Near-Optimum Blind Decision Feedback Equalization for ATSC

ETRI Journal, Volume 26, Number 2, April 2004 Hyoung-Nam Kim et al. 101

This paper presents a near-optimum blind decision feedback equalizer (DFE) for the receivers of Advanced Television Systems Committee (ATSC) digital television. By adopting a modified trellis decoder (MTD) with a trace- back depth of 1 for the decision device in the DFE, we obtain a hardware-efficient, blind DFE approaching the performance of an optimum DFE which has no error propagation. In the MTD, the absolute distance is used rather than the squared Euclidean distance for the computation of the branch metrics. This results in a reduction of the computational complexity over the original trellis decoding scheme. Compared to the conventional slicer, the MTD shows an outstanding performance improvement in decision error probability and is comparable to the original trellis decoder using the Euclidean distance. Reducing error propagation by use of the MTD in the DFE leads to the improvement of convergence performance in terms of convergence speed and residual error. Simulation results show that the proposed blind DFE performs much better than the blind DFE with the slicer, and the difference is prominent at the trellis decoder following the blind DFE.

Keywords: DTV, VSB, ATSC, equalizer, blind DFE.

Manuscript received Apr. 11, 2003; revised Jan. 30, 2004. This work was supported in part by Electronics and Telecommunication Research Institute (ETRI). Hyoung-Nam Kim (phone: +82 51 510 2394, email: [email protected]) is with the Department

of Electronics Engineering, Pusan National University, Busan, Korea. Sung Ik Park (email: [email protected]) and Seung Won Kim (email: [email protected]) are with

Digital Broadcasting Research Division, ETRI, Daejeon, Korea. Jae Moung Kim (email: [email protected]) is with the Graduate School of Information Technology

and Telecommunications, Inha University, Incheon, Korea.

I. Introduction

Decision feedback equalizers (DFEs) are commonly used in digital communication systems to suppress intersymbol interference [1], [2]. Advanced Television Systems Committee (ATSC) digital television (DTV) receivers have also used DFEs to equalize the 8-vestigial sideband (VSB) signal, which is the transmission standard of ATSC terrestrial DTV [3]. In a conventional DFE, the data passed into the feedback section is the slicer output and, hence, no longer contains any noise, thus increasing the accuracy of the interference cancellation. However, this advantage is meaningful only when the slicer output is correct. When there is no training signal and the channel eye is closed, the DFE may have a problem converging its tap coefficients since the probability that the slicer might decide incorrectly increases. Such decision errors result in error propagation throughout the feedback loop [4].

In a DFE for ATSC DTV receivers, the error propagation phenomenon may seriously affect the convergence performance because a blind equalization or decision-directed equalization using slicer outputs has to be carried out in most received symbols. When the training sequence exists, the DFE uses the training sequence for the feedback filter input. However, when there is no training sequence during the data segments, the slicer output is generally fed into the feedback section. As the symbol error rate (SER) can be as high as 0.2 and the training sequence is very short in the terrestrial DTV receiver, error propagation is unavoidable during the reception of data symbols [5]. This results in deterioration of the performance in terms of convergence speed and residual mean-square error (MSE) because the advantage of the DFE is no longer valid.

In [6], the error propagation phenomenon existing in the

Near-Optimum Blind Decision Feedback Equalization for ATSC Digital Television Receivers

Hyoung-Nam Kim, Sung Ik Park, Seung Won Kim, and Jae Moung Kim

102 Hyoung-Nam Kim et al. ETRI Journal, Volume 26, Number 2, April 2004

DFE of ATSC DTV receivers and the performance upper-limits of the DFE were analyzed and presented by comparing error-propagation and no-error-propagation cases. For one approach to the performance limit, the authors considered a blind DFE adopting a trellis decoder (TD) with a trace-back depth (TBD) of 1 as a decision device. The TBD has been set to 1 to remove symbol delay caused by the TD because the low-order tap coefficients of the feedback filter have a large impact on the equalizer performance.

While adoption of the TD in the DFE decreases the decision-error probability, it results in an increase of computational complexity due to the twelve TDs required for trellis code deinterleaving [7]. In this paper, to reduce the computational complexity without performance loss, we modify the conventional TD by using the absolute distance instead of the squared Euclidean distance for computing branch metrics. The modified TD provides a near-optimum DFE to minimize the error propagation as a near-best decision device. Compared to the conventional slicer, the MTD lowers decision-error probability and thus reduces error propagation in the DFE. The reduction of error propagation enhances the performance of the DFE, approaching the performance level of an optimum DFE.

This paper is organized as follows. In section II, we introduce the DFE commonly used for ATSC DTV receivers and address the error propagation effects in a DFE. As an effective method to overcome the error propagation, in section III we present a blind DFE adopting the MTD with a trace-back depth of 1 for the decision device. The performance enhancement of the proposed method is presented through simulation results in section IV. Finally, section V concludes this paper.

