On time-varying cyclic delay diversity

EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONSEuro. Trans. Telecomms. 2006; 17:361–370Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/ett.1124

Special Issue

On time-varying cyclic delay diversity

Gerd Richter1*, Martin Bossert2, Elena Costa2 and Martin Weckerle2

1Department of TAIT, Albert-Einstein-Allee 43, University of Ulm, D-89081 Ulm, Germany2Siemens AG, Com MN PG NT RI4, Sankt-Martin Street 76, D-81541 Munich, Germany

SUMMARY

Cyclic delay diversity (CDD) was introduced in 2001 to obtain spatial diversity in an orthogonal frequencydivision multiplexing (OFDM) based transmission system. In contrast to space-time codes, CDD introducesno additional effort at the receiver side, since CDD changes only the channel impulse response seen by thereceiver by increasing the frequency selectivity. Furthermore, CDD has the advantage that there is no rateloss even for more than two transmit antennas. In this paper, we analyse CDD for an orthogonal frequencydivision multiple access (OFDMA) based transmission system. To increase not only the frequencyselectivity but also the time selectivity, we introduce time-varying cyclic delay diversity (TV-CDD), whichchanges the cyclic shift with each OFDM symbol. Especially in systems, where each user can only allocatea few subcarriers for data transmission, TV-CDD improves the performance of the OFDMA-basedtransmission system significantly. Copyright # 2006 AEIT.

1. INTRODUCTION

One simple method to use spatial diversity is called delay

diversity (DD), which was introduced in References [1]

and [2]. Here, the non-delayed signal is transmitted over

the first antenna, while over the second or each additional

antenna a delayed version of the signal is transmitted. In

OFDM, delay diversity can be used to increase the fre-

quency diversity. A forward error correction (FEC) code

can pick up this increased frequency diversity, and thus

lowers the bit error rate (BER) and the frame error rate

(FER). However, the main disadvantage of this scheme

is that delay diversity causes intersymbol interference, if

the delay is too large. Hence, the maximum delay is lim-

ited by the length of the guard interval minus the maximal

channel delay.

To avoid this disadvantage, CDD was proposed in

References [3], [4], or in [5], where the signal on the sec-

ond or each additional antenna is not delayed but cycli-

cally shifted. Therefore, no intersymbol interference can

occur and thus there are no limits for the cyclic shifts.

Another advantage of CDD is that there is no additional

complexity needed in the receiver. Furthermore, there is

no rate loss even for a large number of antennas in contrast

to other space-time codes.

For a frequency selective channel and OFDMA, the use

of CDD is investigated in Reference [6]. There, it is

assumed that each user allocates adjacent subcarriers for

data transmission. Since CDD only increases the fre-

quency diversity, there is nearly no performance gain for

frequency selective fading channels and for OFDMA,

where several non-adjacent subcarriers are allocated to

each user. Therefore, we extend CDD to time-varying cyc-

lic delay diversity (TV-CDD), a time variant version of

CDD.

The paper is organised as follows: We recall the princi-

ples of CDD and show the error distributions of an

uncoded OFDM system without and with CDD in

Section 2. In Section 3, we introduce the extension of

CDD, namely TV-CDD, which is suitable for OFDMA

Received 30 October 2005

Revised 31 January 2006

Copyright # 2006 AEIT Accepted 1 March 2006

* Correspondence to: Gerd Richter, Department of TAIT, University of Ulm, D-89081 Ulm, Germany. E-mail: [email protected]/grant sponsor: European Union.

systems and can be utilised for all kind of channels. After

that, we visualise the error distribution of the OFDMA sys-

tem with TV-CDD. In Section 4, we show the performance

improvement by using CDD and TV-CDD for frequency

selective channels. Furthermore, we demonstrate how an

increasing number of transmit antennas lowers the BER

in Section 4. Finally, we conclude the paper in Section 5.

2. CYCLIC DELAY DIVERSITY

Figure 1 shows the principle of CDD for NT transmit

antennas.

