Intercarrier Interference CancellationUsing Complex Conjugate Technique

for Alamouti-Coded MIMO-OFDM SystemsAurupong Yiwleak and Chaiyod Pirak

Communications Engineering Program, The Sirindhorn International Thai-German Graduate Schoolof Engineering(TGGS), King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand

1518 Pibulsongkram Road, Bangsue, Bangkok 10800, Thailandemail: aurupong@tot.co.th and chaiyod.p@gmail.com

Abstract—This paper proposes an Alamouti coded orthogonalfrequency division multiplexing (OFDM) scheme combining withthe intercarrier interference (ICI) conjugate cancellation schemein order to mitigate ICI caused by frequency offset in MIMOsystem. The proposed system provides advantages of a conjugatecancellation scheme, such as backward compatibility with theexisting Alamouti coded OFDM system and low receiver complex-ity. Simulation results show that the proposed scheme achievesa lower bit error rate (BER) compared with existing Alamouticoded OFDM system in both AWGN and fading channels.

I. INTRODUCTION

An orthogonal frequency division multiplexing (OFDM)communication system is widely known as the promisingcommunication technique in the current broadband wirelesscommunication systems because of the high spectral efficiencyand robustness in multipath fading channel. However, one ofthe major impairments of such system is the sensitivity ofits performance to synchronization error such as frequencyoffset or phase offset. The frequency offset causes from acarrier frequency synchronization error between oscillatorsin the transmitter and receiver as well as a Doppler shift.Such frequency offset leads to a loss of orthogonality amongsubcarriers that introduce intercarrier interference (ICI).

Currently, there are four different approaches for miti-gating ICI which have been proposed including, frequency-domain equalization [1], time-domain windowing [2], ICIself-cancellation [3],[4], and two-path conjugate cancellation[5],[6]. All of such approaches are developed for one transmitand one receive antenna, excepting [7] introduces ICI self-cancellation scheme in Multiple-Input and Multiple-Output(MIMO) case. However, this study has focused on space-frequency codes, and [8] has proposed Alamouti coded incooperative systems with ICI self-cancellation scheme. Sincethere is a lack of applying ICI complex conjugate cancellationscheme in multiple antennas system, it motivates us to studyin this area.

In this paper, the ICI conjugate cancellation in multipleantennas OFDM systems is proposed. Since, the users haveless space to equip two antennas, then a case of two-transmitand one-receive antennas in OFDM system is focused onthis paper. As compared to a standard Alamouti-codedOFDM system, at high-frequency offset situations, the

lX0X

-1NX -1Nx

0x

P/SS/P

(a)

IFFT

ˆkX

0X

-1ˆ

NX -1ˆNx

0xˆ

lXP/SS/P

ML

Decoding

(b)

FFT

Figure 1. Structure of a baseband OFDM system, (a) Transmitter, (b)Receiver

Alamouti-coded with ICI conjugate cancellation achievesbetter performance than the standard Alamouti-coded OFDMsystem.

The rest of this paper is organized as follows. Section II, themathematical model of OFDM signal with frequency offsetand the conjugate cancellation scheme proposed in [5] aredescribed. Section III presents the proposed Alamouti-codedMIMO-OFDM system with ICI conjugate cancellation. Sec-tion IV provides simulations to verify the theoretical analysis.The results of the paper are summarized in Section V.

II. OFDM SIGNAL MODEL WITH FREQUENCY OFFSET

A. OFDM Signal Model

Fig.1 shows the block diagram of a baseband OFDM systemwith Single-Input and Single-Output (SISO). Denote Xl(l =0, ..., N−1) as the modulated symbols on the lth transmittingsubcarrier of OFDM symbol at transmitter, which are assumedindependent, zero-mean random variables, with average powerσ2

X . The complex baseband OFDM signal at output of theIFFT can be written as

xn =1√N

N−1∑

l=0

Xlej 2π

N nl, n = 0, . . . , N − 1 (1)

where N is the total number of subcarriers and the OFDMsymbol duration is T seconds.

