SVD-AidedPowerAllocationandIterativeDetection...

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2011, Article ID 505606, 8 pagesdoi:10.1155/2011/505606

Research Article

SVD-Aided Power Allocation and Iterative DetectionScheme for Turbo-BLAST System with Imperfect ChannelState Information

Xiaomin Chen,1 Xiangbin Yu,1, 2 and Dazhuan Xu1

1 College of Information Science and Technology, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China2 National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China

Correspondence should be addressed to Xiangbin Yu, [email protected]

Received 4 November 2010; Revised 20 April 2011; Accepted 9 June 2011

Academic Editor: Ananda Sanagavarapu Mohan

Copyright © 2011 Xiaomin Chen et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

A new technique that combines adaptive power allocation and iterative detection based on singular value decomposition (SVD) isintroduced for the modified Turbo-BLAST system with imperfect channel state information (I-CSI). At the transmitter, in order tomaximize the capacity performance, the MIMO channel is decomposed into several parallel eigen subchannels by SVD, and thenproper power based on the water-filling principle is allocated to every subchannel subject to the total transmit power constraint. Atthe receiver, the modified MMSE detector taking the CSI imperfection into account is used to remove the coantenna interference,and then the turbo idea is employed for iterative detection to lower the system BER. As a result, the BER performance is effectivelyenhanced. Numerical results show that the introduced SVD-aided adaptive power allocation method is valid to improve not onlythe capacity but also the BER performance in the presence of channel state information imperfection, while the iterative detectorcan further lower the BER results.

1. Introduction

Multiple-input multiple-output (MIMO) systems can pro-vide a significant capacity increment over the conventionalone through appropriate space-time processing [1, 2]. Belllabs layered space-time (BLAST) structure is one of thepromising architectures thanks to the advantages of lowdetection complexity and high data rates [3]. The new systemwhich combined BLAST structure with turbo idea is calledTurbo-BLAST that can offer a reliable and practical solutionto high data-rate transmission for wireless communications[4].

One of the attractive features of MIMO system is a multi-plexing gain and consequently a higher capacity performanceover single-input single-output system. When channel stateinformation (CSI) is perfect, the water-filling power alloca-tion strategy [5–7] is optimized to improve the capacity per-formance for MIMO systems. Practically, CSI at the receiveris subject to the error due to nonreal time data processing,and so forth [8]. For the modified Turbo-BLAST system,

the task of designing the effective link adaptive techniquebecomes more challenging in the presence of CSI imperfec-tion. Recently, various contributions have also considered theMIMO transceiver design problem for systems with eitherpartial or imperfect CSI at the transmitter [9–12]. In thesereferences, the effect of I-CSI on the capacity performance ofMIMO system is investigated in [9, 10]. Based on the perfectand imperfect CSI, the performance of adaptive modulationschemes in MIMO systems is analyzed in [11]. The transmitpower allocation for a two-input multiple-output system ispresented in [12] by minimizing the BER, but the schemeis only suitable for the systems with two-transmit antennas.The above references, however, consider the uncoded MIMOsystem only, and thus the superiority of channel codingis not fully utilized. Especially, the Turbo-BLAST structurewith superior performance is not considered. As a result, theperformance improvement is limited.

Motivated by the reason above, we will study the perfor-mance of Turbo-BLAST system in this paper and developa new SVD-aided adaptive power allocation strategy and

2 International Journal of Antennas and Propagation

Inputdata

stream

Outputdata

stream

Channelencoder

Modulator Demultiplexer

Demultiplexer

Powerallocator

Inputsignalshaper

Channelestimator

SISOchanneldecoder

DemodulatorMultiplexer

MMSEdetector

Transmittingsymbol

estimator

Orthogonalconvertor

· · ·

...

......

...

...

...

...

...

