Bidirectional Equalizer Arbitrated by Viterbi Decoder ... - IEEE Xplore
IEEE Transactions on Consumer Electronics, Vol. 53, No. 1, FEBRUARY 2007
60
Bidirectional Equalizer Arbitrated by Viterbi Decoder Path Metrics Hae-Sock Oh, and Dong Seog Han, Member, IEEE Abstract — A bidirectional decision feedback equalizer (DFE) is proposed with the arbitration of the Viterbi decoder. The proposed DFE uses the minimum path metric between Viterbi decoders for the forward and reverse DFEs in the arbitration process. It has over 2 dB SNR gain against the conventional bidirectional DFE and the single DFE.1 Index Terms — Bidirectional DFE, Viterbi decoder, path metric.
I. INTRODUCTION In packet data communications with a small cell size like wireless LANs, a bidirectional decision feedback equalizer (DFE) has been developed to enhance the output signal-tonoise ratio (SNR) and to be robust over pre-ghost signals [1-3]. Various bidirectional DFEs consist of a forward DFE (F-DFE) and a reverse DFE (R-DFE) have been proposed according to the selection method of the F-DFE and R-DFE outputs. Ariyavisitakul [1] proposed a parallel equalizer to select the final decision symbol between the F-DFE and R-DFE outputs. The reverse of the received signal converts the minimum phase roots into the maximum phase roots. The output with the smaller mean square error (MSE) is chosen as the final output between the two DFE outputs. Since the selection is made with a packet data, the accuracy is degraded in dynamic channels. Meanwhile, Balakrishnan et al. [2] tried to improve the performance of an equalizer by combining the F-DFE and the R-DFE outputs using the minimizing MSE (MMSE) criterion. Recently, Nelson et al. [3] proposed a bidirectional arbitrated decision feedback equalizer (BAD) that selects the decided output that shows the smaller MSE by comparing the FDFE and the R-DFE outputs with the received signal after passing through an estimated channel filter. The BAD provides a very improved performance over the conventional systems. The conventional BAD requires the exact channel estimation [4], which is not easy work even in static channel conditions due to a short training sequence and noise components. Moreover, the BAD has high probability of error in the signal reconstruction process in dynamic channel conditions because the training sequence for the channel estimation is periodic. Consequently, the performance of BAD could be degraded. Therefore, it is required that a bidirectional DFE without any channel estimation and an improved selection algorithm between the F-DFE and R-DFE. 1
This work was supported by the Brain Korea 21 project. Hae-Sock Oh is with Samsung Electronics CO., LTD., Suwon 443-742, Korea and Dong Seog Han is with the School of Electrical Engineering and Computer Science, Kyungpook National University, Daegu 702-701, Korea (e-mail: [email protected], [email protected]). Manuscript received January 15, 2007
A bidirectional DFE without channel estimation is proposed in this paper. Most of communication systems, like IEEE 802.11x, DMB, and ATSC 8-VSB, use a convolutional coding to reduce the error rate in the received signal, and the Viterbi decoder is used as the decoder. The output of the Viterbi decoder is fed back to the feedback filter (FB) to reduce the error propagation effect and to enhance the equalizer output SNR [5]. The proposed bidirectional DFE uses the Viterbi decoder path metrics to select the outputs between the F-DFE and RDFE without any channel estimation. The bidirectional DFE and the selection algorithm are proposed with the Viterbi decoder path metrics. The proposed system is analyzed and compared with the conventional BAD in the typical urban 6 (TU6) channel [6] which is a typical channel model for the performance evaluation in the mobile communication systems. II. PROPOSED BIDIRECTIONAL DFE The conventional BAD [3] goes through the received signal reconstruction stage with the estimated channel filter and the arbitration stage that selects the output between the F-DFE and the R-DFE. The exact channel estimation is not easy work with a short training sequence in fading channel conditions. Moreover, the arbitration process of the conventional BAD could be inaccurate in dynamic channel conditions. Therefore, a robust bidirectional DFE should be developed that is independent of the channel estimation and has a symbol-bysymbol arbitration process. The proposed bidirectional DFE arbitrated by Viterbi path metrics (BI-VI) is shown in Fig. 1. In the symbol arbitration process in Fig. 1, the proposed bidirectional DFE uses path metrics of resulting parameters of Viterbi decoding. Since path metrics in the Viterbi decoder are used for the maximumlikelihood symbol detection [5, 7], the proposed bidirectional DFE selects the outputs between the F-DFE and the R-DFE by monitoring the path metrics for the two DFEs. In addition, the Viterbi decoder operates every output symbol of the F-DFE and the R-DFE, the symbol arbitration can be a symbol-bysymbol process. The symbol-by-symbol process guarantees the robustness of the proposed bidirectional system to the channel variation in dynamic channels. In this section, we explain channel estimation and the algorithm for adaptive weight activation using a data-recycling algorithm. Then, the operation of the proposed sparse equalizer is described with the application of the results obtained from the aforementioned processes.
