Performance of Cyclic Delay Diversity in Ricean Channels

PERFORMANCE OF

CYCLIC DELAY DIVERSITY

IN RICEAN CHANNELS

Armin Dammann, Ronald Raulefs, Simon PlassGerman Aerospace Center (DLR)Institute of Communications and NavigationOberpfaffenhofen, 82234 Wessling, Germany

{Armin.Dammann,Ronald.Raulefs,Simon.Plass}@DLR.de

Abstract Cyclic delay diversity (CDD) provides additional diversity in Rayleigh fadingchannels, and therefore, improves system performance. Forline-of-sight (LOS)propagation, e.g. the additive white Gaussian noise channel, the implementa-tion of CDD yields to a performance loss. Therefore, we investigate CDD forRicean channels with different Ricean factors. To combat the SNR loss for sig-nificant LOS propagation we propose the principle of antennapower weighting.The idea is to feed different power levels into the multiple transmit (TX) an-tenna branches rather than distributing the TX power uniformly among the TX-antennas. We exemplarily implement CDD with antenna power weighting to theterrestrial digital video broadcasting system (DVB-T). Simulation results showthat antenna power weighting significantly reduces the SNR loss in LOS propa-gation by the cost of a slight degradation of the SNR gain in non-LOS scenarios.

1. Introduction

Multiple antenna transmission schemes have gained a high attraction sincethey offer a capacity which rises proportional to the minimum of the numberof transmit (TX) and receive (RX) antennas from informationtheory point ofview [1]. In the recent years, several approaches have been proposed, whichtake advantage of multiple TX- respectively RX-antennas. One representativeof multiple antenna schemes is cyclic delay diversity (CDD)[2]. CDD is a vari-ant of delay diversity (DD) [3] and adapted to communications systems withcyclic extensions as guard intervals such as orthogonal frequency division mul-tiplexing (OFDM) for instance. Signal delays in DD may causeintersymbolinterference. In contrast, CDD prevents such additional intersymbol interfer-ence by using cyclic signal shifts. Typically, multi TX/RX-antenna techniques

2 A. Dammann, R. Raulefs, S. Plass

like Space-Time coding [4, 5] require signal processing in both the transmitterand the receiver. However, CDD as well as DD can be implemented solelyat the transmitter, the receiver or both sides. The fact thatthe counterpart —e.g. the RX in case of a TX sided implementation — need not be aware ofthe implementation makes these techniques standard compatible. I.e. they canbe implemented as an extension for already existing systemswithout changingthe standard.

CDD has extensively been investigated for Rayleigh fading channels. Itcan be shown, that CDD can be considered as channel transformation, whichincreases the number of propagation paths and the delay spread of the channel,observed at the transmitter. This improves the system performance in multipathRayleigh fading scenarios. A line-of-sight (LOS) propagation, e.g. an AWGNchannel, however, would be transformed into a static multipath channel, whichdefinitely decreases performance. Therefore, it is of high interest to investigatethe performance of CDD for propagation environments where both LOS andnon-LOS (Rayleigh) components occur. In this paper, we investigate CDDfor the terrestrial digital video broadcasting standard (DVB-T, [6]) in Riceanmultipath channels with different Ricean factors and propose antenna powerweighting as a method to combat the system degradation of CDDfor extremeLOS propagation scenarios.

2. System Description

Compared to wireless communications systems, LOS propagation in TVbroadcasting is more distinct. Transmit (TX) antennas are typically located onhigh masts and for fixed reception users often install rooftop antennas. There-fore, the propagation conditions for TV broadcasting covera large variety ofscenarios, described by multipath Rayleigh fading channelmodels with non-LOS, Ricean fading channels (mixed LOS and non-LOS) and, as pure LOSpropagation, the AWGN channel. Subsequently, we show the application ofCDD to DVB-T and define the channel model, which is used for ourinvestiga-tions.

2.1 DVB-T and Cyclic Delay Diversity

The physical layer of a DVB-T transmitter comprises three main parts,which are (i) MPEG-2 source coding and multiplexing, (ii) outer coding withinterleaving and (iii) inner coding, interleaving, framing and modulation. TheDVB-T standard defines a target bit error rate (BER) of2 × 10−4 after decod-ing of the inner channel code, which yields to a quasi error free data streamafter decoding of the outer Reed-Solomon code. Therefore, we are interestedin the inner DVB-T and model the data stream at the input of theinner systemas pseudo random binary sequence. Figure 1(a) shows the block diagram of a

