Engineering, 2009, 2, 91-98
doi:10.4236/eng.2009.12010 Published Online August 2009 (http://www.SciRP.org/journal/eng/).
Optimal Power Allocation Strategy for TBLAST
Based 4G Systems
Wu YIN1, Pei XIAO2
1ZTE corporation, Shenzhen, China
2The Institute of ECIT, Queen’s University, Belfast, UK
Received May 21, 2009; revised July 13, 2009; accepted July 20, 2009
ABSTRACT
There is a big demand for increasing number of subscribers in the fourth generation mobile communication
systems. However, the system performance is limited by multi-path propagations and lack of efficient power
allocation algorithms in conventional wireless communication systems. Optimal resource allocation and in-
terference cancellation issues are critical for the improvement of system performance such as throughput and
transmission reliability. In this paper, a turbo coded bell lab space time system (TBLAST) with optimal
power allocation techniques based on eigen mode, Newton and convex optimization method and carrier-
interference-and-noise ratio (CINR) are proposed to improve link reliability and to increase throughput with
reasonable computational complexity. The proposed scheme is evaluated by Monte-Carlo simulations and is
shown to outperform the conventional power allocation scheme.
Keywords: Carrier Interference and Noise Ratio (CINR), Convolutional Turbo Coded Bell Space Time
(TBLAST), Eigen Mode (EM), Optimal Power Allocation (OPL), Automatic Differentiation
(AD), Symbolic Derivative (SD)
1. Introduction
This decade has witnessed incredible development in
mobile wireless communications. Multiple-input and
multiple-output (MIMO) techniques and adaptive an-
tenna system (AAS) have been adopted in the 4th gen-
eration (4G) systems, e.g., worldwide interoperability
microwave access (WiMAX) and long term evolution
(LTE) systems. It is well known that wireless communi-
cation systems are interference limited, i.e. their through-
put and quality of service are largely affected by various
impairments such as multiuser inference (MUI), inter-
symbol interference (ISI) and spatial correlation, etc..
MIMO and orthogonal frequency division multiplex-
ing (OFDM) techniques have been adopted in 4G sys-
tems. OFDM technique transforms a frequency selective
fading channel into parallel flat fading channels which
provides an efficient way to improve MIMO and AAS
system performance. The single-carrier frequency divi-
sion multiple access (SC-FDMA) and orthogonal fre-
quency division multiple access (OFDMA) have been
employed in the uplink of the WiMAX (IEEE802.16e)
and LTE systems, respectively, to mitigate the effect of
channel fading and interference. In 4G systems, the
channel quality is measured by the carrier-interferer-
noise-ratio (CINR), defined by the ratio between the
power of useful subcarriers in the OFDM and the power
of noise plus interference.
The issues of allocating power among subcarriers in
OFDM systems have been investigated extensively [1,2].
The power control of an OFDM system and its sub-
channels is an efficient way to improve system perform-
ance such as maximizing system capacity and reducing
bit error ratio (BER). Thus, the power allocation
schemes and their application in the MIMO-OFDMA as
well as AAS systems have attracted a lot of attention
from both academia and industry.
It has also been reported that in 4G systems, there ex-

