Study of Cyclic Delay Diversity for Single Frequency Network using DRM Standard Vincent Savaux ∗ ECAM

∗† ,

Mo¨ıse Djoko-Kouam ∗ , Alexandre Skrzypczak and Yves Lou¨et †

‡

Rennes - Louis de Broglie, Campus de Ker Lann - Bruz 35 091 Rennes Cedex 9, France † IETR - SUPELEC, Campus de Rennes 35 576 Cesson - S´evign´e Cedex, France ‡ Zodiac Data Systems 2 rue de Caen, 14740 Bretteville l’Orgueilleuse, France

Abstract—This paper presents a study of cyclic delay diversity (CDD) for a single frequency network (SFN) using digital radio mondiale (DRM) standard. Flat fading over the bandwidth can entirely disrupt the signal during several orthogonal frequency division multiplexing (OFDM) symbols. In such conditions, channel encoding can only partially recover the sent information. In order to overcome this problem, CDD artificially increases the frequency selectivity of the channel by adding a phase to the signal at the emitter side. We describe the principle in the case of two transmit antennas, and for a more complete network model, where three values of phase shifting are considered. We measure the gain provided by CDD for one process on one hand and in average on the other hand. In order to complete the study, we show the effect of the increase of frequency selectivity on the channel estimation performance. Index Terms—COFDM, delay diversity, single frequency network, digital radio mondiale.

I. I NTRODUCTION OFDM, used with channel encoding (COFDM) is very robust in frequency selective channels context. Furthermore, the addition of a guard interval (GI) avoids the intersymbol interference (ISI). In SFNs, the signal is emitted at the same frequency from all transmit antennas. In the overlapping area between two adjacent cells, the channel which disrupts the signal can be composed of several paths with short delays. In the frequency domain, it causes flat fading which can affect the complete bandwidth, and during several OFDM symbols. In such conditions, even COFDM does not reduce the errors enough at the receiver to obtain an acceptable signal quality. This article deals with cyclic delay diversity, which increases the frequency selectivity and avoids flat fading. The considered SFN uses the digital radio mondiale (DRM) standard, extended to DRM+ [1], designed for the radio transmission below 30 MHz (DRM) and until 174 MHz (DRM+). References [2]–[4] cover the usual spatial diversities. In [2], some subcarriers are clustered and emitted by independent antennas. This is not applicable in our SFN context. In [3], delay diversity (DD) is presented. By adding a delay to the signal, it artificially increases the frequency selectivity at the receiver. However, this method is limited by the length of the GI. To overcome this problem, [4] proposes phase diversity

(PD), in which phase shifting is added in the frequency domain, what also increase frequency selectivity. Equivalently to PD, [5] presents cyclic delay diversity (CDD) in digital video broadcasting-terrestrial (DVB-T) [6] context. It also shows that the phase shifting can be performed at the receiver side. In [7], a comparison between delay diversity and Alamouti scheme [8] is studied. Although Alamouti diversity scheme is more efficient in slow fading environments, its performance is degraded in fast varying environments. [9] discuss channel estimation in case of transmission with CDD. Indeed, the receiver has to adapt the channel estimation to the increase of frequency selectivity. [10], [11] present recent studies on DD measurements in DRM+ context. In this article, we propose a theoretical study of CDD in a SFN context with DRM standard. We describe the problem in a simple example (two transmitters), and we extend to the use of CDD in a more general SFN context. When several cells are considered, we show that three different values of phase shifting are needed at least to perform CDD. Furthermore, in DRM/DRM+ standard, such as in other standards, pilots carriers are sparse in the frame, so an interpolation on the time and frequency axis is required to obtain the channel estimation all over the frame. We also study the effect of the increase of the frequency selectivity due to CDD on the performance of the system. The rest of the paper is organized as follows: Section II describes the system model for two transmit antennas, Section III presents CDD and extends the problem for a multiple transmitters SFN. In Section IV simulations results show the effects of CDD and channel estimation on the performance of the system. Finally, we draw conclusions in Section V. II. S YSTEM M ODEL A. Transmission Model As depicted in Fig. 1, we consider a mobile receiver Rx in the overlapping area between two antennas Tx1 and Tx2 in a single frequency network (SFN). Let us assume that, in this area, the power of the signal from Tx1 is equal to the power of the one from Tx2 . Furthermore, the delays of arrival of the signal from the two antennas can be very short, what may

cause flat fading in the considered bandwidth. A more general SFN network model will be presented in Section III-C.

