Performance of hybrid OCA-FD/CDMA for cellular mobile communications

J. Lee R. Tafazol I i B.G.Evans

Indexing terms: FDICDMA, Overlapped carriers, Edang capacity, Adjacent carrier, E&,

Abstract: The performance is investigated of cellular hybrid FD/CDMA (frequency division/ code division multiple access) with the overlapped carrier allocation (OCA) scheme in the reverse link of a cellular radio system. Of primary interest are the effect of chip waveform, the number of carriers and the degree of overlapping between adjacent carriers on the system capacity. To take into account the bandlimited waveform, the analysis is conducted in the frequency domain. It is shown that OCA compensates for capacity loss incurred in the subdivision of the available spectrum for frequency division multiplexing, and that it also achieves even higher capacity for chip waveforms with a smooth spectral shape at no extra system complexity while the merits of FDICDMA are still fully exploited.

1 Introduction

Direct-sequence code division multiple access (DS- CDMA), which has been widely studied in the past two decades as a multiple access technique, is a promising candidate for third-generation mobile communication systems. Disjoint carrier allocation (DCA) FDICDMA (frequency divisionicode division multiple access), illus- trated in Fig. lb , is currently being considered for the third-generation mobile and personal communication systems. In this approach, the available spectrum is subdivided into multiple subspectra and CDMA is employed in each subspectrum. A CDMA receiver, operating under multi-user interference, extracts the desired signal while interfering signals are left spread. To guarantee perfect rejection of interference arising from adjacent carriers in FDICDMA, guard bands are imposed between adjacent carriers in DCA-FDI CDMA. By subdivision of the available bandwidth into narrower carriers, the chip rate can be reduced com- pared with ordinary CDMA, and system complexity is

0 IEE, 1998 IEE Proceedings online no. 19982280 Paper first received 25th July 1996 and in revised form 29th August 1997 J. Lee was with the University of Surrey and is now with Philips Consumer Communications, 91 New England Ave, F’iscataway, NJ 08854-4142, USA R. Tafazolli and B.G. Evans are with the Mobile Communication Research Group, Centre for Communication Systems Research (CCSR), University of Surrey, Guildford, Surrey GU2 5XH, UK

correspondingly decreased. However, lit has been reported that capacity is significantly relduced as the spectrum is subdivided 111.

I . a

. . . I , , .......

fo f l fz C 4

available spectrum Fig. 1 a Ordinary SC-CDMA b DCA-FDICDMA

Hybrid FD/CDMA ,schemes under consideration

c OCA-FDICDMA

Sousa in [2] introduced the overlapping carrier allo- cation (OCA) scheme, depicted in Fig. IC, which per- mits overlapping between adjacent subspectra. He also derived the variance of adjacent carrier interference over the additive white Gaussian noise channel. Capac- ity gain due to OCA applied to hybrid FDlICDMA has been investigated previously [3, 41. Hybrid FDICDMA with OCA and DCA are referred to as OCA-FDI CDMA and DCA-FDKDMA, respectively. We have previously reported on the capacity gain based on the signal-to-noise ratio (SNR) by the overlapping of adja- cent carriers 141, but the analysis was limited to the rel- ative gain of capacity without consideration of absolute capacity. Although the analysis was not carried out in a comprehensive scenario, OCA turns out to improve capacity compared to DCA.

Fig. 1 a illustrates ordinary single carrier CDMA (SC-CDMA) and hybrid FDICDMA witlh DCA and OCA. Universal frequency reuse [5-71 is assumed. All the available N , carriers are allocated to each cell. Hence every signal is subject to other-cell and intra-cell interference from the co-carrier (i.e. the carrier by which the message of interest is delivered) and adjacent carriers. As depicted in Fig. 2a, if at the base station one amplifier is used for the signals from all1 N, carriers at the base-station transmitter, hybrid FDICDMA would encounter intermodulation distortion. Nonlinear distortion occurs at the transmitter power amplifier since the input signal is amplified in the class BC or class C region for higher power efficiency. ]For this rea-