W. YIN ET AL. 92
ists carrier frequency offset which destroys the orthogo-
nality between subcarriers, leading to inter-carrier inter-
ference [3] which can deteriorate system performance
significantly. In addition, spatial correlation has more
impact on the uplink than on the downlink [4] of 4G
systems. Interference cancellation (IC) techniques have
been recommended as an efficient solution to tackle this
problem. In 4G systems, optimal resource allocation
(OPL) can be implemented by adaptive modulation and
coding (AMC) as well as with channel state information
at the transmitter (CSIT). Precoding (beamforming) with
CSIT is a technique that can effectively utilize optimal
resource to maximize throughput or improve transmis-
sion link quality.
In 4G systems, CINR [5] gives an indication for the
underlying channel condition, and has been used in Wi-
MAX and LTE systems as feedback information from
mobile terminals to base station. Conventional optimal
methodologies usually have prohibitive computation
complexity which prevents them from practical imple-
mentation. Eigenvalue mode (EM) has been regarded as
an efficient way to achieve desirable performance with
reasonable complexity. For these reasons, we consider
the use of CINR and develop an EM based algorithm in
this paper.
Space time coding (STC) and spatial multiplexing
(SM) also called the BLAST have been considered in the
4G standards [6]. In this paper, we investigate BLAST
techniques, which can achieve good performance with
low computational complexity by successive interference
cancellation (SIC) algorithm [7]. The disadvantage of
Vertical BLAST is the lack of diversity for transmission
link. To tackle this problem, parallel convolutional cod-
ing (PCCC) coded BLAST can be employed to compen-
sate the diversity loss in the conventional VBLAST.
Turbo BLAST (TBLAST) was proposed in [6] to reduce
the complexity of such systems. The principle is to re-
peat the process of passing soft information instead of
hard decision between the MIMO detector and the chan-
nel decoder. As such, the system performance can be
improved in an iterative manner.
However, the OPL and interference cancellation tech-
niques as well as TBLAST have not been considered in
the current WiMAX and LTE standards. This paper pro-
vides a feasibility study of utilizing the OPL and
TBLAST techniques on the transmitter and receiver side,
respectively. It is reasonable to believe that the results
obtained from this study are of direct relevance to the
future development of 4G standards.
2. Literature Review
2.1. Review of CINR Utilization
Channel estimation and resource optimisation are the
two key issues that can determine the physical layer sys-
tem performance in both LTE and WiMAX systems.
Recently, major equipment vendors issued a proposal
that involved Physical CINR and power allocation to
improve the WiMAX system performance [8,9] in Wi-
MAX Forum. Channel estimation is performed based on
CINR. CSIT or PCINR information can be in the form of
precoding matrix index (PMI) in both WiMAX and LTE
systems.
The eigen mode relies on the analysis of CINR, which
is equivalent to one form of Shannon capacity [9]. In [10,
11], compensation-booting assisted OPL and AMC have
been used to improve wireless system performance.
However, there is lack of specific methodologies and
application in 4G systems. In WiMAX beamforming or
LTE precoding techniques, eigen mode based techniques
can be considered for weight calculation or code book
selection in the precoding mode of transmission in base
station. OPL can be achieved by feedback of fast feed-
back (FFB) channel and CSIT from customer premise
equipment (CPE) in a closed-loop system.
2.2. Review of Water-Filling (WF) and SVD in
Wireless Communication
Power allocation schemes for the wireless communica-
tion systems mainly fall into three categories, i.e. equal
power allocation, water filling power allocation that
based on singular value decomposition SVD and Newton
and convex optimization method based power allocation.
The principle of SVD can be described briefly with the
following equations:
*()*()diag diag

Hλvλ (1)
12n 1 2n
],






where H is a normalised channel complex matrix,
each element of which represents the complex channel
gain with zero mean and unit variance;

are eigen-
values of H corresponding to the power of each sub-
channel, and the relevant eigenvectors that can be re-
garded as weights in the beamforming or choice of PMI
are as follows:
mn 

i

v = [v1 , v2···vn] (2)
which can be utilized to form precoding matrix in MIMO
systems. Water-filling (WF) or water pouring schemes

W. YIN ET AL. 93
Figure 1. Block diagram of the proposed transmit system.
[12] have been proposed as iterative power allocation for
transmit antennas after acquiring eigenvectors following
channel estimation, covariance matrix calculation and
SVD operation. In the water-filling scheme, the iterative
power allocation is implemented for each user and can
be expressed as
 miλPp
m
i
ici 2,1
1
1









 (3)


H
ctrP QQ (4)
where m is the number of transmit antennas; is the
transmit power constraint; Q denotes the ith signal se-
quence in the transmit system;

are the power allo-
cated to individual sub-streams in the transmitter and the
c
P

