An Adaptive MIMO Transmission Technique forLDPC Coded OFDM Cellular Systems

Kwang Soon Kim, Yun Hee Kim, and Jae Young AhnElectronics and Telecommunications Research Institute (ETRI)

161 Gajeong-Dong, Yuseong-Gu, Daejeon 305-350, KoreaTel: +82-42-860-6702Fax: +82-42-869-6732

E-mail: kskim@ieee.org

Abstract— In this paper, an adaptive MIMO transmissionscheme using QAM and LDPC code is proposed for an OFDMcellular system employing FDD. By approximating the LLRdistribution to a Gaussian distribution, only two parameters, themean and the normalized standard deviation, are required to besent to the transmitter, which requires only a few more bits thanthose required in currently used single carrier cellular systems,such as cdma2000-1x EV-DO. It is shown by computer simulationthat the proposed adaptive transmission scheme can provide upto 2 ∼ 3dB gain over the conventional system using the meanSNR only, at the expense of only 3 more bits in the feedbackinformation.

I. I NTRODUCTION

In order to meet the explosively increasing demand onreliable and high-rate service over wireless channel, orthogo-nal frequency division multiplexing (OFDM) has been widelyaccepted as the most promising radio transmission technologyfor the next generation wireless communication systems dueto its advantages such as the robustness to multipath fading,granular resource allocation capability, and low complexity[1]. In addition, in order to enhance the system capacity aslarge as possible, a multiple input multiple output (MIMO)technique, such as spatial multiplexing (SM) [2], and the linkadaptation using adaptive modulation and coding have beenconsidered as key technologies for the next generation wirelesscommunication systems [3][4]. The basic idea of the adaptivemodulation and coding is that the transmitter selects one ofthe pre-defined modulation and coding set (MCS) by the aidof the channel state information, which is reported to thetransmitter by the receiver in frequency division duplexing(FDD) systems.

In OFDM systems, the bit-loading algorithm is knownto be optimum. However, the transmitter has to know thechannel state information of all sub-carriers, which is im-practical in wireless OFDM systems using large number ofsub-carriers. Thus, block-wise adaptive transmission schemeswere proposed as sub-optimum algorithms [3][4]. In cellularsystems employing FDD, however, even the amount of thefeedback information required for the block-wise adaptivetransmission schemes is far from that can be supported inpractical situations since both high frequency selectivity andhigh mobile speed should be supported. Thus, for practi-cal OFDM cellular systems, a simple adaptive transmission

Fig. 1. The system model for the proposed adaptive transmission.

scheme is required with low feedback rate comparable to thatin currently employed cellular systems, such as cdma2000-1xEV-DO. However, in frequency-selective fading channels, thesystem capacity would degrade significantly if only the meansignal to noise power ratio (SNR) over the whole sub-carriersis used as in a single-carrier system.

In this paper, an adaptive MIMO transmission scheme,based on the knowledge of the received log-likelihood ratio(LLR) distribution, is proposed for an OFDM cellular systemusing SM, quadrature amplitude modulation (QAM), and lowdensity parity check (LDPC) code. By approximating the LLRdistribution to a Gaussian distribution, only two parameters,the mean and the normalized standard deviation, are requiredto be sent to the transmitter, which requires only a few morebits than those required in currently used single carrier cellularsystems. This paper is organized as follows: In Section 2, thesystem model considered in this paper is shown. The proposedadaptive transmission algorithm is presented in Section 3,and the performance of the proposed scheme is evaluated bycomputer simulation in Section 4. Finally, concluding remarkis provided.

II. SYSTEM MODEL

A physical layer frame is comprised of a number of con-secutive data slots, in which pilot symbols of each transmitantenna are well distributed in both frequency- and time-domain. In case of multiple access system, all sub-channelsin a data slot are also well-distributed in a data slot. In Fig.1, the system model considered in this paper is shown. In the

Fig. 2. The Gray encoded 4-QAM and 16-QAM constellations using multipletransmit antennas.

transmitter side, pilot symbols of allNT transmit antennasare transmitted with fixed powerPpilot. At the receiver sideemployingNR receiving antennas, the channel is estimated bythe channel estimator. With the estimated channel, the channelstate information (CSI) is generated and sent to the transmitterside. At the transmitter, the MCS and the transmit power (TP)are determined from the received CSI and the pre-determinedrequired SNR table. In case of multiple access system, thereare a number of receivers with their own CSIs. Then, basedon each user’s pre-determined quality of service (QoS) andthe reported CSI, active users are selected with correspondingMCS and TP by the MCS and TP selector. Then, the adaptivelytransmitted signal is received and the LLR is calculated fromthe received symbols with the estimated channel at the receiverside. Finally, the LDPC decoder extracts the transmitted infor-mation.

