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On the transmitter-based preprocessing for 2-D OFDM-CDMA forward-link systems over time-varying Rayleigh fading channels

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1968 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 3, MAY 2008

Fig. 5. Effect of the pilot placement with M = 2 (200-Hz Doppler frequency).

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[9] J. Gao and H. Liu, “Decision-directed estimation of MIMO time-varying Rayleigh fading channels,” IEEE Trans. Wireless Commun., vol. 4, no. 4, pp. 1412–1417, Jul. 2005.

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On the Transmitter-Based Preprocessing for 2-D OFDM-CDMA Forward-Link Systems Over Time-Varying Rayleigh Fading Channels

Chih-Cheng Kuo, Student Member, IEEE,

Wern-Ho Sheen, Member, IEEE, Chung-Ju Chang, Fellow, IEEE, and Chang Lung Hsiao, Member, IEEE

Abstract—Transmitter-based preprocessing is investigated for 2-D

or-thogonal frequency-division multiplexing code-division multiple-access (OFDM-CDMA) forward-link systems for improving performance and shifting signal processing complexity from a mobile unit to a base station. Preprocessing schemes that are based on zero forcing (ZF) with power normalization, minimum mean square error (MMSE), and ZF with mul-tiuser water filling (ZF-MWF) criteria are jointly investigated with 2-D spreading pattern optimization and multiuser scheduling from an informa-tion-theoretic viewpoint. Numerical results show that 1) the performance of preprocessing is quite sensitive to the 2-D spreading pattern for SNRs of interest, for example, 20% degradation on the sum data rate is observed for MMSE preprocessing if the spreading pattern is not properly selected; 2) ZF-MWF may substantially outperform the other two criteria de-pending on the SNRs; and 3) multiuser scheduling provides a significant performance improvement on the system sum data rate.

Index Terms—Forward-link systems, sum data rate, transmitter

pre-processing, two-dimensional (2-D) orthogonal frequency-division multi-plexing code-division multiple access (OFDM-CDMA).

I. INTRODUCTION

Orthogonal frequency-division multiplexing code-division multiple access (OFDM-CDMA) is a promising radio access technology for the next-generation mobile communication systems thanks to its ability to overcome intersymbol interference that is incurred in high-data-rate transmission, its ability to provide universal frequency reuse in a multicell environment, and its ability to achieve high-order diversity gain by spreading data over frequency and time domains [1]–[5]. Traditionally, OFDM and CDMA are combined in a 1-D fashion, that is, a data symbol is spread either in frequency or time domain (see [1] and references therein). Recently, 2-D OFDM-CDMA, where data are spread over time and frequency domains, has been proposed to improve the performance of the 1-D one by simultaneously exploiting the temporal and spectral characteristics of the fading channels [2]–[5]. Transmitter-based preprocessing, on the other hand, has been pro-posed for improving performance and shifting signal processing com-plexity from a mobile unit to a base station in mobile communication systems [6]–[13]. Zero forcing (ZF) [6], [7] and prerake [8], [9] preprocessing methods with a different degree of receiver complexity were proposed for direct-sequence CDMA (DS-CDMA) systems. In addition, transmitter preprocessing schemes that are based on the MMSE [11], [13] or ZF [10]–[12] were investigated for broadcast multiple-input–multiple-output (MIMO) systems.

This paper aims to design 2-D OFDM-CDMA forward-link systems with transmitter preprocessing to improve system performance. Three preprocessing methods, including ZF with power normalization (ZF-PN), the MMSE, and ZF with multiuser water filling (ZF-MWF), Manuscript received August 7, 2006; revised June 11, 2007, July 10, 2007, and August 13, 2007. The review of this paper was coordinated by Prof. J. Choi. The authors are with the Department of Communication Engineering, National Chiao Tung University, Hsinchu 300, Taiwan, R.O.C. (e-mail: cckuo. cm90g@nctu.edu.tw; whsheen@cm.nctu.edu.tw; cjchang@cc.nctu.edu.tw; clhsiao@itri.org.tw).

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2007.909256 0018-9545/$25.00 © 2008 IEEE

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Fig. 1. RRUs.

are jointly investigated with spreading pattern optimization and multi-user scheduling from an information-theoretic viewpoint. An ergodic sum data rate serves as the performance index for performance com-parisons under the assumption of perfect channel state information (CSI). Numerical results are given to illustrate the superiority of ZF-MWF over the other two methods, the key role that the spreading pattern plays to the system sum data rate, and the performance gain that is obtained through multiuser scheduling.

