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218 IEEE TRANSACTIONS ON BROADCASTING, VOL. 44, NO. 3, SEPTEMBER 1998 Block Sequential quares Feedback Equalization Algorit Application to Terrestrial Chun-Ming Zhao, member, IEEE, Xiao-Yu Hu, student member, IEEE, and Xiao-Hu Yu, senior member, IEEE

Abstruct- Due to the very high of terrestrial does not perform well on channels with spectral nulls in the HDTV systems, up to now there exist no equalization so- frequency response characteristics , to compensate for the lutions with sufficiently low hardware complexity and sat- isfactory performance for commercial applications. In this channel distortion the LE places a large gain near the spec- paper, we present a block sequential least squares decision tral nulls, which enhances the additive noise. In contrast, feedback equalization algorithm with application to over- the DFE can compensate for amplitude distortion without the-air HDTV channels. The proposed adaptive algorithm as much as noise enhancement as a LE by inclusion of a is derived on the basis of minimization of least squares crite- rion, thereby achieving faster convergent and tracking rate decision-feedback section which eliminates the intersymbol relative to the recommended LMS algorithm. Meanwhile, interference from previously detected symbols. good numerical stability is guaranteed because it success- In the literature of adaptive equalization, the coefficients fully eliminates time updates of the flltering coefficients, which is the main cause of instability of FTF-like algo- of a DFE are usually adjusted by adaptive algorithms, such rithms, Also of great significance is its drastic reduction as LMS and RLS. Although the LMS is computationally in computational complexity by means of block operation, efficient, its convergence rate is dependent on the chan- taking advantage of the slowly time-varying nature of ter- restrial broadcasting channels. Simulation results show that nel characteristics and is especially slow on channels which the equalizer achieves almost 3.5dB SNR improvement at contain spectral nulls. In contrast, the convergence rate a bit error rate of 3 x lo-' without significant increase in of the RLS algorithm is not affected by the channel char- computational complexity, as compared to the conventional LMS decision feedback equalizer (DFE) when applied to the acteristics, it can provide consistently fast convergent and equalization of over-the-air HDTV channels. tracking properties. However, the computational burden proportional to N2 (N is the total order of the equalizer), is prohibitively expensive for HDTV applications. I. INTRODUCTION It has been reported by Cioffi [7][8]that FTF can provide HE vulnerability of terrestrial HDTV broadcasting lower bound of computational requirement for the prewin- T systems with respect to linear distortion caused by dowed sample-by-sample fast recursive least squares algo- multipath propagation can greatly be reduced by the use rithms. The computational load of FTF can be reduced to of adaptive equalizers [1][2][3].The choice of the equalizer 7N,approximately three to four times that of the LMS al- structure and of its adaptation algorithm is heavily influ- gorithm. Nevertheless, several authors [9][10] pointed out enced by the baud rate of the system and by the technol- that the FTF-like algorithms are numerically instable, and ogy available for the implementation. An equally impor- divergence may occur after a large number of iterations. tant factor is the characteristics of terrestrial broadcasting This paper is concerned with the algorithm of block se- channels, namely, currently existing NTSC bands. quential least squares (BSLS) adaptive decision feedback In the over-the-air HDTV applications using TCM-8VSB equalizer and the performance of its application to Grand transmission with very high symbol rate (10.76 M sym- Alliance TCM-8VSB terrestrial HDTV broadcasting sys- bols/s), a major problem is the presence of large intersym- tem. Not only the average operations of the proposed bo1 interference (ISI) due to time dispersion. The reason equalizer can be drastically reduced, but also better equal- for the time dispersion is that a received signal is the sum ization performance can be achieved because of the fast of the multipath signals with different delay. It is well rec- convergence and tracking properties of least squares crite- ognized a decision feedback equalizer (DFE) has a better rion. Moreover, it will be shown that numerical stability is bit-error-ratio (BER) performance than a linear equalizer also well guaranteed, which is very important for practical (LE), especially on time-varying multipath fading channels. applications. Decision feedback equalization is widely employed as an ef- The remainder of this paper is organized as follows. Sec- fective countermeasure to eliminate IS1 when the channel tion I1 briefly describes the overall system and a reason- distortion is too severe for an LE to handle. Since the LE able channel model for terrestrial HDTV broadcasting, pro- viding a background to evaluate equalization performance. The authors are currently with National mobile Communications Research Laboratory(NCRL), Southeast University, Nanjing 210096, The algorithm of BSLS decision feedback equalizer is de- P.R. China. e-mail: hxyQseu.edu.cn. This work was supported in rived in Section 111, in which geometric approach will be part by the Transcentury Talent Foundation of State Education Com- employed. Section IV evaluates the performance of the pro- mission of China and the Climbing Program-National Key Project for Fundamental Research in China, Grant NSC 92097. posed equalizer by computer simulation in comparison with Publisher Item Identifier S 0018-9316(98)08 0018-9316/98$10.000 1998 IEEE