363 IEE Proc.-Commun.. Vol. 145, No. 5, October 1998

son, hybrid FDICDMA encounters intermodulation. A perfect solution to eliminate intermodulation is to use a separate power amplifier and antenna for each carrier [8], as depicted in Fig. 26, at the expense of high hardware cost. The number of carriers N, for FDI CDMA (typically less than IO) i s not as great as that for narrow-band FDMA. When a single common power amplifier is used, high output back-off from the amplifier can mitigate intermodulation. On the receiv- ing end, since the arriving signal level variations are small, due to power control and attenuation through the propagation channel, a low-noise amplifier operat- ing in the class A region is assumed, and so the issue of nonlinearity may be avoided.

carrier 0

carrier 1 --I.--

carrier N,-1

b Fig. z Buse station transmitter structures a One common amplifier for all carriers b Separate amplifier for each individual carrier

In this paper, attention is focused on the perform- ance of the reverse link (mobile terminals to base sta- tion), which is the limiting direction. The analysis is carried out for bandlimited waveforms, particularly those generated by the raised cosine (RC) pulse-shap- ing filter which satisfies the Nyquist criterion. The results of the analysis are exploited to trade-off the sys- tem capacity and adjacent carrier interference, which is due to changes in the degree of overlap between adja- cent carriers as the result of changes in the processing gain.

2 System model

2. I Transmitter model The reverse link of terrestrial cellular radio systems is our primary concern. Without a strong pilot, phase synchronisation is extremely difficult. Although only a fraction of power is allocated to a pilot, power effi- ciency becomes low. For this reason, M-ary orthogonal modulation and noncoherent reception are more realis- tic for the reverse link [6, 91. However, for brevity, sys- tem model and performance analysis are carried out for binary phase shift-keying (BPSK) modulation and coherent reception, and the result is extended to M-ary orthogonal modulation and noncoherent reception.

The number of chips per bit, referred to as the processing gain, is defined by N = TIT,, where T and

364

T, denote bit duration and chipping period, respec- tively. The transmitted signal by the kth user employ- ing BPSK modulation is expressed in the form

.

s(') ( t ) = Re { d x b ( ' " ) ( t )

(1) where 6") (mod 2 4 denotes the uniformly distributed random phase of the oscillator and A(k) denotes the fre- quency deviation of the carrier, which delivers the mes- sage of the kth user, fromfo. Without essential loss of generality, the first user (whose message is delivered by the pth carrier whose frequency is fo) is taken as the reference. The complex low-pass equivalent form with respect to the pth carrier frequency is then given by

Superscript '(k)' denotes the kth user. The baseband signal for BPSK, generated by the impulse modulator and pulse-shaping filter, is

b(" ( t ) = { 9 d ~ ~ ) N , 0 . p 6 ( t - ZT,) * h(t) ( 3 ) 2 = - - 0 0 I

where the coded data sequence (d,'k)) generated in every T seconds and the signature sequence (a,'k)) generated in every T, seconds are assumed to randomly take val- ues of -1 or + l . The function h(t) denotes the impulse response of the pulse-shaping filter with its transfer function H(R. It is assumed that 1HV>l2 satisfies the Nyquist pulse-shaping criterion [lo] and has the raised cosine form, i.e.

for (1-p) <_ I J ' ~ 5 ~ (1+P)

(4)

2 T c 2T , -

elsewhere

For notational convenience, let b,ck) = d[$Ll a,(k). M-ary orthogonal modulation is discussed elsewhere

[9-111. The input binary data stream passes through the channel encoder, and then its coded output is inter- leaved in order to make successive symbols memoryless and to mitigate the burst error due to fading. log,M successive coded and interleaved bits constituting a -

symbol are mapped to one of the A4 orthogonal wave- forms. The A4 orthogonal waveforms are generated by the impulse-modulating Walsh-Hadamard sequence corresponding to the M-ary symbol [lo, 111 and by applying the pulse-shaping filter to the sequence.

2.2 Multipath fading channel model Transmitted signals are impaired by both multipath and additive white Gaussian noise through the propa- gation channel. In this paper, the well known tapped delay line model [lo] is chosen as the multipath channel model. In the tapped delay line model, the complex lowpass equivalent impulse response of the multipath channel for the kth user is expressed as

..

r, - 1

1=0

where a{") denotes the ith path gain, and @,(k) denotes the uniformly distributed random phase through the lth

IEE Pvoc -Commun Vol 145, No 5 Octobev 1998

path. A constant multipath profile, i.e. E{(a{k))2) = 2~7: for any I, is assumed. L denotes the maximum number of resolvable paths and is given by

(6)

where T, denotes the RMS delay spread [lo].