0

overlapping area

−10

10

Tx1

0

Tx2

−10 −20

Rx

20log10(|H|)

−20 −30 −40

−30

−50 −60 −40

−70 −80

Fig. 1.

100

Simplified SFN network, with two transmitters Tx.

80

30

From the receiver Rx point of view, the contribution of the signal from the two transmitters is a signal emitted over a single channel. After the removal of the cyclic prefix and the 𝑀 -points discrete Fourier transform (DFT), the received signal is U = CH + W,

(1)

where C is the 𝑀 ×𝑀 diagonal matrix of the emitted symbols, W is the 𝑀 × 1 complex vector of the white Gaussian noise such as each sample 𝑊𝑚 , 𝑚 = 0, 1, ..., 𝑀 − 1 follows a distribution 𝒩 (0, 𝜎 2 ). H is the 𝑀 × 1 vector of the frequency response of the channel, whose characteristics are given in Section II-B. We express the samples 𝐻𝑚 , 𝑚 = 0, 1, ..., 𝑀 −1 of the frequency response of the equivalent channel as the sum of the two channel contributions:

𝐻𝑚

= =

𝐿−1 ∑

ℎ𝑙 𝑒−2𝑗𝜋

𝑙=0 𝐿∑ 1 −1 𝑙1 =0

𝑚𝜏𝑙 𝑀

(2)

𝑚𝜏𝑙

ℎ𝑙1 𝑒−2𝑗𝜋

𝑀

1

+

𝐿∑ 2 −1

𝑚𝜏𝑙

ℎ𝑙2 𝑒−2𝑗𝜋

𝑀

2

, (3)

𝑙2 =0

where ℎ𝑙 , ℎ𝑙1 , ℎ𝑙2 are the time-varying path weights, which are zero mean Gaussian random processes. 𝜏𝑙 , 𝜏𝑙1 , 𝜏𝑙2 are the corresponding sampled path delays. 𝐿 is the number of paths of the equivalent channel. We assume that each channel has the same number of paths and 𝐿 = 𝐿1 + 𝐿2 . In our model, we consider short delays 𝜏𝑙 . In such conditions, the gains ∣𝐻𝑚 ∣ can be deeply reduced over a large number of consecutive carriers. As made in [5], we illustrates these wide fading in Fig. 2, over 103 carriers and for 30 consecutive OFDM symbols. A dynamic representation of the phenomenon is available following this link 1 . When too many consecutive carriers (in the frequency and time axis) are disrupted by the deep fading, the decoding of the COFDM signal becomes inefficient even if bit interleaving is used, and a large number of decision errors occurs. Considering such corrupted signals, the maximum transmission rate is not reached. 1

http://www.youtube.com/watch?v=cyy1bVE8W24&feature=relmfu

20

40

15 10

20 carriers

Fig. 2.

−50

25

60

5 0

0

−60 OFDM symbols

Frequency Response of the Equivalent Channel, without Diversity.