The rest of this paper is organized as follows. Section II describes the system model. Section III derives the considered transmitter preprocessing methods. Section IV gives the numerical results, and finally, conclusions are given in Section V.

II. SYSTEMMODEL

A. RRUs

To apply 2-D spreading, the time–frequency radio resource in a data frame is divided into nonoverlapped gf× gt rectangular radio

resource units (RRUs), as shown in Fig. 1, where gf and gt are

the frequency- and time-domain spreading factors, respectively. G 

gf × gt> 1 is the overall spreading factor. In an RRU, subcarriers

and OFDM symbols are assumed to be adjacent to each other. Users with the same overall spreading factor can share an RRU in a code-division fashion, and users with different overall spreading factors utilize different RRUs. Since RRUs are nonoverlapped, without loss of generality, only one RRU will be explicitly treated in the rest of this paper. Note that for gt= 1, the system degenerates to the

multicarrier CDMA (MC-CDMA) system, and for gf = 1, the system

degenerates to the multicarrier DS-CDMA (MC-DS-CDMA) system that is described in [1]; MC-CDMA and MC-DS-CDMA are special cases of the considered 2-D OFDM-CDMA system.

Different spreading patterns, which are characterized by the pair (gf, gt), can be employed for a particular G. Fig. 2 depicts such

possibilities for G = 16 with different selections of gf and gt. For

example, (gf = 2, gt= 8) and (gf = 4, gt= 4) are two legitimate

spreading patterns. Different spreading patterns result in different performance, depending on the frequency and time selectivity of the channel, as will be shown in Section IV. In fact, how the spreading

Fig. 2. Example of spreading patterns.

patterns perform against each other for a fixed G is one of the issues that interest us in this paper.

Let G also denote the number of users sharing an RRU. (Recall that

G is the overall spreading factor.) In a data frame, with orthogonal

spreading codes, an RRU can be simultaneously shared by all the

G users in a code-division fashion, i.e., one code for each user (the

single-code case), or the RRU can be shared by the G users in a time-division fashion, i.e., some users are scheduled to transmit in a frame, and others are scheduled in other frames. In a time-varying fading environment, by scheduling those users who are in a good channel condition in a particular frame, one can take advantage of multiuser diversity to increase the system throughput [11]. In this paper, to investigate the multiuser diversity gain, we allow K  G users to be scheduled in a frame. For that case, each scheduled user utilizes G/K spreading codes (the multicode case) for data transmission, where

G/K is a positive integer. B. Channel Model

A discrete-time wide-sense stationary uncorrelated scattering Rayleigh channel is considered. The complex equivalent low-pass response for the ith user is given by

h(i)(t; τ ) =

L



l=0

h(i)l (t)δ(τ− lTs), i = 1, . . . , K (1)

where h(i)l (t) is the lth path gain, δ(·) is the Dirac delta function,

lTs is the propagation delay for the lth path, Ts is the sampling

duration of the system, and K is the number of scheduled users.

h(i)l (t) is a complex Gaussian variable with zero mean and variance

σ2

l,{h

(i)

l (t)} L

l=0are independent for different l’s, and users experience

independent identically distributed (i.i.d.) channel characteristics. The channel is assumed to remain constant over an OFDM symbol and to vary symbol-by-symbol based on the channel time variation.

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1970 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 3, MAY 2008

Fig. 3. (a) Transmitter. (b) Receiver. Thus, (1) can be simplified as

h(i)(n; τ ) =

L



l=0

h(i)l (n)δ(τ− lTs), i = 1, . . . , K (2)

where n is the OFDM symbol index. Furthermore, the power delay profile of the multipath channel follows the exponential decay model

σ2

l = σ

2

0· exp(−10l/L), l = 1, 2, . . . , L (3) with σ2

0 = 1− exp(−10/L), and it leads to the unit of total power. Last, the Clarke 2-D isotropic scattering model for{h(i)l (n)} will be used to model the time variation of channels in this paper [14].