At the receiver, the received OFDM signal is mixed withlocal oscillator signal, with the frequency offset deviated fromΔf the carrier frequency of the received signal owing tofrequency estimation error or Doppler velocity, the receivedsignal is given by

xn = (xn ⊗ hn)ej 2πN nΔfT + zn (2)

where hn, ej 2πN nΔfT , and zn represent the channel impulse

response, the corresponding frequency offset of received signalat the sampling instants: ΔfT is the frequency offset tosubcarrier frequency spacing ratio, and the AWGN respec-tively, while ⊗ denotes the circular convolution. Assumingthat a cyclic prefix is employed; the receiver has a perfecttime synchronization. Note that a discrete Fourier transform(DFT) of the convolution of two signal in time domain isequivalent to the multiplication of the corresponding signals inthe frequency domain. Then the output of the FFT in frequencydomain signal on the kth receiving subcarrier becomes:

Xk =N−1∑

l=0

XlHlUl−k + Zk, k = 0, . . . , N − 1

= XkHkU0 +N−1∑

l=0,l �=k

XlHlUl−k + Zk (3)

The first term of (3) is a desired transmitted data symbolXk. The second term represents the ICI from the undesireddata symbols on other subcarriers in OFDM symbol. Hk is thechannel frequency response and Zk denotes the frequency do-main of zn. The term Ul−k is the coefficient of FFT (IFFT ),is given by

Ul−k =1N

N−1∑

n=0

ej 2πN n(l−k+ΔfT ) (4)

when the channel is flat, Ul−k can be considered as a com-plex weighting function of the transmitted data symbols infrequency domain.

B. Conjugate Cancellation Scheme and Its Property

According to [5], a conjugate cancellation algorithm is totransmit the standard OFDM symbol and its conjugate overtwo transmission paths that provide weighting factors withopposite polarities at the zero crossing point. The detectedsymbol is an average detected symbol of both paths, thestructure of conjugate cancellation will be shown in SectionIII. Assuming that the frequency offset is a constant over thetwo-path time interval.

The property of the complex conjugate cancellation with thecomplex weighting function is expressed as follow [5]

Ul−k + Vl−k

2≈{

1 if l = k0 if l �= k

(5)

where Vl−k is the complex weighting function of the conjugatepath, is given by

Vl−k =1N

N−1∑

n=0

ej 2πN n(l−k−ΔfT ) (6)

III. PROPOSED CONJUGATE CANCELLATION IN MIMOSYSTEM

A. System Model for MIMO System

In this section, we propose a conjugate cancellation(CC) scheme in Multiple-Input and Multiple-Outputsystem (MIMO) system as shown in Fig.2. The modulatedsymbols Xl(l = 0, ..., N − 1) are encoded with Alamoutispace time coding [9], transmitted frequency domainsignal on lth transmitting subcarrier from antenna oneis denoted by D1,l = (X0,−X∗

1 , ...,XN−2,−X∗N−1, for

l = 0, ..., N−1, respectively) and from antenna two is denotedby D2,l = (X1,X

∗0 , ...,XN−1,X

∗N−2, for l = 0, ..., N − 1,

respectively). Assuming that the cyclic prefix is employed; thereceiver has the perfect time synchronization. Note also thatthe frequency offset is constant over all-path time interval.The received time domain signal is given by

xn = (d1,n ⊗ h1,n + d2,n ⊗ h2,n)ej 2πN nΔfT + zn (7)

Then the frequency domain receiving signal of standardOFDM on kth receiving subcarrier expressed in (3) changesto

Xksd

=N−1∑

l=0

D1,lH1,lU1,l−k +N−1∑

l=0

D2,lH2,lU2,l−k +Zk (8)

The conjugate path is also shown as follow

Xkcc

=N−1∑

l=0

D1,lH∗1,lV1,l−k +

N−1∑

l=0

D2,lH∗2,lV2,l−k +Z∗

k (9)

Assuming that the channel frequency response is constant overtwo consecutive transmitted symbols and two transmissionpaths.

B. Conjugate Cancellation Scheme for MIMO

The averaged received signal of the standard OFDM andthe conjugate cancellation can be described as

Rk =12(Xk

sd+ Xk

cc) (10)

Rk =12(D1,kH1,kU1,0 +D2,kH2,kU2,0

+D1,kH∗1,kV1,0 +D2,kH

∗2,kV2,0)

+ Ik +Wk (11)

where

Ik =12

N−1∑

l=0,l �=k

(D1,lH1,lU1,l−k +D2,lH2,lU2,l−k

+D1,lH∗1,lV1,l−k +D2,lH

∗2,lU2,l−k) (12)

andWk =

12(Zk + Z∗

k) (13)

The first term on the right hand side of the (11) is the desiredsignal, Ik is ICI, and Wk is the AWGN.

