iterative compensated mmse channel estimation in lte systems

7/27/2019 Iterative Compensated MMSE Channel Estimation in LTE Systems

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Iterative Compensated MMSE Channel Estimation

in LTE Systems

Yang LIUSequans Communications

Email: [email protected]

Serdar SEZGINERSequans Communications

Email: [email protected]

AbstractIn this paper, an iterative channel estimation algo-rithm is considered in LTE systems. In order to take advantageof null sub-carriers (guard band) in LTE systems and make thealgorithm simpler, an iterative compensated MMSE (IC-MMSE)channel estimation algorithm is proposed in frequency domain.Together with a simple linear interpolation in time domain,channel estimates are obtained in an iterative way with lowercomplexity. Theoretical analysis shows that the compensationprocess does not affect the accuracy of iterative MMSE channelestimation. Simulation results confirm that the proposed channel

estimation has very robust performance and approaches the bestachievable performance.

I. INTRODUCTION

In recent years, with the appearance of turbo principle [1],

iterative receivers are becoming more and more popular and

promising because of their excellent performances. Different

mechanisms have been proposed and studied, for example,

iterative detection, iterative multi-input multi-output (MIMO)

equalization, etc. However, these iterative mechanisms are

seriously affected by channel estimator. For example, in [2], it

has been shown that an iterative MIMO equalizer is sensitive

to channel estimation, and the traditional non-iterative channelestimators cannot provide sufficiently accurate channel esti-

mates. This necessitates more accurate channel estimates to

improve system performances.

Recently, iterative channel estimation is being considered

to improve the accuracy of channel estimation, which uses

the soft information of data to improve channel estimation

performance. This type of channel estimation algorithms is

particularly helpful for systems which have fewer and/or

lower powered pilot symbols. For example, in Long Term

Evolution (LTE) systems, at most 2 orthogonal frequency-

division multiplexing (OFDM) symbols carry pilots in a given

resource block (RB = minimum allocation unit over 7 OFDM

symbols with normal cyclic prefix and 12 sub-carriers) and thisdecreases to 1 OFDM symbol for MIMO transmission [3].

With this sparse pilot arrangement, the iterative channel es-

timation can be a good candidate to improve channel esti-

mation performance. Moreover, for future standards, one of

the key features will be power efficiency and, in this manner,

decreasing the power of pilots is one of the possible ways to

improve the power consumption efficiency. In such systems,

the channel estimation algorithms used in current systems will

have less accuracy and more robust algorithms will be needed.

Some iterative channel estimators have already been pro-

posed for OFDM systems by using the soft information from

decoder. Among these iterative algorithms, the iterative mini-

mum mean square error (MMSE) channel estimator provides

excellent performances which approach the performance with

perfect channel state information (CSI). The iterative MMSE

is based on the traditional MMSE channel estimator defined

in [4] and improves the accuracy of channel estimation by

using the soft information from channel decoder. However,the complexity of the iterative MMSE channel estimator is

high due to the matrix inversion which has to be performed at

each iteration. Furthermore, in LTE systems, the distributed

resource allocation is used to vary RB positions in differ-

ent OFDM symbols. With the iterative MMSE algorithm,

the allocated RB positions have to be pinpointed and the

matrix to be inverted is different from one OFDM symbol

to another one. This process adds more complexities to the

iterative MMSE algorithm. Therefore, a novel iterative MMSE

algorithm which is not sensitive to RB positions is desirable.

In order to solve these problems, we propose a so-called

iterative compensated MMSE (IC-MMSE) channel estimation

algorithm. This method takes advantage of the null sub-carriers to reduce the complexity and to improve the accuracy

of the MMSE channel estimation. In the sequel, we refer to

LTE systems as an example. However, it is worth mentioning

that the idea can be generalized to any OFDM(A)-based

communication system.

The rest of the paper is organized as follows. In Section II,

the interpolation based channel estimation method in LTE

systems is briefly explained. Next, in Section III, the proposed

IC-MMSE algorithm is described in both single-input multi-

output (SIMO) and MIMO transmission systems. Then, the

impact of the compensation process and the complexity of the

proposed algorithm are analyzed in Section IV and Section V,

respectively. Simulation results are shown in Section VI.Finally, conclusions are drawn in Section VII.

I I . INTERPOLATION METHOD IN LTE

In a practical system, in order to have simple channel

estimation, usually we implement 2x1D interpolation method.