3 Signal-to-noise ratio and bit error rate

Our performance analysis is based on the Gaussian approximation of interference and zero-mean random signature sequence. Under the Gaussian approximation of interference, the first and second moments of the received signal are sufficient to derive the signal-to- noise ratio (SNR), and by applying the SNR to the well known relation between the bit error rate (BER) and Gaussian noise [lo], the BER is obtained. It is known [lo, 111 that BPSK with a coherent maximal ratio combiner (MRC) and M-ary orthogonal modula- tion with a square-law equal gain combiner (SL-EGC) have the same bit-energy-to-interference ratio denoted by Eb/Io. First, the SNR is derived for BPSK with MRC, and then it is used to derive the BER for orthogonal modulation with SL-EGC.

(k) a LR-I

(k) ,i4 LR -1

Fig. 3 Low-puss equivalent RAKE receiver structure

Fig. 3 depicts a low-pass equivalent form of a LRth order RAKE receiver. The input to the RAKE finger is coherently demodulated, passed through the matched filter, sampled in every chipping period T, at the peak of the chip waveform, multiplied by signature sequence, and the successive Nb samples are summed. Finally, the path gain is multiplied for MRC. The decision variable of the first user takes the following form

LR-1

2 = G Q Z , (7) m=O

where 2, denotes the output of the mth finger of the RAKE receiver and consists of three components:

Zm zz um + Is,, + Io , , + N m ( 8 ) where U, is the useful output; I,,, is the self-generated interference due to the multipath; Io,, is the interfer- ence arising from other users; and Nw, is the back- ground noise.

Those components are expressed in the form

t=O U , = N d X h ( t ) * h(-t)l

= N d z / m -00 IH(f)12df (9)

IEE Proc -Commun , Vol 145, No 5, October 1998

where self-generated interference is given bly

II;; and other user interference is given by

L-3

k f l m=O

The function n(t) denotes background noise with its autocorrelation function

1 2

R,,(T) = -E [n*(t)n(t + T ) ] = N o S ( ~ ) (15)

dk) in eqn. 14 accounts for asynchronous transmission among different users. Note that inter-chip interference is not included in eqn. 8 since the Nyquist pulse-shap- ing filter eliminates it. Although the Nyquist criterion is not met, inter-chip interference has proved to be neg- ligible. In eqn. 9, Parseval's theorem is invoked.

Let us turn our attention to E(ZJ and Var(Z,>. Ran- dom phase +"(l) - q5{k) + @) included in eqns. 10 and 11 can be represented simply by q5{k) since the three components are independently uniformly distributed over [0 2x1. Recalling that the signature sequence (a ik)) is random with zero mean leads to E(2,) = Uq. Moreo- ver, uncorrelatedness between (a,")) and an other user's signature sequence (an(k)), k z 1 or its delayed replica (a $& ), h

} (16)

Var(I0,%) and Var(N,) can be expressed in a similar manner to eqn. 16. It is obvious that io(t) ;and n(t) are wide-sense stationary. Var(Z0J and Var(NJ are easily solved by using the following relation:

0 leads to

Var(ls,,) = AV x Vur {t5,m(i) * h(-%)l t=O

00

V a r { 4 ) / t=O } = s_, Szz(f)clf (17)

where x(t) is a wide-sense stationary random process and S,,cf> is its power spectral density. From Example A-I6 in [12] and our eqn. 14, it is straightforward to obtain the power spectral density of io(t) as

(18)

(19) and

where the operation F denotes Fourier transform. Sn, ( f ) = F{fLn(7-)) = No

365

By invoking the relation in eqn. 17 for the power spec- tral density after performing the matched filter @@, we obtain

(20)

Var(NL) = N * No IH(f)12df (21)

and 00

Recall that E(a{"))* = 20:. In eqn. 13, iJ,m(t) is not wide-sense stationary. However, similarly to the deriva- tion of eqn. 9, without inter-chip interference due to the Nyquist filter, it is straightforward to obtain

Var(&) = 203v(L - 1 ) N (11 ,H(i)12df)2

(22) Let us turn our attention to the BER. A random PN sequence forces the delayed replicas to be mutually independent. Hence the definition of the SNR given by eqn. 10-5-6 in [13].