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data data Reed-Solomon data trellis - randomizer - encoder - interleaver - encoder

-_ - pilot VSB RF multiplexer - insertion - modulator - upconverter

~ rejection phase qualiae detector filter tracker -

trellis data Reed-Solomon data L- decoder -de-int erleaver decoder de-randomizer &

Fig. 2. Block diagram of Grand Alliance HDTV TCM-8VSB receiver respectively. Tab. I illustrates some important parameters used in computer simulation. the LMS DFE recommended by Grand Alliance. Some im- portant issues regarding practical implementation, such as TABLE I computational complexity, convergence rate, are also ad- MAIN PARAMETERS USED IN SIMULATION dressed. Finally, a brief summary concludes this paper.

11. SYSTEMOVERVIEW AND CHANNELMODEL A. system description The Grand Alliance high-definition standard for terres- trial broadcasting (TCM-8VSB) over the taboo channels uses a digital vestigial sideband technique with additional features that enhance it when reception is difficult [11]-[16]. Forward error correction in the form of Reed-Solomon and trellis coding, along with 1/6 data field interleaving, pro- B. channel model vide a rugged system that can endure both white noise and interference environment. At the suppressed carrier In order to evaluate the performance of adaptive equal- frequency of 310k Hz from the lower band edge, a small izer, it is of great significance to establish a reasonable pilot added to the VSB signal assists robust carrier recov- mathematical model for over-the-air HDTV channels. The ery in the receiver even under the occasionally extreme Institute for Telecommunication Sciences (ITS) has com- conditions of terrestrial broadcasting. In order to maxi- pleted a program to measure the impulse responses of mize service area and alleJriate co- or adjacent-channel in- VHF/UHF channels that would probably be used in over- terference from NTSC signal, an comb/rejection filter is the-air HDTV. Based on these measurements, Hufford [17] employed in the receiver. In addition, a powerful adap- developed a simple statistical model which needs only two tive equalizer is designed to compensate for severe linear parameters-the “strength” and the “spread” of the “mul- channel distortion, such ara tilt and ghosts, whether these tipath tail”. Given an archetype region, the equivalently distortions come from the transmission channel or from im- low-pass complex impulse response of HDTV broadcasting perfect components within the receiver. Fig. 1 and Fig. 2 channel can be written in the form show the transmitter and tlhe receiver block diagrams of the TCM-SVSB terrestrial broadcasting transmission system, 中国科技论文在线 http://www.paper.edu.cn