According to different strategies, we can perform interpola-

tions first in frequency domain or in time domain. In this paper,

we will focus on the approach where frequency interpolation

is applied first, as depicted in Fig. 1. For time domain

IEEE ICC 2012 - Wireless Communications Symposium

978-1-4577-2053-6/12/$31.00 2012 IEEE 4862


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interpolation, we consider the simple linear interpolation;

for frequency domain channel estimation, an MMSE based

iterative algorithm will be discussed in the following.

Frequency domain interpolation

Time domain interpolation

Channel estimates on RS

Fig. 1. Conventional interpolation based channel estimation in an LTE sub-frame.

III. ITERATIVE COMPENSATED MMSE CHANNEL

ESTIMATION

A. Traditional Iterative MMSE

By considering the soft information from the decoder, the

traditional iterative MMSE channel estimation at the (i + 1)th

iteration h(i+1)MMSE can be formulated as

h(i+1)MMSE = L

LR(i)NNL +

2C1gg

1LX(i)y, (1)

where ()

stands for transpose-conjugate and ()

stands for

complex conjugate. Here, y represents the received signal

vector, L is a matrix consisting of the first L (L representing

the delay spread of channel) columns of the FFT matrix,

X(i) represents a diagonal matrix of soft symbols containing

a posteriori probabilities (APPs) of the data Xkk at the ith

iteration, the matrix R(i)NN is defined asR(i)

NN =CQ

AP Pi(X = C)CC. (2)

Here, Q represents the set of all possible codeword matrices of

X and the matrix C stands for one realization from Q. Cgg is

the auto-covariance matrix of channel impulse response g and

2 denotes the noise variance. From (1), the complexity of the

traditional iterative MMSE channel estimator is high due to the

matrix inversion of size L L which has to be performed at

each iteration of the estimation process, because the value of

the matrix

R

(i)NN changes at each iteration. Furthermore, in

LTE systems, the distributed resource allocation is used to vary

RB positions in different OFDM symbols. With the traditional

iterative MMSE algorithm, the allocated RB positions have to

be pinpointed and the matrix to be inverted is different from

one OFDM symbol to another one. This process adds more

complexities to the traditional iterative MMSE algorithm.

B. Iterative Compensated MMSE (IC-MMSE)

In order to solve the problems of the traditional iterative

MMSE, we propose an iterative compensated MMSE channel

estimation algorithm.

1) Compensation Process: One key feature is the com-

pensation process which is applied on the values of the

estimates which correspond to the null sub-carriers, as shown

in Fig. 2. By using some kind of initial channel estimation

algorithms, it is possible to obtain channel estimates over

all sub-carriers based on pilot symbols. For example, the

simple least square (LS) channel estimation can be a candidate.

This initial channel estimate is noted as h(0), which can be

separated into two parts

h(0) =

h(0)TN , h

(0)TDP

T, (3)

where the vector h(0)DP represents the channel estimates on

modulated sub-carriers, including data and pilot symbols and

vector h(0)N represents the channel estimates on the null sub-

carriers. Since the null sub-carriers normally exist at both sides

of bandwidth, the channel estimates h(0)N can be expressed as

h(0)N =

h(0)TN,1 , h

(0)TN,2

T, as shown in Fig. 2.

Compensate

Compensate

h(i)DP

h(i+1)IC-MMSEh

(i)IC-MMSE

h(i)N,0

h(i)

N,1 EP

h(i)

N,1

X(i) DP

y

EPh(i)N,0

Fig. 2. Compensation process of IC-MMSE.

In the traditional iterative MMSE channel estimation, soft

information is produced by channel decoder during current

iteration and used in the next iteration to build soft symbolsX(i)DP. However, no soft information is available on the nullsub-carriers, since no symbol is transmitted on this part. In

order to simplify the calculations made during the iterations,

we propose to copy the channel estimates on the null sub-

carriers from the current iteration h(i)N to the next (i + 1)th

iteration at the same positions as in the (i)th iteration. It isalso assumed that, for the copied part, the channel estimates

are obtained from pilot symbols and the transmitted power on

this part is equal to the power of pilot symbols, denoted as

EP. With this assumption, it can be seen as pilot symbols are

transmitted on the null part where, actually, no symbol exists.