can be applied to our case. The average bit-energy-to- interference ratio for MRC, obtained by taking the average of eqn. 23 with respect to path gains of the reference user, is thus

(26) It is known [lo] that for binary orthogonal modulation and the L,th order of SL-EGC, the BER is related to the average SNR per path 7, as follows:

pb

(27)

r c = E(Yb)/LR (28) where

366

4 Erlang capacity

In this Section, we discuss the Erlang capacity [lo] for the reverse link, taking into account source activity and imperfect power control. The Erlang capacity is defined as the average number of users requesting service which leads to the blocking condition [lo]. It is assumed that the system is fully loaded. The number of users in any sector and carrier is i i d Poisson-distributed. Suppose that the carriers are equally spaced by A. When source activity and other cell interference are taken into account, eqn. 24 leads to the average bit-energy-to- interference-density ratio for the reference user whose information is delivered by the pth carrier

N,-l

(Unlike eqn. 24, the reference user is included in other user interference; this approximation facilitates analy- sis). Kq and vJk) denote the number of users in the ref- erence sector, which is a Poisson-distributed random variable with a Poisson arrival rate of Acallsis and average service duration per call U p s , and source activ- ity of the kth user served by the qth carrier with Pr(v = 1) = p and Pr(v = 0) = I - p , respectively, and

(IiS),, q = 0, 1, 2, ..., N, - 1 is an i.i.d. random variable defined by eqn. 7 in [6] and denotes interference arising from the gth carrier of other cells or sectors. When power control is imperfect, PJk) and PP(l) are randomly ,

distributed. Let us assume that they are log-normally distributed with standard deviation 0,. ,,(Ic) can then be expressed in the form

The random variables &Jk) and &P(l) account for Gaus- sian distributed power control error and K = ln(10)/10.

The outage probability may be defined as the proba- bility that EblIo of the reference user is less than the required bit-energy-to-interference ratio for an accepta- ble BER (Eb/l0),, i.e.

P o u t = pr ( E b / l o 5 ( E b / l o ) r )

Pout = PT(V > 4)

(32)

( 3 3 )

By using eqn. 29, eqn. 32 can be changed to

where

(34) and

As in [5] , invoke the Gaussian approximation for deriv- ing Erlang capacity as follows:

IEE Proc.-Commun., Vol. 145, No. 5, October 1998

-c - E ( V )

m Pout FZ Q ( ) (36)

30

25

L 2o

15

10

5 -

From eqn. 31, xJk) has the form where the random variable - &Jk) is Gaussian with zero mean and variance 20:, and its first and second moments are E&,'k)) = eKZuc2 and E& q (k))2 = e4K2uc2, respectively. By using the upper bound of the variance and mean of (NS)? given by eqn. 14 in [6], it is straightforward to obtain the mean and variance of V:

N, ~ 1

E(V) I (d/Du)(exP{ (mY} + 0.247) CE(lrl-Plq q=o

(37) and

V a r ( V ) N, -1

I ( P X l D ) (exp (4(nad2} + 0.139) c t 2 0 4 -PIA) q=o

(38) Since E(1q - plA) < 1 for q s p , OCA helps to decrease Var(V), as shown in eqn. 38. By solving eqn. 36 for the given outage probability with respect to Up, the Erlang capacity is obtained in the form

-

-

-

-

-

x - 1 = 2 PO,'*

( - A 4- dB2 - 4AC 2 il

N,-l

X J ( exP(4 (m)2) + 0.139) t2(14 -PIA) q=o

(41)

5 Numerical results

Fig. 4 shows E(A) against carrier spacing A. A is nor- malised to the chip rate. As discussed in the preceding Section, the sharp roll-off spectrum exhibits higher K O ) , whereas it exhibits lower HA) from roughly A = 0.55T;' onwards. This implies that the sharp roll-off is less affected by adjacent carrier interference than the smooth roll-off. whereas it is more affected by interfer- ence from the same carrier. For a rectangular pulse K O ) becomes 213, and then eqn. 24 leads to the well known SNR in [ 141.

