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On Modelling Cellular Interference for Multi-Carrier based Communication Systems Including a Synchronization Offset Gunther Auer

Armin Dammann, Stephan Sand, Stefan Kaiser

DoCoMo Euro-Labs, Landsberger Str. 312, 80687 M¨unchen, Germany. Email: [email protected]

German Aerospace Center (DLR), Institute of Communications & Navigation, 82234 Wessling, Germany.

Abstract— We address the downlink of a cellular multi-carrier CDMA (MC-CDMA) system. The nature of celluar interference is dependent on the synchronization mismatch between interfering base stations (BS). For an unsynchronized system the interference observed at a certain subcarrier stems from all interfering subcarriers, so the interference can be modeled as white Gaussian noise. For a perfectly synchronized system, on the other hand, orthogonality between subcarriers is preserved and the interference can be described on the subcarrier level, which may not be Gaussian. In this paper the performance of a cellular MC-CDMA system is analysed in the presence of a synchronization offset between two interfering BS. Furthermore, models to simplify the simulation of interference are examined.

approximate the entire signal received from an interfering BS by WGN, known as Gaussian approximation (GA). A more sophistiated model is obtained, by separating the received signal after OFDM demodulation into two parts, an ICI part modeled by WGN and a remaining signal part, the cellular system can be modeled in the frequency domain. The outline of the paper is as follows: after introducing the cellular MC-CDMA system to be analysed in section II; section III discusses models to describe cellular interference in the frequency domain; and simulation results are presented in section IV.

I. I NTRODUCTION

II. S YSTEM & C HANNEL M ODEL

Multi-carrier modulation, in particular orthogonal frequency division multiplexing (OFDM) [1], has been successfully applied to various digital communications systems. OFDM can be efficiently implemented by using the discrete Fourier transform (DFT). Furthermore, for the transmission of high data rates its robustness in transmission through dispersive channels is a major advantage. For multi-carrier CDMA (MCCDMA), spreading in frequency and/or time direction is introduced in addition to the OFDM modulation [2–4]. MC-CDMA has been deemed a promising candidate for the downlink of future mobile communications systems [5, 6]. If a multi-carrier based communication system, e.g. OFDM or MC-CDMA, is to be employed as a cellular system with high frequency reuse factor, the effects of the cellular interference needs to be thoroughly analysed. The nature of the cellular interference on the downlink is dependent on the synchronization offset between interfering base stations (BS). While for large synchronization offsets the interference can be classified as white Gaussian noise (WGN), for small synchronization offsets this may not be the case. The reason is that for large synchronization offsets inter-carrier interference (ICI) is the dominiant source of interference which is observed as WGN. For small or no synchronization offsets, the major part of the interference stems from a single subcarrier, which is in general non-Gaussian. For a perfectly synchronized MC-CDMA, orthogonality between subcarriers is preserved, and simulations can be conveniently performed in the frequency domain, i.e. the subcarrier level. Unfortunately, for a unsynchronized system this is not the case. The most simple cellular FD model is to

Fig. 1.a shows the block diagram of a MC-CDMA transmitter with Nc subcarriers for Nu users. The bit stream for each user is encoded with a convolutional code, bit interleaved by the outer interleaver πout , and fed to the symbol mapper. The symbol mapper assigns the bits to complex-valued data symbols according to different alphabets, like PSK or QAM with the chosen cardinality. A serial-to-parallel converter allocates the modulated signals to Nd ≤ Nc /L data symbols per user. If Nd = Nc /L, all available subcarriers are assigned to this data stream. Alternatively, other independent data streams, termed user groups in [4], may be accommodated in case that Nd < Nc /L. Subsequently, each of the Nd data symbols is spread with a Walsh-Hadamard sequence of length L ≥ Nu . Given the vector, dk = [d(k1 ) , · · · , d(kNu ) ]T , consisting of the k th symbol of all users, the spreading operation results in sk = CL dk , ∈ CL , 1 ≤ k ≤ Nd

(1)

where CL represents a L × Nu spreading matrix. The system load of the MC-CDMA system is Nu /L, and can be adjusted between 1 and 1/L. Subsequently, the block s = [s1 , · · · , sNd ]T is frequency interleaved by the inner interleaver πin over one OFDM symbol to maximize the diversity gain. We choose a randome interleaver for πin . The interleaved symbol of the `th OFDM symbol, at subcarrier i, is denoted by X`,i . One frame consists of Nframe OFDM symbols, each having Nc subcarriers. If Nd < Nc /L, the free subcarriers are assigned to symbols from other independent data streams, such that all subcarriers are equally loaded. In order to destinguish signals from different BS and to further randomize the transmitted signal, X`,i is scrambled by a cell specific

SF

Nc

(0)

Sync Off

(0)

h (τ,t)

(0)

(0)

xl,n

h (τ,t)

yl,n OFDM Demod

DeScr

Yl,i

1/∆E

(I)

(I)

(I)

Fig. 2.