i
p


1
i

are the water-filling levels.
However, the WF scheme is suboptimal for multiuser
MIMO systems since it only considers separated power
allocation for each user rather than joint power allocation
for all the users [13,14]. More details can be seen in the
following section of the proposed optimal method in the
third part of the system model. In addition, the previous
publications and research on the optimal power alloca-
tion of the VBLAST systems [14,15] have heavy compu-
tational complexity that prevents their application in
practice. Furthermore, these researches only focus on
uncoded VBLAST systems. In this paper, coded
VBLAST systems with high efficiency have been inves-
tigated and the comparison with the previous optimal
power allocation schemes will be addressed in the fol-
lowing section of the proposed optimal method.
3. System Model and the Proposed Power
Allocation Scheme
In this section, we describe the proposed transceiver sys-
tem.
3.1. Review of Transceiver System and Conven-
tional Power Allocation Scheme
In Figure 1, the data source is first separated into m sub-
streams and then encoded by different PCCC encoders.
Subsequently, each coded substream can be beamformed
by weight or coded by PMI mode. An inverse fast Fou-
rier transform (IFFT) is then applied to the signal and
each coded sub-stream is independently fed into its an-
tenna. In addition, the power of the transmitted signals
can be controlled by base station through closed-loop
optimal power allocation based on CINR and the feed-
back of CPE.
Figure 2 illustrates the proposed TBLAST receiver
structure. The communications channel with the highest
signal-to-noise ratio (SNR) is chosen for detection by a
linear adaptive MMSE scheme. In the decoder, a maxi-

W. YIN ET AL. 94

Figure 2. Block diagram of the proposed receiver system.
mum aposteriori (MAP) or aposteriori probability (APP)-
based algorithm is utilized to extract the data from the
received signal. After deriving soft decision and recon-
structing each transmitted sub-stream, the detected signal
is removed from the received signal by successive inter-
ference cancellation (SIC) algorithm before proceeding
to the next iteration.
In WiMAX beamforming (BF) or LTE precoding
techniques, eigenvalue base techniques can be used for
weight calculation or code book selection in the precoder
design at base station. The conventional OPL algorithms
are designed according to utility functions using SINR,
BER performance or system capacity. The cost function
of signal to interference and noise ratio (SINR) can be
expressed as [16,17]:

2
2
2
2
j
ii
i
jj i
ji
ii i
ikjj
ji
ap
pbp n
p
vp















vH
vH
(5)
where

denotes the processing gain;

i
a


j
bdenotes the
channel coefficient;

is a zero mean Additive White
Gaussian Noise (AWGN); is the nulling vector and
is the power allocated to individual sub-streams in
the transmitter.

i
n
i
v

i
p
The maximum signal to noise ratio (MSNR) based
precoding scheme is equivalent to the maximum capacity
based scheme. The system capacity can be presented as
follows [18]:















N
n
nk
H
SINR
C
1
,
2
1log
detlog IHQH 
(6)
where H is a normalised complex-valued channel
nm 
matrix with unit variance, Q is the covariance matrix of
the information data bits and the 2

denotes the variance
of the noise
In MIMO systems, the ergodic capacity, defined as the
maximum average mutual information for identical inde-
pendent distribution (i.i.d) complex Gaussian channels
with perfect CSI at receiver and no CSI information in
transmitter can be expressed as [18]:
























2 1
H
2
1log
1
b/s/HzIdetlog




ii
m
i
Hi
p
m
m
Epf HQH
(7)
where

denotes the average SNR;

stands for the
complex conjugate operator. The channel gain is normal-
ized so as to meet the constant power constraint, m is the
number of transmit antennas.
H
VBLAST is a technique that selects the received layer
with the highest signal noise ratio (SNR) and then re-
moves the relevant layer by SIC till the last layer is de-
tected. Therefore, the first layer detection is critical to
BLAST system performance. The principle of the opti-
mal power allocation in the proposed BLAST system is
to allocate more power to the layers with high SNR, and a
good system performance can be achieved in this manner.
3.2. Review of Optimal Theory on Wireless
Communications
Most optimization problems in practical wireless com-
munication environments fall into the category of convex
optimization. IPM (interior point method), which con-
sists of quasi Newton method and Lagrangian method,
has been regarded as the most efficient method in the
optimal sense for resolving optimal convex problems
with certain constraints.
The applications of IPM are classified into three cata-
logues, i.e. primal IPM, dual IPM and primal dual IPM
methods. The optimal source management solutions in
practical wireless communication systems can be dealt
with by optimal primal-duality IPM theory that is actu-
ally a minimum-maximum or minmax problem [17] with
power constraint:
  


m
i
iiii pgkpf
1
max (8)
The automatic differentiation (AD) method is highly
efficient to achieve optimal solution with low computa-
tion complexity compared to the conventional optimal
schemes. In the wireless communication systems, it can
be described in terms of multiple variables as follows