When the channel is quasi-static and flat, the frequencyresponse of the channel H1,l and H2,l always equals to 1

lX

0D

-1ND

0D

0d

0d

S/P

S/P

IFFT

IFFT P/S

P/S

TDM

TDM

(a)

*( )

*( )

STC

-1Nd

-1Nd-1ND

ˆkR

ˆkS

ˆ sdkX

ˆ cckX

0X

-1ˆ

NX

0x

-1ˆNxˆlX

TDMP/SFFTS/P

st1 path

nd2 path

ICI CancellingAlamouti

Combining

ML

Decoding

*( )

(b)

Figure 2. Structure of an Alamouti-coded MIMO-OFDM system with ICI conjugate cancellation, (a) Transmitter, (b) Receiver

[10], i.e. an AWGN channel, and if the channels are real-valued then H∗

l,l = H1,l and H∗2,l = H2,l [8]. Assuming that

the frequency offset is a constant over two-transmit and one-receive antennas, then U1,l = U2,l = Ul and V1,l = V2,l = Vl.The received signal Rk of kth receiving subcarrier becomes:

Rk =12(D1,kH1,k(U0 + V0) +D2,kH2,k(U0 + V0))

+12

N−1∑

l=0,l �=k

(D1,lH1,l(Ul−k + Vl−k)

+D2,lH2,l(Ul−k + Vl−k)) +12(Zk + Z∗

k)

=12(D1,k +D2,k)(U0 + V0)

+12

N−1∑

l=0,l �=k

(D1,l +D2,l)(Ul−k + Vl−k)

+12(Zk + Z∗

k) (14)

With the property of conjugate cancellation from (5), The ICIterm is mitigated, then the term Rk becomes:

Rk =12(D1,k +D2,k) +

12(Zk + Z∗

k)

(15)

And, it is straightforward to get Rk+1 of (k+1)th receivingsubcarrier from (15):

Rk+1 =12(D1,k+1 +D2,k+1) +

12(Zk+1 + Z∗

k+1)

(16)

The Alamouti combining scheme is used to combine pair ofconsecutive received signals. The following combined signalwill be sent to the maximum likelihood detector:

Sk = H∗1,kRk +H2,k+1R

∗k+1, k = 0, 2, . . . , N − 2 (17)

Sk+1 = H∗2,kRk −H1,k+1R

∗k+1, k = 0, 2, . . . , N − 2 (18)

Note that modulated symbols are assumed independent,zero-mean random variable. When the channel is quasi-staticand flat, from (14),(17), and (18), the carrier to ICI power ratio(CIR) of CC algorithm in MIMO, as the function of frequencyoffset, can be expressed by

CIR =|U0 + V0|2∑N−1

l=1 |Ul + Vl|2(19)

It is important to note that this CIR is precisely the CIR of CCalgorithm in SISO. From (19), the CIR of the conventionalOFDM in MIMO is straightforward to get the followingequation:

CIR =|U0|2∑N−1

l=1 |Ul|2(20)

Note also that CIR in (20) is for the conventional OFDMin SISO. Considering the complex conjugate cancellationproperty of weighting function in (5), it is obvious that thedenominator in (19) is approaching to zero and CIR is thenincreased when the frequency offset is small, that means theICI is significantly mitigated.

IV. SIMULATION RESULTS

In this section, the performance of the proposed ICI con-jugate cancellation in MIMO-OFDM system with Alamoutispace time coding is verified through a computer simulation.The simulation is conducted under both in an AWGN anda frequency-selective Rayleigh fading channels. Jake’s model[11] is employed with a normalized Doppler shift of 5,000Hz. The same channel parameters are applied to the standardpath and its conjugate path with the six paths Typical Urban(TU) delay profile [12]. Assuming that the receiver has perfectknowledge of the channel and the channel is real-valuedfading channel, the cyclic prefix is employed; the receiver

0 5 10 15 20

10−5

10−4

10−3

10−2

10−1

100

Bit Error Rate (BER) vs. SNR(dB)