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where T denotes symbol duration, r and T are selectable weighted linear combination of the input signal sequence parameters of multipath tail and where the zi are complex- ykPn, _n = -NI -+ 1,.. . , -1,O, and of the previous outputs valued random variables. All the zi are pairwise indepen- -Tk-1,1k-2,-..,Ik-~~. Thus dent and their real and imaginary parts are independently 0 N2 Gaussian variables with zero means and standard devia- .fk = cjyk-j + ~.jfk-j (3) tions equal to fi. In consequence , the amplitudes are j=-Ni+l j=1 Rayleigh distributed and the phases uniformly distributed. The equalizer is assumed to have NI taps in its feedforward The first term here is the direct wave which has been nor- section and N2 taps in its feedback section. According to malized to an in-phase unit impulse. The subsequent sum- specifications of Grand Alliance, the tap coefficients are mation is then a “tail” of randomly sized multipath com- adjusted recursively by using LMS algorithm. That is, ponents. The parameter T measures the strength of the multipath tail, namely the ratio of the energy in the tail &k+1 ck+ pekpk (4) to that in the direct signal. T is a measure of the delay where the vector Ck consists of the tap coefficients spread of the tail-after a time 7, the expected power will C-N~+~,...,C-~,C~,C~,...,CN~,the vector vk consists of have dropped by a factor l/e. A reasonable selection for - the data ?/k+Nl-l,. . ,yk, 4-1, - . . , I~-N~,p denotes the “worst-case” multipath propagation in HDTV channel may step size, and the error is either be R = -3dB and ~=5ps,where the capital letter R de- notes the strength, T, in decibel. €k = ak - Ik (5) The inadequacy of Eq.(l) lies in that it does not take nr maximal multipath time delay an important factor -.. T~~~~ €k = Ik - Ik (6) determining the needed number of adaptive equalizer taps, into account. From references [18] and [19] , one can know depending upon whether the equalizer is operating in ini- that multipath time delay spreads in urban areas can span tial training mode or in decision-directed mod:, respec- 6-8ps, and up to 17ps in mountainous terrain. Therefore, in tively. (ak denotes the training sequence and 1, denotes the worst case a reasonable maximal multipath time delay the decision of the estimate fk) rmazmight take 18ps. Thus the modified version of Eq.(l) As mentioned earlier, the performance degradation can be rewritten as caused by slow convergence rate of LMS algorithm can be alleviated by LS-type algorithms. The proposed BSLS DFE algorithm inherits the transversal BSLS algorithm de- veloped by one of the authors [20]. This algorithm achieved the exact LS solution by keeping track of some correla- The amplitude profile of this typical simulated channel are tion vectors instead of directly adapting tap coefficients. depicted in Fig. 3. The basic idea is to utilize the time-updating quantities to transfer the information from block to block, and to derive at the edge of each data block the LS solution for tap coefficients of equalizer by an order-recursive proce- dB dure. Since the fixed computational burden for the order- 0 I I I I I I I I recursive procedure is distributed over a block, usually cov- -10 1 ers a relatively long time interval, the total computational 1 complexity will be greatly reduced. It is noteworthy that -20 each order-recursive procedure is independent, there is no -30 error propagation between each procedure for deriving tap coefficients, so numerical stability is also guaranteed by the -40 BSLS algorithm, which is of great significance for HDTV

-50 applications. For convenience, we limit our discussions to the so-called I I I I I I I I -60 prewindowed case, where the first N1 samples are assumed 0 2 4 6 8 10 12 14 16 18 to be zero. This assumption sacrifices the fast start feature of the LS criterion to a certain extent, but it has the ad- echo (ps) vantage of leading to significant reduction in computation, which is of major importance for real-time applications. Fig. 3. Amplitude profile of the simulated channel, representing the Based on the input signal yk and the training sequence ak worst-case: R=--JdB, 7=5ps, T~~~ = 18ps over time interval j 5 IC 5 n, the LS problem can be stated as the determination of an N x 1 (N = N1+ Nz) weighting vector, W$;,i:n,for which 111. BSLS DFE ALGORITHM n 2 - @)‘ E(2) In a typical decision feedback equalizer, the tstimate fUk + y$)t(k)w~~,j:nl - N,j:n N,j:n (7) of the symbol at the lcth signaling interval, 4, is a k= j+Nl-l 中国科技论文在线 http://www.paper.edu.cn

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is minimized, where some notations are defined as Then one gets the projection-update recursions as follows

Without loss of generality, the tap number of feedback sec- 0 I t "2 -1ztpcv tion in a decision feedback equalizer is typically larger than K[zlYIV = ( KyV ) -I- ( -K~Z) (' pY ) Y that of feedforward section, i.e., N2 > N1, then define a (15: quantity L = NZ- NI. For M = O,l,. ,N1, there exits

Yj+M-l Yj+M-2 *" Yj aj+M-z aj+~-3 ... aj-L-1 Yj+M Yj+M-l .'. Yj+l aj+M-l aj+M-2 . . . Uj-L