First, an OFDM modulation is done, which includes

FEC, interleaving, modulation and an inverse fast Fourier

transformation (IFFT). After the IFFT, the signal is split in

NT antenna branches. The cyclic shift of the first antenna is

set to zero, while in the other branches the signal is cycli-

cally shifted by an antenna-specific cyclic shift �n,n ¼ 1; . . . ;NT � 1. The equivalent representation in the

frequency domain, which is called phase diversity (PD),

can directly be calculated from the IFFT with length NF

and corresponds to

sðlÞ ¼ 1ffiffiffiffiffiffiNF

pXNF�1

k¼0

SðkÞ � ej 2pNF

kl

sðl� �nÞ|fflfflfflfflffl{zfflfflfflfflffl}CDD signal

¼ 1ffiffiffiffiffiffiNF

pXNF�1

k¼0

e�j 2p

NFk�n � SðkÞ|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}

PD signal

�e j 2pNF

kl

where l, k, s(l) and S(k) denote the discrete time, the discrete

frequency, and the complex-valued signals in time-domain

and frequency-domain respectively and l� �n is calculated

modulo NF . Figure 2 illustrates the difference between DD

and CDD in the time domain. The reference signal on the

antenna Tx 1 is undelayed, while the signal on the antenna

Tx 2 is delayed by one subcarrier ai; i ¼ 1; . . . ;NF for DD

and cyclically shifted by one subcarrier ai for CDD.

After the cyclic shift, the prefix of the shifted signal is

added to fill the guard interval. The signals of the different

transmit antennas superimpose on the channel and the

receiver processes the sum signal by simply removing

the guard interval and by performing the inverse OFDM

(IOFDM), which contains the fast Fourier transformation

(FFT), the demodulation, the deinterleaving and the

decoding. This is possible, since the cyclic shifts appear

as multipaths at the receiver and thus, no special combin-

ing and no additional effort is necessary except for the

channel estimation, because only the characteristics of

the channel seen by the receiver is changed.

Figures 3 and 4 show the error distribution for the

first 200 subcarriers of an uncoded transmission with two

OFDMGuard

Guard

δ1

δN−1 Guard

∑Guard IOFDM

...

Figure 1. Orthogonal frequency division multiplexing (OFDM) with cyclic delay diversity (CDD).

Guard 1

Guard 1

Guard 1 OFDM symbol 1

OFDM symbol 1

Guard 2

Guard 2

Guard 2

discrete time

Tx 2: CDD signal

Tx 2: DD signal

Tx 1: Reference

OFDM symbol 1

a1aNF

a1 a2 aNF

a1 a2 aNF

aNF−1

δ1

Figure 2. Difference between delay diversity (DD) and CDD.

362 G. RICHTER ET AL.

Copyright # 2006 AEIT Euro. Trans. Telecomms. 2006; 17:361–370

transmit antennas in the frequency-time plane for a

transmission over a time-invariant multipath channel with-

out CDD and with CDD, respectively. The error distribu-

tion of the remaining subcarriers shows a similar

behaviour. The cyclic delay on the second antenna is

�1 ¼ 200 (in samples) and the number of subcarriers is

NF ¼ 512.

We can conclude from Figures 3 and 4 that the fre-

quency selectivity increases by the use of CDD. The trans-

mission without CDD results in error bursts that contain

Figure 3. Errors of an uncoded transmission without CDD (� errors).

Figure 4. Errors of an uncoded transmission with CDD (� errors).

ON TV–CDD 363


many adjacent subcarriers. These error bursts are separated

by the use of CDD into several error bursts that only con-

tain a few subcarriers. The number of errors remains

approximately the same for both transmissions. The use

of CDD virtually changes, for example, a channel with

25 paths into a channel with 50 paths.

3. TIME-VARYING CYCLIC DELAY DIVERSITY

In this section, we introduce a new method suitable for

OFDMA transmission, called TV-CDD. In OFDMA only

a few subcarriers are assigned to each user. As we can see

in Figures 3 and 4, there occur many errors in some sub-

carriers, while other subcarriers are nearly error free. Thus,

some users suffer from deep fading, while other users

enjoy a nearly error-free transmission. However, this is

not desirable for a multiuser system, since fairness among

users is not taken into account.

