Effective Multi-Mode Equalization for ATSC Receivers

Elias Nemer Intel Corporation Technology Office. Consumer Electronics Group. 2200 Mission College Blvd Santa Clara, CA 95054 U.S.A email: [email protected]

Abstract— This paper presents a new equalization scheme for VSB-based digital video broadcasting (DVB) receivers used in the F F F slicer Current North-American ATSC standard. The proposed equalizer symb consists of switching between multiple modes of adaptation, depending on its convergence state. The contribution described in Coefficient Adaptation FBF this paper is about a novel criteria to switch between a “blind” and a “decision-directed” adaptation, and is based on the 4th order statistics (the kurtosis) of the slicer error (the error past symbol(s) between the received soft symbols and their estimated hard Next symbol levels). Simulation in adverse channel conditions shows the scheme is effective and very robust in the presence of high levels of noise and the echo sets specified in the Grand Alliance requirements [9] for DTV broadcast. Comparison to other known methods showed this scheme is more reliable and accurate in FFF : changing channel conditions, thus ensuring proper equalizer - removes the pre-cursor ISI of the next symbol FBF : convergence in all practical situations. - combines the energy of the current symbol removes the post-cursor ISI of the (from the past few samples) past symbol(s) Keywords: DVB. ATSC receiver. Equalizer. Figure 1 : Pre and post echoes and an equalizer structure I. INTRODUCTION Digital video broadcasting (DVB) is designed to deliver B. Equalization Challenges for ATSC high fidelity pictures and sound, to create a true ‘home-theatre’ experience for the end user. A number of standards for To cover the worst case set specified in the Grand Alliance terrestrial [10][11] satellite [12][14] and cable broadcasts [15] tests [9], an equalizer total length of roughly 400 taps is have been defined over the past few years. The north-American required. The challenges in using such a long equalizer for terrestrial standard (ATSC) uses an 8-level Vestigial Sideband 8VSB are: modulation (VSB) to transmit roughly 10 Msymb/s in the • The long convergence time to properly adapt the 2 traditional 6 MHz band used for analog TV channels. filters. • A. Overview The error propagation effects, due to bad slicer decisions being fed back in the FBF and cause either The nature of the terrestrial TV channel causes long signal instability or poor convergence. multipaths at the receiver and leads to two types of inter- symbol interference (ISI) as shown in figure 1: • The high AWGN level (15 – 18 dB) which makes decision directed adaptation (DD) sometimes unusable • post-cursor ISI: The falling tail causes past symbols to and makes it critical to have a proper non-DD interfere with the current one. adaptation for a long enough period to “open the eye”. • pre-cursor ISI: The rising edge causes future symbols to interfere with the current one. Given the above challenges, a number of equalization schemes have been proposed in the literature: For these reasons, it is customary to consider an equalizer • Blind-only adaptation: this type of adaptation [3] is that has both a feed-forward filter (FFF) and a feedback one guaranteed to converge and is not susceptible to high (FBF); the first equalizes the pre-cursor ISI and the latter the levels of noise which cause unreliable slicer decision. post-cursor ISI). It is arguable however that a long-enough FFF Various blind adaptation schemes, based on variations can also equalize some of both the ISI’s as well, though the of the classical Sato, Goddard and other newly derived added advantage of using a sliced decision and a feedback sign errors [8], have been proposed for terrestrial DVB structure provides an added de-noising effect of the clean past receivers. The drawback of blind-only adaptation is a decisions. limited effectiveness: it has a relatively large residual error and thus cannot achieve as good of an SNR as in SatoErr[k] = ~y[k] − R ⋅ sign{}~y[k] decision-directed adaptation. 2 R = E (a (k ) ) E ()a (k ) = 5.25 • Stop-and-Go (SAG) adaptation schemes that consists of adapting the equalizer during ‘reliable’ conditions