YTl Yn-1 "' Yn-M+l an-1 an-2 an-M-L

By substituting YN~,~:~and 0 into Eq. 13 and 14, we have

It is easily verified that both PN,,~:,and P&l,j:nsatisfy idempotency, thus recognized to be orthogonal projection operator. Motivated by Eq. 10 - 12, we will approach the sequential LS problem by geometric projections, which have proved to be very pciwerful means to eliminate unnec- essary or redundant compiutations [6][7][8].Let U,V, Y, 2 be arbitrary matrices having the same column length, and let [Y,Z] be the matrix formed by Y and 2 taken together. The corresponding projection operators are introduced as 中国科技论文在线 http://www.paper.edu.cn

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- t (2) t (2) (2) y(2),r * $:nLM - * YM,j+l:nKM,j+l.n 3:n-M TABLE I1 - (Yn-M,%--M-L) -y~'t(.)K~~j+i.n~(.~~r~ THESUBSTITUTIONS FOR THE DERIVATIONS OF ORDER-RECURSIVE PROOEDURE

= G~~l(n)TL+ltBgj:n-l

(Z),f - y!2),' tPC , y.(2),' 'm,j:n - 3+m:n md:n-1 3+m:n

€:libn - y!2)? tPC . y.(.2hT - 3:n-m m,3+1:n 3.n--m (2) ym,jZn = *'P;,j:nu where T is the so-called permutation matrix, which meets

[YE;+l:nlq?:TM] TL+l - YM+l,j:n(2)

(2)J (2) - (2) [Y3fM:nIYM,j:n-,l] %+I - YM+l,j:n and m denotes a running variable rather than a fixed one. All of the quantities are classified into two categories: the time-updating ones, and the order-updating ones. As we have mentioned, the basic idea of the BSLS algorithm is to utilize the time-updating quantities to transfer the infor- mation from block to block, and to derive at the edge of each block the LS solution by an order-recursive procedure. The desirable order-recursive procedure can be derived by using Eq. 13, 14, 15, and the definitions in the foregoing order-updating quantities. After a series of substitutions for U,V, Y,and 2 in Eq. 13, 14, 15, which are detailed shown in Tab. 11, we obtain the order-recursive procedure for BSLS algorithm as follows: Up until now, the main derivation procedure is complete. The order-recursive procedure: Combining the order-recursive procedure with the time- E'orM=O,l,...,N1 -1 DO updating quantities, one immediately established the BSLS algorithm, whose overall flowchart description is provided b(') = ~M+l(n)~ifi+~BM,~,~(2) M,jn (19) in Fig. 4.

(2) ~ yw (2) pM7j:n - Aj+M:n M+l,j:nBM,j:n It has been observed by several authors [9][10] that the - QA4+l,j;mT!4+lBA4,j:*(2) FTF-like algorithms are numerical instable, and divergence - (2) (20) may occur after a large number of iterations. Although some rescue procedures were proposed by several authors to avoid this disastrous effect, a "blind period" for the algo- rithms will happen, which is extremely undesirable to high- speed applications such as terrestrial HDTV broadcasting. In contrast, the stability problem can be well solved by the BSLS algorithm. The reason is that time updates of tap CO- efficients in the FTF-like algorithms have been eliminated, which have been shown to be the main cause leading to nu- merical instability. The round-off errors for tap coefficients of the BSLS decision feedback equalizer are accumulated only in each independent order-recursive procedure and do 中国科技论文在线 http://www.paper.edu.cn

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Shown in Fig. 5 is the comparison of computational com- begin plexity of the two equalizers. The average multiplications ir' and additions (MADs) required for the BSLS decrease with the length of block (LOB). We infer from Fig. 5 that the operations required by BSLS can be reduced to the level new data point of LMS's, provided that LOB> 8N is satisfied. In practi- is available cal environments, the choice of LOB depends on the time- variations of channels. For slowly-varying channels, the LOB can be set to be relatively large, and vice versa. rder-recursiv implement

MSE(dB) yesigno1 I I I I I I I

' dex=LOB

0 . Fig. 4. A flowchart description of the BSLS DFE algorithm

-5 - -

not propagate from block to block, so divergence will not -io - occur. -15 I I I I I IV. COMPUTERSIMULATION 100 200 300 400 500 600 700 800 900

