i
8
3
10
I?
1;
1;
114
Reference
1L
EslNo dB (per receive antenna)
Vahid Tarokh, Nambi Seshadri and A. R. Calderbank, “Space -Time Codes for High Data Rate Wireless Communication: Performance Criterion and Code Construction,” IEEE Trans. Inform. neoty, vol. 44, no. 2, pp. 744-765, March 1998,
Fig. 3 GLST system with 4 transmit and 4 receive antennas
Vahid Tarokh, Ayman Naguib, Nambi Seshadri and A. Robert Calderbank, “Combined Array Processing and Space -Time Coding,” IEEE Trans. In/ortn. Theory, vol. 45, no. 4, pp. 1121 - 1 128, May 1999, Da-shan Shiu 62 Joseph M. Kahn, “Layered Space-Time Codes for Wireless Communications Using Multiple Transmit Antennas,” ICC’99, vol.1, pp.436-440, 1999,
P. W. Wolniansky, G. J. Foschini, G. D. Golden, and R. A. Valenzuela. “V-BLAST: An Architecture for Realizing Very High Data Rates Over the Rich -Scattering Wireless Channel,” invitedpuper, Proc. ISSSE-98, Pisa, Italy, Sept. 29, 1998,
(L
LL Lu
1o-?
M. Tao, R. S. Cheng, “LOW complexity post-ordered iterative decoding for generalized layered space-time coding systems,” ICC 2001,Finland, June 200 I , 10.3
8
9
10
11 12 13 14 EslNo dB (per receive antenna)
15
16
17
G . J. Foschini, “Layered Space-Time Architecture For Wireless Communication in a Fading Environment When Using Multi -Element Antennas,” Bell Lalis TechnicalJoournal, Autumn 1996,
Fig. 4 GLST system with 8 transmit and 8 receive antennas
0-7803-7097-1/01/$l0.00 02001 IEEE
N. Sharma, Hsuan-Jung Su, E. Geraniotis, “A Novel Approach For Multi-Antenna Systems,” ICC 2000, vo1.3, pp.1264 - 1269, 2000.
1710