II. DFE for ATSC DTV Receivers

The 8-VSB signal is transmitted in “frames,” as shown in Fig. 1. Each data frame is composed of two data fields, each containing 313 “segments,” of which the first segment is the “field sync” segment, followed by 312 “data segments.” Each data segment is composed of 832 symbols, of which the first four symbols are the “segment sync” symbols (5, -5, -5, 5) and the remaining 828 symbols are Reed-Solomon-encoded, interleaved, and trellis-encoded symbols drawn from the 8-level pulse amplitude modulation constellation (±1, ±3, ±5, ±7) [3]. The field sync segment is used for the training sequence of the equalizer.

During the field sync segment, the DFE operates without error propagation because the known signal is fed into the feedback filter. However, since the field sync segment arrives only once every field, corresponding to 24 ms, the overall rate of convergence of the equalizer can be quite slow if the adaptation

Fig. 1. An 8-VSB data frame.

313

segm

ents

(=24

.2 m

s)31

3 se

gmen

ts(=

24.2

ms)

Field sync #1

Data+ FEC

Data + FEC

4 828 symbols

Segm

ent

sync

Field sync #2

1 segment (= 77.3 µs)

of the equalizer is carried out only during the field sync segment. In addition, such an adaptation policy is not efficient for time-varying channels. Decision-directed (DD) adaptation at the data segments does not work well. Since the SER of the symbols obtained from the equalizer output signal is about 0.2 at the threshold of visibility (TOV) [5], and the DFE has 200 more taps, one error feedback can affect 200 more outputs. To deal with time-varying channels and compensate for the shortness of the training sequence, blind equalization algorithms have been introduced for the DFE during the data segments [5], [8].

The DFE can be adapted by using the least-mean-square (LMS) algorithm or the recursive-least-squares (RLS) algorithm in the training mode, and by using one of the blind algorithms such as the constant modulus algorithm, the stop-and-go (SAG) algorithm, or the SAG dual-mode constant modus algorithm for the data segments [8]. Let ][kx be the equalizer input at time ,k then the output of the DFE at time k ,

][ky , is given by

∑∑=

−

=

−−−=ab N

jj

N

ii jkykcikxkbky

1

1

0

],[ˆ][][][][ (1)

where )1,,1,0(][ −= bi Nikb L are the forward equalizer taps at time k , ),,1(][ aj Njkc L= are the feedback taps at time ,k and ][ˆ ky is the slicer output, which is the constellation point closest to ].[ky The LMS update algorithm for the feedforward and feedback filter taps are given by


],[ˆ][][]1[],[][][]1[jkykekckc

ikxkekbkb

Djj

Dii

−+=+−−=+

µµ

(2)

where µ is the step size and ][ˆ][][ kykykeD −= is the DD error. In the blind mode, using the SAG algorithm, the filter tap coefficients are updated via

].[ˆ][][][]1[],[][][][]1[jkykekfkckc

ikxkekfkbkb

Djj

Dii

−+=+−−=+

µµ

(3)

The SAG flag ][kf is defined as

≠=

=]},[sgn{]}[sgn{0]}[sgn{]}[sgn{1

][kekeifkekeif

kfSD

SD (4)

where }sgn{⋅ is a signum function defined by

>+=<−

=,0when 1

0when 00when 1

}sgn{xxx

x

and ][keS is the Sato error given by

]}.[sgn{][][ kykykeS γ−= (5)

Here, γ is a constant defined by

,|]][[|]|][[| 2

kaEkaE

=γ (6)

where ][ka is the transmitted symbol. Note that the slicer output in (1), (2), and (3) is replaced with the training symbol during the training mode.

In many circumstances of DTV receivers, the DFE operates under the additive white Gaussian noise condition of signal-to-noise ratio (SNR) values between 20 dB and 30 dB. When we consider multi-path fading channels, the SNR condition worsens at the equalizer output because the DFE does not completely compensate for the multi-path channel effect. When the SNR is lower than about 18 dB, the eyes of the 8-VSB signal are closed and thus error propagation occurs during the data segments. This results in deterioration of the convergence performance of the blind DFE [6].

To overcome this problem, it is necessary to analyze the error propagation effect and reduce it. In [8], a selective feedback scheme was proposed to reduce the performance degradation of the blind DFE caused by error propagation. Though the performance of the blind DFE can be improved by introducing the selective feedback scheme, the degree of improvement is not large and error propagation still exists. The analysis presented in [6] shows that the SER performance of the blind

DFE can improve by more than 2 dB if we minimize error propagation.