C. Transmitter and Receiver

The transmitter of the considered OFDM-CDMA forward-link system is sketched in Fig. 3(a). Recall that only one RRU will be explicitly treated. The lth data symbol of user i, i.e., s(i)l ,

i = 1, . . . , K, l = 1, . . . , G/K is first spread over time and

frequency domains by a 2-D spreading code c(i)m,n(l), m = 1, . . . , gf, n = 1, . . . , gt, and the spreading chip is preprocessed by multiplying

the complex-valued gain p(i)m,n(l). The respective chips from all data

symbols in an RRU are summed together before being allocated to the time–frequency plane, which is done, along with chips from other RRUs, by time–frequency mapping. Last, the inverse fast Fourier transform (IFFT) is performed on the allocated chips, and these chips are sent for further operations such as parallel-to-serial

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conversion, cyclic-prefix insertion, and analog/RF front-end processing.

As shown in Fig. 3(b), at the receive end of the ith user, after RF/analog processing, synchronization, cyclic-prefix removal, and serial-to-parallel conversion, the fast Fourier transform (FFT) and time–frequency demapping are performed on the received signal. The demapped chips of the considered RRU are passed through simple 2-D despreading because most of the signal processing has been shifted to the base station. The despread signals are then forwarded for further demodulation and/or decoding.

D. Signal Models

For notational simplicity, only the single-code case, i.e., K = G, one spreading code for each user, is explicitly treated in this section. The extension to the case of multicodes is straightforward. Assuming that the cyclic prefix is larger than the maximum delay spread, and perfect frequency/time synchronization is achieved at the receiver, then the demapped signal of the (m, n)th chip of the ith user is given by

r(i) m,n(1) =  G  j=1 s(j)1 p(j) m,n(1)c (j) m,n(1)  H(i) m,n+ N (i) m,n m = 1, . . . , gf, n = 1, . . . , gt, i = 1, . . . , G (4) where Hm,n(i) = L  l=0 h(i)l (n)e−j2πlmNFFT (5)

is the frequency-domain channel gain, NFFTis the size of IFFT/FFT, and Nm,n(i) is a Gaussian variable with zero mean and variance σN2.

For convenience, we rearrange the 2-D chip index (m, n) into the 1-D one by using k = (n− 1)gf+ m, n = 1, . . . , gt, m = 1, . . . , gf,

and it leads to k = 1, . . . , G. With this new indexing notation and (4),

r(i)1 can be rewritten as the following matrix form:

r(i)1 =. 

r(i)1 (1),· · · , r(i)k (1),· · · , rG(i)(1) T = H(i)(P C)s + n(i) (6) where P = [p(1), . . . , p(G)], p(j)= [p(j) 1 (1), . . . , p (j) G(1)] T, s = [s(1)1 , . . . , s(G)1 ]T, n(i)= [N(i) 1 , . . . , N (i) G ] T, C = [c(1), . . . , c(G)], c(j)= [c(j) 1 (1), . . . , c (j) G (1)]

T, and H(i) is a diagonal matrix with

elements{H1(i), . . . , HG(i)}.  and [·]Tdenote the Hadamard product

(element-by-element multiplication) and the operation of transpose of a vector and/or a matrix, respectively, s is the symbol vector with the covariance matrix σ2

sIG, n(i)is a complex Gaussian vector with

the covariance matrix σ2

NIG, σs2 is the transmit signal power, σ2N

is the noise power for each chip, and IG is the identity matrix of

dimension G.

Let d(i)1 be the decision variable of the ith user. Then

d(i)1

.

= c(i)Hr(i)1 = c (i)H

H(i)(P C)s + c(i)Hn(i) (7) where [·]H is the conjugate transpose operation, and{c(i)Hn(i)}G

i=1

are i.i.d. Gaussian variables, provided that orthogonal codes are used.

III. TRANSMITTERPREPROCESSING

For a multiple-access system, the sum data rate is the maximum data rate of all users supported by the system from an information-theoretic viewpoint [11, ch. 6 and 8]. The sum data rate will be adopted here as the performance index for the design and the comparison of different preprocessing methods.