III. T HE ADAPTIVE TRANSMISSION SCHEME

A. Received LLR distribution in SISO case

For a given LDPC code and a decoding algorithm, theperformance is determined by the received likelihood distri-bution [5]. Thus, the transmitter can expect the performanceof each MCS option if the received LLR distribution is known.In addition, by parametric modelling of the received LLRdistribution, the LLR distribution parameters can be used asa CSI. In this paper, we assume that the LLR distribution isGaussian. Then, the mean and variance of the LLR distributioncan be used as the CSI and the performance of each MCSoption can be well expected by the transmitter with only twoparameters.

In this paper, we consider Gray encoded 4-QAM and 16-QAM for modulation options (shown in Fig. 2) and themaximum value approximation of the maximum likelihood(Max-ML) method for LLR calculation algorithm. However,it can be easily extended to higher order QAM modulations,such as 64-QAM.

First, we consider the 4-QAM case in single input singleoutput (SISO) environment. Letxl be the lth transmittedsymbol in a data slot. Then, thelth received symbol at thereceiver is given by

yl = Ahlxl + nl, (1)

whereA2 is the transmit power,hl and nl are the complexchannel gain and the additive complex Gaussian noise withmean zero and variance2σ2 at the lth symbol location in adata slot, respectively. Then, the decision variable of thelthsymbol,zl is given by

zl = h∗l yl/|hl| = A|hl|xl + n

′

l, (2)

wheren′

l = h∗l nl/|hl| is also a complex Gaussian noise with

mean zero and variance2σ2.In the Gray encoded 4-QAM, the LLR distributions of the

two bits in a symbol are the same. Letzl = zl,i + jzl,q andxk

l be and thekth bit in xl. Then, the LLR ofx0

l , Λ(

x0

l

)

, isgiven by

Λ(

x0

l

)

= log

(

maxxl∈X0,0

Pr {zl|xl, hl}Pr{xl})

− log

(

maxxl∈X0,1

Pr {zl|xl, hl}Pr{xl})

=

√2A|hl|zl,i

σ2,

(3)

whereXk,m denotes the set of symbols in which thekth bitis m. Since the distribution ofzl,i when x0

l = 0 is Gaussianwith mean A|hl|√

2and varianceσ2, the distribution ofΛ

(

x0

l

)

when x0

l = 0 is Gaussian with meanA2|hl|2σ2 and variance

2A2|hl|2σ2 . Note that the distribution ofΛ

(

x1

l

)

is the same tothat ofΛ

(

x0

l

)

. Then, the mean of the LLR distribution over thewhole code block when the all-zero codeword is transmittedis given as

E{

Λ(

x0

l

)}

=1

L

L−1∑

l=0

A2|hl|2σ2

= 2mSNR,

(4)

wheremSNR = 1

L

∑L−1

l=0

A2|hl|22σ2 . Also, we have

E{

Λ2(

x0

l

)}

=1

L

L−1∑

l=0

(

A4|hl|4σ4

+2A2|hl|2

σ2

)

(5)

and

V ar{

Λ(

x0

l

)}

= E{

Λ2(

x0

l

)}

− E2{

Λ(

x0

l

)}

= 4mSNR + 4m2

SNRσ2

SNR,(6)

where σSNR is defined as σSNR =√

1

m2

SNRL

∑L−1

l=0

(

A2|hl|22σ2

)2

− 1. Thus, we can see that

the meanmSNR and the normalized standard deviationσSNR

of the received SNR are sufficient statistic for determiningthe received LLR distribution.