only and freezing the adaptation the rest of the time. 64 sym field Sync Correlator Decision Logic These approaches [4] prevent an erroneous adaptation Blind / DD / Soft Symbols training which may throw the equalizer out of the convergence Slicer Err mode path. However, the drawback is that the equalizer may Input get caught in an un-reliable condition and never get Symbols FFF : N Taps ~ x(n) y[k] yˆ[k] adapted; Given the very noisy conditions, such Slicer methods have very limited effectiveness in practical Hard Symbols terrestrial broadcast environments. Old FFF, FBF • Dual-mode adaptation: These schemes [5][6] are the Soft Symbols Soft FBF : M Taps most effective and consist of changing dynamically Symbols Blind Adaptation 3:1 between blind adaptation and decision-directed Slicer MUX DD Err field Sync Adaptation adaptation, depending on various criteria. The blind FS Training Training New FFF, FBF adaptation is used as a ‘cold start’ to open the eye of mode Err Adaptation the constellation, and once in a semi-converged state, mode the equalizer is switched to a decision-directed to minimize an MMSE error , which results in the best Figure 2 : Multi-mode equalizer structure achievable constellation SNR. The challenge in these schemes is to have a reliable and robust way to switch 2. A decision-directed state: used when the equalizer has between these modes. Erroneous, late or pre-mature almost converged. This mode allows the error to be switching can cause instability or failure to converge. minimized and thus leads to a maximization of the In this paper, we present a generalized multi-mode SNR. The adaptation is done based on the slicer error: equalizer that switches between blind, decision-directed and training modes at the proper times in a changing channel + = − µ ⋅ ⋅ − FFFi [k 1] FFFi [k] DD SlicerErr[k] x[k i] conditions. We propose a novel and effective scheme for FBF [k +1] = FBF [k] − µ ⋅ SlicerErr[k]⋅ yˆ[k − j] switching between blind and decision-directed, based on the j j DD fact that the slicer error distribution is significantly different where: between a non-converged and a nearly-converged state. As a result, the 4th order statistics of this error is used to discriminate yˆ[k] = Slicer{}~y[k] the distribution shape and determine the correct mode. SlicerErr = ~y[k] − yˆ[k]

i = 1: N j = 1: M II. PROPOSED EQUALIZATION SCHEME k iteration index A. Generalized Multi-mode Adaptation 3. A training state: whenever an apriori known field sync The general equalizer structure is shown in figure 2 below. (FS) sequence is sent from the transmitter and detected The soft output of the equalizer is given by: at the receiver, the equalizer switches to this state and

N M derives its error from the training symbols. ~y[k] = ∑ FFF[i]⋅ x[k − i] + ∑ FBF[ j]⋅ FBF _ Memory[k − j] = = + = − µ ⋅ ⋅ − i 1 j 1 FFFi [k 1] FFFi [k] T TrainErr[k] x[k i] The proposed scheme is a generalization of the dual-mode FBF [k +1] = FBF [k] − µ ⋅TrainErr[k]⋅ FS[k − j] adaptation (described above), namely, the equalization control j j T ~ logic can be viewed as a state machine with transition where: TrainErr = y[k]− FS[k] dynamically between 3 states (fig. 3): In addition, the control logic includes an initialization state, 1. A blind adaptation state: used for ‘cold start’ and which occurs at start up (or reset) and entails starting the whenever the equalizer is not in a converged state. The equalizer with a given coefficient set. This could simply be an coefficients are updated based on a blind error that does impulse set. not require an estimate of the transmitted symbol. For example, Sato-based adaptation [3] is carried out as:

FFF [k +1] = FFF [k] − µ ⋅ SatoErr[k]⋅ x[k − i] i i S + = − µ ⋅ ⋅ ~ − FBF j [k 1] FBF j [k] S SatoErr[k] y[k j] where: • The value of the equalizer soft symbol: this scheme is based on the reasoning that values lying far from (all) Train constellation points are usually wrong, and an Sync Sync detected indication of non-convergence. The scheme in [2] is detected based on several heuristics and empirical boundaries, End-of- sync but is not proven robust or effective in all cases.

Initialize Blind DD Convergence lost B. Criteria based on slicer error statistics

Near-convergence The proposed scheme is based on the observation that the statistical distribution of the slicer error is an effective and robust way to distinguished between a converged and a non- • Initialize : an intial set of coefficients is downloaded converged state. The graphs below (fig. 4) show the • Blind : adaptation based on Blind error (Sato) • DD : LMS adaptation based on slicer error (decision-directed) distribution (histogram) of the slicer error during both the • Train : LMS adaptation based on the training error converged and non-converged states. Graphs are shown for the case of added noise, as well as noise-free scenarios.