From (7), the decision variable for the ith user can be rewritten as

d(i)1 = c(i)HH(i)p(i) c(i)s(i) 1  desired signal + G  j=1,j=i c(i)HH(i)p(j) c(j)s(j) 1  MAI + c(i)Hn(i)  noise . (8)

The multiple-access interference (MAI) term can be approximated as a zero-mean Gaussian variable under the assumption of large G [11]. Therefore, the achievable maximum reliable data rate C(i)for the ith user, given H(i), is presented by (9), shown at the bottom of the page [11], where q(i)= p(i) c(i), andc(i)2= 1 for i = 1, 2, . . . , G. As a result, the sum data rate C, which is the sum of the individual rates, is obtained by (10), shown at the bottom of the page.

With the performance index in (10), our problem becomes finding the set of optimum preprocessing weight vectors{ q(i)}, for a given

C(i)= 1 Glog2            1 + E 

c(i)HH(i)q(i)s(i) 1  2 E    G  j=1,j=i c(i)H H(i)q(j)s(j) 1 + c(i) H n(i) 2            b/s/Hz (9) C = G  i=1 C(i)= 1 G G  i=1 log2          1 + σ 2 s· q(i) H

H(i)Hc(i)c(i)HH(i)q(i)

σ2 s G  j=1,j=i q(j)H H(i)H c(i)c(i)H H(i)q(j)+ σ2 N          (10)

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1972 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 3, MAY 2008

{H(i)}, to obtain the maximum sum data rate by solving the following constrained optimization problem:

{ q(i)} = arg  max {q(i)}C  , s.t. G  i=1 q(i)2= G. (11) After obtaining the sum data rate for a particular{H(i)}, the average sum data rate, called the ergodic sum data rate in [11, ch. 6 and 8], is evaluated by Cerg= E[C], where the expectation is taken over all channels{H(i)}.

The following investigates three transmitter preprocessing methods based on ZF-PN, MMSE, and ZF-MWF criteria under the perfect knowledge of CSI of every user. Since the optimization formulation in (10) and (11) is similar to the one investigated in [11] and [12] for MIMO systems, only sketches of the derivations are given here.

A. ZF-PN

The basic idea of this method is to completely eliminate the MAI at the outputs of despreading of each user by properly choosing the transmitter preprocessing matrix Q = P C at the base station under the power constraint given in (11).

Define d to be the aggregated decision variables from all users. From (7) d=.   d(1)1 .. . d(G)1  =   c(1)H H(1)Qs + c(1)H n(1) .. . c(G)H H(G)Qs + c(G)H n(G)   =  c (1)H H(1) .. . c(G)H H(G)  Qs +  c (1)H n(1) .. . c(G)H n(G)   = RQs  signal + n noise (12) where R =  c (1)H H(1) .. . c(G)H H(G)   n =  c (1)H n(1) .. . c(G)H n(G)  .

With zero MAI, RQs = s, which results in!

!

Q = RH(RRH)−1= R. + (13) where R+is the right pseudoinverse of matrix R. On the other hand, according to (11), the total transmit power needs to be normalized to

σ2

sG, that is, E[Qs 2] = σs2· G. Therefore,Q =

GR+/R+

F

[6], where · F stands for the Frobenius norm of a matrix.

B. MMSE

In this method,Q is selected to minimize the MSE between the

decision vector d and the transmitted symbol vector s under fixed transmit power. The associated constrained optimization problem can be formulated as follows: Q = arg  min Q E " d−s2#, s.t.Q2 F= tr{Q HQ}=G (14) where E"d − s2#= E"RQs + n − s2# = σ2 str $" QHRH− I G # [RQ− IG] % + Gσ2 N. (15) Therefore, (14) can be rewritten as

Q = arg  min Q tr $" QHRH− IG # [RQ− IG] % s.t.Q2 F = tr{Q HQ} = G. (16)

By applying the theory of Lagrange multiplier to solve the above constrained optimization problem, the solution is [13]

Q = (RHR + λ· I

G)−1RH (17)

and λ satisfiesGi=1(λi/( λ + λi)2) = G, where{λi} are the

eigen-values of the matrix RHR.