To avoid this, we introduce TV-CDD, which is a time

variant version of CDD. Figure 5 shows the block diagram

of an OFDM system with TV-CDD.

The only difference between CDD and TV-CDD is that

the cyclic shifts �nðtÞ at the second and each additional

antenna is now a function of the time (or the number t of

the transmitted OFDM symbol). The cyclic shift �nðtÞ can

take any random integer value, �nðtÞ 2 1; . . . ;NF � 1, in

an IFFT modulation of length NF for any OFDM symbol

t 2 Z. Hence, the TV-CDD signal in time domain and its

representation in the frequency domain can be expressed

as follows:

sðl� �nðtÞÞ|fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}CDD signal

¼ 1ffiffiffiffiffiffiNF

pXNF�1

k¼0

e�j 2p

NFk�nðtÞ � SðkÞ|fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl}

PD signal

�e j 2pNF

kl

We can see that by artificially cyclical shifting the

signal with an arbitrary integer number �nðtÞ for every

OFDM symbol, the received signal varies in the phase

from symbol to symbol. Therefore, we make the

channel artificially time-variant even though the channel

is time-invariant or a slow-fading channel. The error

distribution in the frequency-time plane of an unco-

ded transmission with two transmit antennas over a

time-invariant multi-path channel with TV-CDD is

shown in Figure 6. The cyclic shift �nðtÞ is randomly

chosen for each OFDM symbol.

In comparison to Figure 4, we can see that the long error

bursts in some subcarriers due to deep fading are broken

into shorter ones and are scattered to the adjacent subcar-

riers. The channel still shows a frequency selective

fading, but no deep fades extend over long periods of

many OFDM symbols. Furthermore, we can see that in

Figures 3, 4 and 6 the number of errors are approximately

the same. But the error distribution changes and that is

what the FEC code can gain from.

It is shown in Reference [7] that the diversity order of a

CDD transmission system over a Rayleigh fading channel

is equal to the minimum of the number of transmit anten-

nas NT and the minimum Hamming distance of the code.

Since the channel shows frequency selective fading, the

diversity order for each subcarrier by a transmission with-

out TV-CDD is only one during one codeword. In a similar

way as CDD for Rayleigh fading channels, the diversity

order of one subcarrier can be increased by using more

transmit antennas and TV-CDD. Figure 7 shows the error

distribution with TV-CDD and four transmit antennas.

Here, the errors are nearly randomly distributed and no

frequency selective fading characteristics can be ob-

served. Thus, the FEC code benefits from almost full diver-

sity, which results in a lower BER.

4. SIMULATION RESULTS

In this section, we show simulation results for an OFDMA

transmission system without CDD, with CDD and with

TV-CDD. We use a wide-sense stationary un-correlated

scattering channel model with 25 paths. The power delay

profile is exponentially decreasing with a maximum delay

OFDMGuard

Guard

δ1(t)

δN−1(t) Guard

∑Guard IOFDM

...

Figure 5. OFDM with TV-CDD.



�max ¼ 5 ms. Similar results can be obtained for all kinds of

frequency-selective channel models. The parameters for

the OFDM transmission are summarised in Table 1.

In all simulations an interleaver is used that permutes

the bits randomly over one codeword. Furthermore, we

assume a quasi-static channel that remains constant over

one codeword.

In a conventional OFDMA system, the subcarriers allo-

cated to a user, are either a set of adjacent subcarriers or

several non-adjacent subcarriers. For the simulations, we

Figure 6. Errors of an uncoded transmission with TV-CDD (� errors).

Figure 7. Errors of an uncoded transmission with TV-CDD and four transmit antennas (� errors).

ON TV–CDD 365


use three different mapping schemes to allocate the sub-

carriers to the users as described in the following.

Mapping scheme 1 represents the extreme case, where

each user only gets one subcarrier for transmission. Hence,

the number of users is equal to the number of subcarriers

and a codeword of one user is spread over 200 consecutive

OFDM symbols. As we know from the error distributions

of the uncoded transmission (see, e.g. Figure 3) some users

get a very good subcarrier, while some others have a very

poor subcarrier available for data transmission.