0098 3063/07/$20.00 © 2007 IEEE
H.-S. Oh and D. S. Han: Bidirectional Equalizer Arbitrated by Viterbi Decoder Path Metrics
Received sequence
r [n ]
Feedforward Transversal Filter w ff [n ]
DT R
61
DT R
z fwd [n ] Decision
FB2
FB1
Viterbi Decoder l min.fwd [n ]
bˆfwd [n ] bˆdec.fwd [n ] in
TR Feedforward Transversal Filter w ff [n ]
TR
z rvs [n ]
r [n ]
Decision
FB2
FB1
Recovered sequence
bˆBI-VI [n ]
control
bˆrvs [n ]
Reverse Viterbi Decoder
AB
out
l min.rvs [n ] TR: Time Reverse AB: Arbitrator FB: Feedback Transversal fb [n ] Filter w fb [n ] w DT R: Time reverse delay
brvs [n ]
bˆdec.rvs [n ]
Fig. 1. The proposed bidirectional DFE arbitrated by the Viterbi decoder path metrics.
Since the path metric reveals a similarity between the equalizer output and the transmitted symbol, the arbitration process could be performed by comparing the minimum path metrics between the F-DFE and the R-DFE without channel estimation. DTR in Fig. 1 is the required time for reversing the incoming order of a packet. The transmitted signal b[n] is passed through the channel h[n] and added by the additive white Gaussian noise
(AWGN) in the receiver. Therefore the received sequence { r[n]} at a time n in Fig. 1 is expressed as r[ n ] =
L2
∑
k =− L1
h [ k ] b [ n − k ] + w[n], 0 ≤ n ≤ N − 1
(1)
where h[n] is a discrete channel that has a length of L1 + L2 + 1 symbols, w[n] is AWGN with zero mean and a
noise variance of σ w2 and N means a packet size. The received sequence is transferred to the F-DFE and the R-DFE, respectively, where the sequence is reversed for the R-DFE. The F-DFE output zfwd [n] and the R-DFE output zrvs [n] are directly fed back to the FB1 and the FB2, respectively. The Viterbi decoder outputs bˆdec.fwd [n] and bˆdec.rvs [n] of the F-DFE and the R-DFE are fed back to the FB1 and the FB2 with a traceback delay time D of the Viterbi decoder, respectively. Consequently, the output of each DFE is expressed into three parts as zfwd [n] = +
K2
∑
k =− K1 M
∑
k = D +1
and
D
wff [ k ] r [ n − k ] + ∑ wfb [ k ] bˆfwd [ n − k ] k =1
wfb [ k ] bˆdec.fwd [ n − k ], 0 ≤ n ≤ N − 1
(2)
zrvs [n] = +
K2
D
∑
k =− K1
w% ff [ k ] r% [ n − k ] + ∑ w% fb [ k ] b%rvs [ n − k ]
M
∑
k = D +1
k =1
(3)
w% fb [ k ] bˆdec.rvs [ n − k ], 0 ≤ n ≤ N − 1
where r%[n] is the rearranged sequence form of the received sequence r[n] as r%[n] = r [ N − 1 − n ] , 0 ≤ n ≤ N − 1 (4) wff [ k ] , w% ff [ k ] , wfb [ k ] , w% fb [ k ] in eqs. (2) and (3) are the
feed forward filter (FF) and the FB tap weights of the F-DFE and the R-DFE, respectively, and expressed as w ff = { wff [ k ] , − K1 ≤ k ≤ K 2 } (5) % ff = { w% ff [ k ] , − K1 ≤ k ≤ K 2 } w
(6)
w fb = { wfb [ k ] , 1 ≤ k ≤ M }
(7)
% fb = { w% fb [ k ] , 1 ≤ k ≤ M } w
(8)
where K1 + K 2 + 1 and M are the length of the FF and the FB, respectively. bˆfwd [ n] and b%rvs [n] are the decided signal of the F-DFE and the R-DFE outputs and bˆ [n] and bˆ [ n] dec.fwd
dec.rvs