B. System Parameters This study is based on the parameters taken from the digital radio mondiale (DRM/DRM+) standard [1]. DRM, and its extension DRM+, is designed for the broadcast of the digital radio over the current AM and FM bands. We here consider the DRM parameters, that is the transmission below 30 MHz, but the study is applicable to all SFN such as DRM+ or DVB-T [5]–[7], [11]. The considered signal is emitted with the robustness mode B in a channel bandwidth 𝐵 = 5 kHz. Each OFDM symbol is composed of 103 carriers, and each frame of 15 symbols. The bit stream is mapped with a 4QAM constellation. The symbol and cyclic prefix durations are 𝑇𝑠 = 21.33 ms and 𝑇𝐶𝑃 = 5.33 ms respectively. The Reed Solomon code rate is equal to 0.5. For both channels, we consider a simple model inspired from the 𝐶𝐶𝐼𝑅 𝑝𝑜𝑜𝑟, described in [1]. It is a two pathschannel with a uniform gain profile and following the wide sense stationary uncorrelated scattering (WSSUS) model. This channel modeling is sufficiently relevant for our transmission scenario in Fig. 2 as it represents the case of a channel with a LOS (line of sight) path and a path corresponding to one ionospheric reflection. The maximum delay 𝜏𝑚𝑎𝑥 is fixed so that 𝜏𝑚𝑎𝑥 = 1/2𝐵 = 0.1 ms, which allows to simulate a flat fading. Each path has a Gaussian Doppler spectrum, and the maximum Doppler frequency is equal to 2 Hz. It corresponds to a mobile velocity roughly equal to 72 km/h. III. S PATIAL T RANSMIT D IVERSITY In order to overcome the problem of deep fading on a wide bandwidth, inserting some spatial diversity may consequently increase the frequency selectivity of the channel. In this case, the channel is disrupted by many fading, but each one affects a limited bandwidth. By using a channel coding and a bit interleaving, it becomes possible to limit the errors at the receiver. We here present the two main spatial diversities: the

delay diversity (DD) and its equivalent form in frequency, the phase diversity (PD) or cyclic delay diversity (CDD) [4], [5].

0

A. Delay Diversity

10

The principle of CDD or PD is to directly apply the phase shifting in the frequency domain. In the discrete formalism, the delay becomes Δ = 𝑘𝑇𝑠 /𝑀 and the frequency is 𝑓 = 𝑚/𝑇𝑠 . The phase shifting −2𝜋𝑓 Δ then becomes −2𝜋𝑘𝑚/𝑀 . If the condition 𝑇𝐶𝑃 > 𝜏𝑚𝑎𝑥 +Δ, DD, CDD and PD are equivalent, as shown in [5]. However, CDD or PD does not necessitate any constraint on the guard interval 𝑇𝐶𝑃 > 𝜏𝑚𝑎𝑥 + Δ. Since Tx1 and Tx2 play the same role in our problem formulation, the phase shifting is applied on Tx2 , without loss of generality. Let us denote Φ𝑚 = −2𝜋𝑘𝑚/𝑀 the phase applied on the 𝑚𝑡ℎ carrier. From (3), we express the resulting frequency response as

=

𝐿∑ 1 −1

𝑚𝜏𝑙

ℎ𝑙1 𝑒−2𝑗𝜋

𝑀

1

+

=

𝑙1 =0

−30 −30

−40 −50 −40

−60 −70 −80

−50

100 80

𝐿∑ 2 −1

𝑚𝜏𝑙

ℎ𝑙2 𝑒−2𝑗𝜋

𝑀

2

40

𝑚𝜏𝑙

ℎ𝑙1 𝑒−2𝑗𝜋

15 10

20

carriers

−60

20 5 0

OFDM symbols

0

C. Extension to a Multi-Transmitters SFN Network In this section, we consider a multiple transmit-antennas network, as depicted in Fig. 4. In the proposed model, we alternate transmitters without CDD (marked with an empty circle, such as 𝐵𝑆1 ) with transmitters with CDD (marked with a full circle or a cross, such as 𝐵𝑆2 and 𝐵𝑆3 ). Obviously, the phase of 𝐵𝑆2 noted Φ𝑚2 is different from the one of 𝐵𝑆3 noted Φ𝑚3 . Furthermore, the arrangement is made so that two adjacent areas do not share the same phase shifting. Should the opposite occur, the received frequency response would be given by

𝑒𝑗Φ𝑚 𝐻𝑚 =

𝑀

1

+

𝐿∑ 2 −1

ℎ 𝑙2 𝑒

𝑚(𝜏𝑙 +𝑘) 2 −2𝑗𝜋 𝑀

. (4)

𝑙2 =0

ℎ𝑙 𝑒

−2𝑗𝜋

𝑚𝜏𝑙 𝑀

)

𝑒𝑗Φ𝑚 .