OFDM Mod

(I)

...

...

Scr

Sync Off

Block diagram of the cellular MC-CDMA system.

(0) ˜ ( 0 ) = p( 0 ) X`,i . The scrambler random sequence, p`,i , to yield X `,i `,i has caridinality Ms , and the Ms discrete singal points are chosen according to a PSK constellation. An inverse DFT with NFFT ≥ Nc points is performed on each block, to yield the time (0) ˜ ( 0 ) }, and subsequently a guard domain signal x`,n = IDFT{X `,i interval (GI) having NGI samples is inserted, in the form of a cyclic prefix.

A. Describing cellular interference including a carrier frequency offset A block diagram of the downlink of the considered cellular MC-CDMA system is shown in Fig. 2. After D/A conversion, the transmitted signal of BS m, x( m ) (t) is propagating through a mobile radio channel with response h( m ) (t, τ ). We assume accurate timing synchronization, i.e. the guard interval exeeds the timing offset plus the maximum delay of the channel [7]. Define the carrier frequency offset between the local oscillators of BS m and the mobile by ∆f ( m ) . Then the received signal of the equivalent baseband system at sampling instants t = [n + `Nsym ]Tspl is the superposition of signals received from NBS BS, is given by NBS X (m) 4 ( m ) j2πnTspl ∆f z`,n e +n`,n (2) y`,n = y([n+`Nsym ]Tspl ) = m=1

where n`,n represents a sample of additive white Gaussian noise (AWGN), Nsym = NFFT +NGI accounts for the number of samples per OFDM symbol, and Tspl is the sampling duration. The received signal of BS m, can be expressed as ¯ Z ∞ ¯ (m) z`,n = h( m ) (t, τ ) · x( m ) (t − τ ) dτ ¯¯ (3) −∞

1

Yl,Nc

π−1 in Nc

DET

DET

Demap

π−1 out

LLR calc

Channel decoding

user 1

Demap

π−1 out

LLR calc

Channel decoding

user Nu

1 SF

Nc

Block diagram of the MC-CDMA system, (a.) transmitter, (b.) receiver. nl,n

Interfering Signal

Xl,i

Xl,Nc

(0)

Scr

...

...

Xl,i

xl,n

Spread

Yl,1

...

sym mapper

πin

(b.) ...

MUX

Fig. 1.

OFDM Mod

Spread ...

πout

Channel Coding

user Nu

Xl,1

1

sym mapper

...

πout

Channel Coding

user 1

DMUX

(a.)

t=[n+`Nsym ]Tspl

We limit our discussion to one interfering BS, so NBS = 2. The signal components corresponding to the desired and interfering BS will marked by the superscript (0) and (I), respectively. The signal from the desired and interfering BS are received with energy per symbol of Es and Es /∆E, respectively. So, ∆E accounts for the difference in received signal power between the two interfering BS. After sampling the guard interval is removed and a DFT on the received block of NFFT signal samples is performed, ˜ to obtain © ªthe output of the OFDM demodulation Y`,i = DFT y`,n . The last NFFT −Nc DFT outputs of Y˜`,i contain

zero subcarriers which are dismissed. Subsequently, the cell 0) ∗ ˜ specific scrambling sequence is removed, Y`,i = p(`,i Y`,i . We assume the guard interval to be longer than the maximum delay of the channel including a possible the timing synchronization offset. Assuming perfect synchronization for the moment, the received signal after OFDM demodulation of OFDM symbol ` at subcarrier i is in the form 0) ∗ I) p(`,i · p(`,i (I ) (I ) (0) (0) X`,i H`,i + N`,i (4) Y`,i = X`,i H`,i + √ ∆E (·) (·) where X`,i , H`,i , and N`,i , denote the transmitted symbol, the channel transfer function (CTF), and AWGN with zero mean and variance N0 . B. Data detection A block diagram of a MC-CDMA receiver after OFDM demodulation is depicted in Fig. 1.b. After deinterleaving with the inner interleaver πin the vector rk = [rk,1 , · · · , rk,L ]T is obtained, containing the k th spread symbols of the Nu users. The detector comprises a linear MMSE one tap equalizer and the despreader, yielding the received data vector b k = CH G rk ∈ CNu d (5) L