are the Viterbi decoder and the reverse Viterbi decoder outputs in eqs. (2) and (3). The weight adaptation algorithm considered in this paper is the least mean squares (LMS) algorithm [8] considering robustness and convenience of hardware implementation. The weight adaptations of the F-DFE and the R-DFE are expressed as wff [ k ] = wff [ k − 1 ] + μ1efwd [n]r [ n − k ] , − K1 ≤ k ≤ K 2 (9) wfb [ k ] = wfb [ k − 1 ] + μ 2 efwd [n]bˆfwd [ n − k ] ,1 ≤ k ≤ D wfb [ k ] = wfb [ k − 1 ] + μ 2 efwd [n]bˆdec.fwd [ n − k ] , D +1 ≤ k ≤ M (10)
IEEE Transactions on Consumer Electronics, Vol. 53, No. 1, FEBRUARY 2007
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%ff [ k −1] + μ1ervs[n]r% [ n − k ] , −K1 ≤ k ≤ K2 (11) w%ff [ k ] = w w% fb [ k ] = w% fb [ k − 1] + μ2ervs [n]b%rvs [ n − k ] ,1 ≤ k ≤ D w% fb [ k ] = w% fb [ k − 1] + μ2ervs [n]bˆdec.rvs [ n − k ] , D+1 ≤ k ≤ M (12) where μ1 and μ2 are the step sizes of the FF and the FB, respectively. The error signals efwd [n] and ervs [n] in eqs. (9) to (12) are
efwd [n] = b[n] − zfwd [n] e [n] = b%[n] − z [n] rvs
b[n] = δ ( n mod 2 ) beven [n] + δ ( ( n mod 2 ) − 1 ) bodd [n], 0 ≤ n ≤ N − 1
(20)
where δ ( x ) is defined as ⎧ 1, when x = 0 ⎩ 0, otherwise
δ ( x) = ⎨
(21)
and N means a packet size. The state diagram of the convolutional encoder according to eqs. (18) and (19) is depicted in Fig. 2.
(13)
rvs
during the training sequence and
efwd [n] = bˆfwd [n] − zfwd [n] e [n] = b% [n] − z [n] rvs
rvs
(14)
rvs
during the payload data. b% [ n ] is the reversed sequence of the transmitted signal as
b%[n] = b[ N − 1 − n ] , 0 ≤ n ≤ N − 1
(15)
The decided output of the R-DFE is reversed to be the final output of the R-DFE as
bˆrvs[n] = b%rvs [ N −1 − n ] , 0 ≤ n ≤ N −1
(16)
At a symbol time n , the arbitrator of BI-VI in Fig. 1 selects the outputs between the F-DFE, bˆ [n] , and the R-DFE, fwd
bˆrvs [n] by comparing the minimum path metrics of each
Viterbi decoder, λmin.fwd [n] and λmin.rvs [n] . Because the minimum path metrics of the Viterbi decoders can be an indicator for the confidence of the decoded data, the BI-VI uses the minimum path metrics for path arbitration. The final selected output of BI-VI, bˆBI-VI [n] is
⎧⎪ bˆfwd [n], λmin.fwd [n] < λmin.rvs [n] bˆBI-VI [n] = ⎨ ⎪⎩ bˆrvs [n], λmin.fwd [n] > λmin.rvs [n]
(17)
Since another time reverse is required to the output of the R-DFE be put into the arbitrator in Fig. 1, the arbitrator can be operated after decoding a packet. Therefore, the delay time between the DFE outputs and the calculation of the minimum path metrics does not mattered. It is assumed that a convolutional encoder with a code rate of 1/2 and a constraint length of 3 for explaining the proposed BI-VI. The generated payload data brand [n] is encoded by two generator polynomials beven [n] for the even bit and bodd [n] for the odd bit defined as and
beven[n] = 1+ brand [ n −1] + brand [ n − 2]
(18)
bodd [n] = 1 + brand [ n − 2 ] ,
(19)
respectively. Therefore, the transmitted data b[n] is
Fig. 2. State diagram used for the forward Viterbi decoder.