Figure 3 : State machine control of equalization modes

Ensemble A, no noise After convergence Ensemble A, no noise Before convergence III. EFFECTIVE MODE SWITCHING CRITERIA

A. Reported Methods Switching back and forth between Blind and DD at the correct time is critical and has to be done dynamically: Ensemble A, 18 dB • Given the severity of the echoes (and the high level of After convergence

noise), blind adaptation is needed to “open the eye”. If Ensemble A, 18 dB the switch to DD is done prematurely, the equalizer Before convergence cannot converge and will lead to a poor SNR. • Once in a DD state, the equalizer must be able to revert back to the blind state, if the channel abruptly changes. If the equalizer remains erroneously in the DD state, it will not converge or become unstable. Figure 4: The PDF of the slicer error before and after convergence (with and without noise). • If the equalizer remains in a blind adaptation mode for From the observation above, we note that: more than needed, it delays a proper receiver ‘lock’, i.e. a low enough Bit Error rate. In adverse multipaths • The distribution of the slicer error has a Gaussian conditions, keeping the equalizer indefinitely in ‘blind’ shape (or close to Gaussian) once the equalizer has just adaptation may not achieve the desired SNR that is converged, whether noise is present or not. We note required for a Threshold of Visibility (TOV) [9]. here that the inherent clipping of the error to ±1due to the modulo operation of the slicer causes high histograms values at the edges when added noise is Various known schemes have been proposed as the used. This prevents a perfect Gaussian shape, but that deciding criteria to switch between blind and DD adaptation: shape is nevertheless distinct from the case of non- convergence. • The value of the slicer error [7]: this metric is not reliable in a high-noise environment because the error • The distribution of the slicer error has a non-Gaussian value is too high, even in a full converged state. and near-uniform shape during the non-convergent state, whether noise is present or not. • The value of the blind error: the blind errors (such as Sato or Goddard) are statistical errors, that average to • The slicer error by itself (i.e. the level or energy value) zero when in a converged mode, however their cannot be a reliable metric since the level of input instantaneous values are never small. Using long term noise of 15 dB makes this error quite large, whether the average of these values is not convenient or effective. equalizer is converged or not. • The correlation of the signs of the slicer and blind Thus, detecting convergence can be achieved thru a metric error: there is no clear evidence that the correlation that characterizes (or discriminates) the shape of the between the sign of the 2 errors will be significantly distribution of the error. To this end, we consider the 4th order different in a converged state. statistics of the slicer error (SE), defined as: 2 K[]SE = E[]SE 4 − 3()E []SE 2 Eq 1

Kurtosis of the slicer Error State flag This metric is attractive for 2 reasons: Tain • The kurtosis of a Gaussian process is zero: []= K SEGnoise 0 DD • For the case of uncorrelated processes, the kurtosis of the sum is the sum of the kurtosis : Blind K [SE ]= K [SE ]+ K []SE reflection s+noise reflection s noise = []+ K[se] not in [-0.4:0.1] for 100 symb K SE reflection s 0

Thus, the value of the kurtosis of the slicer error is near Blind DD zero once the equalizer starts converging and non-zero when not converged. This is true whether noise is present or not, since the value of the kurtosis of Gaussian noise is zero. K[se] in [-0.4:0.1] for 15,000 symb

C. Robustness of mode switching in noise Figure 6 : Transition between blind and DD using the kurtosis The value of the kurtosis for the case of an echo set (ensemble F in [9]) without any noise, and the case where IV. SIMULATION RESULTS 18dB AWGN is added are shown in figure 5 below. The plots illustrates that the general behavior of the kurtosis is similar An ATSC transmitter-receiver model using the above regardless of the added noise. Clearly, the value in the case of equalizer was implemented and the echo profiles specified in noise does not go to the ideal zero, but is small enough to allow [9] were simulated. The following figures show the switching a detection scheme. In both sets of plots, the kurtosis has a of the equalizer between the 3 states for some of the static large value while the equalizer is not converged and decreases ensembles with noise added. gradually near convergence. In this case, the equalizer is In each of the 2 figures (7 and 8) below, the soft symbols adapting based on a blind scheme using Sato error [3]. The are shown (though not visible due to the added noise). The kurtosis is computed from the incoming data using time value of the kurtosis is shown, along with the training error averaging to approximate the statistical expectations in Eq 1. (when the equalizer is in the Train state). The plot in the lower Equalizer output soft symbols Equalizer output soft symbols right corner shows the transition flag between the 3 states (0: Ensemble F, 18 dB noise Ensemble F, no noise Blind; 1: DD; 2: Train). The 2 figures are meant to illustrate that with the required noise level (between 17 dB and 18.44 dB), the behavior is similar and this illustrates the robustness of the proposed scheme. In this case, the echo profile (ensemble A), is specified in the GA specs and consists of a set of 6 multipaths, each with a given attenuation and phase shift.