Binary orthogonal signalling with the SL-EGC is assumed. If 64-ary orthogonal signalling is employed, the computation to obtain numerical results is cumber- some. Our purpose is to investigate the relations among the diversity scheme, degree of overlapping and capac- ity, and hence binary orthogonal modulation is suffi- cient to achieve our objective. It is known from Section 5-4-3 and 14-4-3 in [lo] that noncoherent reception of the M-ary signal exhibits a lower BER as M increases for both non-fading and fading channels. Around 5-7 dB SNR gain is expected when 64-ary orthogonal sig- nalling is employed instead of binary.

A (normalised to chip rate) Fig.4 EjA) against A

O = O

/ 3 = 1

. . . . . . , , . __ /3 = 0.4 ~~-~

450 I

150

100

-

a 35 I 1

O L 0 2 4 6 13 10

number of carriers b

Fig. 5 Imperfectly power-controlled multi-cell system with binary orihog- onal signalling and square-law combiner Outage probability 1%, L, = L, p = 318, U, = ISdB, BER s 1W2, &/No = 12.04dB + (Eh/IJr)

DCA og= I . ... . x P = O . 4 __ OCA + p = o a N, x (UP) b L when points in a are obtained

Fig. 5 shows the Erlang capacity and other parame- ters for a given number of carriers ranging from 1 to 10. The multipath diversity order L, is assxmed equal to L, i.e. the maximum number of resolvable paths determined by the chipping period. The available band- width of the system, the RMS delay spread, and the data bit rate are assumed to be SOMHz, 0 . 6 2 5 ~ ~ and 8kbit/s, respectively. Received E,,INo is assumed to be E,/No = 12.04dB + (&/Io ),, i.e. sufficiently large that background noise is negligible.

Fig. 5a shows the Erlang capacity for the available spectrum, i.e. N , x (Up), the product of the Erlang capacity per carrier and the number of carriers. The Erlang capacity IJp is computed for the LNc/2J-th car-

IEE Proc.-Commun., Vol. 145, No. 5, October 1998 367

rier, for which 22i1E(\q - p(A) attains its maximum value among p = 0, 1 , 2, ..., N , - 1. For OCA, the Erlang capacity is found by searching for the maximum N p for N ranging from BW/N,(l + /3) to (BW/(l + /3))/ ( 1 + (N, - 1)/2), i.e. the maximum N , which does not allow overlapping among three successive carriers, for the given number of carriers Ne and the available band- width BW. For DCA, at N = BW/N,(l + /3), i.e. the maximum N without overlapping between adjacent spectra, the Erlang capacity is achieved. Fig. 5b shows L corresponding to the Erlang capacity achieved in Fig. Sa. Fig. 6a shows the relative (EbllJr of DCA and OCA compared to SC-CDMA, i.e.

6 (&/Io ) v , DC A = (&/Io ) T , DC A - (& / 1, ) T , sc - c D M A

(42)

b ( - % / l o ) T , ~ ~ ~ = ( - % / l o ) T , ~ ~ ~ - ( E b / l o ) T , ~ ~ - ~ ~ ~ ~ (43)

corresponding to the capacity achieved in Fig. 5a. Fig. 66 plots the capacity increase in YO by overlapping computed by

corresponding to the Erlang capacity achieved in Fig. 5a.

1.50 I 6 0 $

I ."" a

160 i

0 2 4 6 8 10 number of carriers

b

Fig. 6 Imperfectly power-controlled multi-cell system with binary orthog- onal signalling and square-law combiner Outage probability 1%, L, = L, p = 318, uc = 1.5dB, BER 5

DCA 12.04dB + (Eb/Io)i) o g = 1 x p = 0.4 __ OCA + /3=0 a G(Eb1I0), b W J P )

EdNo = ..... .

368

In DCA, N, x (Np) is inversely proportional to N,. In particular, the rate of decreasing of Ne x (Up) for the smooth roll-off spectrum is higher. By introducing the OCA scheme, the capacity of OCA-FDICDMA is comparable to or even higher than that for single wide- band CDMA(SC-CDMA). In OCA, N, x ( U p ) increases as N, increases towards 4 and decreases from N , = 5 onwards. Curves of relative (&/& plotted in Fig. 6a are nearly symmetric about the x-axis. In a heuristical manner, it is obvious that relative (Eb/IJv is a important factor to account for the relative capacity of DCA and OCA to SC-CDMA and OCA to DCA. A change of (Eb/Zo)v, ranging from -1.2SdB to +l.SdB, affects the Erlang capacity dramatically.