For the proposed BI-VI, it is proposed that the reverse Viterbi decoding structure for the R-DFE. The structure of the reverse Viterbi decoder is shown in Fig. 3. In the R-DFE, the input sequence to the Viterbi decoder is reversed comparing with the original sequence. To decode the reversed sequence, it should be done a ‘2-bit reverse’ operation at before and after the reverse Viterbi decoding. For the reverse Viterbi decoding in Fig. 3, the state diagram of Fig. 2 should be redrawn as in Fig. 4. As depicted in Fig. 4, all the four states a, b, c, and d, and the input-to-output relationship are the same as the original state diagram in Fig. 2. Consequently, the reverse Viterbi decoding can be operated by using the state diagram in Fig. 4.
Fig. 3. The reverse Viterbi decoding scheme.
III. SIMULATION RESULTS
Comparison among the F-DFE, BAD, and BI-VI is performed in the TU6 channel [6] with slight modification considering BPSK and QPSK modulations. The TU6 channel is proposed by the COST207 project, which investigates and analyzes channel characteristics. Three kinds of channels, TU, hilly terrain (HT), rural area (RA) are modeled in the COST207 project. The TU6 channel presented in Table 1 is a
H.-S. Oh and D. S. Han: Bidirectional Equalizer Arbitrated by Viterbi Decoder Path Metrics
suitable model of the urban area communication environments. Each path of the TU6 channel suffers the Rayleigh fading and has a Doppler frequency. In the simulation, the Doppler frequency is fixed at 22.2 Hz in the TU6 channel with a carrier frequency of 470 MHz when a vehicle moves by 60km/h.
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the R-DFE could have similar probability of error in the equalizer output. Therefore, the BI-VI makes a diversity effect. SERs in Fig. 5(b) are for QPSK modulation. The results are similar to the BPSK case of Fig. 5(a). The BI-VI shows about 0.5 dB SNR gain over the F-DFE and the BAD. -1
10
Symbol Error Rate
-2
10
-3
10
F-DFE BAD BI-VI
-4
10
3
4
5
6
Fig. 4. State diagram used for the reverse Viterbi decoder.