In order to evaluate ithe performance of the proposed number of iterations BSLS adaptive decision feedback equalizer, we adopt the LMS decision feedback equalizer (DFE) recommended by Grand Alliance as a benchmark. As recommended by Fig. 6. The training curves of the two adaptive equalizers at a SNR Grand Alliance, the LM13 DFE consists of two parts, a 64 of 25dB tap feedforward transversal filter followed by a 192 tap de- cision feedback section. To make sense, the proposed BSLS Generally speaking, the convergence and tracking rate of DFE also has 256 taps, with 64 in feedforward section and BSLS algorithm is faster than LMS, since the BSLS min- 192 in feedback section. imizes LS criterion rather than MSE, leading to drastic performance improvement, especially for severely distorted or fast fading channels. Fig. 6 clearly accounts for this MADS point. In accordance with GA specifications, the train- I I ing period uses 828 symbols, equivalent to the length of a LMSDFE Frame Sync. Referring to Fig. 6, The training curve of BSLSDFE -b- LMS is almost flat, exhibiting slow convergence and track- 2000 ing properties. Conversely, the training curve of BSLS is very steep, and the MSE of BSLS algorithm at the end of training is significantly smaller than that of LMS. By 1600 the way, we also found in computer simulations that, the range of the step size for which LMS can properly work is 1200 very narrow, rendering an appropriate selection of step size quite difficult. Here, the step size for the LMS algorithm 800 was selected as 0.00005, which represents a good trade-off between convergence rate and stability. Shown in Fig. 7 are the bit-error-ratio (BER) curves 400 1 2 3 4 5 6 versus various signal-to-noise rate (SNR) for the proposed BSLS decision feedback equalizer and the LMS DFE recom- p (LOB=pxN) mended by Grand Alliance. All these results are calculated over 10' data samples and 8-bit soft decision in Viterbi Fig. 5. Computational complexity comparison of the two adaptive algorithm for decoding the trellis is adopted. The SNR equalizers in terms of average MADs required for each data point is defined as the average transmitted power at the input

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0 0 ... 0 0

... 0 0 ... aj-2 ... aj-1 aj

... an-L-1 an-,!,

OLXL J

Since there is no occurrence of yk in this equation, the two- channel BSLS problem can be decomposed into a transver- sal LS problem. Using almost the same notations in [ZO], we summarize the initial procedure for BSLS DFE as fol- lows: Form =O,l;..,L- 1 DO: SNR (dB)

Fig. 7. Performance comparison of the two adaptive equalizers; the LOB for BSLS DFE is 3x256.

of the receiving low-pass filter over the average additive- noise power at the same point. It is evident that about 3.5dB SNR improvement at the bit error rate of 3 x lop6 is achieved by using BSLS decision feedback equalizer.

V. CONCLUSIONS

A BSLS adaptive decision feedback equalizer for terres- trial IHDTV broadcasting has been proposed in this paper. Computationally efficient block operation are employed to facilitate easy implementation and low cost. Not only the average MADS of the proposed equalizer for each data point can be drastically reduced, but also it exhibits distinct per- formance improvement over the LMS DFE recommended by Grand Alliance. In addition, numerical stability is also guaranteed due to each independent order-recursive proce- dure on a block-by-block basis, which looks very promising for terrestrial HDTV broadcasting.

APPENDIX

To properly use the proposed BSLS DFE algorithm, IF m = L - 1 then some initial values are necessary. The derivation of the initial procedure is closely related transversal BSLS algo- rithm [20]. Under prewindowed condition, we have 中国科技论文在线 http://www.paper.edu.cn

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Bt,j:n [ F?-;,j:n ] - [ ] [17] G. Hufford, “A Characterization of the Multipath in the HDTV Channel,” IEEE %ns. Broadcasting, vol. 38, no. 4, pp. 252-255, 1992. + [ -ql,j:n ] (Epf,j:n)--lkLA_Bl,j:n [18] M. Sablatash, R. K. Tiedemann, K. W. Moreland, “A Multipath RF Propagation Model for Computer Simulation of Complex Im- B - (1) pulse Response of Broadcasting Teletext Channel,” IEEE Jour. BL,j :n - BL,j :n on Selec. Areas in Commu., vol. SAC-5, no. 2, 1313.286-298, Feb. B - (1) 1987. FL,j:n - FL,j:n [19] CEPT/GSM Recommendations, Ser. 05. 05. [20] Xiao-Hu Yu and Zhen-Ya He, “Efficient Block Implementa- With the above quantities, we can set the initial condition tion of Exact Sequential Least-Squares Problems,” IEEE Rans. of the order recursive procedure for two dimension algo- Awust., Speech, Signal Processing, vol. ASSP-36, pp. 392-399, Mar. 1988. [21] G. A. Clark, S. K. Mitra, and S. R. Parker, “Block Implementa- tion of Adaptive Digital Filter,” IEEE ’Ibans. Awust., Speech, Signal Processing, vol. ASSP-29, pp. 744-752, June 1981. [22] G. A. Clark, S. K. Mitra, and S. R. Parker, “A Unified Approach to Time- and Frequency-Domain Realization of FIR Adaptive Digital Filters,” IEEE %ns. Awust., Speech, Signal Process- ing, vol. ASSP-31, pp. 1073-1083, Oct. 1983.