Performance of CDD in Ricean Channels 3

IFFT1

2

CDD Extension

CyclicPrefix

cyc

1

CyclicPrefix

Frame

AdaptationMOD

Pilot &

TPS

Signals

CODCC(171,133)

Inner DVB-T Transmission System

(a) Transmitter with 2-TX-antenna CDD frontend

removeCyclicPrefix

CE

DEMODFFT

Pilot Symbols

Data

SymbolsDeframing

CSI

DECODCC(171,133)

(b) Receiver

Figure 1. Block diagram of the inner DVB-T system

DVB-T transmitter with 2-TX-antenna CDD. The binary data isencoded, us-ing a convolutional code with generator polynomials(171, 133) in octal form.The mother code of rateR = 1/2 may be punctured in order to achieve highercode rates. After interleaving and modulation, the complexvalued data sym-bols together with scattered pilot symbols, continuous pilot carriers (CPC) andtransmission parameter signalling (TPS) data are arrangedin an OFDM frame,which consists of 68 OFDM symbols. The OFDM symbols are transformedinto a time domain signal by an inverse fast Fourier transformation (IFFT).The time domain signal is normalized and split into the TX-antenna branchesin such a way, that the overall transmitted power is independent of the num-ber of TX-antennas. In each TX-antenna branch the signal is shifted cyclicallyby δcyc

i before the guard interval as cyclic prefix is added. Considering oneOFDM symbol, the antenna specific TX signals are

si(k) =1√NT

· s(k − δcyci mod NFFT)

=1√

NT · NFFT

NFFT−1∑

ℓ=0

e−

j2π·δcyci

·ℓ

NFFT · S(ℓ) · e−j2π·k·ℓNFFT (1)

For the time intervalk = −NG, . . . , NFFT − 1 we get the OFDM symboltogether with the cyclic prefix.S(ℓ) are the complex valued frequency domainsymbols, carrying data or pilots.

4 A. Dammann, R. Raulefs, S. Plass

Table 1. Main DVB-T coding and modulation parameters

Parameter Specified Values

FFT length NFFT 2048 (2k), 8192 (8k)Relative guard interval lengths NG/NFFT 1/4, 1/8, 1/16, 1/32Inner convolutional code rates R 1/2, 2/3, 3/4, 5/6, 7/8Modulation 4-QAM, 16-QAM, 64-QAM

The receiver is shown in Figure 1(b). First, the guard interval is removedfrom the received time domain baseband signal

r(k) =

NT−1∑

i=0

Nmax∑

m=0

hi(m) · si(k − m) + n(k). (2)

n(k) denotes complex valued additive white Gaussian noise (AWGN) withvarianceσ2 andNmax is the maximum channel delay spread. The remainingOFDM time domain symbol is transformed into frequency domain by an FFT,which yields to

R(ℓ) =1√

NFFT

NFFT−1∑

k=0

r(k) · ej2π·k·ℓNFFT

= S(ℓ) · 1√NT

NT−1∑

i=0

Hi(ℓ) · e−j2π·δ

cyci

·ℓ

NFFT

︸ ︷︷ ︸

=H(ℓ)

+N(ℓ). (3)

with Hi(ℓ) =∑NFFT−1

k=0 hi(k) · ej2π·k·ℓNFFT and the AWGN termN(ℓ) again with

varianceσ2. Eq. (3) shows that CDD can be described as anequivalent channeltransfer functionH(ℓ). For this reason, a receiver cannot distinguish whethera propagation path results from CDD or the channel itself. The deframing unitseparates data- and pilot symbols. From the pilots the complex valued channelfading coefficients for each subcarrier are estimated. Withthis estimation andthe received data symbols, the demodulator provides soft information in formof log-likelihood (LL) ratios by applying the MAX-Log-MAP algorithm [7].The deiterleaved LL values are used as soft input for the Viterbi algorithm[8], which provides a maximum likelihood estimation of the information bits.Table 1 shows possible coding and modulation parameters according to theDVB-T standard.

2.2 Channel Model

For our investigations, we useIndoor Commercial – Channel Bmodel asdefined in [9]. This 7-path multipath Rayleigh fading channel models large

Performance of CDD in Ricean Channels 5

-4.6 dB

0 dB

-4.3 dB

-6.5 dB

-3 dB

-15.2 dB

-21.7 dB

0 100 200 300 400 500 600 700 800Delay [ns]

-25

-20

-15

-10

-5

0

Pow

er [d

B]

Figure 2. Power-delay profile of the Indoor Commercial – Channel B

open centers, such as shopping malls and airports. Its power-delay profile isshown in Figure 2. The Doppler spectrum of the fading processes is uniformwith bandwidths in the range offDmax = 2 . . . 5 Hz.