7 Eb/N0 [dB]
8
9
10
11
8
9
10
11
(a) BPSK case
0.0 0.2 0.5 1.6 2.3 5.0
-3 0 -2 -6 -8 -10
Rayleigh Rayleigh Rayleigh Rayleigh Rayleigh Rayleigh
For the DFE, the length of the FF and the FB taps is 300, respectively. The step size of the FF and the FB is set at 0.00005 considering the convergence of all the DFEs. Since the depth of the Viterbi decoder is usually set over 5 times the constraint length of the encoder [9], it is set at 20 in the simulations. The LMS algorithm is used in the training sequence and the direct decision is adopted in the payload data. The simulation time is set as 20,000 packet times and one packet is consisted by 500 symbols as [3]. The training sequence is 10 % per packet. The conventional BAD assumes perfect channel estimation in the static channel condition and the window size of the arbitrator is 30 symbols [3]. Comparison of the symbol error rate (SER) among the FDFE, BAD, and BI-VI is shown is Fig. 5 in the static TU6 channel with the Doppler frequency of 0 Hz. SERs in Fig. 5(a) are for BPSK modulation. The BAD shows similar performance to the F-DFE in Fig. 5(a). From the simulation results, since the rate of selecting the F-DFE in the BAD varied from 50 % to 90 % according to the input SNRs, the arbitrator of the BAD can not select correctly. The proposed BI-VI is superior to the BAD by an SNR of about 0.5 dB in Fig. 2(a) and the rate of selecting the F-DFE maintains about 50 %. Because the TU6 channel has several strong ghosts and one pre-ghost,
0
10
-1
10 Symbol Error Rate
Path 0 1 2 3 4 5
TABLE I TU6 CHANNEL PROFILE Delay [us] Amplitude [dB] Doppler frequency [Hz]
-2
10
-3
10
F-DFE BAD BI-VI
-4
10
3
4
5
6
7 Eb/N0 [dB]
(b) QPSK case Fig. 5. Symbol error rate with static TU6 channel.
The SERs of the F-DFE, BAD, and BI-VI are shown in Fig. 6 in the TU6 channel shown in Table I. In Fig. 6(a) with the BPSK modulation, the BAD shows 1.5 dB SNR degradation over the F-DFE. It is because the possibility to select a more reliable output by the arbitrator is not guaranteed in the BAD by the lack of the training sequence and inaccurate channel estimation. The BI-VI is superior to the BAD by an SNR of about 2.3 dB in Fig. 6(a). In Fig. 6(b) with QPSK modulation, the BI-VI shows over 1.4 dB SNR gain against the BAD while the BAD is inferior to the F-DFE by 0.8 dB. From the simulation results, the proposed BI-VI using Viterbi decoder path metrics can operate correctly regardless of the channel variations.
IEEE Transactions on Consumer Electronics, Vol. 53, No. 1, FEBRUARY 2007
64 0
10
REFERENCES [1]
[2]
Symbol Error Rate
-1
10
[3] -2
10
[4] F-DFE BAD BI-VI
-3
10
8
9
[5] 10
11
12 Eb/N0 [dB]
13
14
15
16
(a) BPSK case
[6] [7] [8]
0
10
[9]
Hae-Sock Oh was born in Daegu, Korea on August 8, 1975. He received the B.S., M.S, and Ph. D degrees from Kyungpook National University, Daegu, Korea, in 1999, 2001, and 2006, respectively. Since 2006, he has been with Samsung Electronics Co., LTD. His main research interests are spread-spectrum technique, adaptive array, digital communications, and DTV systems.
Symbol Error Rate
-1
10
-2
10
F-DFE BAD BI-VI
-3
10
S. Ariyavisitakul, “A decision feedback equalizer with time-reversed structure,” IEEE J. Select. Areas Commun., vol. 10, no. 3, pp. 599-613, Apr. 1992. J. Balakrishnan and C. R. Johnson, Jr., “Bidirectional decision feedback equalizer: infinite length results,” in Proc. Asilomar Conf. on Signals, Systems, and Computers, vol. 2, Pacific Grove, CA, USA, pp. 14501454, Nov. 2001. J. K. Nelson, A. C. Singer, U. Madhow, and C. S. McGahey, “BAD: Bidirectional Arbitrated Decision-Feedback Equalization,” IEEE Trans. Commun., vol. 53, no. 2, Feb. 2005. D. S. Han, “Serially connected bi-directional DFE suitable for 8-VSB modulation,” IEEE Trans. Broadcasting, vol. 52, no. 1, Mar. 2006. G. D. Forney, Jr., “Maximum likelihood sequence estimation of digital sequences in the presence of intersymbol interference,” IEEE Trans. Inform. Theory, vol. 18, no. 3, pp. 363-378, May 1972. TeamCast, DVB-H Validation Task Force – Final Report, Jan. 2005. G. D. Forney, Jr., “The Viterbi algorithm,” Proc. of the IEEE, vol. 61, no. 3, pp. 268-278, Mar. 1973. S. U. H. Qureshi, “Adaptive equalization,” Proc. of the IEEE, vol. 73, no. 9, pp. 1349-1387, Sep. 1985. I. A. Glover and P. M. Grant, Digital Communications, London, UK: Prentice Hall, 1998.