(5)

In that case, whatever the value of the phase shifting Φ𝑚 , (5) is equivalent to a transmission without CDD (3). Three different values of phase shifting are then required to develop the network. Although Fig. 4 is still a theoretical representation, it highlights the three different overlapping areas between the cells: two areas between cell with and without CDD (presented in previous Section III-B) and one area between cells with CDD. In that case, we express the resulting frequency response as

𝐻𝑚

=

(𝐿 −1 1 ∑

𝑚𝜏𝑙

ℎ 𝑙1 𝑒

−2𝑗𝜋

𝑀

𝑙1 =0

+

(𝐿 −1 2 ∑

1

)

𝑚𝜏𝑙

ℎ 𝑙2 𝑒

−2𝑗𝜋

𝑀

2

𝑙2 =0

= http://www.youtube.com/watch?v=p5vyyNpYIgo

(𝐿−1 ∑ 𝑙=0

In order to obtain the expected increase of destructive and constructive superposition, we keep the condition 𝑘 > 2. Fig. 3 illustrates the frequency selectivity brought by CDD with 𝑘 = 6. The snapshot is obtained on 103 carriers and during 30 OFDM symbols. Compared with Fig. 2, the frequency fading is higher, but the channel finally corrupts less consecutive carriers and less consecutive OFDM symbols. To complete the observation, the dynamic evolution of channel with CDD can be consulted following this link 2 . The channel is exactly the same as before, and CDD has been added, with 𝑘 = 6. In such condition, an efficient channel estimation [12], [13], combined with coded-OFDM with bit interleaving, largely allow to reduce the errors of decision at the receiver [2]– [5]. However, this model with only two transmit antennas is very simple. In practice, several antennas must be taken into account to accurately describe a SFN network. 2

30 25

60

𝑙2 =0

𝑙1 =0

𝐿∑ 1 −1

−20

−20

Fig. 3. Frequency Response of the Equivalent Channel, with Cyclic Delay Diversity.

B. Cyclic Delay Diversity

𝐻𝑚

−10

20log10(|H|)

The principle of delay diversity is to transmit the signal from one antenna with a delay Δ. This time shifting is equivalent to a phase shifting in the frequency domain, which increases the frequency selectivity. In order to get the expected effect, [4] indicates that the condition on the delay Δ > 2/𝐵 must be respected. In the following, we note Δ = 𝑘/𝐵, with 𝑘 > 2. The problem of DD is that from the receiver point of view, it increases the maximum delay to 𝜏𝑚𝑎𝑥 + Δ. Moreover, if 𝜏𝑚𝑎𝑥 + Δ > 𝑇𝐶𝑃 , it creates intersymbol interference (ISI). A solution is to lengthen the guard interval, which consequently leads to a reduction of the useful data rate.

−10

0

𝐿∑ 1 −1 𝑙1 =0

ℎ𝑙1 𝑒−2𝑗𝜋

𝑚(𝜏𝑙 +𝑘1 ) 1 𝑀

𝑒𝑗Φ𝑚1 )

𝑒𝑗Φ𝑚2

+

𝐿∑ 2 −1 𝑙2 =0

ℎ𝑙2 𝑒−2𝑗𝜋

𝑚(𝜏𝑙 +𝑘2 ) 2 𝑀

(6).

𝐵𝑆1

𝐵𝑆2

𝐵𝑆3

100

90

Percentage of disrupted carriers

no CDD with CDD

20log10(|H|) = −10 dB

80

70

60

50

40

30

20

10

0

overlapping areas Fig. 4.

SFN Network, with multiple transmitters Tx.