Now, consider the 16-QAM case. Since we use the Max-MLmethod, the LLR of a bit in a symbol is proportional to thedifference of the followings: one is the minimum Euclideandistance between the received symbol and the constellationpoints where the bit is 0, and the other is the minimum

one between the received symbol and the constellation pointswhere the bit is 1. Then, we obtain the follows:

Λ(

x0

l

)

=

4A|hl|zl,i√10σ2

+ 4A2|hl|210σ2 zl,i ∈ C0,

2A|hl|zl,i√10σ2

zl,i ∈ C1 ∪ C2,4A|hl|zl,i√

10σ2− 4A2|hl|2

10σ2 zl,i ∈ C3,

(7)

and

Λ(

x2

l

)

=

{

2A|hl|zl,i√10σ2

+ 4A2|hl|210σ2 zl,i ∈ C0 ∪ C1,

−2A|hl|zl,i√10σ2

+ 4A2|hl|210σ2 zl,i ∈ C2 ∪ C3.

(8)

Note thatΛ(

x1

l

)

= Λ(

x0

l

)

andΛ(

x3

l

)

= Λ(

x2

l

)

except thatzl,i and Cn are replaced withzl,q and Rn, respectively. Inaddition, the distribution ofzl,i when xk

l = 0, fzl,i(y), is

given by

fzl,i(y) =

{

1

2φ(y; vl, σ

2) + 1

2φ(y; 3vl, σ

2), k = 0,1

2φ(y;−vl, σ

2) + 1

2φ(y; vl, σ

2), k = 2,(9)

where vl = A|hl|/√

10 and φ(y;m,σ2) is defined as theGaussian distribution with meanm and varianceσ2. Then,after tedious mathematical calculations, we obtain follows:

E{

Λ(

x0

l

)} ∼= 5v2

l

σ2,

E{

Λ2(

x0

l

)} ∼= 10v2

l

σ2+

34v4

l

σ4,

E{

Λ(

x2

l

)} ∼= 2v2

l

σ2,

E{

Λ2(

x2

l

)} ∼= 4v2

l

σ2+

4v4

l

σ4.

(10)

Thus, it is seen again that the mean and the normalizedstandard deviation of the received SNR are sufficient statisticfor determining the received LLR distribution.

B. Extension to MIMO case

Let xl be theNT × 1 transmitted symbol vector of thelthsymbol in a data slot. Then, theNR(≥ NT )×1 received vectorof the lth symbol at the receiver is given by

yl =A√NT

Hlxl + nl, (11)

whereHl is theNR×NT complex channel gain matrix, whose(i, j)th element is denoted ashl,i,j , at thelth symbol locationin a data slot, andnl is theNR×1 additive complex Gaussiannoise vector with mean zero and variance2σ2I at the lthsymbol location in the data slot.

Then, by applying the singular value decomposition on thechannel gain matrixHl, we obtainHl = UlDlV

Hl , where

Ul andVl are unitary matrices andDl is the diagonal matrixwhose diagonal elements are the singular values ofHl, λ

1/2

l,i ,i = 0, · · · , NT − 1. Then, we obtain

yl = ADlxl + nl, (12)

where yl = UHl yl, A2 = A2/NT , xl = VH

l xl, and nl =UH

l nl. Thus, the MIMO channel is equivalent toNT parallelchannels with channel gains ofλ

1/2

l,i , i = 0, · · · , NT −1. Also,

sinceUl andVl are unitary, the Euclidean distance betweenany two constellation vectors or noise vectors is invariantunder the transformation defined by the matrixUl or Vl.Thus, the SNR of theith spatial channel at thelth symbollocation,νl,i, is defined as

νl,i =A2λl,i

2NT. (13)

Then, the mean and the normalized standard deviation of thereceived SNR in MIMO case are given as

mSNR =1

LNT

L−1∑

l=0

NT −1∑

i=0

νl,i (14)

and

σSNR =

√

√

√

√

1

m2

SNRLNT

L−1∑

l=0

NT −1∑

i=0

ν2

l,i − 1. (15)

Therefore, in MIMO case also,mSNR and σSNR are suffi-cient statistic for determining the received LLR distributionregardless of the MCS option and the number of transmit andreceiving antennas.

