multiuser-CoMP OFDM systems with low-complexity estimation of multiple CFOs

2012 International Conference on Systems and Informatics (ICSAI 2012) Independent Component Analysis Based Semi-Blind Equalization for Multiuser-CoMP OFDM Systems

with Low-Complexity Estimation of Multiple CFOs

Yufei Jiang??,Xu Zhu?,Enggee Lim?,Wenfei Zhu??,Linhao Dong?and Yi Huang?

?Department of Electrical Engineering and Electronics,The University of Liverpool Brownlow Hill,Liverpool,L693GJ,U.K.

Email:{yufei10,xuzhu}@https://www.360docs.net/doc/4914183947.html,

?Department of Electrical and Electronic Engineering,Xi’an JiaoTong Liverpool University,Suzhou,China215123

Abstract—We propose a low-complexity carrier frequency offset(CFO)estimation method and an independent component analysis(ICA)based semi-blind equalization structure for mul-tiuser and coordinated multi-point(CoMP)OFDM systems.A group of orthogonal sequences is employed to enable separation and simultaneous estimation of multiple CFOs,dividing the multi-dimensional search into series of low-complexity mono-dimensional searches.The ICA is used for equalization,with a small number of pilot symbols employed for ambiguity elimination in the ICA equalized signals.The proposed semi-blind equalization structure slightly outperforms the previous precoding aided scheme,with a lower complexity.It also provides a almost same BER performance to the case of zero forcing(ZF) and minimum mean square error(MMSE)based equalization with perfect CSI and no CFO at the receiver.

Index Terms—independent component analysis(ICA),coordi-nated multi-point(CoMP),OFDM,CFO

I.I NTRODUCTION

Coordinated multi-point(CoMP)transmission which has been adopted by3GPP LTE-Advanced[2]is a promising technique to reduce intra-cell interference and improve the coverage of data rate services,by enabling the multiple geographically separated base stations to jointly process the multiuser’s signal in wireless communication.

Channel estimation and multiuser signal detection play an important role in multiuser-CoMP OFDM systems.Indepen-dent component analysis[3][4],as one of higher order statistic(HOS)based blind source separation approaches,can be employed to estimate the data directly from the statistics of received signal,without knowing the channel state information (CSI).However,the ambiguity problem exists in the ICA equalized signal.In[5],the statistical correlation between subcarriers is used to resolve the frequency dependent permu-tation problem but incurs ambiguity error propagations across subcarriers.In[6],a precoding is employed to eliminate the permutation and phase ambiguities without consuming extra bandwidth.However,it has a good BER performance only when data frame size is large enough.

One of the main drawbacks of OFDM systems is their sensitivity to the carrier frequency offset(CFO)due to the imperfect local oscillators between the transmitter and re-ceiver,destroying the orthogonality among the subcarriers and inducing the additional intercarrier interference(ICI).In the multiuser-CoMP system,multiple CFOs exist between mobile terminals and each base station,introducing multiple access interference(MAI).The optimum maximum likelihood(ML) based CFO estimation is proposed in[7]but its complexity is prohibitive in real systems.A low-complexity algorithm is proposed in[8],suf?cient samplings are generated,incapable of the practical implementations.In[9],a sub-optimal esti-mation using constant amplitude zero autocorrelation(CAZA) sequences is proposed,however the error?oor is suffered.

In this paper,we propose a low-complexity CFO estimation method and an ICA based semi-blind equalization structure for multiuser-CoMP OFDM systems.Our work is different in the following aspects.First,a group of orthogonal sequences are employed for multiple CFO separations and estimations during the preamble,dividing the multidimensional search into a serials of low-complexity mono-dimension searches. Second,an ICA based semi-blind equalization structure is proposed,where a small number of pilot symbols are used to eliminate the permutation and quadrant ambiguities induced by ICA exploring the cross correlation between the original and equalized pilot symbols.Simulation results show that the proposed pilot aided and ICA based semi-blind equalization scheme provides a better bit error rate(BER)performance than the precoding aided ICA based equalization scheme in [6].It also requires a lower complexity than the method in[6] as the permutation and quadrature ambiguities can be solved sequentially,rather than separately.The proposed semi-blind equalization scheme is also shown to be more robust against channel variations.