...

nR

nTPV

1

1

UH

Figure 1: An illustrative diagram of the modified Turbo-BLAST system.

iterative detection scheme for modified Turbo-BLAST sys-tem in the presence of CSI imperfection. At the transmitter,aiming at maximizing the capacity performance of theoverall system, MIMO channel is decomposed into severalparallel eigen subchannels by singular value decomposition(SVD) [13–16], and then appropriate power based on water-filling principle is allocated to each subchannel subject to thetotal transmit power constraint. At the receiver, the iterativeturbo strategy is employed for signal detection to enhancethe BER performance. The theoretical analysis and numericalresults show that the proposed SVD-assisted transmit powerallocation (TPA) approach is an effective method to improveboth the capacity and the BER performance. Furthermore,the corresponding BER results of the modified Turbo-BLAST system can be further enhanced through the iterativedetection.

This paper is organized as follows: after the introductionin Section 1, the channel model and system descriptionare briefly introduced in Section 2. Section 3 is concernedwith SVD-aided power allocation scheme in the presenceof imperfect CSI. Section 4 presents an iterative detectionalgorithm for the modified Turbo-BLAST system withadaptive power allocation. The numerical results are givenin Section 5. Finally, Section 6 summarizes the conclusion ofthe paper.

2. Channel Model and System Description

2.1. Channel Model. Consider a Turbo-BLAST system withnT transmit antennas and nR receive antennas (nT ≤ nR)as depicted in Figure 1. Based on CSI obtained from thefeedback channel, the transmitter optimally varies its power

allocation parameters as will be detailed in Section 3. Weadopt a CSI imperfection model from [8]. The CSI isestimated at the receiver and sent to the transmitter by feed-back channel. To assist the receiver in performing channelestimation and symbol detection, known pilot symbols areperiodically inserted at the transmitter—a technique that isknown as pilot symbol assisted modulation (PSAM) [17].At the receiver, the samples corresponding to the knownpilots are extracted, based on which CSI is interpolated usingoptimal Wiener filtering [17].

The imperfect CSI is represented by the complex channelmatrix H, which is related to the true channel matrix H as

H = H + Ξ, (1)

where Ξ is a complex matrix related to the imperfect CSI.Note that the same CSI is known to both the transmitterand receiver. The elements of both H and Ξ can be modeledas independent complex Gaussian variables [8], whichsubsequently lead to the entries of H as complex Gaussianvariables, and furthermore, H and Ξ are independent toeach other [8, 11]. Thus we can express their statistical

distributions as ei j ∼ CN (0, σ2e ), hi j ∼ CN (0, 1 − σ2

e ),and hi j ∼ CN (0, 1), which are all distributed by complexGaussian law with σ2

e indicating the accuracy of the CSI.

In order to maximize the capacity of the Turbo-BLASTsystem, the MIMO channel is decomposed into severalparallel eigen subchannels by SVD. In practice, true CSIcannot be obtained, so H is treated as the true channel matrixwhich can be decomposed as

H = UΛVH , (2)

International Journal of Antennas and Propagation 3

where (·)H denotes a matrix conjugate transpose, U andV are the unitary matrices with left and right singularvector of H as their columns, Λ is a nonnegative and

diagonal matrix, {√λi}nTi=1 are the main diagonal elements

of Λ, and {λi}nTi=1 are eigenvalues of HHH , respectively. Theleft singular vector V is used for the input signal shapingat the transmitter and the conjugate transpose of rightsingular vector U is used for orthogonal transform at thereceiver.

2.2. System Description. In this part we propose a sys-tem model for a modified Turbo-BLAST system using anovel SVD-assisted power allocation strategy with imperfectCSI.

Figure 1 shows an illustrative diagram of a modifiedTurbo-BLAST system. At the transmitter, the input datastream is firstly encoded and then mapped into a symbolstream that is subsequently demultiplexed into nT sub-streams, and the transmit power at each eigen subchannel isvaried according to the instantaneous values and/or statisticsof the subchannel gains under an total transmit power con-straint.

Let x = [x1, . . . , xnT ]T and r = [r1, . . . , rnR]T denoteinput and output column vectors at a sampling instant, re-spectively. Similarly, n = [n1, . . . ,nnR]T is a column vector,where each component is independent and identically dis-tributed (i.i.d) zero-mean complex Gaussian variables withvariance σ2

n .