Subsequently, we are interested in propagation scenarios,which containLOS, therefore we define an additional propagation path at delay zero withpower |h|2. The average channel impulse response power of the resulting amultipath Riceean fading channel model is normalized to one, i.e.,

|h|2 +

NP−1∑

p=0

E{|hp|2} != 1, (4)

whereE{|hp|2} is the average power of the fading processhp for propagationpathp. We define the power ratio of LOS and non-LOS propagation paths asthe Ricean factor

K = 10 · log |h|2∑NP−1

p=0 E{|hp|2}(4)= 10 · log |h|2

1 − |h|2 [dB] (5)

Note thatK = −∞ results in the original indoor Rayleigh fading model(Fig. 2), whereasK = +∞ yields to an AWGN channel.

3. Antenna Power Weighting

LOS propagation is a severe problem for CDD since the constant (LOS)paths of the channel are transformed into a static frequencyselective one.Using 2-TX-antenna CDD, for instance, transforms an AWGN channel withCTF Hi(ℓ) = 1 into an equivalent channel with an absolute square CTF|H(ℓ)|2 = 1 + cos(2π · δcyc

1 · ℓ/NFFT) according to (3). This is depictedfor δcyc

1 = 10 samples in Figure 3 with graph∆P = 0 dB, where frequency

6 A. Dammann, R. Raulefs, S. Plass

0 1 2Frequency [MHz]

10-3

10-2

10-1

100

|H|2

1-TX2-TX, ∆P = 0dB2-TX, ∆P = 3dB2-TX, ∆P = 6dB2-TX, ∆P = 10dB2-TX, ∆P = 20dB

Figure 3. Equivalent CTF|H(f)|2 for pure LOS (AWGN), 2-TX CDD,δcyc1 = 10 samples

IFFT

Front end of a generic OFDM Transmitter

Cyclic Delay Diversity Extension

CyclicPrefix

CyclicPrefix

CyclicPrefixT

cyc

1N

cyc

1

T 1( )N

s k

1( )s k

0 ( )s k

0

1

1T

N

Figure 4. Principle of antenna power weighting

f = ∆f ·ℓ can be calculated from subcarrier indexℓ and the subcarrier spacing∆f = 4464 Hz of the considered DVB-T 2k mode. We can clearly observedeep fades, which degrade the system performance compared to the 1-TX an-tenna case. The reason for these deep fades is the equal powerdistributionamong the TX-antennas.

A solution to overcome this problem is to weight the signal ateach TX-antenna branch by different factorsαi. The implementation principle is shownin Figure 4. To keep the transmitted power independent of thenumer of TX-antennas yields to the normalization

NT−1∑

i=0

E{|αi|2} != 1. (6)

Performance of CDD in Ricean Channels 7

First of all, the implementation shown in Fig. 4 allows a flexible allocation ofpower to the different TX-antenna branches with several degrees of freedom.In order to describe the power distribution by one parameter, we define

∆P = 10 · log |α0|21 − |α0|2

[dB] (7)

as the TX power ratio between the first TX antenna and the CDD extension,i.e., TX-antennas1 . . . NT − 1. The parameter∆P allows to switch on/offCDD softly. Note that∆P = +∞ completely switches off the CDD exten-sion. Subsequently we investigate 2-TX antenna CDD by simulation. For that,definition (7) provides a unique description of the power distribution. For pureLOS (AWGN) and 2-TX antenna CDD, the equivalent CTF is

|H(ℓ)|2 = 1 +2 ·

√∆Plin

1 + ∆Plin· cos

(2π · δcyc

1 · ℓNFFT

)

, (8)

which is shown in Figure 3 forδcyc1 = 10 and different TX antenna power

ratios. ∆Plin = |α0|2

1−|α0|2is the linear representation of∆P . For more than

2-TX antennas, the power distribution within the CDD extension part is stillambiguous, and therefore, provides room for optimization.

4. Results

In this section, we provide simulation results for CDD with antenna powerweighting applied to the inner DVB-T system as introduced inSection 2.1.We use the 2k mode with a subcarrier spacing of∆f = 4464 Hz, 16-QAMmodulation and an inner code rate ofR = 3/4. The guard interval lengthis NG = 1/32 · NFFT = 64 samples, which equals7 µs for 8 MHz chan-nels. This parameter set results in a net bit rate after the outer Reed-Solomondecoder of18.1 Mbit/s for 8 MHz channels. We consider 1-TX and 2-TXantenna CDD withδcyc

1 = 10. Results in [2] have shown that no further gain isachievable for the considered channel model if we further increase the cyclicdelayδcyc

1 . The Doppler spectrum of the Rayleigh (non-LOS) componentsisuniform with a bandwidth offDmax = 4.464 Hz, which is 0.1% of the subcar-rier spacing and thus negligible in terms of intercarrier interference.