II.SYSTEM MODEL

Throughout the paper,we consider an uplink multiuser-CoMP OFDM system.The K users transmit different signal simultaneously using the same set of N subcarriers to the M separated base stations.Only single antenna is assumed for each base station and user.Each receiver experiences

multiple CFOs from K users.The source signal of each user is transmitted in terms of frames containing N s blocks of QPSK symbols,while each symbol block is prepended with a cyclic pre?x (CP)of length L cp before the transmission and removed at the receiver to avoid inter-block interference.

We de?ne the k -th user’s signal in the i -th block as s k (i )=[s k (0,i ),s k (1,i ),...,s k (N ?1,i )]T where s k (n,i )denotes the symbol on the n -th subcarrier (n =0,1,...,N ?1)in the i -th (i =0,1,...,N s ?1)block transmitted by the k -th user.F H and F are the N -point unitary IDFT and DFT matrix respectively.The channel is assumed to be quasi-static block fading and the CSI remains constant for the duration of a frame.h m,k is the channel impulse response between the k -th user and m -th base station with L paths.At the m -th receiver,after the removal of cyclic pre?x,following [9],the received signal y m (i )=[y m (0,i ),y m (1,i ),...,y m (N ?1,i )]T in the i -th block combined with all K users with multiple CFOs in the time domain is expressed as

y m

(i )=

K ?1∑k =0

E (?

m,k

)?h

m,k F H s k (i )+z m (i )(1)

where E (?m,k )=diag (1,e j 2π?m,k

N ,???,e

j 2π(N ?1)?m,k

N )is the normalized CFO matrix on N subcarriers with diag (?)denot-ing the diagonal matrix.?m,k is the normalized CFO which is de?ned as ?m,k =△f m,k /f 0where △f m,k is the CFO between the k -th user and the m -th base station,and f 0is the

subcarrier spacing.?h

m,k is the circular matrix obtained from h m,k .z m (i )is the additive white Gaussian noise (AWGN).The entries of the vector z m (i )are independent identically distributed (i.i.d.)complex Gaussian random variables with zero mean and variance of σ2.Equation (1)is transformed to frequency domain by taking the N -point DFT of y m (i ):

Y m (i )=Fy m

(i )=

K ?1∑k =0

FE (?m,k )??h

m,k

?F H s k (i )+Z m (i )

=

K ?1∑k =0C m,k H m,k s k (i )+Z m (i )

(2)

where Y m

(i )=[Y m

(0,i ),Y m

(1,i ),...,Y m

(N ?1,i )]T

is

the frequency domain received signal at the m -th base station.C m,k =FE (?m,k )F H is the ICI matrix caused by the CFO between the k -th user and the m -th base station.H m,k =F ?h

m,k F H is the relevant channel frequency response between the m -th base station and the k -th user.Z m (i )=Fz m (i )is the frequency domain noise matrix.

The entry [c m,k ]u,v denotes the ICI term on the u -th row and v -th column of C m,k having such properties:

Property I:C m,k is circulant matrix transformed from diagonal matrix E (?m,k )[10].

Property II:the sum of the elements on any row or any column is equal to one.That is ∑N ?1u =0[c m,k

]u,v =1,∑N ?1v =0[c m,k ]u,v =1and ∑N ?1u =0∑N ?1v =0[c

m,k

]u,v =N .III.O RTHOGONAL S EQUENCES B ASED M ULTIPLE CFO S

E STIMATION During preamble,a simple and viable method to reduce the computational complexity consists of separating the k -th user’s ICI matrix along with channel frequency response matrix C m,k H m,k at the m -th receiver accomplished by the application of a group of different orthogonal sequences on N subcarriers and K users.The ICI property is used to estimate the channel frequency response matrix of H m,k ,and then each user’s ICI matrix of C m,k at the m -th base station is decoupled.Finally,the multiple CFOs can be estimated in the frequency domain at M base stations simultaneously by searching for the value closest to the real CFO.