The transmitted signals are received by the nR antennasat a sampling instant which can be expressed as

r = UH(

HVPx + n)= UHHVPx + UHn, (3)

where P = diag(√P1, . . . ,

√PnT ) is the diagonal transmit

power matrix with total power constraint∑nT

k=1 Pk =nT .

At the receiver, an iterative detection strategy based onthe “turbo” principle is used for the symbol detection.The encoding and demultiplexing for the data stream canbe equivalently viewed as a serially concatenated encodingprocess as depicted in Figure 1. The concatenated code canbe decoded using a low-complexity iterative decoder whichis similar to the iterative decoder for a serially concate-nated turbo code. For the iterative decoding, the optimaldecoding process can be separated into two stages, that is,soft-input/soft-output (SISO) detector and SISO channeldecoder, respectively, which mutually exchange the extrinsicinformation sent from one stage to another iteratively untilthe decoding process converges.

3. Power Allocation Scheme withImperfect CSI

3.1. Equivalent System Model. In this subsection, we proposean equivalent system model under the conditions of imper-fect CSI for the modified Turbo-BLAST system.

With the channel model and the SVD technique intro-duced aforementioned, when the CSI is imperfect, thereceived signal at a sampling instant can be formulated as

r = UH(

H + Ξ)

VPx + UHn = UHHVPx + UHΞVPx + UHn

= UHUΛVH VPx + UHΞVPx + UHn

= ΛPx + UHΞVPx + n′

= ΛPx + n,(4)

where n′ = UHn, U is the unitary matrix with the rightsingular vectors of H as its columns, thus n′ = UHn isalso a column vector of additive Gaussian noise variables,where each component is i.i.d zero-mean complex Gaussianvariables with the variance of σ2

n , n = UHΞVPx + n′ isan equivalent additive noise consisting of the interferencecaused by the channel estimation errors and the complexGaussian noise, respectively. Here we make an approxima-tion that assumes that the entries of x are i.i.d. Gaussianvariables, that is, xi ∼ CN (0, 1) [11]. Under this assumption,the variance of the equivalent noise n can be calculated asfollows.

Firstly, let G = UHΞV, the mean and variance of G canbe evaluated as

ε{G} = ε{

UHΞV}= UHε{Ξ}V = 0nR×nT ,

ε{

GGH}= ε

{UHΞVVHΞHU

}= ε

{UHΞΞHU

}= UHε

{ΞΞH

}U = σ2

e InR .

(5)

Clearly, the components of G are i.i.d zero-mean complexGaussian variables with the variance of σ2

e : thus we canexpress the statistical distributions as

gi j ∼ CN(0, σ2

e

),

ε{gqkg

∗qi

}= σ2

e δ(k − i).(6)

Then let f be denoted as follows:

f = GPx =

⎡⎢⎢⎢⎢⎢⎢⎢⎣

g11 g12 · · · g1nT

g21 g22 · · · g2nT

......

. . ....

gnR1 gnR2 · · · gnRnT

⎤⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎣

√P1 0 · · · 0

0√P2 · · · 0

......

. . ....

0 0 · · · √PnT

⎤⎥⎥⎥⎥⎥⎥⎥⎦

×

⎡⎢⎢⎢⎢⎢⎢⎢⎣

x1

x2

...

xnT

⎤⎥⎥⎥⎥⎥⎥⎥⎦ =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

nT∑k=1

g1k√Pkxk

nT∑k=1

g2k√Pkxk

...nT∑k=1

gnRk√Pkxk

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦=

⎡⎢⎢⎢⎢⎢⎢⎢⎣

f1

f2

...

fnR

⎤⎥⎥⎥⎥⎥⎥⎥⎦.