W. YIN. ET AL. 95





1112n
mm12n
F(p)=f(p ,p,p,)
F(p) =
F(p)=f (p,p,p,)








(9)
The derivative matrix that depends on the Jacobian ma-
trix can be described as
F(p)
=
p
J
j

 (10)
111
1
12 n
mm m
n
12 n
F (p)F (p)F (p)
ypp p
=
F(p) F(p)F(p)
ypp p
J
 



 



 



 












(11)
where the function is set up to meet the require-
ments of the wireless communication system functions;
 p
i
F


m,, pppp 21
 is the allocated power in the trans-
mission system.
The symbolic derivative (SD) method has been re-
garded as a new area in mathematics and has been
widely applied in industry, commerce and academia. It
can be implemented by the solver package, which is an
efficient software depending on IPM method, for resolv-
ing optimal convex solution by Newton method, in the
processing of derivative. SD algorithms calculate deriva-
tive and estimate an approximate optimal solution in the
formulas with less computational complexity and accu-
racy compared to conventional optimal schemes.
3.3. Proposed Optimal Method and Comparison
with Conventional Schemes
In the classical single-user or multi-user Waterfilling
scheme, the power is allocated for each individual sub-
stream in the transmitter iteratively until all Karush-
Kuhn-Tucker (KKT) conditions are satisfied, which is a
necessary condition and resolved by first order deriva-
tive in a non-linear equation and is actually a simplified
application of IPM [19]. However, the conventional wa-
terfilling schemes have many issues that will prevent
their application and will be explained in the following
paragraphs.
The proposed optimal power allocation scheme in the
BLAST systems is different from the conventional wa-
terfilling or any other power allocation schemes. Firstly,
in the classical waterfilling scheme, the power will be
cut off when the power allocated for individual sub-
stream is less than the waterfilling level u
  0,max uppi (12)
Consequently, the classical waterfilling will result in a
reduced spectral efficiency due to the loss of spatial mul-
tiplexing gain when applied to the BLAST systems. Sec-
ondly, considering the error propagation problem inher-
ent in the interference cancellation based receiver, the
first layer detection is crucial for the system performance
in terms of achievable system capacity and BER per-
formance. For this reason, the substream with the highest
SNR should be allocated more power. Thirdly, the con-
ventional BLAST detection algorithms are only deter-
mined by the SINR. However, in coded BLAST systems
with variable transmission rate, the choice of channel
code and code rate in each substream will affect the
BLAST systems performance significantly.
The conventional optimal power allocation algorithms
for VBLAST have been investigated in [14,15], the
SINR that can be expressed as

2
2
2
2
p
ap ii i
ii
pibp n
jj i
ji vp
ikjj
j
ji








 





vH
vH
(13)
where


i
a denotes the processing gain;


j
bdenotes the
fading channel gain;


i
n is a zero mean AWGN; is
the nulling vector and
i
v


i
p is the power allocated to in-
dividual substream in transmitter.
The BER


ie pP can be approximated and reduced to a
simplified formula as [22, 23]













 12
5.1
exp
5
1
i
R
i
p
i
p
e
P

(14)
where is the data rate of the transmit stream. The
derivatives are subsequently taken for the Equations (3)-
(41) subject to (3)-(39)
i
Rth
i












0
i
dp
i
p
e
Pd
i
dp
i
pfd
i
dp
i
pJd 
(15)
Then the power allocation solution can be derived
from an exhaustive search [23]


p
p
p
i
i
R
ii
ln2625.0 1















ij
jm
i
R
paf
pM i
1
2125.3
1
1

(16)
where

W. YIN ET AL. 96
 

 

































m
ii
j
jm
i
R
m
ii
i
R
p
af
pm
p
p mi
i
1
1
1
1
1
1
1
2125.3
ln
2
6.1
exp




(17)
where the power allocation can be derived by an adap-
tive method such as LMS
 





k
i
ii
i
p
pJ
iukpkp 1
 





















m
ii
k
p
i
pJ
m
i
k
p
i
pJ
m
iuk
i
p
1
2
11
)
(18)
where denotes the step function and m is the trans-
mit antenna size.