With the known k ′-th (k ′=0,1,???,K ?1)user’s orthog-onal sequences of size N ×P ,the combination T m,k ′of the ICI matrix and channel frequency response matrix for the k ′-th user at the m -th receiver is separated from other users:

T m,k ′

=

1P

Y m ort?[s k ′ot?]H

(3)

where Y m ort?is the received pilot during preamble at the m -th receiver.s k ot?and s k

′

ot?are the orthogonal sequence matrix of the k -th user and the k ′-th user respectively which can be obtained from a group of well studied Hadamard matrix [6].They satisfy

s k ot?[s k ′ot?]H

={

P I N k =k ′0N ×N k =k ′(4)

Shown from (4),any two different users are orthogonal to each other on all subcarriers.Substituting (4)into (3)yields

T m,k ′

=C m,k ′

H m,k

′

(5)

Since C m,k ′

is a circulant matrix [10]and H m,k ′

is a

diagonal matrix,based on the property II of the ICI ma-trix,∑N ?1u =0[c m,k ′

]u,v =1,the channel frequency response ?H m,k ′

(v )on the v -th (v =0,1,???,N ?1)subcarrier between the m -th receiver and the k ′-th user is decoupled as

?H

m,k ′

(v )=

N ?1∑u =0

[T m,k ′

]u,v

(6)

where [T m,k ′

]u,v denotes the entry on the u -th row and v -th column of T m,k ′

.Combining and rearranging the channel frequency responses on N subcarriers,the channel frequency

response matrix ?H

m,k ′between the m -th receiver and the k ′-th user is estimated as

?H

m,k ′

=diag ([?H m,k ′(0),?H m,k ′(1),???,?H m,k ′(N ?1)])(7)

The channel frequency response matrix in (7)is taken into (5),

the ICI matrix C

m,k ′

caused by CFO between the k ′-th user and the m -th base station is obtained with very low complexity as:?C

m,k ′

=T m,k ′[?H m,k ′]H (8)

Since C =FE (?)F H ,the CFO ??

m,k ′between the k ′-th user and the m -th base station ??m,k ′is estimated by searching for the minimum distance between ?C

m,k ′

and C as ??

m,k ′=arg min ?∈(?0.5,0.5)

?C m,k ′

?C 22=arg min ?∈(?0.5,0.5)

?C

m,k ′?FE (?)F H 22(9)where ∣∣?∣∣denotes the L-2norm.In reality,the value of

CFO △f ,is less than the half of subcarrier spacing [10],so the normalized CFO is searched in the range from ?0.5to 0.5.The multiple CFOs can be estimated simultaneously by using (9),dividing the multidimensional search into a serial of low-complexity mono-dimension searches.After the multiple CFOs are estimated during the preamble,they can

be compensated for correctly by multiplying [?C

m,k ′]?1in the frequency domain.The novelty of the proposed method is that it can separate and estimate the multiple CFOs when the number of users is greater than the number of base stations.

IV.ICA B ASED S EMI -B LIND E QUALIZATION

With CFO estimation and compensation,the received signal is a linear mixture of transmitted signal.The separated base stations jointly detect and equalize the multiuser’s signal by employing ICA [4]on each subcarrier.However,as the instinct drawback of ICA models,the permutation and phase ambigu-ities exist in the ICA separated signal.In order to eliminate the ambiguity problem,the de-rotation process is ?rst used to correct some possible phase shifts in the ICA separated signal,enabling the signal to have a same phase rotation in a data frame.Second,the pilots of length N pil ,known at the receiver,are extracted to resolve the problem of permutation and phase ambiguities,by using the cross-correlation between equalized and original pilot symbols.The received signal Y (n,i )=[Y 0(n,i ),Y 1(n,i ),???,Y M ?1(n,i )]T on the n -th subcarrier is re-expressed as

Y (n,i )=QH (n )s (n,i )+Z (n,i )

(10)

where s (n,i )=[s 0(n,i ),s 1(n,i ),???,s K ?1(n,i )]T is the K users on the n -th subcarrier .Q is the estimation error between the estimated and the real CFO.H (n )and Z (n,i )are the M ×K channel frequency response matrix and M ×1noise vector on the n -th subcarrier,respectively.A.Independent Component Analysis