By factorizing 𝑒𝑗Φ𝑚1 or 𝑒𝑗Φ𝑚2 with 𝑒𝑗Φ𝑚1 ∕= 𝑒𝑗Φ𝑚2 , the expression (6) is equivalent to (4):

𝐻𝑚

=

(𝐿 −1 1 ∑

𝑚𝜏𝑙

ℎ𝑙1 𝑒−2𝑗𝜋

𝑀

1

𝑙1 =0

+(

𝐿∑ 2 −1

𝑚𝜏𝑙

ℎ 𝑙2 𝑒

−2𝑗𝜋

𝑀

2

)𝑒

𝑗Φ𝑚2 −𝑗Φ𝑚1

𝑙2 =0

)

𝑒𝑗Φ𝑚1 . (7)

Finally, whatever the considered overlapping area, the study amounts to the same thing. Only the phase shifting will be different: Φ𝑚1 , Φ𝑚2 or Φ𝑚2 − Φ𝑚1 . IV. S IMULATIONS R ESULTS A. Measurement of the Fading In a first time, we study the effect of CDD on the width of the channel fading, independently to the rest of the system (channel estimation, channel encoding etc.). To do so, we measure the maximum number of consecutive carriers disrupted by deep fading, i.e. the percentage of consecutive carriers disrupted by a channel gain 20𝑙𝑜𝑔10 (∣𝐻𝑚 ∣) equal or less than -10 dB. Fig. 5 displays the value of this measure versus time (sampled in OFDM symbols), with and without CDD. The comparison is given for one simulation run and during 420 consecutive OFDM symbols, corresponding to a signal time duration equal to 11.20 s. In this example, we fixed 𝑘 = 6. For one process, we observe on Fig. 5 that the maximum percentage of consecutive carriers disrupted by fading less than -10 dB can reach 100%, and that during several consecutive OFDM symbols. In that case, the channel decoding becomes inefficient and a large number of errors in bit stream occurs. Considering the same transmission with CDD on one Tx, we observe a decrease of this maximum to 40%. As a consequence, we suppose that the number of errors is less than in a transmission without CDD. On the other hand, for a transmission without CDD, we observe that it is possible to obtain a flat channel (no carriers under -10 dB), what

0

Fig. 5.

50

100

150

200 250 OFDM symbols

300

350

400

450

Percentage of disrupted carriers over 420 OFDM symbols.

tallies with a perfect transmission with only AWGN. In this conditions, for the transmission with CDD, we observe that the percentage reaches around 8%. The effect of CDD is then to globally keep at low value the maximum percentage of consecutive carriers disrupted by fading. Table I shows the average values of the percentages for two different shifting values 𝑘1 = 3 and 𝑘2 = 6. The use of two shifting values allows to describe the model of Section III-C: one transmitter without CDD, and two transmitters with 𝑘1 ∕= 𝑘2 . By choosing 𝑘2 = 2𝑘1 , we simplify the number of cases to consider because 𝑘1 = 𝑘2 −𝑘1 . Two thresholds -10 and -20 dB are considered. Furthermore, in order to complete the study, we test CDD with variable values of 𝑘 during the transmission. To simulate it, we consider that the delay 𝑘 alternately takes the value 𝑘 − 1, 𝑘 and 𝑘 + 1. Each of the three values has a probability equal to 1/3. The average is calculated with 100 simulation runs. For a transmission without CDD, the average of maximum percentage of consecutive carriers disrupted by fading is 22.6% at -10 dB and 7.34% at -20 dB. TABLE I AVERAGE OF CONSECUTIVE CARRIERS DISRUPTED BY FADING AT -10 OR -20 D B. C OMPARISON IN FUNCTION OF DIFFERENT DELAY VALUES .