Kurtosis of the slicer Error Kurtosis of the slicer Error

Equalizer output soft symbols Kurtosis of the slicer Error

Figure 5: value of the kurtosis of the slicer error in the case of an echo Training error State flag set with and without added noise Tain

In general, switching between DD and Blind adaptation modes can be done based on the value of the kurtosis (K[SE]): DD - From the blind mode: If K[SE] is in the interval [0.4:0.1] for 15,000 consecutive symbols, go to DD Blind - From the DD mode: If K[SE] falls outside the interval [-0.4:0.1] for 1000 or more symbols, go to blind. Figure 7: Blind-DD-Train switching – Ensemble A + 18.44 dB noise Equalizer output soft symbols Kurtosis of the slicer Error

REFERENCES [1] W. Lee et al. “ Convergence Analysis of the Stop-and-Go Blind Equalization Algorithm”. IEEE Transactions on communications, Vol. 47, No. 2, Feb. 1990. [2] L. R. Litwin et al. “ Blended CMA : Smooth, Adaptive transfer from CMA to DD-LMS”. IEEE 1999 Training error State flag Tain [3] M. Ghosh. “Blind Decision Feedback Equalization for Terrestrial Television Receivers”. Proceedings of the IEEE, Vol. 86, No. 10 Oct 1998. [4] C. Tseng and C. Lin. “A Stop-and-Go Dual-Mode Algorithm for Blind DD Equalization”. IEEE 1996. [5] V. Weerackody and Salem Kassam. “Blind Adaptive Equalization Using Dual-Mode Algorithm”. 1990. [6] V. Weerackody and Salem Kassam. “Dual-Mode Type Algorithms for Blind Blind Equalization”. IEEE transactions on communications, Vol. 42, Figure 8: Blind-DD-Train switching – Ensemble A with 17 dB noise. No. 1 , Jan 1994. [7] H. Kim et al. “Blind Decision Feedback Equalization for VSB-based Finally, the figure 9 shows the case where the channel DTV Receivers”. IEEE 2002. abruptly changes while the equalizer is running. The purpose is [8] M. Ghosh. “A Sign-error algorithm for Blind Equalization of Real to illustrate the ability to switch back to the Blind state from the Signal”. IEEE 1998. DD state, when a sudden change in the channel requires it. In [9] Grand Alliance requirements. Advanced Television Technology Center. this case, the channel is switched from the preset ensembles A “Evaluation of ATSC 8-VSB receiver performance in the presence of to C to D. simulated multipaths and noise”. Doc #99-04A. Sept 1999. [10] A/53. “ATSC standard: digital television standard, revision B”. Kurtosis of the slicer Error Advanced Television Systems Committee (ATSC). Aug 2001. [11] EN 300-744. “Digital video broadcasting. Framing structure, channel Equalizer output soft symbols modulation for digital terrestrial television”. ETSI V1.4.1 2001-01. [12] EN 300 421. “Digital video broadcasting (DVB). Framing structure, channel coding and modulation for 11/12 GHz satellite services”. ETSI. V1.1.2. 1997 – 08. [13] EN 302 307. “Digital video broadcasting: second generation framing structure, coding and modulation systems for broadcasting, interactive services, news gathering and other broadband satellite applications. State flag ETSI. DVBS2-74r15. 2004. Tain [14] ITU-R BO.1516. “Common functional requirements for the reception of digital multi-programme television emissions by satellite operating in A C D the 11/12 GHz frequency range”. DD [15] ITU-T J.83. “Digital multi-programme systems for television, sound and data services for cable distribution”. 1998. NO AWGN

Blind

Figure 9: Abrupt channel changes through ensembles A, C, D

V. CONCLUSION This paper presented a new scheme for multi-mode equalization for an ATSC receiver. The proposed equalizer transitions between various adaptation modes as needed to ensure stability and improved SNR in all channel conditions. The key criteria for switching between a blind and decision- direction adaptation is based on the kurtosis of the slicer error and allows dynamic and effective switching when channel conditions abruptly change. Simulation showed this criterion is robust and works effectively in all the echo ensembles specified by the Grand Alliance spec [9]. Note: A patent application based on this work is filed by Intel Corporation (P21333).