ICA aimes to extract the original source data from the linear mixture based on the statistics of received signal.JADE [3],as one of the well-established methods in ICA,resulting in pa-rameter free and shorter data sequences,is employed in this pa-per.To obtain the spatially uncorrelated signals,principal com-ponent analysis (PCA)[3]is used ?rstly to whiten the received signal.The whitening matrix W (n )is obtained from the eigen-value decomposition of the autocorrelation matrix of received signal as R xx (n )=E {Y (n,i )Y H (n,i )}=U (n )Λ(n )U H (n ).The whitening matrix is given as W (n )=Λ?1/2(n )U H (n )such that W (n )E {Y (n,i )Y H (n,i )}W H (n )=I K .JADE is

applied on each frame of length N s to get the unitary matrix

V (n )on the n -th subcarrier.The separated signal ?s (n,i )on the n -th subcarrier and in the i -th OFDM symbol is given by:

?s (n,i )=V (n )W (n )Y (n,i )+?Z

(n,i )(11)

where ?Z

(n,i )=V (n )W (n )Z (n,i )is the output noise ma-trix from the ICA based equalization.However,there exists ambiguity matrix G (n )in ?s (n,i ),compared with s (n,i )as

?s (n,i )=G (n )s (n,i )

(12)

The N s symbols in a data frame on the n -th subcarrier has a same ambiguity matrix G (n )composed of two indeterminacies as

G (n )=P (n )D (n )(13)with P (n )denoting the permutation ambiguity matrix and

D (n )denoting the quadrant ambiguity matrix.The ambiguity which remains in the ICA separated signal can be resolved by the proposed pilot aided method described as below.B.Phase Deviation Correction

First,the de-rotation process can correct possible phase deviations in the ICA separated signal,to ensure that all of the data,including the separated pilot and source symbols in a frame,has a same phase rotation on each substream.The equalized signal ˇs (n,i )after phase deviation correction is denoted as

ˇs (n,i )=?s (n,i )[αk (n )/∣αk (n )∣]

(14)where αk (n )={1N s ?1

∑N s i =0[?s k (n,i )]4}?14e j π

4is the de-rotation factor obtained from the statistical characteristics of ?s (k,i )with QPSK modulation.The de-rotation process

introduces a phase rotation of θ(θ∈{0,π2,π,3π

2})in ˇs (n,i ),

which might vary from frame to frame,and from user to user.C.Permutation and Quadrant Ambiguity Resolution After the de-rotation process,the data in a frame for each separated user on one subcarrier has the same quadrant and permutation ambiguities which can be resolved by the cross correlation property between the original and equalized pilot symbols.The cross correlation ρπk (n ),k (n )between the ICA equalized pilot symbols ˇs pil,πk (n )(n,i )and the original pilot symbols s pil,k (n,i )on the n -th subcarrier for the k -th user is de?ned as

ρπk (n ),k (n )=1

N pil N pil ?1∑i =0

{[ˇs pil,πk (n )(n,i )e jθπk (n )]s ?pil,k (n,i )}(15)

where θπk (n )=π

2l l ∈{0,1,2,3}is the possible phase rotation for the πk (n )-th separated user on the n -th subcarrier.In the noiseless case σ2=0,∣ρπk (n ),k (n )∣=1only when πk (n )=k ,while the absolute value of cross correlation is less than 1when πk (n )=k .The phase rotation of θπk (n )on

the πk (n )-th user can be found as e jθπk (n )=s pil,k (n,i )

ˇs pil,πk (n )(n,i ).In the presence of noise,we can search for the largest real part of cross correlation in equation (15)to ?nd the correct

[θcor πcor k

(n ),πcor k

(n )]=arg max θπk (n ),πk (n )

?e (ρπk (n ),k )=arg max θπk (n ),πk (n )?e {1N pil N pil

∑i =1{[ˇs pil,πk (n )(n,i )e jθπk (n )]

?s ?pil,k

(n,i )}}

(16)

The reason that we choose the real part of ρπk (n ),k is because the real part is less than one while the value of imaginary part βim (n )is not zero any more due to the noise.Thus,the πcor k (n )and θcor

πcor k

(n )are considered as the highest possibility

of being the correct order and the correct phase rotation when the real part is the largest one.