For real multiuser systems, we do not assign each user to

only one subcarrier, since the performance is very bad and

the data rate may not be sufficient. Instead, we allocate, for

example eight subcarriers to each user. Thus, a codeword

of one user is spread over 8 subcarriers and 25 consecutive

OFDM symbols. In mapping scheme 2, every user can use

eight adjacent subcarriers, while mapping scheme 3 is the

interleaved assignment, where the subcarriers are periodi-

cally assigned to each user one by one. The latter two map-

ping schemes for the OFDMA transmission can be

considered in Figure 8.

Figure 9 shows the BERs of an uncoded transmission

without CDD, with CDD and with TV-CDD.

Here, we can see that all three error rates are approxi-

mately the same. Thus, CDD and TV-CDD do not lead

to better performance without FEC. This is due to the fact

that CDD and TV-CDD only change the error distribution,

but not the total number of errors.

The coded BERs for mapping Scheme 1 without CDD,

with CDD and with TV-CDD with NT ¼ 2 transmit anten-

nas are depicted in Figure 10. Also, the BERs for TV-CDD

with NT ¼ 3 and NT ¼ 4 transmit antennas can be seen

in this figure. In addition, the uncoded BER is shown in

Figure 10.

Here, we can see that without CDD and with CDD no

coding gain can be achieved, since there is no diversity

within one subcarrier. In contrast, by the use of TV-CDD

additional diversity is introduced for every subcarrier and

thus better performance can be achieved with TV-CDD.

We also see that an increasing number of transmit antennas

lowers the BERs for the case of TV-CDD because the

diversity order is increased with every additional antenna.

Also an error floor can be observed for the transmission

with NT ¼ 4 and TV-CDD. This is due to the fact that

the phase of the 0th subcarrier does not change from

Table 1. Parameters of the OFDMA Transmission.

Carrier frequency 5.5 GHzSystem Bandwidth 20 MHzFFT length 512Guard interval length 128OFDM symbol duration 25:6 msGuard interval duration 6:4 msMaximum channel delay 5:0msConvolutional Code (171 133)Codelength 200Modulation BPSK

user64user1 user4user3user2

user1 user2 user64

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 64

. . . . . .

. . . . . .

504 512

451 452449 450 512

. . .

. . .

. . . . . .

user1 user4user3user2 user64 user1user2

65 66

Scenario 2

Scenario 3

Figure 8. Mapping schemes for an OFDMA transmission.



OFDM symbol to OFDM symbol. We can get rid of this

error floor by not using the 0th subcarrier for transmission

as it is done in some OFDM-based transmission systems,

for example IEEE 802.11.a.

Figure 11 shows the BER in dependence of the constant

cyclic shift (CCS) (in samples) for Eb=N0 ¼ 10 dB for

mapping scheme 2 and for mapping scheme 3 for

NT ¼ 2 and the use of CDD.

10-3

10-2

10-1

100

0 5 10 15 20

BE

R

Eb/N0 [dB]

No CDDCDDTV-CDD

Figure 9. BERs of an uncoded transmission.

10-6

10-5

10-4

10-3

10-2

10-1

100

0 5 10 15 20

BE

R

Eb/N0 [dB]

Uncoded (NT = 1)No CDD (NT = 2)CDD (NT = 2)TV-CDD (NT = 2)TV-CDD (NT = 3)TV-CDD (NT = 4)

Figure 10. BERs of a coded transmission (Mapping scheme 1).

ON TV–CDD 367


In this figure, we can see that for mapping scheme 2 the

performance with CDD is improved by increasing the CCS

from 0 to approximately 100. After this, increasing the

CCS does not lead to better performance. From approxi-

mately CCS¼ 412 the BER gets larger, when the CCS is

further increased. This is due to the fact that the frequency

selectivity is increased when the signal on the second

antenna is cyclically shifted by a high CCS to the left or

to the right. The small peak for a CCS of 256 occurs,

because the PD signal transmitted over the second antenna

is either SðkÞ for an even k or �SðkÞ for k odd. The signals

of the two antennas superimpose, which may lead to a

destructive interference for every second subcarrier and

to a constructive interference for the other subcarriers.