(7)


Clearly, f is a zero-mean complex Gaussian column vectorwith its components fq =

∑nTk=1 gqk

√Pkxk, (q = 1, . . . ,nR),

whose variance can be evaluated as

σ2q = ε

(fq f

∗q

)= ε

⎧⎨⎩⎡⎣ nT∑k=1

gqk√Pkxk

⎤⎦⎡⎣ nT∑i=1

gqi√Pixi

⎤⎦∗⎫⎬⎭=

nT∑k=1

Pkε[(gqkg

∗qk

)(xkx

∗k

)]=

nT∑k=1

Pkε{∣∣∣gqk∣∣∣2

}ε{|xk|2

}

= σ2e

nT∑k=1

Pk = nTσ2e .

(8)

Thus the component of n is given as nq = fq + n′q, (q =1, . . . ,nR) by the aforementioned definition with the variancecalculated as

σ2nq= ε

{nqn

∗q

}= ε

{(fq + n′q

)(fq + n′q

)∗}

= ε{∣∣∣ fq∣∣∣2

}+ ε{∣∣∣n′q∣∣∣2

}= nTσ

2e + σ2

n .

(9)

Given the proposed equivalent system model, a SVD-assisted transmit power allocation scheme aiming at maxi-mizing the capacity of the whole system in the presence ofCSI imperfection will be described in the next part.

3.2. SVD-Aided Power Allocation Strategy. In the presence ofchannel state information imperfection, the channel capacityfor Turbo-BLAST system with SVD-assisted power allocationscheme can be expressed as [1]

C(λ)=

nT∑k=1

log2

[1 +

PkλknTσ2

e + σ2n

], (10)

where λ = diag[λ1, . . . , λnT ] and Pk is the transmit power

allocated for the k-th subchannel. The capacity subject to anoptimization problem is given as

[P1, . . . ,PnT

]opt = arg max

⎧⎨⎩nT∑k=1

log2

[1 +

PkλknTσ2

e + σ2n

]⎫⎬⎭subject to

nT∑k=1

Pk = nT .

(11)

The Lagrange multiplier method is employed to find theoptimized power allocation matrix that can maximize theoverall capacity with total power constraint. By solving theequation in (11), we can find that the transmit powerallocated for the k-th subchannel is

Pk =[μ− (nTσ2

e + σ2n

)λ−1k

]+, (12)

where (x)+ � max{x, 0} and μ is the Lagrange multiplierrestricted by

nT∑k=1

[μ− (nTσ2

e + σ2n)λ−1

k

]+ = nT . (13)

In a flat fading MIMO channel, the channel capacity is

the statistical mean of λ approximately in the presence of CSIimperfection

C=ελ

{C(λ)}=ε

⎧⎨⎩nT∑k=1

log2

(1 +

Pkλkσ2n

)⎫⎬⎭=ε

⎧⎨⎩nT∑k=1

log2

(μλk

)⎫⎬⎭.(14)

Because {λi}nTi=1 is i.i.d and has the same probability density

function p(λk), formula (14) can be expressed as

C = nT

∫ +∞

0

[log2

(μλk

)]+p(λk)dλk. (15)

Since singular values are random variables, it is hard toachieve the function of its probability density straightly. Weuse the algebraic mean to achieve the capacity results in thesimulation which can be expressed as

C ≈ ε

⎧⎨⎩nT∑k=1

log2

[1 +

PkλknTσ2

e + σ2n

]⎫⎬⎭≈ 1

N

N∑i=1

⎧⎨⎩nT∑k=1

log2

[1 +

Pk,iλk,i

nTσ2e,i + σ2

n,i

]⎫⎬⎭,

(16)

where N is the number of channel estimation matrix which isused for simulation, {Pk,i}nTk=1 is the transmit power sequence

for i-th channel matrix Hi, {λk,i}nT

k=1 are eigenvalues ofHiHH

i , σ2e,i, and σ2

n,i are the variances of channel estimationand AWGN, respectively.