Compared with the actual pilot symbols, these pilot symbols

are considered as virtual pilot symbols. This copy process is

called compensation, as shown in Fig. 2. The compensation

process can be described as:

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1 In the initial channel estimation, use pilot symbols to

obtain channel estimates over all sub-carriers in the

vector h(0);

2 Split current vector h(i) (i = 0, 1, 2, ) into two sub-

vectors

h(i)N , h

(i)DP

, where the sub-vector h

(i)DP relates to

data and pilot symbols and the sub-vector h(i)N relates to

null sub-carriers;

3 Copy the channel estimates on null sub-carrier parth(i)N to the next iteration by considering the power of

virtual pilot symbols EP;4 Implement iterative MMSE channel estimation by con-

sidering soft symbols (X(i)), actual pilot symbols(XP), and virtual pilot symbols, as shown in Sec-

tion III-B2;

5 Make i = i + 1 and repeat step 2), 3), 4) and 5).

2) IC-MMSE: With the compensation process described in

section III-B, the IC-MMSE channel estimation at the (i+1)thiteration h

(i+1)IC-MMSE can be written as

h(i+1)

IC-MMSE =L L EP, R(i)NDPNDPL + 2C1gg

1

L

EPh

(i)N ,

X(i)DP y , (4)where EP = EPINNDP and INNDP stands for an identitymatrix of size N NDP, N and NDP being the number of

all sub-carriers and the number of modulated sub-carriers

respectively, the matrix

EP, R(i)NDPNDP represents a diagonalmatrix defined as

EP,

R(i)NDPNDP

=

EP, 1 0

R

(i)NDPNDP

0 EP, 2

, (5)

andEPh

(i)N ,

X(i)DP y is an N1 vector, where EP, 1 and EP, 2correspond to h

(i)N,1 and h

(i)N,2, the diagonal matrix

X(i) includesall soft symbols and pilot symbols and the vector y represents

the received symbols. Compared with the traditional iterative

MMSE channel estimation in (1), due to the compensation

process, (4) replaces the matrix R(i)NN with

EP, R(i)NDPNDP

and replaces the vector X(i)y with EPh(i)N , X(i)DP y. The di-agonal entries of the matrix

EP, R(i)NDPNDP and the elements

of the vector

EPh

(i)N ,

X(i)DP y

are arranged corresponding to

the correct pattern of pilot and data arrangement.Then, considering that the average transmit powers over all

sub-carriers are the same, (4) can be approximated as

h(i+1)IC-MMSE L

L

L +2

EavC1gg

1L

constanth(i)N ,

R(i)1NDPNDP

X(i)DP y= Lg

(i+1)IC-MMSE, (6)

where Eav stands for the average power of transmitted symbols,

g(i+1)IC-MMSE stands for the time domain channel estimate in the

(i + 1)th iteration, which will be used in section IV. From(6), it can be seen that the first part, which includes a matrix

inverse, is always constant and we do not need to perform

matrix inversion at each iteration. This is the simplification

which allows the reduction of the calculation complexity.

Furthermore, with distributed resource allocation, since the

positions of the allocated non-null part are varying from

one OFDM symbol to another one, the traditional iterative

MMSE channel estimation algorithm in (1) has to choose

different FFT matrices L for each OFDM symbol, resulting

in more calculations. With the proposed IC-MMSE, thanks

to the compensation process, we do not need to choose the

corresponding partial FFT matrices and to re-calculate the

matrix inversion anymore. Thus, the proposed IC-MMSE has

a much lower complexity than the traditional iterative MMSE

channel estimation.

3) IC-MMSE in MIMO: The IC-MMSE algorithm is pro-

posed in SIMO transmission, and it can also be used in MIMO

transmission. With transmit diversity (taking two transmitantenna system as an example), the received symbols on the

rth receive antenna are

yr =

1t=0

Xthrt + nr (0 r 1) , (7)

where Xt stands for the transmitted symbols on the tth

transmit antenna, and hrt represents the channels between

the tth transmit antenna and the rth receive antenna. In the

(i + 1)th iteration, to estimate the channel vector hrt, thereceived symbol vector yrt is approximated as

y(i)rt = yr X(i)1th(i)r(1t) (0 r 1, 0 t 1) , (8)

where X(i)1t and h(i)r(1t) stand for the soft symbols and chan-nel estimates respectively which contain soft information from

the ith iteration. Then, substituting (8) into (6), we obtain IC-

MMSE channel estimates in transmit diversity transmission.