Another reason for the increase of the Erlang capac- ity due to OCA is explained in terms of processing gain. If effective processing gain for OCA-FD/CDMA is defined by PGoci! = N,(TIT,,ocA), i.e. processing gain per carrier multiplied by the number of carriers, the ratio between PGocA and the processing gain of ordinary SC-CDMA (denoted by PGsc) is given by

Nc(1 + P ) (1 + P ) + ( N , - 1) .

(45) -- - PGOCA

PGsc . A where TCaOcA denotes the chipping period of OCA-FDI CDMA for the given N,. When carrier spacing is fixed to qj Tc,OcA-l regardless of Ne, the ratio increases as N , increases towards infinity. The increase of the effec- tive processing gain accounts for the capacity gain.

400 L 350 300 1

," 200

3 150

.- E /

a I

number of carriers b

Fig. 7 Imperfectly power-controlled multi-cell system with binury orthog- onal signalling and square-law combiner Outage probability 1%, LR = max(4, L), p = 318, U, = 1.5dB, BER s IO-', E*/ No = 12.04dB + (Eb/I,Jr) og= 1 . . . . . . . DCA x p = 0.4 __ OCA + p = o a Ne x (UP) b L when points in a are obtained

IEE Proc.-Commun.. Vol. 145, No. 5, Octobev 1998

There is similar discussion for multi-carrier CDMA elsewhere [15]. In multi-carrier CDMA, more subcarri- ers means higher processing gain per carrier, and in turn this achieves greater capacity since the bandwidth of the carrier and the order of diversity remain con- stant. As Fig. 5b shows, L varies from 2 to 32 accord- ing to N,. Fig. 6b shows a dramatic percentage capacity increase due to overlapping, whereas 6 (EblIo)r varies between -1.25dB and +1.5dB in Fig. 6a.

In Fig. 7, the Erlang capacity and L corresponding to the Erlang capacity are plotted in the same way as in Figs. 5 and 6, except that the multipath order is given by LR = max(4, L). When L > 4, a larger difference between them degrades the capacity more since the desired signal energy is not fully exploited. As a result of subdivision of the spectrum, L is decreased. For j3 = 1.0, L is equal to or less than 4 from N, = 5 onwards in Fig. 7b, and so the Erlang capacity is reduced as N , increases towards 10, as in Figs. 5 and 6. Where N, 2 5, the Erlang capacity is dramatically increased by OCA.

Let us turn our attention to the variation of trans- mission range due to OCA in hybrid FDICDMA. The primary factor which determines the minimum power required from the mobile terminal to just overcome the background noise is (Eb/Io)r [7] . In hybrid FDKDMA, because of the variation of the chipping period depend- ing on N,, B W and the degree of overlap, S(EbIIJr var- ies within a certain range, as verified in Fig. 6a. Let us compute how much 6(EblIo), affects transmission range and in turn cell coverage. Consider the worst case in which the mobile terminal is at the boundary between adjacent cells. When there is a change of SNR as large as 6(EblI,),, the relative transmission range F is given by

where v denotes the path loss exponent of the propaga- tion channel, and 6(&,/&), is given in dB. Relative cell coverage area is given by i2. As illustrated in Fig. 8, when 6(Eb/I0), is between -1.25dB and +1.5dB, relative cell coverage area is up to 80%.

22k 0 2.01 P A

0 0.5 1.0 1.5 2.0 2.5 3.0

Relative cell coverage area against 6(Edlo), (= y ) for various vs Y! dB

Fig.8

6 Conclusions

The effect of the chip waveform, carrier bandwidth and degree of overlap between adjacent carriers on the Erlang capacity of hybrid OCA-FD/CDMA has been investigated. We have shown that the {capacity loss introduced by subdivision of the available spectrum when it is applied to FDiCDMA is recovered through hybrid OCA-FDKDMA. The capacity gain due to OCA is accounted for by higher spectral efficiency, i.e. higher effective processing gain and less bit-energy-to- interference ratio required for an acceptable BER. Moreover, this scheme does not require any extra sys- tem complexity compared with that of FD/CDMA and could be a potential access scheme candidate suitable for the third-generation mobile cellular cornmunication systems. OCA affects the transmission range greatly since a variation occurs of required EblIo, a primary factor to determine the transmission range.

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