4. Iterative Detection Algorithm forthe Modified Turbo-BLAST System

In this section, the iterative detection strategy is employedfor the modified Turbo-BLAST system with imperfect CSIto enhance the BER performance. The iterative decodingstructure of serially concatenated turbo codes provides theprincipal model for the iterative decoding algorithm [4].

In practice, true CSI cannot be obtained, so the receivertreats H as the true channel matrix and n as the equivalentnoise. The iterative detection scheme for the modifiedTurbo-BLAST system will be described next.

Let xk be the k-th transmitted signal at a sampling epoch,with (4), the received symbol vector r corrupted by thechannel noise and interferences is given as

r = λk√Pkxk + ΛkPkxk + n, (17)

where λk is the k-th column of the matrix Λ and

Λk =[λ1, . . . , λk−1, λk+1, . . . , λnT

],

xk =[x1, . . . , xk−1, xk+1, . . . , xnT

]T,

Pk = diag(√

P1, . . . ,√Pk−1,

√Pk+1, . . . ,

√PnT

).

(18)


With (18), the decision statistic of k-th substream using alinear filter wk can be expressed as

yk = wHk λk

√Pkxk︸︷︷︸

qk

+ wHk ΛkPkxk︸︷︷︸

dk

+ wHk n︸︷︷︸zk

, (19)

where qk, dk, and zk are the desired response obtained bythe linear filter, the coantenna interference, and the phase-rotated noise, respectively.

The coantenna interference can be removed from yk bythe proposed multisubstream detector and soft interferencecancellation based on MMSE principle. The improvedestimation of the transmitted symbol xk can be formulatedas

xk = wHk r− dk, (20)

where xk is the estimate of the symbol xk, and dk is the linearcombination of the interfering substreams. The estimationerror is defined as Δxk = xk−xk. The weighted vector wk and

the interference estimation dk are optimized by minimizingthe mean-square estimation error of Δxk between eachsubstream and the related estimate by the following costfunction (

wk, dk

)= arg min(

wk ,dk

)ε[∥∥xk − xk

∥∥22

], (21)

where the expectation is taken over the equivalent noise nand the statistics of the data sequence x.

We use standard minimization techniques to solve theoptimization problem formulated in (21). In order to arriveat the solution, we write the cost function as

Cost = ε[∥∥xk − xk

∥∥22

]= ε

[∥∥∥wHk r− dk − xk

∥∥∥2

2

]

= wHk ε(

rrH)

wk − wHk ε[

r(dk + xk

)∗]

− ε[

r(dk + xk

)∗]Hwk + ε

[(dk + xk

)(dk + xk

)∗],

(22)

where

ε[

rrH]= ε

[λk√Pkxk + ΛkPkxk + n

×(λk

√Pkxk + ΛkPkxk + n

)H]

= PkλkλH

k + ΛkPkε(xkx

Hk

)(ΛkPk

)H+(nTσ

2e + σ2

n

)InR ,

ε[

r(dk + xk

)∗] = ε[(

λk√Pkxk + ΛkPkxk + n

)(dk + xk

)∗]= λk

√Pk + ΛkPkε

(xk

)d∗k .

(23)

By (23), the cost function in (22) can be further evaluated as

Cost = wHk

{Pkλkλ

H

k +(ΛkPk

)ε[xkx

Hk

](ΛkPk

)H+(nTσ

2e + σ2

n

)InR

}wk

− wHk

[λk√Pk + ΛkPkε

(xk)d∗k

]

−[Pkλ

H

k + dkε(xk)H(

ΛkPk

)H]wk

+ ε[dkd

∗k + dkx

∗k + xkd

∗k + xkx

∗k

].

(24)

The linear combination of interfering substreams dk andthe weighted vector wk is obtained from (24) by letting

∂Cost/∂d∗k = 0 and ∂Cost/∂w∗k = 0, respectively,

dk = wHk

(ΛkPk

)ε(

xk

),

wk =[

Q + S +(nTσ

2e + σ2

n

)InR]−1

(λk√Pk

),

(25)

where

Q =(λk√Pk

)(λk√Pk

)H,

S =(ΛkPk

){I(nT−1) − diag

[ε(

xk

)ε(

xk

)H]}(ΛkPk

)H.