iu
It can be observed that the disadvantage of this opti-
mal power allocation scheme is its heavy computational
load to obtain the derivatives in the equation, which is
impractical for real time communication environments.
One solution is to employ the SD, which is efficient in
the derivation and differential algebraic operations for
optimal solution with less computational complexity
compared to the conventional optimal methods.
The power allocated to each individual sub-stream can
be expressed in the form of eigenvalues as

gppkp
m
iic iii
il
 
 (19)
where

are the lagrangian coefficients. Subsequently,
we can obtain the first order of derivative as:

i
k
dl(p,k,r )df(p,r)dg(p,r )
k
dp dpdp
iii iiii
ii
ii
e
i
i
(20)
we can then derive the following equations
1
() ()
m
iii
i
f
pkg


p
)
i
(21)
where and are the gradient of the func-
tions and . The allocated power {} can
be derived from solving following equations

i
pf

i
pf
i
g

i
p
i
gi p
1212 12
{}(
mi
pp psolveeeeggg
 (22)
In the conventional VBLAST detection algorithm, the
ordering procedure that is determined by SINR is ex-
pressed as [13]







 HH
GHIHH 1
2
maxarg 
(23)
With optimal power allocation, the equation for ordering
selection is replaced by




HH
GHPIHPHP1
2
1

 
(24)
Finally, we obtain the eigenmode power allocation for
individual substream in the transmission system as




mi pppdiagP  21 , (25)
Table 1. Simulation environment.
Simulation model
Transmit antenna Receive
antenna
Fading channel
Doppler
frequency
Encoder & rate
Data modulation
Decoding
algorithm
Constraint length
Feedback
polynomial
Feedforward
polynomia
Number of
iterative
CSI
System
Monte Carlo
3 elements
6 elements
Rayleigh. Jakes model
20 Hz
CTC 1/2
OFDM QPSK
Log-Map,
extrinsic information transfer
(EXIT)
4, 6
111 (L=4), 11011 (L=6)
101 (L=4), 11001 (L=6)
6
Perfect known
PCCC, Closed-loop
Figure 3. BER Performance comparison: OPL versus equal
power allocation.

W. YIN. ET AL. 97
11.5 22.5 33.5 4
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
Signal to Noise Ratio (SNR) in dB
Spectral Efficiency (Bits/Sec/Hz)
Optimal power allocation
Uniform power allocation
Figure 4. Comparison of spectral efficiency: OPL versus
uniform power allocation.
In the VBLAST system, we selected the layer with the
highest SINR and perform SIC to remove the detected
layer. This procedure continues for subsequent iterations
of detection and decoding process till the last substream
is detected layer. The solution can be derived by setting
Equation (9) to zero, then we can perform optimal search
within certain steps or iterative number that depends on
the AD method [16]. As a result, the derived solution can
be applied to the transmitter to optimize resource alloca-
tion or relocate the power to the modulation and coding
of transmission in the base station.
4. Numerical Results
In this section, the performance of different systems is
evaluated by computer simulations and numerical results
are provided to demonstrate the effectiveness of the pro-
posed schemes. The simulation parameter setting is tabu-
lated in Table 1.
In Figure 3, we show the comparison of the BER per-
formance between the proposed OPL and the equal
power allocation scheme. Simulation results indicate that
there is a considerable improvement by the proposed
scheme compared to the conventional equal power
scheme. A gain of 4.5 dB has been observed at target
BER= , and the gain becomes more obvious as SNR
increases.
3
10
One can also see from Figure 4 that the spectral effi-
ciency, which depends on received CINR, can be im-
proved by the proposed scheme compared to the equal
(uniform) power allocation. This is due to the fact that
more power in the base station is allocated to the trans-
mit layers with high SNR, leading to the improved sys-
tem performance with SIC based layered processing.
In practical wireless communication systems such as
LTE and WiMAX IEEE802.16e, only equal power allo-
cation has been considered so far. However, this simple
algorithm is highly suboptimal as indicated by our re-
sults. Also considering the fact that the conditions for
performing iterative water-filling can not always be ful-
filled in practical situations, the proposed algorithm pro-
vides an effective means to allocating transmit power
for the 4G systems.
5. Conclusions
In this paper, a closed-loop TBLAST system with eigen
mode and optimal power allocation is proposed and
evaluated by means of simulations. Results show that it
achieves a substantial performance gain in system per-
formance with reasonable computational complexity
compared to the conventional schemes. The work pre-
sented in this paper provides a useful source of informa-
tion for the optimization of power allocation in the future
4G systems.
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