IV. IMPACT OF COMPENSATION

Define an L L matrix Q as

Q =

L

L +2

EavC1gg

1(9)

and an LN matrix A as A = QL. Then, the IC-MMSEchannel estimate in the time domain in (6) can be expressed

as

g(i+1)IC-MMSE A

h(i)N ,

R(i)1NDPNDP

X(i)DP y . (10)According to the arrangement of null sub-carriers, the matrix

A can also be divided into two parts

A =

ANLNN , ADPLNDP

LN

, (11)

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where AN = QLN

, ADP = QLDP

, and NN + NDP = N.Then, (10) can be written as

g(i+1)IC-MMSE ANh

(i)N + ADP

R(i)1NDPNDP

X(i)DP y. (12)With Appendix A, (12) can be expressed as

g(i+1)IC-MMSE N g

(i)IC-MMSE + DP g

(i)DP , (13)

where 0 < N < 1, 0 < DP < 1, and N + DP 1.With the assumption of high SNR, we have perfect APPs of

transmitted symbols. Therefore, the channel estimate g(i)DP will

not change with different i and we denote g(i)DP = gDP. Then,

in the (i + t)th (t > 1) iteration, the time domain channelestimate can be written as

g(i+t)IC-MMSE

t

N g(i)IC-MMSE + DP gDP

t1n=0

nN . (14)

When t , we have

g(i+t)IC-MMSE 0 + DP gDP

1

1 N gDP. (15)

From (15), we see that, through sufficient iterations, IC-MMSE

algorithm can have the same performance as the traditional

iterative MMSE algorithm using only the modulated part.

However, the proposed IC-MMSE algorithm has much lower

complexity, which will be discussed in the next section.

V. COMPLEXITY

In order to assess the complexity of the IC-MMSE, we

check the number of complex multiplications needed in the

traditional iterative MMSE and the IC-MMSE. In (1), for

each iteration, the number of complex multiplications is

N2DPL + NDPL2 +O L

3

. For IC-MMSE in (6), the constantpart can be done offline and will keep the same value for alliterations and all OFDM symbols. Therefore, at each iteration,

the IC-MMSE only needs N2 complex multiplications. Fur-

thermore, if we consider i iterations, the difference between

the traditional iterative MMSE and the IC-MMSE becomes

i

N2DPL + NDPL2 +O

L3 N2

.

VI . SIMULATION RESULTS

To assess performances of the proposed iterative channel es-

timation algorithms, simulations are conducted over extended

vehicular A (EVA) channel model with 5Hz Doppler frequencyand extended typical urban (ETU) channel model with 70HzDoppler frequency which are defined in [5]. The main parame-

ters are summarized in Table I. We simulate 10MHz bandwidthas defined in [5]. Two strategies of resource allocation are

simulated: full allocation which allocates all RBs to one single

user and distributed allocation which allocates only 2 RBs to

one single user and varies positions of allocated RBs from

one OFDM symbol to another one. For the first iteration, the

simple LS channel estimation is used to get channel estimates

over all sub-carriers. With this LS initial channel estimation,

the proposed algorithm is named as LS+IC-MMSE. In order

to obtain channel estimates on the whole sub-frame, linear

TABLE ISIMULATION PARAMETERS.

Parameter Value

FFT size 1024

Number of modulated sub-carriers 600

Allocated RB 50/2

Cyclic prefix 80

Transmission mode SIMO (1 2) / MIMO (2 2)

Modulation scheme 16-QAM

Channel coding rate 1/2

Channel coding type Duo-binary turbo code

Channel typeEVA5/ETU70 (modified Jakes

Doppler spectrum [6])

time interpolation is implemented after IC-MMSE frequency

domain channel estimation.

In Fig. 3, the packet error rate (PER) performance is

shown over ETU70 channel model with 50RB full allocation.

We see that, in SIMO transmission system, even though

the performance of the first iteration with LS is bad, after

5 iterations, the PER performance of the proposed LS+IC-

MMSE algorithm approaches that of perfect channel state

information (PerCSI). Even with 2RB distributed resource

allocation, after 6 iterations, we obtain good performance

which is close to that of PerCSI, as shown in Fig. 4.

10-3

10-2

10-1

100

4.0 6.0 8.0 10.0

PER

Es/N0 (dB)

1x2 50RB 16QAM 1/2 ETU70 PerCSILS+IC-MMSE iter 1LS+IC-MMSE iter 3LS+IC-MMSE iter 5

Fig. 3. Packet error rate with 50RB full allocation over SIMO transmission.

In Fig. 5, the PER performance is shown over MIMO

transmission. Here, the 50RB full allocation strategy is simu-

lated. From this figure, we see that, over MIMO transmission,

the proposed LS+IC-MMSE algorithm also have good perfor-

mances which approaches the performance with PerCSI, even

though the received symbols for a pair of transmit and receive

antennas have to be estimated based on soft information.