The MMSE equalizer G is a diagonal matrix with entries H (0) ³ `,i ´ Gi,i = (6) (0) 2 (0) 2 0 + σ( I ) 2 |H`,i | + NLu · N Es + σICI (0) 2 The quatities σICI and σ ( I ) 2 = Es /∆E denote the ICI power due to a synchronization offset and the power of the interfering signal, respectively. In case of vanishing interference and (0) disappear and the perfect synchronization, both σ ( I ) and σICI standard MMSE equalizer is obtained [4]. Subsequently, all data symbols of the desired user, db(k1 ) , are combined to a serial data stream. The symbol demapper maps the data symbols into bits, by also calculating the LogLikelihood-ratio (LLR) for each bit, based on the selected alphabet. The codebits are deinterleaved and finally decoded using soft decision algorithms [4].

C. Channel model We consider a time-variant, frequency selective fading channel, modeled by a tapped delay line with Q0 non-zero taps [8]. The channel impulse response (CIR) is defined by h( m ) (t, τ ) =

Q0 X

h(qm ) (t) · δ(τ − τq( m ) ) ,

m = {0, I}

(7)

q=1

where h(qm ) (t) and τq( m ) are the complex amplitude and delay of the q th channel tap. It is assumed that the Q0 channel taps are mutually uncorrelated. Due to the motion of the moblile h(qm ) (t) will be time-variant caused by the Doppler effect,

being band-limited by the maximum Doppler frequency νmax . However, the channel impulse response (CIR) needs to be m) approximately constant during one OFDM symbol, so h(`,q = (m) (m) th hq (`Tsym ). The channel of the q tap, h`,q , impinging with time delay τq( m ) , is a wide sense stationary (WSS), complex Gaussian random variable. We consider two cases, a channel with line of sight (LoS) and without. Without LoS all Q0 channel taps are zero mean and the Rayleigh fading channel is m) obtained. With LoS part the first channel tap h(`,1 is assumed to (m) be Ricean distributed. That is, h`,1 consists of a constant part ¯ ( m ) = E{h( m ) } and a Rayleigh fading part h0 ( m ) , such that h `,1 `,1 `,1 m) ¯ ( m ) +h0 ( m ) . The ratio between constant and Rayleigh =h h(`,1 `,1 `,1 fading part is defined by © (m) 2ª ¯ | E |h 4 `,1 K = © 0(m) 2ª (8) E |h`,1 | m) In any case, for all other taps h(`,q is assumed to be zero mean. The CTF is the Fourier transform of the CIR. Sampling the result at time t = `Tsym and frequency f = i/T , the CTF becomes Q0 X (m) (m) m ) −j2π τq i/T H`,i = H ( m ) (`Tsym , i/T ) = h(`,q e (9)

q=1

where Tsym = (NFFT +NGI )Tspl and T = NFFT Tspl represents the OFDM symbol duration with and without the guard interval. III. M ODELLING C ELLULAR I NTERFERENCE IN THE F REQUENCY D OMAIN For simulation purposes, the notation for the perfectly synchronized system from (4) motivates a simplified implementation of the MC-CDMA sytem. Instead of computing (m) a convolution of the time domain signal z`,n in (3), the (m) (m) (m) equivalent frequency domain signal Z`,i = X`,i H`,i can be computed direcly by using (9). A. Perfectly snychronized system Provided a perfectly synchronized system (4) can be direclty applied. This model does not take into account any synchronzation offset, neither between BS and mobile nor between interfering BS. This model is straightforward to implement. However, it may be insufficient to accurately model an unsynchronized system.