(26)

Therefore the weighted vector wk is used for the modifiedTurbo-BLAST system in the presence of imperfect CSI. Thus(20) can be rewritten as

xk = wHk r− dk =

{[Q + S +

(nTσ

2e + σ2

n

)InR]−1

(λk√Pk

)}H

×[

r−(ΛkPk

)ε(

xk

)].

(27)

For the first iteration, we assume that ε(xk) = 0, and thusthe linear MMSE detection for the k-th substream becomes

xk ={[(

λk√Pk

)(λk√Pk

)H+(ΛkPk

)(ΛkPk

)H

+(nTσ

2e + σ2

n

)InR

]−1(λk√Pk

)⎫⎬⎭H

r

=(λk√Pk

)H[(ΛP

)(ΛP

)H+(nTσ

2e + σ2

n

)InR

]−1

r.

(28)

Next, we assume that ε(xk) → xk with the increasing numberof iterations, where the MMSE interference canceller forthe modified Turbo-BLAST system using SVD-based powerallocation with imperfect CSI is

xk =(λk√Pk

)H[(λk√Pk

)H(λk√Pk

)+(nTσ

2e + σ2

n

)]−1

×[

r−(ΛkPk

)xk

].

(29)


The MMSE detector gets the estimation of all thetransmit signal using (29) and generates soft estimates of thecoded bits conditioned on the received signal. The iterativedecoder depicts message passing between the MMSE detectorand SISO channel decoder. During the first iteration, theinitial intrinsic probabilities of all symbol bits are assumedto be 1/2 (i.e., equally likely). The posteriori information iscomputed and fed back to the SISO channel decoder as theintrinsic information of its all coded bits. Then the SISOmodules, in turn, process the soft information and computerefined estimates of soft information on both coded andinformation bits, based on the trellis structure of the channelcodes, which is the channel code constraint. The SISOchannel decoders are implemented by using the generalizedBCJR algorithm [18].The soft information is sent to MMSEdetector for interference cancellation [4]. Steps above arerepeated until the decoding algorithm converges.

5. Simulation Results

In this section we compare the capacity and the BERperformance of the traditional and modified Turbo-BLASTsystems, where the proposed adaptive SVD-aided powerallocation strategy is adopted in the latter case. At thetransmitter, the data stream is first encoded by a rate-1/2convolutional code with generator (7, 5), then modulatedby 4-QAM scheme, whose capacity performance over a largenumber of channel realizations is exhibited in Figures 2 and3, extra capacity, which is defined as the capacity gap betweenthe modified Turbo-BLAST system and the conventionalone, is given in Figure 4, and finally BER performanceis presented in Figure 5, respectively, with the traditionalTurbo-BLAST system adopting the equal power allocationstrategy, denoted by “EPA”, and the modified Turbo-BLASTsystem employing the proposed transmit power allocation,denoted by “TPA”, respectively.

Figure 2 shows that the capacity performance of themodified Turbo-BLAST system outperforms the traditionalone in all cases under the same conditions. This indicatesthat the proposed SVD-aided power allocation strategy is aneffective means to improve capacity performance even withthe imperfect CSI. For example, at Eb/N0 = 10 dB, there are0.8 (bit/s/Hz) and 1 (bit/s/Hz) capacity gains for σ2

e = 0.04and σ2

e = 0.1, respectively.

Figure 3 shows that the capacity degradation is relativelyinsensitive to the CSI imperfection when CSI is moreaccurate. Only when σ2

e increases to nearly 10−2, thecapacity starts to fall. The over SNR degrades as the noisecontribution due to the use of imperfect CSI increases whichdetermine the detection performance. Figure 3 also showsthat the impact of CSI imperfection on the capacity resultsis higher for larger Eb/N0.