test test test test

1 2 3 4

k = 3: 0 k = 6: I 0 I 0 I

fixed k: 0 var. k: I 0 0 I I

% -10 dB 15,17 10,50 15,59 10,78

% -20 dB 4,52 3,19 4,55 3,53

In average, we observe that the maximum percentage of consecutive carriers disrupted by fading decreases compared to transmission without CDD, whatever the threshold, and for the two values 𝑘 = 3 and 𝑘 = 6. It confirms the observations made for one simulation run. When varying delays 𝑘 is used, we find almost the same results as for fixed 𝑘. Indeed, in average, 𝐸 {𝑘} (when 𝑘 varies) is equal to the fixed 𝑘 value, 𝐸 {.} being the mathematical expectation. At the receiver, varying 𝑘 would increase the difficulty of making an efficient estimation, or requires methods which do not depend on the variations of

the channel parameters as [14]. We then finally recommend the use of fixed 𝑘 delays.

transmission without CDD at BER=10−3 , the gain in SNR is 2dB for CDD with 𝑘 = 3 and 3 dB for 𝑘 = 6.

B. Bit Error Rate Performance

0

10

AWGN no CDD CDD, k=3 CDD, k=6 −1

10

BER

We now characterize the performance of the global system, including channel encoding and channel estimation. We use a Reed-Solomon code with rate 1/2. A least square (LS) estimation is performed on the pilot tones, and a cubic spline interpolation allows to get the channel estimation all over the bandwidth. Fig. 6 depicts the bit error rate (BER) as a function of OFDM symbols, for a transmission duration of 11.20 s (420 symbols). Two independent processes are displayed, in which the transmission of the signal without CDD is compared to the one with CDD, for the same channel. We used a delay 𝑘 = 6, and the signal to noise ratio is set equal to 10 dB.

−2

10

−3

10

−4

10 0.2 no CDD CDD

Fig. 7.

0.05

0

0

50

100

150

200 250 OFDM symbols

300

350

400

450

0

50

100

150

200 250 OFDM symbols

300

350

400

450

0.07 0.06 0.05 BER

−2

0

2

4

6 SNR (in dB)

8

10

12

14

16

BER versus SNR for transmissions with and without CDD.

0.1

0.04 0.03 0.02 0.01 0

Fig. 6.

BER versus OFDM symbols, for two process.

For the two processes, we clearly observe a decrease of the BER for the transmission with CDD compared to the one without CDD. Indeed, two effect are noticeable. Firstly, the symbols with non-null BER are sparsely distributed in transmissions with CDD, while they occur a lot more and consecutively appear in transmissions without CDD. Thus, on the figure at the top, the duration of consecutive OFDM without CDD symbols with non-null symbols is roughly equal to 1.5 s, while the BER is null during all the transmission duration with CDD. Secondly, the BER value is lower if diversity is used: on the figure at the bottom, the BER reaches 0.025 (with CDD) against 0.065 without CDD. In the context of radio transmission with DRM/DRM+, we conclude that the use of CDD allows to get a listening time with almost inaudible disruptions. Fig. 7 displays the BER curves of transmission without CDD compared to the one with CDD, for 𝑘 = 3 and 𝑘 = 6. As a lower bound reference, we also added the BER performance of a transmission over a flat channel with AWGN. The simulation has been performed on 500 simulations runs, corresponding to 2.106 bits. We observe, for SNR values from -4 to 16 dB, the gain provided by CDD. Indeed, compared to

In order to study the effect of CDD on the performance of the global system, it is important to show the impact of the increase of frequency selectivity on the channel estimation performance. The distribution of the pilot tones in the frame is one for seven carriers in the frequency axis and one for four symbols in the time axis (see [1]). A least square (LS) estimation is performed on pilot tones and an interpolation is made to obtain the channel estimation all over the frame. Thus, Fig. 8 compares the BER curves of channel estimation made with a spline interpolation and with a linear interpolation, in the case of transmissions without CDD, and CDD with 𝑘 = 6. Spline interpolation is more efficient than linear, but also more complex: 𝒪(𝑀 2 ) for spline and 𝒪(𝑀 ) for linear interpolation. 0

10

AWGN no CCD, spline CDD, k=6, spline no CDD, linear CDD, k=6, linear

−1

10

BER

BER

0.15

−4

−2

10

−3

10

−4

10

−4

−2

Fig. 8.

0

2

4

6 SNR (in dB)

8

10

12

14

16

BER versus SNR, effect of the interpolation.