C. Cellular interference taking into account a carrier frequency offset Consider a signal having a carrier frequency offset between the local oscillators of the BS and the mobile. In the absence (m) of ISI (correct timing synchronization), the DFT of z`,i from (3), which represents the received signal from BS m = {0, I}, can be expressed as [7] NX c −1 (m) (m) (m) (m) (m) (m) (m) (11) Z`,i = Ji,i H`,i X`,i + Jk,i H`,k X`,k k=0 k6=i

|

{z

}

ICI

where

(m)

m) sin(π²(k,i ) ejπ²k,i 1 · (12) Jk,i = · (m) (m) jπ² /N NFFT e k,i FFT sin(π²k,i /NFFT ) accounts for the ICI from subcarriers k to i. The crosssubcarrier and subcarrier local frequency offsets are (m)

m) ²(k,i = ∆f ( m ) T + k − i

An even simpler approximation is to model the entire interference as Gaussian noise, by appropriately scaling the variance of the AWGN term. By applying the Gaussian approximation (GA) the received signal after OFDM demodulation is approximated by (10)

where η`,i denotes the resulting AWGN term having the Es Nu variance ση2 = N0 + ∆E L . Compared to the received signal of the synchronized system (I ) of (4), the Gaussian approximation is justified if Z`,i is an (I ) (I ) AWGN process, which implies that either X`,i or H`,i are (I ) Gaussian. In general this is not the case, since X`,i is randomly

(13)

The effect of a frequency offset is: first, a loss of orthogonality between subcarriers, resulting in inter-carrier interference m) (ICI); second, the amplitude of Y`,i is reduced by sinc(π²(i,i ); (m) third, a subcarrier symbol rotation proportional to ²i,i . If ∆f ( 0 ) 6= 0, i.e. there is a frequency offset between the desired BS and the moblile, the subcarrier rotation is to be tracked by the channel estimator. To efficiently simulate the effects of a carrier frequency offset, the ICI term in (11) may be modeled as WGN [7]. Thus, the received signal after OFDM demodulation including the desired and interfering signal of subcarrier i can be approximated as (0) (0) (0) 0) Y`,i ≈ Ji,i H`,i X`,i + n(ICI `,i

B. Gaussian approximation

(0) (0) Y`,i ≈ X`,i H`,i + η`,i

(I ) taken from a finite set of complex values, while H`,i is Gaussian (for Rayleigh fading) but not white, since adjacent subcarriers and OFDM symbols are strongly correlated. However, in the considered MC-CDMA system scrambling, (I ) spreading and interleaving decorrelate H`,i . So the Gaussian (I ) approximation may be sufficient, if H`,i can be sufficiently decorrelated. This model is most efficient to implement, since no information about the interfering signal apart from the averate singal strength is required.

(14)

I) p( 0 ) ∗ ·p(`,i (I ) (I ) (I ) √ + `,i (Ji,i H`,i X`,i ∆E

I) ) + n(ICI `,i

+N`,i (m)

where nICI`,i denotes an AWGN term that models the ICI, having the variance (m) 2 (m) 2 σICI = Es · (1 − |Ji,i | ),

m = {0, I}

(15)

It can be observed that for perfect synchronization ∆f ( m ) = 0, m) so (13) simplifies to ²(k,i = k −i. Then the ICI terms in (14) disappear and (4) is obtained. However, if the interference is received with a large sync offset, the ICI term of will be significant. Then, the interference is dominated by WGN and (14) approaches the Gaussian approximation of (10).

TABLE I MC-CDMA SYSTEM PARAMETERS −1

R MCC b

101.5 MHz 768 1024 268 7.4 ns 64 8 {1, 4, 8, 16} L QPSK CC 1/2 6 512

∆P: decay between adjacent taps

... ∆τ: tap spacing

Fig. 3.

time

Q0: number of non-zero taps

10

uncoded TD FD

−2

BER

B Nc NFFT NGI Tspl Nframe Ms L Nu

10

−3

10

L=8 Eb/N0 = 10 dB

coded −4

10

0

0.1

Fig. 4.