C. Proposed adaptive transmission algorithm

The CSI is defined as the mean and the normalized standarddeviation of the received SNR in a data slot and the SNR isestimated from the received pilot symbols. Then, the CSI indi-cates the received LLR distribution when the transmit poweris Ppilot. Now, let SNRk and ∆k,µ be the required meanSNR and the required additional power when the normalizedstandard deviation of the received SNR isµ for the kth MCSoption, respectively. Then, the required transmit power whenthe kth MCS option is used,PT,k, is obtained as follow:

PT,k = Ppilot + SNRk − mSNR + ∆k,σSNR(dB). (16)

Here, SNRk and ∆k,µ can be pre-determined by computersimulation or field-test. From (16), the transmitter can evaluatehow much power is required for each user and each MCSoption. Then, any optimization process for selecting active userset and MCS option for each user can be adopted.

IV. SIMULATION RESULTS

In Fig. 3 the packet error probabilities of the MCS optionusing 2x2 spatial multiplexing, 4-QAM and 1/2-rate LDPCcode is shown. Here, the ITU-R pedestrian A fading channelis used and the transmit power is controlled to keep the meanof the received SNR in a packet constant. Also, the packeterror probability of the conventional scheme using the meanof the received SNR only, denoted as ’All’ in the figure, isalso plotted for comparison. In this figure, the normalizedstandard deviation is quantized into 3 bits (denoted as std2∼std7 in the figure). Note that the performance curves for thestd0 and std1 cases are missing due to their rare occurrence.From the result, it is seen that the packet error probabilityincreases as the normalized standard deviation increases.Inaddition, when the normalized standard deviation is small (std2

0 2 4 6 8 1010

−4

10−3

10−2

10−1

100

2x2 QPSK 1/2 LDPC code

Es/No

PE

Rstd2std3std4std5std6std7All

Fig. 3. The packet error probability of the MCS option using 2x2 SM,4-QAM, and 1/2-rate LDPC code.

0 5 10 15 20 25 300

1000

2000

3000

4000

5000

6000

Average Es/No (dB)

Ave

rage

Tra

nsm

issi

on R

ate

(Kbp

s)

Average Throughput

Prop. SISOConv. SISOProp. 2x2 SMConv. 2x2 SM

Fig. 4. The performance of the proposed adaptive transmissionscheme.

case), the proposed scheme requires 4dB less transmit powercompared to the conventional scheme at the target packet errorprobability of 1e-2.

In Fig. 4, the performance of the proposed adaptive trans-mission schemes is shown in SISO and 2x2 SM cases,respectively. The MCS options used in this simulation aresummarized in Tables I and II. From the result, it is seen thatthe performance of the proposed scheme is up to2 ∼ 3dBbetter than that of the conventional scheme using the mean ofthe received SNR only, at the expense of only 3 more bits inthe feedback CSI.

V. CONCLUDING REMARK

In this paper, an adaptive MIMO transmission scheme, usingQAM, LDPC code, and SM, was proposed for OFDM-basedcellular systems. By assuming the received LLR distribution asGaussian, the received LLR distribution could be representedby two parameters: the mean and the normalized standarddeviation. Also, it was shown that the mean and the normalizedstandard deviation of the received SNR in a packet were thesufficient statistic for the received LLR distribution. Then,

TABLE I

SUMMARY OF THE MCS OPTIONS USED IN THESISOSIMULATION

MCS option Modulation Code Rate Transmission Rate

0 QPSK 1/6 0.384 Mbps1 QPSK 1/3 0.768 Mbps2 QPSK 2/3 1.536 Mbps3 16-QAM 1/2 2.304 Mbps4 16-QAM 2/3 3.072 Mbps5 16-QAM 5/6 3.840 Mbps

TABLE II

SUMMARY OF THE MCS OPTIONS USED IN THE2X2 MIMO SIMULATION

MCS option Modulation Code Rate Transmission Rate

0 4-QAM 1/2 2.304 Mbps1 4-QAM 2/3 3.072 Mbps2 16-QAM 1/2 3.840 Mbps3 16-QAM 2/3 4.608 Mbps4 16-QAM 7/12 5.376 Mbps

the MCS option and the transmit power could be determinedwith the pre-determined values of the required mean SNR andthe additional transmit power corresponding to the normalizedstandard deviation for each MCS option. From the simulationresults, it was shown that the proposed adaptive transmissionscheme could provide up to2 ∼ 3dB gain over the conven-tional system using the mean SNR only, at the expense of only3 more bits in feedback information.

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