III. Blind DFE with a Modified Trellis Decoder

The slicer output is usually determined by searching for the symbol closest to the equalizer output, ][ky , in a predetermined transmit symbol constellation. This kind of decision device has the lowest computational complexity but may result in error propagation when the eyes are closed. To improve the correct-decision probability of the slicer, the Viterbi decoder may be a good candidate as a decision device to replace the slicer [9]. It is well known that a trace-back depth of K5≥δ results in a negligible degradation in the performance relative to the optimum Viterbi algorithm [10], where K is the constraint length. Since K is 3 in the ATSC DTV system, the TBD must be no less than 15. Unfortunately, the use of a TD such as the Viterbi decoder with a TBD of 15 may not be effective for the DFE of ATSC DTV receivers due to the long delay1) caused by the TBD and the trellis code de-interleaver [7]. To adopt the TD as a decision device in the blind DFE, the delay caused by the TD has to be minimized because the low-order tap coefficients of the feedback filter have a large impact on the equalizer performance.

According to coding theory, the trellis-coded 8-VSB has better performance than the un-coded 4-VSB at a TBD setting of about 15 [6]. In the case of the DFE, however, trellis coding is valuable only if the output of the TD has better performance than the output of the slicer. Figure 2 shows that the TD with a TBD of 1 has better SER performance than the slicer output by more than 5 dB at an SER of about 0.03. The more important fact

Fig. 2. Symbol error rates of the slicer, the original trellis decoder, and the modified trellis decoder.

Performance of original and modified trellis decoder

10 12 14 16 18 20 22 24 2610-5

10-4

10-3

10-2

10-1

100

SNR (dB)

Sym

bol e

rror r

ate

Slicer output Original TD output (TBD=1)Modified TD output (TBD=1)

1) The delay becomes 12)1( ×−δ , where δ is the TBD. For example, the TBD of 15 produces a 168 symbol delay.


is that the TD with a TBD of 1 does not cause any delay in using the output of the TD for the blind DFE. If we achieve an output SNR of the DFE of only 17 dB, the TD with a TBD of 1 produces an SER of about 0.003. Provided that this SER value is given, the DFE can avoid deterioration by error propagation and approach a state of no-error propagation. However, in the case of the slicer, when the DFE achieves an output signal-to-noise ratio of 17 dB, the SER becomes 0.1, and thus results in error propagation, as shown in Fig. 2. This error propagation makes the convergence speed slow down and the residual MSE increase.

Fig. 3. Trellis-coded modulation scheme for the ATSC 8-VSB system:(a) trellis encoder, (b) state diagram.

RMapper

000

010001

011100101110111

-7-5-3-11357

R

(a)

(b)

D D

m1 m0

χ1

χ2

z0

z1

z2 z2z1z0

00

01

10

11

D0

D1

D1

D2

D2

D3

Current state Next state

00

01

10

11

010(-3) 110( 5 )

010(-3) 110( 5 ) 000(-7)

100( 1 )

001(-5) 101( 3 ) 011(-1)

111( 7 )

011(-1) 111( 7 )

001(-5) 101( 3 )

D0

D3

(m1,m0) (m1,m0)

χ1=1χ1= 0

000(-7) 100( 1 )

Adoption of the trellis decoder in the DFE decreases the decision-error probability but results in an increase of the computational complexity due to the twelve TDs required for trellis code de-interleaving [7]. To reduce the computational complexity without performance loss, we modify the computation method of the branch metric. The modification is explained based on Fig. 3, where the trellis-coded modulation scheme for the ATSC 8-VSB system is illustrated. Figure 3(a) presents the 8-VSB trellis encoder, and Fig. 3(b) shows the state diagram derived from the trellis encoder. In the original TD, the branch metric is obtained by using the squared

Euclidean distance given by

,)][(]],[[ 2ii DkyDkyBM −= (7)

where )3,2,1,0(, =iDi are the branch output symbols of the trellis diagram, as shown in Fig. 3(b). The sum of this branch metric and the path metric of the current state determines the path metric of the next state. After comparing each path metric of four states, the state with the minimum path metric becomes the next state in the trellis state transition [11].

On the other hand, in the modified TD the branch metric is computed using the absolute distance given by

|,][|]],[[BM ii DkyDky −= (8)

and the other decoding schemes are equal to the original TD. This modification reduces the computational complexity by about 1/5 with the substitution of the twelve absolute operations for the twelve multipliers. In spite of this reduction, shown in Fig. 2, the MTD has almost the same SER performance as the original TD and thus provides a near-optimum DFE to minimize error propagation as a near-best decision device.