For more details of the derivations, we refer the interesting readers to [20]. REFERENCES [l] S. U. H. Qureshi, “Adaptive Equalization,” Proc. of the IEEE, vol. 73, no. 9, pp. 1349-1387, Sept. 1985. [2] J. G. Proakis, Digital Communications, McGraw-Hill, New York, 1989. [3] K. Feher, Advanced Digital Communications: Systems and Sig- nal Processing Techniques, Prentice-Hall Inc., Englewood Cliffs, NJ, 1987. [4] B. Widrow, “Adaptive Filters”, in Aspects of Network and Sys- tem Theory, ed. R. E. Kalman and N. DeClaris, Holt, Rinehart, and Winston, pp. 563-587, New York, 1971. [5] A. Feuer, E. Weinstein, “Convergence Analysis of LMS Fil- ters with Uncorrelated Gaussian Data,” IEEE %ns. Awust., Speech, Signal Processing,vol. ASSP-33, pp. 220-230, Feb. 1985. [6] B. Porat, B. E’riedlander, and M. Morf, “Square-root Ladder Algorithms,” IEEE Trans. Automat. Contr., vol. AC-27, pp. 813-829, Au~.1982. [7] J. M. Cioffi and T. Kailath, “Fast, RLS Dansversal Filters for Adaptive Filtering,” IEEE Tmns. Awust., Speech, Signal Pro- cessing, vol. ASSP-32, pp. 304-337, Apr. 1984. [8] J. M. Cioffi and T. Kailath, “Windowed FTF Adaptive Algo- rithms with Normalization,” IEEE Bans. Acoust., Speech, Sig- nal Processing, vol. ASSP-33, pp. 607-635, June 1985. [9] S. Ljung and L. Ljung, “Error Propagation Properties of RLS Adaptation Algorithms, ’ Automatrca, Mar. 1985. [lo] P. Fabre and C. Gueguen, “Improvement of the Fast Recur- sive Least-Squares Algorithms via Normalization: A Compara- tive Study,” IEEE %ns. Acoust.,Speech, Signal Processing, vol. ASSP-34, pp. 296-308, Apr. 1986. [ll] Grand Alliance HDTV System Specification, FCC Advisory Committee on Advanced Television Systems, Feb. 1994. [12] C. Eilers, P. Fockens, The DSC-HDTV Interference Rejection System,” IEEE Trans. on Consumer Electronics, vol. 38, no. 3, pp. 101-107, Aug. 1992. [13] L.-F. Wei, “Precoding Technique for Partial-Response Channels with Application to HD’I’V Transmission,” IEEE Jour. on Selec. Areas in Commu., vol. IL1, no. 1, pp. 127-135, Jan. 1993. [14] G. Sgrignoli, W. Bretl, and R. Citta, “VSB Used for Terrestrial and Cable Broadcasts,” IEEE Trans. on Consumer Electronics, vol. 41, no. 3, pp. 367-382, Aug. 1995. [15] W. Bretl, G. Sgrignoli, and P. Snopko, “VSB Modem Subsystem Design for Grand Alliance Receivers”, IEEE fians. on Consumer Electronics, vol. 41, no. 3, pp. 773-786, Aug. 1995. [16] W. Y.Zou, Y.Wu, and ]VI. Guillet, “Analysis of ATV Transmis- sion Subsystem Field Test Data,” IEEE Trans. on Broadcasting, vol. 42, no. 1, pp. 1-9, Mar. 1996.