Hence, the overall performance decreases. For the follow-

ing simulations we use a CCS¼ 200.

For mapping scheme 3, we can see that the performance

cannot be improved by using CDD, since the channel

shows also a frequency-selective fading characteristics.

Because adjacent subcarriers are correlated, the diversity

for each user can be increased by using the subcarrier allo-

cation as described in mapping scheme 3. Therefore, the

BERs in Figure 11 for mapping scheme 3 are lower com-

pared with the BERs for mapping scheme 2.

The performance without CDD, with CDD and with TV-

CDD for mapping scheme 2 with NT ¼ 2 transmit anten-

nas can be seen in Figure 12. Furthermore, this figure

shows the BERs for a transmission with NT ¼ 3 and

NT ¼ 4 for TV-CDD and with NT ¼ 4 for CDD.

In Figure 12, one can notice that the coded transmission

outperforms the uncoded transmission in any case.

Furthermore, the use of CDD increases the frequency

diversity, and thus the FEC can pick up this diversity and

therefore lowers the BERs. The OFDMA transmission

with TV-CDD shows only slightly better performance than

the transmission with CDD for NT ¼ 2 since CDD also

increases the diversity for adjacent subcarriers and adja-

cent subcarriers are allocated to each user in mapping

scheme 2. For NT ¼ 4 transmit antennas, TV-CDD outper-

forms CDD because the error distribution shows only a

slight frequency selective fading characteristics, which

can be seen in Figure 7.

The performance without CDD, with CDD and with TV-

CDD for mapping Scheme 3 with NT ¼ 2 can be seen in

Figure 13. Furthermore, the BERs for TV-CDD with

NT ¼ 3 and NT ¼ 4 are depicted in this figure.

Here, we can see that better performance is obtained

by using TV-CDD, because the FEC can gain from the

better error distribution of the transmission with TV-

CDD (compare Figure 4 and Figure 6). Using more

antennas can improve the performance for TV-CDD,

while it does not help for CDD. In comparison with

mapping scheme 2 the increase from NT ¼ 2 transmit

antennas to NT ¼ 4 transmit antennas leads only to a

0 50 100 150 200 250 300 350 400 450 5000

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

CCS [samples]

BE

R

Mapping scheme 2Mapping scheme 3

Figure 11. BER in dependence of the CCS.



10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

0 5 10 15 20

BE

R

Eb/N0 [dB]

Uncoded (NT = 1)No CDD (NT = 2)CDD (NT = 2)TV-CDD (NT = 2)TV-CDD (NT = 3)TV-CDD (NT = 4)CDD (NT = 4)


10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

0 5 10 15 20

BE

R

Eb/N0 [dB]

Uncoded (NT = 1)No CDD (NT = 2)CDD (NT = 2)TV-CDD (NT = 2)TV-CDD (NT = 3)TV-CDD (NT = 4)


ON TV–CDD 369


small performance improvement. This is due to the fact

that the FEC achieves already for NT ¼ 2 transmit anten-

nas a relatively high diversity because every user allocates

eight non-adjacent subcarriers for data transmission.

5. CONCLUSIONS

CDD is an elegant diversity technique for OFDM-based

transmission systems, which does not introduce additional

effort in the receiver. For OFDMA systems with many

users, in which each user is assigned only a few isolated

subcarriers or in case of the interleaved assignment,

CDD cannot provide full diversity for one user. Hence, a

new technique, called TV-CDD, was introduced in this

paper. With this technique the diversity can be increased

by using multiple transmit antennas, which leads to lower

bit and frame error rates during an OFDMA transmission.

ACKNOWLEDGEMENTS

This work has been performed in the framework of the ISTproject IST-2003-507581 WINNER, which is partly funded by

the European Union. The authors acknowledge the contributionsof their colleagues, although the views expressed are those of theauthors and do not necessarily represent the project.