C. ZF-MWF

In this method, multiuser water filling is exploited to improve the performance of ZF-PN. This is done in two steps. First, the desired signal power for each user is maximized under the condition of zero MAI. It is equivalent to finding a set of{!q(i)} such that

!

q(i)= arg 

max

q(i) q

(i)HH(i)Hc(i)c(i)HH(i)q(i)  s.t. q(i) G & j=1,j=i N ' H(j)Hc(j)c(j)HH(j)(∀I (18) where N{A} denotes the null space of the matrix A, and ∩ is the operation of intersection. Using{!q(i)} obtained in (18), the sum data rate in (10) becomes C = 1 G G  i=1 log2 ) 1 +σ 2 sα(i)!q(i) 2 σ2 N * (19)

where α(i)is a function of{H(i)} and can be viewed as the equivalent channel power gain that is experienced by the ith user [11], [12]. Second, the principle of multiuser water filling is applied in (19) to obtain the maximum sum data rate. That is, we are seeking

'  q(i)2 ( = arg     '!maxq(i)2 ( G  i=1 log2  1+σ 2 sα(i)!q(i) 2 σ2 N    s.t. G  i=1 !q(i)2= G. (20) Again, by applying the theory of Lagrange multiplier, it can be shown that  q(i)2=  1 + 1 G G  j=1 σ2 N σ2 sα(j) σN2 σ2 sα(i) + ∀i (21) where [x]+= max{x, 0}.

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TABLE I SYSTEMPARAMETERS

IV. NUMERICALRESULTS

This section presents and compares the ergodic sum data rate of the considered preprocessing methods. The system parameters are summarized in Table I. Recall that there are a total of G users in the system; however, they may not all be scheduled to transmit in a frame.

K G denotes the actual number of scheduled users. For K < G, G/K codes are allocated to each user (multicode transmission), and

the system can exploit the multiuser diversity gain to increase the sum data rate. The user scheduling is performed on a frame-by-frame basis. As given in Table I, a frame-by-frame consists of 64 OFDM symbols. The Hadamard–Walsh orthogonal codes are used throughout this paper.

In Table I, ∆f /Bcand TOFDM/Tcare defined as the normalized

frequency and time selectivity, respectively, where Bcis the coherent

bandwidth, and Tcis the coherent time of the channel. In this paper, Bc= 1/(50στ), and Tc= 1/(50fD), where στ is the

root-mean-square delay spread, and fD is the maximum Doppler spread of the

channel [14]. By changing the path number L and fD, we can obtain

the desirable frequency and time selectivity designated in Table I. For example, L = 7, 13, and 26 correspond to ∆f /Bc= 1/8, 1/4, and

1/2, and fD= 250, 500, and 1000 Hz correspond to TOFDM/Tc=

1/8, 1/4, and 1/2, respectively. The number of channel samples that are used to evaluate the ergodic sum data rate is over 20 000.

Fig. 4 shows an example effect of spreading patterns on the performance of the preprocessing methods for the case of SNR = 29 dB. Similar results are observed for other SNRs. Obviously, the best spread pattern is the one that reduces the channel selectivity in time and frequency domains. In other words, the spread pattern has to be selected to reduce the MAI for better performance. In this example, gf = 4, gt= 4 is the optimum one, regardless of the channel

selectivity. The loss in the ergodic sum data rate can be quite large if the spreading pattern is not properly selected; for example, over 20% loss is observed for MMSE preprocessing. Also shown in the figure is that the channel selectivity degrades system capacity; the degradation is the most significant for MMSE preprocessing.

Fig. 5 compares the ergodic sum data rates for different SNRs in selective channels with K = 16. Frequency-domain spreading with two values of the channel selectivity, that is, ∆f /Bc= 1/4 and 1/2,

is used as the example. As shown in the figure, the channel selectivity

Fig. 4. Example effects of spreading patterns on the ergodic sum data rate with different degrees of selectivity with σ2

s/σN2 = 29 dB.

Fig. 5. Comparisons of the ergodic sum data rate for different preprocessing methods with ∆f /Bc= 1/4 and ∆f /Bc= 1/2.

decreases the ergodic sum data rate; the more severe the channel selectivity, the smaller the ergodic sum data rate. This phenomenon is more prominent for the MMSE in the high SNR region because in the MMSE, there is a residual MAI, which becomes more dominant in performance at the high SNR region. The ZF-MWF could significantly outperform the other two criteria, depending on the channel selectivity, and the operating SNR. ZF-PN performs less favorably than the other two criteria in the low SNR region. Nevertheless, it outperforms the MMSE in the high SNR region where the MAI is the dominant factor.