8.7 or 0.76.7 or 1.34.7 or 3.32.7 or 5.3

6.6 or 1.44.6 or 3.42.6 or 5.40.6 or 7.4

9.5 or 1.57.5 or 0.55.5 or 2.53.5 or 4.5

5.2 or 2.83.2 or 4.81.2 or 6.80.8 or 8.8

1.8 or 6.20.2 or 8.22.2 or 10.24.2 or 12.2

0D

1D

2D3D

0.71.33.32.7

1.43.42.60.6

1.50.52.53.5

2.83.21.20.8

1.80.22.24.2

0D

1D

Computation of the branch metric

Selection of the minimum branch metric

00

01

10

11

0.7 1.4 1.5

3.3 2.62.5

3.4

0.7

3.3

0.6

2.1

3.3

3.9

6.7

3.6

4.6

1.5

1.5

4.8

5.4

1.2

6.0

4.8

1.2

0.8

6.20.8

5.4

1.8 7.8

1.8

8.0

0.2 5.0

0.2 5.6

2D3D

Fig. 4. Example of trellis decoding with the modified trellis decoder.

To easily compare the performance and operational principle between the conventional slicer and the MTD, we present a simple example in Fig. 4. The transmitted symbols and the input of the conventional slicer and the MTD are assumed to be as follows:


Transmitted symbols: (1.0, 1.0, 1.0, –3.0, –5.0) Slicer/MTD input symbols: (1.7, –0.4, 2.5, –1.8, –5.2)

The initial state is “00” and the path metric of this state is 0.0. The path metrics of the other states are all infinite. After the decoding process, shown in Fig. 4, the outputs of the conventional slicer and the MTD are obtained as follows:

Slicer output: (1.0, –1.0, 3.0, –1.0, –5.0) MTD output: (1.0, 1.0, 1.0, –3.0, –5.0)

While all the MTD output symbols are the same as the transmitted symbols, three of the slicer output symbols do not match the transmitted symbols. This result verifies the superiority of the MTD over the conventional slicer.

Figure 5 is the proposed blind DFE adopting the MTD with a TBD of 1. When we use the LMS algorithm in the training mode, the output SNR of the equalizer at the end of the training mode fails to reach 17 dB. In this case, to raise the SNR, the use of blind algorithms in the data segments is required. On the other hand, with fast algorithms, such as the RLS, we can obtain an SNR of higher than 17 dB, but only in the training mode. In such a case, we can use DD equalization for the DFE instead of blind algorithms.

Fig. 5. DFE with the modified trellis decoder.

Modified trellisdecoder

with a TBD of 1)(zB][kx ][ky ][ˆ ky

][keD

++

)(zC

–

–

Finally, note that the blind DFE with the trellis decoder does not cause any problems in the correlation of the noise sequence at the DFE output addressed in [5] because we do not assume any no-error propagation. Therefore, the analysis results given in [5] suggests that this DFE will converge toward the minimum-mean-square-error taps derived using the error propagation model and actually reduce the noise correlation at the DFE output; hence, the loss through the trellis decoder is reduced.

IV. Simulation Results

We performed extensive computer simulations to verify the equalization performance of the proposed blind DFE for ATSC DTV receivers. The transmitted data symbols were generated in “frames,” as shown in Fig. 1. The symbols of the first segment were the same as those of the field sync segment specified by the ATSC standard [3]. The other segments were unknown data segments comprised of 8-level trellis-encoded

Fig. 6. Simulation block diagram of the generation of the equalizer inputs based on the baseband-equivalent VSB channel model.

nngng 1cos][2*][ ω

][nw

Pulse shaping

Baseband- equivalent

VSB channel

Up sampling by M

Down sampling by 1/M

Matched filtering & VSB demod.

][ka ][ns

][ng ][nhR

][kx

symbols from 2-bit data ),( 21 xx , shown in Fig. 3(a), which were generated from uniformly distributed random numbers. These symbols correspond to ][ka , in Fig. 6, which is the simulation block diagram of the generation of the input symbols of the DFE based on the baseband-equivalent VSB channel model presented in [12].

The received SNR was obtained based on the signals shown in Fig. 6 and is defined as

,]|][cos][2][[|

]|][][][[|SNR2

1

2

nwnngngEnangnhE R

∗∗∗∗=

ω (9)

where ∗ is a convolution operator and n is a sample time index over-sampled by an integer value, ,M that is,

10),)1(( −≤≤+−= MiiMkn MT . Here k is a symbol time

index and T is a symbol period of 1/10.76 MHz (0.093 µs) specified by the ATSC transmission standard [3]. In (9), ][nhR is an impulse response of the baseband-equivalent VSB channel model, ][ng is the raised cosine filter with the roll-off factor of 0.0576, ][ng is the square-root raised cosine filter corresponding to ][ng , ][na is a transmit symbol sequence,

][nw is a white Gaussian noise process, and 38.521 ×= πω MHz (Refer to [12] for a detailed description).

The channel profile used for this simulation was Ensemble D having five echoes with amplitudes, delays, and phases as specified by the Advanced Television Technology Center (ATTC) [13], which is shown in Table 1.