REFERENCES

1. Seshadri N, Winters JH. Two signaling schemes for improving theerror performance of frequency-division-duplex (FDD) transmissionsystems using transmitter antenna diversity. International Journal ofWireless Information Networks 1994; 1(1):49–59.

2. Wittneben A. A new bandwith efficient transmit antenna modulationdiversity scheme for linear digital modulation. In IEEE InternationalConference onCommunications (ICC), Vol. 3, May 1993, 1630–1633.

3. Bossert M, Huebner A, Schuehlein F, Haas H, Costa E. On cyclicdelay diversity in OFDM based transmission schemes. In OFDMWorkshop, 2002.

4. Dammann A, Kaiser S. Standard conformable antenna diversitytechniques for OFDM systems and its applicationn to the DVB-Tsystem. In IEEE Globecom, November 2001, 3100–3105.

5. Dammann A, Kaiser S. Low complex standard conformable antennadiversity techniques for OFDM systems and its application to theDVB-T system. In 4th International ITG Conference on Sourceand Channel Coding, January 2002, 253–259.

6. Bauch G, Malik JS. Orthogonal frequency division multiple accesswith cyclic delay diversity. In ITG Workshop on Smart Antennas,Munich, Germany, March 2004.

7. Dammann A. On Antenna Diversity Techniques for OFDM Systems.PhD thesis, University of Ulm, Germany, January 2005.

AUTHORS’ BIOGRAPHIES

Gerd Richter was born in Kosching, Germany, in 1974. He received his Dipl.-Ing. degree in Electrical Engineering from the Uni-versity of Ulm, Germany, in 2002. Since 2002, he has been a research assistant in the Department of Telecommunications and AppliedInformation Theory at the University of Ulm. His research interests are in the field of reliable data transmission, concentrating on low-density parity-check codes and rank codes. Furthermore, he is interested in diversity methods for OFDM.

Martin Bossert was born in Pforzheim, Germany, in 1955. He received his Dipl.-Ing. degree in Electrical Engineering from the Tech-nical University of Karlsruhe, Germany, in 1981 and the Ph.D. from the Technical University of Darmstadt, Germany, in 1987. After a1-year DFG scholarship at Linkoeping, Sweden, he joined AEG Mobile Communication, where he was, among others, involved in thespecification and development of the GSM system. Since 1993, he has been a professor at the University of Ulm, Germany, presentlyas head of the Department for Telecommunications and Applied Information Theory. He is author of several textbooks and his researchinterests are in secure and reliable data transmission. The main focus is on generalised concatenation of codes/coded modulation andsoft decision decoding.

Elena Costa received the Laurea degree in Electronics Engineering and the Ph.D. in Telecommunications Engineering from the Uni-versity of Padua, Italy, in 1997 and 2001, respectively. Her main interests are in the area of wireless communications, with focus on thephysical (PHY) and medium access control (MAC) layers. She has carried out several research works on issues related in particular tomulti-carrier transmission, code division multiple access, channel estimation, channel coding, link adaptation and adaptive resourcescheduling. During her Ph.D. she worked on third generation mobile radio systems. In 2000, she joined Siemens AG, CommunicationsMobile Networks, Munich, where she has developed research and overtaken the management of several internal research projects onbeyond 3G communications. Currently, she co-ordinates Siemens research on the PHY and MAC layers within the IST-WINNERproject.

MartinWeckerle received the Dipl.-Ing. degree in Electrical Engineering in 1997 and the Dr.-Ing. degree in 2002 from the Universityof Kaiserslautern, Germany. From 1997 to 2001, he was with the Research Group for RF Communications of the Universityof Kaiserslautern working on adaptive antenna concepts and multiuser detection schemes for CDMA-based mobile radio systems.In 2001, he joined Siemens AG Communications, Mobile Networks Division, in Munich, Germany, where he is active as a projectmanager in the field of product oriented research on physical layer concepts for future wireless communication systems beyond 3G.Currently, his main research focus is on multi-carrier based air interface solutions, multi-antenna concepts and access network tech-nologies for mobile radio systems.



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On time-varying cyclic delay diversity