SNR(dB)

BE

R

MIMO, FO=0.01CC−MIMO, FO=0.01MIMO, FO=0.1CC−MIMO, FO=0.1MIMO, FO=0.2CC−MIMO, FO=0.2MIMO, FO=0

Figure 3. The curves of BER versus SNR (dB) for AWGN channel

0 5 10 15 20 25 30

10−3

10−2

10−1

100

Bit Error Rate (BER) vs. SNR(dB)

SNR(dB)

BE

R

MIMO, FO=0.01CC−MIMO, FO=0.01MIMO, FO=0.1CC−MIMO, FO=0.1MIMO, FO=0.2CC−MIMO, FO= 0.2MIMO, FO=0

Figure 4. The curves of BER versus SNR (dB) for Rayleigh fading channel

has the perfect time synchronization. The transmitted powerof each path of the conjugate cancellation scheme is halfof the standard OFDM, and total power of the system is 1Watt. The bandwidth efficiency is 1 b/s/Hz, the modulationwith QPSK is employed for the proposed schemes, BPSK isused for standard MIMO-OFDM system for a fair comparison.An OFDM modulation for each system utilizes N = 64subcarriers in all cases. The frequency offset to subcarrierfrequency spacing ratio (ΔfT ) is chosen as 0.01, 0.1 and0.2.

Fig.3 shows the BER versus SNR (dB) for the Alamouti-coded OFDM with ICI conjugate cancellation scheme and thecurve for standard Alamouti-coded OFDM system in AWGNchannel. It is worth noting that, at BER of 10−4 for (ΔfT =0.1), the proposed Alamouti-coded OFDM with ICI conjugatecancellation scheme has 3 dB gain over standard Alamouti-coded OFDM, while at small ΔfT (ΔfT = 0.01), theperformance differences of both systems are not significant.Furthermore, if ΔfT is large (ΔfT = 0.2), the BER of the

0 5 10 15 20 25 30

10−3

10−2

10−1

100

Bit Error Rate (BER) vs. SNR(dB)

SNR(dB)

BE

R

MIMO, FO=0.01CC−MIMO, FO=0.01MIMO, FO=0.1CC−MIMO, FO=0.1MIMO, FO=0.2CC−MIMO, FO=0.2MIMO, FO=0

Figure 5. The curves of BER versus SNR (dB) for Rayleigh fading channel,channel variance of H1,l=1 and channel variance of H2,l=2

ICI Alamouti-coded OFDM is precisely better performancethan that of standard system.

Fig.4 shows the BER versus SNR (dB) for the Alamouti-coded OFDM with ICI conjugate cancellation scheme andthe curve for standard Alamouti-coded OFDM system inRayleigh channel. It is worth noting that, when ΔfT is small(ΔfT = 0.01, 0.1), the Alamouti-coded OFDM with ICIconjugate cancellation scheme is slightly better performancethan that of standard case. Furthermore, if ΔfT is large(ΔfT = 0.2), the BER of the Alamouti-coded OFDM withICI conjugate cancellation scheme gives better performancethan that of standard system about 7 dB at BER of 5 × 10−3.

Fig.5 shows the BER versus SNR (dB) for the Alamouti-coded OFDM with ICI conjugate cancellation scheme and thecurve for standard Alamouti-coded OFDM system in Rayleighchannel. The variance of the channel links between the firsttransmit antenna and the receive antenna is 1, between thesecond transmit antenna and the receive antenna is 2. It isworth noting that the system performance corresponds to theresult as shown in Fig.4 with the better performance in allcases.

V. CONCLUSION

In this paper, an Alamouti-coded MIMO-OFDM systemwith the conjugate cancellation was proposed. OFDM wasused to combat the multipath fading, and an ICI conjugatecancellation scheme was used to mitigate the ICI caused byfrequency offset. The key feature of this new scheme is that itprovides better CIR than the standard Alamouti-coded OFDMsystem. Consequently, the sensitivity of this new scheme to ICIis reduced significantly. Under the same bandwidth efficiency,the proposed scheme performs much better performance thanthe standard Alamouti-coded OFDM system in both AWGNand multipath fading channels. It was also proven by thesimulation that the proposed scheme is robust to a severefrequency offset.

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