In our simulations based on the VSB channel model, we

Table 1. Multi-path profile

Delay (µs) Amplitude (dB) Phase (degree)

–1.8 +0.15 +1.80 +5.70 +18.0

–20 –20 –18 –14 –10

90 55 25 80 90


considered VSB modulation and passband-related effects such as phase information and a carrier frequency under Korean DTV CH 15, for which the center frequency is 479 MHz. The impulse response and the amplitude spectrum of the baseband-equivalent VSB channel corresponding to Ensemble D are shown in Figs. 7 and 8.

A DFE with 40 feedforward and 216 feedback taps was adapted using the LMS or RLS algorithm in the field sync segment and blind equalization algorithms in the data segments. The step sizes of µ in the field sync segment and the data segments were 4100.2 −× and 5100.2 −× ( 5100.1 −× for the DD algorithm under SNR values of less than 21 dB), respectively. The forgetting factor in the RLS was 1.0.

Fig. 7. Impulse response of the equivalent VSB channel corresponding to Ensemble D.

Symbol time (T=0.093 µs)

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200

Am

plitu

de

Fig. 8. Amplitude spectrum of the baseband channel impulse response.Frequency (MHz)

-10 -5 0 5 100

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Am

plitu

de

1. Convergence Performance

The convergence performance was checked by the MSE of the equalizer output, which was computed as follows:

].|][][[|][ 2kakyEkMSE −= (10)

The statistical results come from the average of 100 independent ensembles. For ease of performance viewing, we also used the time average of 50 symbols.

A. LMS in the Training Mode

Figures 9 and 10 show the MSE learning curves of the conventional DFE with the conventional slicer (denoting the conventional DFE), the MTD (denoting the proposed DFE), and no-error propagation (denoting the optimum DFE) at signal-to-noise ratios of 16 to 23 dB. The LMS algorithm was applied in the training mode, and the SAG and DD algorithms were used during the data segments. The result shows that error propagation caused by wrong decisions degrades the convergence performance in terms of both the convergence speed and residual error.

At an SNR of 16 dB, as shown in Fig. 9(a), the output SNR at the end of the training mode2) was about 10 dB, where the symbol error rate of the modified trellis decoder with a TBD of 1 was almost the same as that of the slicer and was greater than 0.4, as can be seen in Fig. 2. Thus, at the starting point of the blind adaptation, error propagation is inevitable even though we use the MTD with a TBD of 1 instead of the slicer for a decision device. However, blind adaptation using the SAG algorithm makes the output SNR improve and thus the performance is better than when the DD algorithm is used. As the blind adaptation using the SAG algorithm proceeds, the output SNR increases and thus the effect of adopting the MTD is prominent compared with the slicer because the difference between the SER of the MTD and that of the slicer grows large.

The effect of error propagation on the equalization performance becomes clearer in Fig. 9(b). Though error propagation exists at the start of blind adaptation, the SAG algorithm adopted in the proposed DFE enhances the output SNR of the DFE and, thus, makes the error propagation decrease. On the other hand, when we use the DD algorithm in the conventional DFE, error propagation caused by slicing error seriously affects the convergence performance. The SAG of the conventional DFE is comparable to the DD of the proposed DFE because blind adaptation of the SAG algorithm in the conventional DFE compensates for the slicing error, and the MTD decreases the decision error probability in the proposed DFE.

In conclusion, as the SNR increases from the low ratios shown in Fig. 9 to the high ratios seen in Fig. 10, the proposed DFE approaches the optimum DFE. We can see that blind equalization is preferable to DD equalization at low SNRs (less than about 18 dB) while DD equalization is superior to blind

2) This corresponds to an 832 symbol time. Actually, the number of the training symbols is 820. In addition, the number may be shortened to 728 if we do not use the reserved symbols. This number is not critical for analyzing performance trend of the DFE.


Fig. 9. Mean-squared error convergence of the DFE (LMS with µ=0.0002 in the field sync segments; SAG or DD with µ=0.00002in the data segments) at an SNR of (a) 16 dB, (b) 17 dB, (c) 18 dB, and (d) 19 dB.

x104

-16

-14 -12 -10

-8

-6

-4

-2

0 MSE learning curve (16 dB)

Number of symbols (a)

Mea

n sq

uare

erro

r (dB

)

0 1 2 3 4 5 6

Optimum DFE

Conventional DFE with DD

Proposed DFE with DD

Conventional DFE with SAG

Proposed DFE with SAG

x104

-18

-16

-14

-12

-10

-8

-6

-4

-2

0MSE learning curve (17 dB)

Number of symbols (b)

Mea

n sq

uare

erro

r (dB

)