In Rayleigh fading channels, CDD provides additional propagation paths,which increases the available diversity. In pure LOS (AWGN), however, theseadditional propagation paths are static, and thus, transform the AWGN channelinto a static frequency selective one, which degrades the system performance.So, the SNR gain turns into a loss if we increase the LOS component in aRicean channel. This can clearly be seen in Figure 5. For the indoor Rayleighfading environment, we get an SNR gain of3.5 dB at BER = 2 · 10−4 for2-TX antenna CDD compared to the 1-TX antenna case (Fig. 5(a)). For the

8 A. Dammann, R. Raulefs, S. Plass

16 17 18 19 20 21 22 23 24 25 26 27 28SNR [dB]

10-6

10-5

10-4

10-3

10-2

10-1

BE

R

1-TX∆P = 0 dB∆P = 3 dB∆P = 6 dB∆P = 10 dB∆P = 20 dB

(a) K = −∞ dB (Indoor Commercial – Channel B)

10 11 12 13 14 15 16 17 18 19 20SNR [dB]

10-6

10-5

10-4

10-3

10-2

10-1

BE

R

1-TX∆P = 0 dB∆P = 3 dB∆P = 6 dB∆P = 10 dB∆P = 20 dB

(b) K = +∞ dB (AWGN channel)

Figure 5. BER after the inner Viterbi decoding of 1-TX and 2-TX CDD, DVB-T 2k-mode,16-QAM, R=3/4, perfect CE

Performance of CDD in Ricean Channels 9

-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30K [dB]

-7-6-5-4-3-2-101234567

SN

R-G

ain

[dB

] vs.

1-T

X

∆P = 0 dB∆P = 3 dB∆P = 6 dB∆P = 10 dB∆P = 20 dB

Rayleigh AWGN

Figure 6. SNR gain of 2-TX CDD compared to 1-TX atBER = 2 · 10−4 versus the Riceanfactor K, DVB-T 2k-mode, 16-QAM, R=3/4, perfect CE, Ricean channel

AWGN channel (Fig. 5(b)), however, we observe an SNR loss of6 dB. As wechange the power distribution among the TX-antennas the SNRloss decreasessignificantly an almost vanishes for∆P = 20 dB. For the Rayleigh fadingchannel the SNR gain decreases. For∆P = 10 dB the SNR loss reduces by5.3 dB to 0.7 dB, whereas the SNR gain for the Rayleigh channel reduced by1.2 dB only. Antenna power weighting allows to find a compromise betweenSNR gains and losses in non-LOS respectively LOS scenarios.Figure 5 hasshown the extremal cases (K = ±∞) of the Ricean channel, introduced inSection 2.2. Our interest now is in on the SNR gain/loss in Ricean channelsfor different Ricean factorsK. These results are shown in Figure 6. As theLOS propagation path increases in power, the SNR gain vanishes and turnsover into an SNR loss forK = 6.5 dB. It is interesting to note that thisturnover point shifts to higher Ricean factors with increasing power weightingratio∆P .

5. Conclusions

CDD is a standard conformable antenna diversity technique,which im-proves system performance of OFDM systems in Rayleigh fading (non-LOS)propagation environments. For LOS propagation, however, there are severeproblems in terms of performance losses. We have introducedthe idea of an-tenna power weighting in order to combat these losses. We have seen that

10 A. Dammann, R. Raulefs, S. Plass

antenna power weighting drastically reduces the SNR loss for Ricean channelwith a significant LOS propagation part by the cost of a slightly decreased SNRgain for non-LOS scenarios. With the approach of antenna power weightingit is possible to switch on/off CDD softly, and therefore, tofind good systemperformance compromises dependent on environment conditions, i.e. the ratiobetween LOS and non-LOS propagation. Investigations by simulation havebeen done for a DVB-T system with 2-TX antenna CDD in an indoorpropa-gation environment. Simulation results indicate that increasing the number ofTX-antennas further increases the SNR gain for non-LOS propagation. There-fore, it will be worth to investigate the system performancewith an increasednumber of TX-antennas for LOS channels with different Ricean factors.

Acknowledgment

This work have been performed in the context of the IST project PLUTO(FP6-2004-IST-4-026902), which is partly funded by the European Union.

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