V.C OMPLEXITY A NALYSIS

In this section,the complexities of the proposed CFO estimation and the pilot aided ICA based equalization are presented in terms of the number of complex multiplications.The complexity of the ML based CFO estimation [7]and the precoding aided ICA based equalization [6]are also analyzed

for comparison.q =1

Δ

is the homogenization of step size Δbetween ?0.5and 0.5for CFO search.As shown in Table I,according to (3)-(9),the multiple CFOs are separated with the complexity order of N 2MKP ,and are estimated simul-taneously with only complexity order of qK ,while the ML based CFO estimator including matrix inversion dominates the computational complexity and its search complexity of q MK increases exponentially with the number of base stations and users.Therefore,the proposed CFO estimation has a much lower complexity than the ML based CFO estimation which requires exhaustive search and is impractical for real systems.For ambiguity elimination problem induced by ICA,the permutation and quadrate ambiguities can be solved simul-taneously by the proposed pilot aided ICA based equalization,rather than separately in [6],having lower complexity order.

VI.S IMULATION R ESULTS

We use simulation results to demonstrate the performance of the orthogonal sequence based CFO estimation and the pilot aided ICA based signal equalization for multiuser-CoMP OFDM systems with K =2users and M =2base stations.A

Fig.1.Normalized MSE of CFO estimation with different sets of CFOs

CP of length L cp =16is used and the number of subcarriers is N =64for the OFDM systems.The Clarke block’s fading channel model [1]with an exponential power delay pro?le is employed,where the CSI remains constant during a frame.Each data frame with QPSK modulation consists of N s =256symbol blocks where the ?rst 6blocks (N pil =6)of each frame are used as pilots,resulting in a training overhead of 2.3%.The root mean square (RMS)delay spread is 86ns.The resulting channel impulse response length is L =7.The orthogonal sequences of length P =32are assigned across on the 16subcarrires to separate and estimate the multiple CFOs on each base station during preamble.The step size Δ=0.001results in q =1000within the range between -0.5and 0.5for CFO search.

Fig.1and Fig.2show the normalized MSE of the multiple CFOs over a range of SNRs,which is de?ned as

NMSE =∑M ?1m =0∑K ?1k =0[(?m,k ???m,k )]2

∑M ?1m =0∑K ?1k =0[?m,k ]2(17)The performances of NMSE demonstrate that the proposed

CFO estimation has ability to estimate the multiple CFOs.The NMSE performances improve as the SNR increase and have no error ?oor at high SNR region.The MSE performance of different CFOs are close together.However,the different values of the multiple CFOs result in the NMSE performance gap in Fig.1.To eliminate the effect of different CFOs on the NMSE performance,the CFO in Fig.2is only set as 0.1or ?0.1.The number of users varies from two to four for two base stations,showing that the proposed CFO estimation can be applied for the scenario where the number of users is more than the number of base stations.With the same NMSE performances,the proposed CFO estimation is also shown to be robust against the change of the number of users.

Fig.3demonstrates the BER performance of the pilot aided ICA based equalization compared with the precoding aid,the ZF based and the MMSE based equalization.The CFO is set to [-0.10.1;0.1-0.1]in Fig.3.With the proposed

Fig.2.Impact of the number of users on the normalized MSE of

CFOs Fig.3.BER performances of semi-blind equalization structures with CFO, in comparison to ZF and MMSE based equalization in the perfect

case Fig.4.Impact of frame size on BER performances of pilot aided and precoding aided semi-blind equalization structures

estimation and compensation,the pilot aided method, close to the ZF based and the MMSE based equalization CFO,and signi?cantly outperforms the precoding

method with optimum selection of precoding constant 0.25in[6],showing the effectiveness of our proposed

in ambiguity elimination.In Fig.4,the precoding

method is shown to be very sensitive to the change frame length from small to medium size,while the pilot method keeps constant at both SNR=10dB and20dB.

the precoding aided approach is related to a statistics, great number of symbols are required to eliminate ambiguity Thus,the precoding aided method has a good BER

only when the frame is large enough.

VII.C ONCLUSION

In this paper,we have proposed a CFO estimation approach and a pilot aided ICA based semi-blind equalization structure multiuser-CoMP OFDM systems.Based on the property orthogonal sequences,the multiple CFOs are separated estimated simultaneously.The multi-dimensional search divided into a serial of one-dimensional searches with lower and higher accuracy.Utilizing the cross-correlation

the original and equalized pilot symbols,the per-

and phase ambiguities due to the ICA model are

simultaneously,without increasing the computational The BER performance of the proposed pilot-aided

equalization structure is not only better than that of precoding aided scheme[6],but is also close to the ideal with perfect CSI and no CFO.

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