0 1 2 3 4 5 6

Optimum DFE Proposed DFE with SAG

Proposed DFE with DDConventional DFE with DD


0 1 2 3 4 5 6x104

-18 -16 -14 -12 -10 -8 -6 -4 -2 0

MSE learning curve (18 dB)

Number of symbols (c)

Mea

n sq

uare

erro

r (dB

) Optimum DFE Conventional DFE with DD




x104

-18

-16

-14

-12

-10

-8

-6

-4

-2


Number of symbols (d)

Mea

n sq

uare

erro

r (dB

)

0 1 2 3 4 5 6

Optimum DFE





Fig. 10. Mean-squared error convergence of the DFE (LMS with µ=0.0002 in the field sync segments; SAG or DD with µ=0.00002in the data segments) at an SNR of (a) 20 dB, (b) 21 dB, (c) 22 dB, and (d) 23 dB.


0 1 2 3 4 5 6x104

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 MSE learning curve (20 dB)


Mea

n sq

uare

erro

r (dB

) Optimum DFE





0 1 2 3 4 5 6x104

-20-18-16-14-12-10-8-6-4-20



Mea

n sq

uare

erro

r (dB

) Optimum DFE




0 1 2 3 4 5 6x104

-22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 MSE learning curve (22 dB)


Mea

n sq

uare

erro

r (dB

) Optimum DFE





0 1 2 3 4 5 6x104

-22-20-18-16-14-12-10-8-6-4-20



Mea

n sq

uare

erro

r (dB

)



Optimum DFE




Fig. 11. Mean-squared error convergence of the DFE (RLS with the forgetting factor of 1.0 in the field sync segments; SAG or DDwith µ=0.00002 in the data segments) at an SNR of (a) 16 dB, (b) 17 dB, (c) 18 dB, and (d) 19 dB.

0 2000 4000 6000 8000 10000-20

-15

-10

-5

0

5



Mea

n sq

uare

erro

r (dB

)

Optimum DFE





0 2000 4000 6000 8000 10000-20

-15

-10

-5

0

5



Mea

n sq

uare

erro

r (dB

)

Optimum DFE





0 2000 4000 6000 8000 10000-20

-15

-10

-5

0

5



Mea

n sq

uare

erro

r (dB

)

Optimum DFE





0 2000 4000 6000 8000 10000-20

-15

-10

-5

0

5



Mea

n sq

uare

erro

r (dB

)

Optimum DFE





Fig. 12. Mean-squared error convergence of the DFE (RLS with the forgetting factor of 1.0 in the field sync segments; SAG or DDwith µ=0.00002 in the data segments) at an SNR of (a) 20 dB, (b) 21 dB, (c) 22 dB, and (d) 23 dB.

0 2000 4000 6000 8000 10000-20

-15

-10

-5

0



Mea

n sq

uare

erro

r (dB

) Optimum DFE





0 2000 4000 6000 8000 10000-20

-15

-10

-5

0

5


Mea

n S

quar

e E

rror (

dB)

Optimum DFE





0 2000 4000 6000 8000 10000-25

-20

-15

-10

-5

0



Mea

n sq

uare

erro

r (dB

)

Optimal DFE





0 2000 4000 6000 8000 10000-25

-20

-15

-10

-5

0



Mea

n sq

uare

erro

r (dB

) Optimum DFE







equalization at high SNRs (more than about 19 dB).

B. RLS in the Training Mode

To raise the output SNR at the end of the training mode, we used the RLS algorithm, and the results are shown in Figs. 11 and 12. Under an SNR of 16 dB, as show in Fig. 11(a), the output SNR at the end of the training mode was about 13.7 dB, where the SER of the proposed DFE was 0.08, as was shown in Fig. 2. While this SER value was about 0.25, seen in Fig. 2, and was smaller than that of the conventional DFE, it still caused error propagation. Accordingly, the performance of the proposed DFE was close to that of the conventional DFE.

The performance of the proposed DFE approached the optimum DFE at an SNR of 17 dB, which can be seen in Fig. 11(b). In this case, the output SNR at the training mode was about 14.7 dB corresponding to an SER of 0.04. When the SNR was greater than 17 dB, the performance of the proposed DFE was almost the same as that of the optimum DFE. From these results, we found that if the output SNR of the DFE with the MTD at the end of the training mode was greater than 15.6 dB, corresponding to an SER of 0.02, error propagation did not affect the convergence performance. However, the conventional DFE suffered from error propagation even when the output SNR was about 19 dB, as seen in Fig. 11(d), because the SER of the slicer output was about 0.05, as was shown in Fig. 2.

Note that the optimum solution of LMS-type algorithms is different from that of LS-type algorithms. As illustrated in Figs. 11 and 12, discontinuities between the training mode and the blind mode appeared because we used LS-type algorithms such as the RLS in the training mode, and LMS-type algorithms such as DD and SAG in the blind mode. The discontinuities become more obvious when either error propagation, caused by slicing error in the conventional DFE, or a low output SNR exists.