In both cases, linear interpolation is less efficient than spline. For CDD, we observe that the SNR gap between spline and linear interpolation is equal to 1 dB at BER=10−3 and 2 dB for BER=10−4 . For linear interpolation, the SNR gap

keeps equal to 0.5 dB. Without CDD, the channel has a low frequency selectivity, so spline and linear interpolation have almost the same performance. However, in presence of CDD with 𝑘 = 6, spline is more efficient than linear. We conclude that the channel estimation method must be taken into account when CDD is used in a network to keep an acceptable BER at the receiver. Although CDD clearly reduces the flat fading in overlapping areas of SFN, the consequence of its use is the increase of complexity of the estimation method. V. C ONCLUSION In this article, we presented the cyclic delay diversity in the context of a SFN in DRM/DRM+ standard. In the overlapping area between two adjacent cells, flat fading may occur, disrupting the signal during several OFDM symbols. CDD artificially increases the frequency selectivity of the channel, reducing the width of the fading. Coded OFDM then allows to recover a signal with a limited amount of errors. We then gave the theoretical expressions of the channel frequency response in presence of diversity. We showed the effect of CDD on the width of the fading, and we confirmed the decrease of BER compared to a transmission without CDD. Furthermore, we studied the effect of the increase of selectivity on channel estimation performance. We showed that it must be taken into account in the global performance of the system. Thus, keeping an expected value of BER could imply an increase of the complexity of the channel estimation method. R EFERENCES [1] ETSI, “Digital Radio Mondiale (DRM);System Specification,” ETSI, Tech. Rep. ETSI ES 201 980 V 3.1.1, August 2009. [2] L. J. Cimini, B. Daneshrad, and N. R. Sollenberger, “Clusteired OFDM with Transmitter Diversity and Coding,” in GLOBECOM, vol. 1, 1996, pp. 703 – 707. [3] Y. Li, J. C. Chuang, and N. R. Sollenberger, “Transmitter Diversity for OFDM Systems and Its Impact on High-Rate Data Wireless Networks,” IEEE Transactions on Selected Areas in Communications, vol. 17, no. 7, pp. 1233 – 1243, July 1999. [4] S. Kaiser, “Spatial Transmit Diversity Techniques for Broadband OFDM Systems,” in GLOBECOM’00, vol. 3, 2000, pp. 1824 – 1828. [5] A. Dammann and S. Kaiser, “Standard Conformable Antenna Diversity Techniques for OFDM and its Application to the DVB-T System,” in GLOBECOM’01, vol. 5, 2001, pp. 3100 – 3105. [6] ETSI, “Digital video broadcasting (DVB) framing structure, channel coding and modulation for digital terrestrial television,” ETSI, Tech. Rep. ETSI EN 300 744 V1.5.1, 2004. [7] H. Schulze, “A Comparison between Alamouti Transmit Diversity and (Cyclic) Delay Diversity for a DRM+ System,” in Proceedings of International OFDM Workshop, Hamburg, Germany, August 2006. [8] S. Alamouti, “A Simple Transmit Diversity Technique for Wireless Communications,” IEEE Trans. on Communications Systems, vol. 16, no. 8, octobre 1998. [9] G. Auer, “Channel Estimation :for OFDM with Cyclic Delay Diversity,” in PIMRC, vol. 3, September 2004, pp. 1792 – 1796. [10] F. Maier, A. Tissen, and A. Waal, “Evaluations and Measurements of a Transmitter Delay Diversity System for DRM+,” in WCNC, Paris, France, 2012, pp. 1180 – 1184. [11] ——, “Evaluations and Measurements of a Single Frequency Network with DRM+,” in European Wireless, Poznan, Poland, April 2012. [12] M. Biguesh and A. B. Gershman, “Training-Based MIMO Channel Estimation: A Study of Estimator Tradeoffs and Optimal Training Signals,” IEEE Transactions on Signal Processing, vol. 54, no. 3, pp. 884–893, March 2006.

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