0.2

∆f⋅T

0.3

0.4

0.5

BER vs ∆f ( 0 ) T for MC-CDMA with and without coding. Eb/N0 = 10dB

νmax= 10-4 Tsym Q0=12 τmax= 177 Tspl ∆τ = 16 Tspl ∆P =1dB

The power delay profile of the used channel model

Since the ICI can be combined with the AWGN source, no further complexity is added with respect to the fully synchronized system from section III-A. IV. S IMULATION R ESULTS The bit error rate (BER) performance of the cellular MCCDMA system is evaluated by computer simulations. The system parameters of the MC-CDMA system and of the channel model were taken from [9], and are shown in Table I and Fig. 3, respectively. Perfect channel knowledge is assumed, so (9) is assumed to be known at the receiver. We assume a fully loaded system throughout the simulations, so Nu = L. The number of modulated symbols per user per OFDM symbol, Nd , was fixed to match a certain block length, independent of L. Quadrature phase shift keying (QPSK) was used for all simulations. For results with outer channel coding, a convolutional code (CC) with rate R = 1/2, memory MCC = 6 and a block length of b = 512 was chosen. All BS are using exactly the same system parameters, i.e. the same number of subcarriers Nc , spreading length L, etc. The Eb /N0 , which defines the average energy per bit divided by the average noise power of AWGN, was set to Eb /N0 = 10 dB. In figs. 4 and 5 a Rayleigh fading channel was employed. This means that all Q0 channel taps are zero mean, which corresponds to a non line of sight scenario. In order to verify the frequency domain approximation, simulation results for MC-CDMA system operating in a single cell scenario are shown in Fig. 4. The frequency domain (FD) model of (14) is compared with the full scale time domain (TD) simulation, both assuming that the interfering signal is set to zero. In Fig. 4 the BER is plotted against the carrier frequency offset, ∆f ( 0 ) normalized to the subcarrier spacing 1/T . For the uncoded case the FD curve closely matches the TD curve, i.e. the FD model accurately models the MC-CDMA system. For the coded case, however, a significant difference

−1

10

−2

BER

Bandwidth # subcarriers FFT length Guard interval (GI) length Sample duration Frame length Scrambler cardinality Spreading Factor # active users Modulation Channel coding Channel coding rate Channel coding memory Block length

10

uncoded L=1 L=4 L=8 L=16 GA

−3

10

−4

10

0

Fig. 5.

coded

5

10

∆ E [dB]

15

20

25

BER vs ∆E for a cellular MC-CDMA system with different L.

between the FD and TD simulation is observed. The accuracy of the FD model is ≤ 0.05·T , and gives a somewhat pesimistic approximation for the true system performance. The reason for the performance difference is due to the fact that the ICI is also subject to fading, i.e. if a subcarrier is in a deep fade, adjacent subcarriers are likely to fade too, which in turn reduces the ICI for that subcarrier. The FD model, on the other hand, assumes a constant average ICI power for all subcarriers, independent of the subcarrier dependent channel state. In the following, results of a 2 cell system are presented, assuming the desired BS and the mobile are perfectly synchrozized, so ∆f ( 0 ) = 0. Fig. 5 shows the BER against the difference in received signal power between the two interfering BS, ∆E, for varying spreading factors L. Curves with solid lines show results for a perfectly synchronized system. For the uncoded MC-CDMA system the performance improves with increasing L, since spreading the transmitted data over several subcarriers utilize the diversity of the frequency selective channel [4]. For the coded system, on the other hand, the performance is more or less independent on L, since the outer channel code also exploits diversity. Results for a system where the cellular interference was modeled by white Gaussian noise (WGN) with appropriate variance, i.e. the Gaussian approximation (GA), are also included in the graph and are marked by ”×”. It can be observed that the GA curves very well match the performance of the cellular system, for the coded as well as for the uncoded case. This is a somewhat unexpected result since on a link level the multiple access interference (MAI) of MC-CDMA cannot be

Rayleigh Rice, K = 10dB Rice, K = 20dB AWGN

−1

10

−2

BER

10

−3

10

−4

10

L=8 Eb/N0 = 10 dB

−5

10

−6

10

0

3

6

∆ E [dB]

9

12

15

Fig. 6. BER vs ∆E for a cellular MC-CDMA system operating in channels with different K factors. −1

10

−2

BER

10

Rayleigh K = 10dB K = 20dB AWGN GA

L=8 ∆ E = 5 dB Eb/N0 = 10 dB

−3

10

−4

10

−5

10

0

0.1

0.2

∆f

0.3

0.4

0.5

Fig. 7. BER vs ∆f ( I ) T for a two cell MC-CDMA system operating in channels with different K factors.

modeled by WGN, especially for low L. Obviously, if results for the GA and a perfectly synchronized system are equivalent, cellular interference with arbitrary synchronization offsets are accurately modeled by the GA. Since the GA accurately describes the system performance even for a fully synchronized system, the signal from the interfering BS is observed as WGN at the mobile. This means (I ) (I ) (I ) that the interfering signal, Z`,i = X`,i H`,i , is sufficiently decorrelated by the inner and outer interleavers. Note that even for L = 1 (which is OFDM) the Gaussian assumption holds. The impact on the chosen channel model on the system performance is examined in figs. 6 and 7. To investigate (I ) scenarios where H`,i is not Rayleigh fading, a line of sight (LoS) path is introduced, as described in section II-C. The strength of the LoS is scaled by the K–factor defined in (8). For vanishing K–factor the Rayleigh fading channel is obtained, while K → ∞ approaches an AWGN channel, i.e. the channel model used in the previous graphs. Note that this modification of the channel model affects the 1st channel tap only, all other channel parameters of Fig. 3 are still valid. Fig. 6 shows the BER vs ∆E of a 2 cell MC-CDMA system with L = 8, for channels with different K–factors. Clearly, the system performance improves with increasing K–factor. For K > 20 dB the BER approaches the performance of an AWGN. The difference between the sync system and the GA is seen to be dependent on the K–factor. For K < 20 dB the GA attains lower BERs than the sync system, while for K > 20 dB the