We also found that DD adaptation and blind adaptation had almost the same performance in the proposed DFE. In the case of the conventional DFE, however, blind adaptation showed a little better performance than DD adaptation in terms of residual MSE at low SNRs, which will be clearly shown in the SER plots presented in the next section.

C. Symbol Error Rate Performance

We carried out simulations to obtain the SER curves of the blind DFE to compare the residual error performance. The number of simulated segments including one field sync segment was 301, and thus the number of data segments was 300, which corresponded to 249,600 symbols. The SER was computed by counting the number of symbol errors existing in the last 180,000 symbols after the tap coefficients converged. In ATSC DTV receivers, we are interested in the performance

Fig. 13. Symbol error rate performance of the DFE: (a) LMS,(b) RLS.

Sym

bol e

rror r

ate

of e

qual

izer

15 16 17 18 19 20 21 22 23 24 2510-3

10-2

10-1

100Equalizer performance in ATTC-D channel

SNR (dB) (a)


Optimum DFE Conventional DFE with SAG Conventional DFE with DD


Sym

bol e

rror r

ate

of e

qual

izer

15 16 17 18 19 20 21 22 23 24 2510-3

10-2

10-1

100Equalizer performance in ATTC-D channel

SNR (dB) (b)

Optimum DFE Conventional DFE wih SAG Conventional DFE wih DD Proposed DFE with SAG Proposed DFE with DD

at SNR values of not more than 25 dB because the trellis decoder following the equalizer can correct most symbol errors at SNR values greater than 25 dB.

Figure 13 shows the SER curves using the LMS and RLS algorithms in the training mode. In both cases, the optimum DFE has a better performance by about 3 dB than the conventional DFE at an SER of 0.2, corresponding to the threshold of visibility (TOV). On the other hand, the proposed DFE was about 2 dB better than the conventional DFE at the TOV value. The performance of the proposed DFE was similar to that of the optimum DFE at most SNR values but degraded to the level of the conventional DFE at very low SNR values when either the LMS or the RLS algorithms in the training mode was used. We found that when error propagation exists, blind adaptation was preferable to DD adaptation in the DFE for ATSC DTV receivers.

We have to note that the performance of the DFE affects the SER performance of the trellis decoder3) following the DFE

3) This trellis decoder is different from the TD used as a decision device in the DFE and generally has a TBD of about 15 to produce the maximum SER performance in the trellis-coded 8-VSB signal.


Fig. 14. Symbol error rate performance of the trellis decoderfollowing the DFE: (a) LMS, (b) RLS.

TCM decoder performance in ATTC-D channel

15 16 17 18 19 20 21 2210-5

10-4

10-3

10-2

10-1

100

SNR (dB) (a)

Sym

bol e

rror r

ate

of T

CM

dec

oder

15 16 17 18 19 20 21 22

SNR (dB) (b)

Sym

bol e

rror r

ate

of T

CM

dec

oder

TCM decoder performance in ATTC-D channel

Optimum DFE Conventional DFE with SAG Conventional DFE with DD Proposed DFE with SAG Proposed DFE with DD

10-5

10-4

10-3

10-2

10-1

100

Optimum DFE Conventional DFE with SAG Conventional DFE with DD Proposed DFE with SAG Proposed DFE with DD

specified in the ATSC terrestrial DTV standard [7]. Figure 14 shows the SER curves of the trellis decoder receiving the output of the DFE and then decoding with a TBD of 15. While the DFE output SER performance of the proposed DFE is similar to that of the optimum DFE, the SER performance of the trellis decoder between them differs by 1 dB. In the conventional DFE, blind adaptation of the SAG algorithm has better performance than DD adaptation at SNR values of less than 22 dB. When the SNR was greater than 21 dB, the SER was smaller than the TOV at the trellis decoder, and thus, the comparison is meaningless.

V. Conclusions

The error propagation phenomenon is unavoidable in the

DFE for ATSC DTV receivers because the training sequence is very short and the symbol error rate of the equalizer output can be as high as 0.2. To reduce the error propagation, we proposed a hardware-efficient blind DFE by incorporating a modified trellis decoder for a decision device. As the MTD uses the absolute distance instead of the Euclidean distance, computational complexity is reduced by 1/5 without performance loss, compared to the original TD. In the proposed DFE, error propagation was apparently reduced, resulting in a faster convergence speed and improved SER performance by more than 2 dB compared with the conventional DFE.

Acknowledgment

The authors would like to thank the anonymous reviewers whose comments improved this paper.

References

[1] S.U.H. Qureshi, “Adaptive Equalization,” Proc. IEEE, vol. 73, no. 9, Sept. 1985, pp. 1349-1387.