VII. CONCLUSION

In this paper, an MMSE based iterative channel estimation

algorithm is proposed in LTE systems. In order to reduce com-

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10-3

10-2

10-1

100

2.0 4.0 6.0 8.0 10.0

PER

Es/N0 (dB)

1x2 2RB 16QAM 1/2 ETU70 PerCSILS+IC-MMSE iter 1LS+IC-MMSE iter 3LS+IC-MMSE iter 6LS+IC-MMSE iter 10

Fig. 4. Packet error rate with 2RB distributed allocation over SIMOtransmission.

10-3

10-2

10-1

100

2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

PER

SNR (dB)

2x2 50RB 16QAM 1/2 EVA5 PerCSILS+IC-MMSE iter 1LS+IC-MMSE iter 3LS+IC-MMSE iter 6

Fig. 5. Packet error rate with 50RB full allocation over MIMO transmission.

plexity and take advantage of null sub-carriers, a compen-

sation process is proposed to simplify the traditional iterative

MMSE channel estimator. After this iterative compensated

MMSE channel estimation in frequency domain, a simple

linear interpolation in time domain is performed to obtain

channel estimates over all OFDM symbols. Simulation results

show that the proposed IC-MMSE channel estimation algo-

rithm has good performances which approach the performance

with perfect channel state information in both SIMO and

MIMO transmission modes.

ACKNOWLEDGMENT

The research leading to these results has received funding

from the European Commissions seventh framework program

FP7-ICT-2009 under grant agreement n 247223 also referred

to as ARTIST4G.

APPENDIX A

DERIVATION OF (13)

In (12), the channel estimate h(i)N is obtained by

h(i)N = LN g

(i)IC-MMSE. (A-1)

Also, we define g(i)DP asR(i)1NDPNDP

X(i)DP y = LDP g(i)DP. (A-2)Then, we get

g(i+1)IC-MMSE ANLN g

(i)IC-MMSE + ADPLDP g

(i)DP. (A-3)

Together with the definitions of AN, we have

ANLN =

L

L +22

EavC1gg

1LN

LN

=

NILL +

22

EavC1gg

1LN

LN . (A-4)

In order to simplify analysis, we assume rectangular channel

profile, which means all taps have the same power1

L. Then,

(A-4) becomes

ANLN =1

N +2L2

Eav

LN

LN . (A-5)

In (A-5), even though LN

LN is not diagonal, we can still

make a diagonal approximation, because its diagonal entries

are more larger than non-diagonal entries. Then, (A-5) can be

further simplified and the scalar value is defined as N:

ANLN NN

N +2L2

Eav

ILL NILL. (A-6)

The same process can be made for ADPLDP and we get

ADPLDP NDP

N +2L2

Eav

ILL DPILL. (A-7)

Since NN + NDP = N, it is evident to have N < 1 andDP < 1. Also, compared with the value of N, the value of2L2

Eavis so small that we can have

N + DP 1. (A-8)

Finally, substituting (A-6) and (A-7) into (A-3), we get (13).

REFERENCES

[1] C. Berrou, A. Glavieux, and P. Thitimajshima, Near shannon limit error-correcting coding and decoding: Turbo-codes, in Proc. ICC93., vol. 2,pp. 10641070, May 1993.

[2] L. Boher, R. Legouable, and R. Rabineau, Performance analysis of

iterative receiver in 3GPP/LTE DL MIMO OFDMA system, in Proc.IEEE ISSSTA08, Aug. 2008.

[3] 3GPP, Evolved universal terrestrial radio access (E-UTRA); physicalchannels and modulation, 3rd Generation Partnership Project (3GPP),TS 36.211, Mar. 2008.

[4] J.-J. van de Beek, O. Edfors, and M. Sandell, On channel estimationin OFDM systems, in Proc. 45th IEEE (VTC95), vol. 2, pp. 815819,Sep. 1995.

[5] 3GPP, Evolved Universal Terrestrial Radio Access (E-UTRA); UserEquipment (UE) radio transmission and reception, 3rd Generation Part-nership Project (3GPP), TS 36.101, Sep. 2008.

[6] Y. Li and X. Huang, The simulation of independent rayleigh faders,IEEE Trans. Commun., vol. 50, no. 9, pp. 1503 1514, Sep. 2002.

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