Fig. 6 shows the performance of the ergodic sum data rate for the nonselective channel with a different number of scheduled users. For comparison purposes, the sum data rate for the additive white Gaussian noise (AWGN) channel is also included in the figure. Clearly, for K 8, a higher ergodic sum data rate is obtained for fading channels than that for the AWGN case because of the exploitation of the multiuser diversity. Nevertheless, the advantage of the multiuser diversity diminishes as the number of scheduled users becomes larger.

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1974 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 3, MAY 2008

Fig. 6. Ergodic sum data rate of ZF-MWF for nonselective channels with multiuser scheduling.

In fact, for K = 16, the ergodic sum data rate of the fading channel is less than that of the AWGN channel, except for very low SNRs.

V. CONCLUSION

Different transmitter-based preprocessing methods are jointly inves-tigated with spreading pattern optimization and multiuser scheduling for the 2-D OFDM-CDMA forward-link systems from an information-theoretic viewpoint. The ergodic sum data rate serves as the perfor-mance index for perforperfor-mance comparisons under the assumption of perfect CSI. Examples are given to illustrate the important issue of spreading pattern optimization. ZF-MWF performs the best among the preprocessing methods that were investigated, including ZF and the MMSE. Moreover, as expected, multiuser scheduling gives a significant performance improvement.

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Interpretation of MIMO Channel Characteristics in Rectangular Tunnels From Modal Theory J. M. Molina-Garcia-Pardo, Member, IEEE, Martine Lienard, Pierre Degauque, Member, IEEE, Donald G. Dudley, Fellow, IEEE,

and L. Juan-Llacer, Senior Member, IEEE

Abstract—We develop a modal approach for analyzing multiple-input–

multiple-output (MIMO) wireless channel propagation in a tunnel with lossy walls. We use parametric methods to study the effects of the number of modes and of the separation among antennas. We evaluate the perfor-mance of the MIMO channel in terms of capacity as a function of range and tunnel size.

Index Terms—Modal theory, modes, multiple-input–multiple-output

(MIMO), propagation in tunnels, ray tracing.

I. INTRODUCTION

This paper builds on the information-theoretic result that multiple-input–multiple-output (MIMO) channels offer a substantial improve-ment over a single channel. Specifically, the Foschini–Telatar MIMO model [1], [2] predicts a dramatic increase in channel capacity over the Shannon single-channel capacity [3, Ch. 11]. An overview of MIMO wireless communications is provided in [4] and [5]. In addition, the ideas have been explored in depth in [6]. Our application of MIMO

Manuscript received January 17, 2006; revised January 30, 2007, June 28, 2007, and August 28, 2007. The work of J. M. Molina-Garcia-Pardo at the University of Lille was supported by the Universidad Politecnica de Cartagena. This work was supported in part by Pole Sciences et Technologies pour la Secu-rite dans les Transports (Science and Technology for Safety in Transportation) and in part by the European Commission (FEDER), the French Ministry of Research, and the Region Nord Pas de Calais. The review of this paper was coordinated by Prof. A. Abdi.

J. M. Molina-Garcia-Pardo was with the Telecommunications, Interferences and Electromagnetic Compatibility (TELICE), Institut d’Electronique de Mi-croelectronique et de Nanotechnologie, University of Lille, 59655 Villeneuve d’Ascq, France. He is now with the Departamento de Technologias de la Información y la Comunicaciones, Technical University of Cartagena, 30202 Cartagena, Spain (e-mail: josemariamolina@upct.es).

M. Lienard and P. Degauque are with the Telecommunications, Interferences and Electromagnetic Compatibility (TELICE), Institut d’Electronique de Mi-croelectronique et de Nanotechnologie, University of Lille, 59655 Villeneuve d’Ascq, France (e-mail: Martine.Lienard@univ-lille1.fr).

D. G. Dudley, deceased, was with the Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ 85721 USA.

L. Juan-Llacer is with the Departamento de Technologias de la Información y la Comunicaciones, Technical University of Cartagena, 30202 Cartagena, Spain.

Digital Object Identifier 10.1109/TVT.2007.913177 0018-9545/$25.00 © 2008 IEEE

數據

Fig. 5. Effect of the pilot placement with M = 2 (200-Hz Doppler frequency).
Fig. 1. RRUs.
Fig. 3. (a) Transmitter. (b) Receiver. Thus, (1) can be simplified as
TABLE I S YSTEM P ARAMETERS
+2

參考文獻

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