[2] N. Al-Dhahir and J.M. Cioffi, “MMSE Decision-Feedback Equalizers: Finite-Length Results,” IEEE Trans. Inform. Theory, vol. 41, no. 4, July 1995, pp. 961-975.

[3] ATSC, ATSC Digital Television Standard, Apr. 2001, Doc. A/53A. [4] A. Fertner, “Improvement of Bit-Error-Rate in Decision Feedback

Equalizer by Preventing Decision-Error Propagation,” IEEE Trans. Signal Processing, vol. 46, no. 7, July 1998, pp. 1872-1877.

[5] M. Ghosh, “Blind Decision Feedback Equalization for Terrestrial Television Receivers,” Proc. IEEE, vol. 86, no. 10, Oct. 1998, pp. 2070-2081.

[6] H.-N. Kim, S.I. Park, and S.W. Kim, “Performance Analysis of Error Propagation Effects in the DFE for ATSC DTV Receivers,” IEEE Trans. Broadcasting, vol. 49, no. 3, Sept. 2003, pp. 249-257.

[7] ATSC, Guide to the Use of ATSC Digital Television Standard, Oct. 1995, Doc. A/54.

[8] H.-N. Kim, Y.-T. Lee, and S.W. Kim, “Blind Decision Feedback Equalization for VSB-Based DTV Receivers,” IEEE Trans. Consumer Electronics, vol. 48, no. 3, Aug. 2002, pp. 602-609.

[9] J.J. Nicolas and J.S. Lim, “Equalization and Interference Rejection for the Terrestrial Broadcast of Digital HDTV,” Proc. ICASSP-93, vol. 4, Minnesota, USA, Apr. 1993, pp. 176-179.

[10] J.G. Proakis, Digital Communications, 4th ed., McGraw-Hill, New York, 2001, p. 485.

[11] E. Biglieri, B. Divsalar, P.J. McLane, and M.K. Simon, Introduction to Trellis-Coded Modulation with Applications, Macmillan, New York, 1991.

[12] H.-N. Kim, Y.-T. Lee, and S.W. Kim, “Mathematical Modeling of VSB-Based Digital Television Systems,” ETRI J., vol. 25, no. 1, Feb. 2003, pp. 9-18.

[13] Comm. Research Center, Digital Television Test Results – Phase I, CRC Report No. CRC-RP-2000-11, Ottawa, Nov. 2000, p. 6.


Hyoung-Nam Kim received the BS, MS, and PhD degrees in electronic and electrical engineering from Pohang University of Science and Technology (POSTECH), Pohang, Korea, in 1993, 1995, and 2000, respectively. From May 2000 to February 2003, he was with Electronics and Telecommunications Research

Institute (ETRI), Daejeon, Korea, developing advanced transmission and reception technology for terrestrial digital television. Since March 2003, he has been an Assistant Professor in the Department of Electronics Engineering at Pusan National University, Busan, Korea. His research interests are in the areas of digital signal processing, adaptive IIR filtering, and radar signal processing, in particular, signal processing for digital television, digital communications, and multimedia systems. Dr. Kim is a member of IEEE and KICS.

Sung Ik Park received the BSEE from Hanyang University, Seoul, Korea, in 2000 and MSEE from POSTECH, Pohang, Korea, in 2002. Since 2002, he has been with the Broadcasting System Research Group, ETRI, where he is a member of Research Staff. His research interests are in the area of error

correction codes and digital communications, in particular, signal processing for digital television.

Seung Won Kim received the BSEE and MSEE from Sung Kyun Kwan University, Korea, in February 1986 and 1988. After graduation, he served in the Korean Army as a reserved officer from August 1988 to February 1989. Since June 1989 he has been employed at ETRI, Korea. He received his PhD from

University of Florida, USA, in May 1999. He is currently a leader of DTV system research team at ETRI. His main research interests are in the areas of digital communication systems, digital signal processing and DTV transmission systems.

Jae Moung Kim received the BS degree from Hanyang University, Korea in 1974, the MSEE degree from University of Southern California, USA in 1981, and the PhD degree from Yonsei University, Korea in 1987. He was a Vice President of Radio & Broadcasting Technology Laboratory and Director of Satellite

Communication System Department at ETRI from September 1982 to March 2003. Since April of 2003, he has been a Professor in the Graduate School of Information Technology and Telecommunications, Inha University. He is a board member of directors of Korean Institute of Communication Science (KICS), a Vice President of Korea Society of Broadcast Engineers (KOSBE) and a senior member of IEEE. His research background is telecommunication systems modeling and performance analysis of broadband wireless access systems, mobile communications, satellite communications and broadcasting transmission technologies.

Documents

Near-Optimum Blind Decision Feedback Equalization for ATSC