It is clear that from Figure 4, we can see that the extracapacity is higher for low SNR and/or large antenna systemsin the presence of CSI imperfection. For instance, at Eb/N0 =4 dB, there are 3.2 (bit/s/Hz) and 1.3 (bit/s/Hz) capacity gainsfor the Turbo-BLAST system with eight and seven transmitantennas, respectively.

0 2 4 6 8 10 12 14 164

6

8

10

12

14

16

18

20

22

Cap

acit

y(b

it/s

/Hz)

TPATPATPATPA

σ2e = 0σ2e = 0.01σ2e = 0.04σ2e = 0.1

σ2e = 0σ2e = 0.01σ2e = 0.04σ2e = 0.1

Eb/N0 (dB)

EPAEPAEPAEPA

Figure 2: Capacity performance of traditional and modified Turbo-BLAST systems with four transmit and four receive antennas underthe conditions of different inaccuracy of channel estimation.

10−4 10−3 10−2 10−1 1002

4

6

8

10

12

14

16

18

20

Cap

acit

y(b

it/s

/Hz)

σ2e

Eb/N0 = 15 dBEb/N0 = 10 dBEb/N0 = 5 dB

Figure 3: Impacts of CSI on the capacity performance of modifiedTurbo-BLAST systems with four transmit and four receive antennasin various values of Eb/N0.

It can be observed from Figure 5 that as the BER resultsconcerned, the modified Turbo-BLAST system outperformsthe traditional system under the same conditions, regardlessof the status of CSI. This implies that the proposed powerallocation strategy is also valid to improve BER performanceeven with the imperfect CSI. For example, at a BER of 10−4,we can see that there are 5 dB gains for the modified systemover the traditional one in the 1st detection iteration underthe condition of perfect CSI, that is, σ2

e = 0. Moreover, theBER results are quickly lowered with the increasing detectioniterations. For instant, at a BER of 10−4, there are 3 dBextra gains attained for the modified Turbo-BLAST systemusing TPA scheme through 3rd iterative detection under thecondition of perfect CSI.


0 2 4 6 8 10−1

0

1

2

3

4

5

6

Ext

raca

paci

ty(b

it/s

/Hz)

nT = 8nT = 7nT = 6

nT = 5nT = 4

Eb/N0 (dB)

Figure 4: Extra capacity results between modified and traditionalTurbo-BLAST systems with eight receive antennas and varioustransmit antennas configuration under the conditions of imperfectCSI (σ2

e = 0.01).

0 2 4 6 8 10 12 14 1610−6

10−4

10−3

10−2

10−1

100

BE

R

σ2e = 0.1 Iter = 1σ2e = 0.1 Iter = 3

σ2e = 0 Iter = 1σ2e = 0 Iter = 3

EPA

TPA

10−5

Eb/N0 (dB)

Figure 5: BER performance of traditional and modified Turbo-BLAST systems with four transmit and four receive antennas underthe conditions of different inaccuracy of channel estimation.

6. Conclusion

In this paper, we propose a new strategy that combines SVDtechnique, transmit power allocation, and iterative detectiontechniques to improve both the capacity results and the BERperformance for the modified Turbo-BLAST system.

Based on the equivalent system model used in this paperand the derived variance of the equivalent noise, the SVD-assisted transmit power allocation strategy is theoreticallyobtained. The Lagrange multiplier method is then employedto find the optimized power allocation matrix which canmaximize the capacity for the whole system subject tothe total transmit power constraint. Finally, the iterative

detection technique is adopted for the modified Turbo-BLAST system to enhance the BER performance. Simulationresults show that the newly introduced method is effectiveto enhance not only the capacity results but also the BERperformance of Turbo-BLAST system in both cases of perfectand imperfect CSI.

Acknowledgments

This paper is supported by Doctoral Fund of Ministry ofEducation of China (no. 20093218120021), Open ResearchFund of National Mobile Communications Research Lab-oratory, Southeast University (no. N200904), and NUAAResearch Funding (NS 2010113). The authors would like tothank the anonymous reviewers for their valuable commentswhich improve the quality of this paper greatly.

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