opposite is true. The difference between GA and sync system is maximum at K = 10 dB but never exeeds 1 dB. In Fig. 7 the BER is plotted against the normalized carrier frequency offset between the interfering BS and the mobile, ∆f ( I ) T . The ratio of the received signal power between desired and interfering BS was set to ∆E = 5 dB. All other system and channel parameters are the same as in the previous graph. Results of the FD model proposed in section III-C and the full scale TD simulation are plotted in solid and dashed lines, respectively. Also shown in the graph is the BER for the GA. The results for the FD and TD simulations are reasonably close. In any case, it is seen that there is only little dependency on ∆f ( I ) T . This is in line with the observations from the previous graphs which showed close match between the GA and the sync system. V. C ONCLUSIONS The performance of a celluar MC-CDMA system on the downlink has been analysed. Particularly, the impact of a synchronization offset was taken into account. While a multicarrier system is very sensitive to a frequency offset between the Tx and Rx local oscillators, a frequency offset between an interfering signal and the receiver does not have a major effect on the performance. In fact, in many cases an interfering MC-CDMA or OFDM modulated signal can be accurately approximated by white Gaussian noise. Furthermore, a simulator was examined which can model a frequency offset in the frequency domain. In order to justify the application of this FD simulator, scenarios need to be identified where interference of a perfectly synchronized system and interference modeled by Gaussian noise result in a significant difference in performance. R EFERENCES [1] S. Weinstein and P. Ebert, “Data Transmission by Frequency Division Multiplexing Using the Discrete Fourier Transform,” IEEE Transactions on Communication Technology, vol. COM-19, pp. 628–634, Oct. 1971. [2] K. Fazel and L. Papke, “On the Perfomrance of Convolutionally-Coded CDMA/OFDM for Mobile Communication Systems,” in Proc. IEEE Int. Symp. Personal, Indoor and Mobile Radio Commun. (PIMRC’93), Yokohama, Japan, pp. 468–472, Sep. 1993. [3] S. Hara and R. Prasad, “Overview of Multicarrier CDMA,” IEEE Communications Magazine, pp. 126–133, Dec. 1997. [4] S. Kaiser, Multi-Carrier CDMA Mobile Radio systems — Analysis and Optimisation of Detection, Decoding, and Channel Estimation. PhD thesis, German Aerospace Center (DLR), Oberpfaffenhofen, Germany, Jan. 1998. [5] S. Abeta, H. Atarashi, and M. Sawahashi, “Performance of Coherent Multi-Carrier/DS-CDMA and MC-CDMA for Broadband Packet Wireless Access,” IEICE Transactions on Communications, vol. E84-B, pp. 406– 414, Mar. 2001. [6] H. Atarashi, S. Abeta, and M. Sawahashi, “Broadband Packet Wireless Access Appropriate for High-Speed and High-Capacity Throughput,” in Proc. IEEE Vehic. Technol. Conf. (VTC’2001-Spring), Rhodes, Greece, May 2001. [7] M. Speth, S. Fechtel, G. Fock, and H. Meyr, “Optimum Receiver Design for Wireless Broad-Band Systems Using OFDM—Part I,” IEEE Trans. Commun., vol. COM-47, pp. 1668–1677, Nov. 1999. [8] J. G. Proakis, Digital Communications. New York: McGraw-Hill, NY, USA, 3rd ed., 1995. [9] H. Atarashi, N. Maeda, S. Abeta, and M. Sawahashi, “Broadband Packet Wireless Access Based on VSF-OFCDM and MC/DS-CDMA,” in Proc. IEEE Intern. Symp. Personal, Indoor and Mobile Radio Commun. (PIMRC 2002), Lisbon , Portugal, pp. 992–996, Sep. 2002.