8
9
10
11
12 Eb/N0 [dB]
13
14
15
16
(b) QPSK case Fig. 6. Symbol error rate with TU6 channel.
IV. CONCLUSIONS
The bidirectional DFE arbitrated by the Viterbi decoder path metrics has been presented in this paper. Without any channel information, the proposed BI-VI effectively selects the output between the F-DFE and the R-DFE by utilizing the Viterbi decoder path metrics. There fore, the proposed BI-VI can obtain the diversity gain to enhance the equalizer output performance. In the TU6 channel, the proposed BI-VI properly selected more exact outputs between the F-DFE and the R-DFE and showed robust performance regardless of the channel variations.
Dong Seog Han was born in Daegu, Korea on February 10, 1966. He received his B.S. degree in electronic engineering from Kyungpook National University (KNU), Daegu, Korea, in 1998, his M.S and Ph.D degrees in electrical engineering form the Korea Advanced Institute of Science and Technology (KAIST), Daejon, Korea, 1n 1989 and 1993, respectively. From October 1987 to August 1996, he was with Samsung Electronics, Co. Ltd., where he developed the transmission systems for QAM HDTV and Grand Alliance HDTV receivers. Since September 1996, he has been with the School of Electronic and Electrical Engineering, Kyungpook National University. Currently he is an Associate Professor in the school of Electronic and Electrical Engineering, KNU. He worked as a courtesy Associate Professor in the electrical and computer engineering, University of Florida in 2004. His main research interests are digital communications and array signal processing.
60
Bidirectional Equalizer Arbitrated by Viterbi Decoder Path Metrics Hae-Sock Oh, and Dong Seog Han, Member, IEEE Abstract — A bidirectional decision feedback equalizer (DFE) is proposed with the arbitration of the Viterbi decoder. The proposed DFE uses the minimum path metric between Viterbi decoders for the forward and reverse DFEs in the arbitration process. It has over 2 dB SNR gain against the conventional bidirectional DFE and the single DFE.1 Index Terms — Bidirectional DFE, Viterbi decoder, path metric.
I. INTRODUCTION In packet data communications with a small cell size like wireless LANs, a bidirectional decision feedback equalizer (DFE) has been developed to enhance the output signal-tonoise ratio (SNR) and to be robust over pre-ghost signals [1-3]. Various bidirectional DFEs consist of a forward DFE (F-DFE) and a reverse DFE (R-DFE) have been proposed according to the selection method of the F-DFE and R-DFE outputs. Ariyavisitakul [1] proposed a parallel equalizer to select the final decision symbol between the F-DFE and R-DFE outputs. The reverse of the received signal converts the minimum phase roots into the maximum phase roots. The output with the smaller mean square error (MSE) is chosen as the final output between the two DFE outputs. Since the selection is made with a packet data, the accuracy is degraded in dynamic channels. Meanwhile, Balakrishnan et al. [2] tried to improve the performance of an equalizer by combining the F-DFE and the R-DFE outputs using the minimizing MSE (MMSE) criterion. Recently, Nelson et al. [3] proposed a bidirectional arbitrated decision feedback equalizer (BAD) that selects the decided output that shows the smaller MSE by comparing the FDFE and the R-DFE outputs with the received signal after passing through an estimated channel filter. The BAD provides a very improved performance over the conventional systems. The conventional BAD requires the exact channel estimation [4], which is not easy work even in static channel conditions due to a short training sequence and noise components. Moreover, the BAD has high probability of error in the signal reconstruction process in dynamic channel conditions because the training sequence for the channel estimation is periodic. Consequently, the performance of BAD could be degraded. Therefore, it is required that a bidirectional DFE without any channel estimation and an improved selection algorithm between the F-DFE and R-DFE. 1
This work was supported by the Brain Korea 21 project. Hae-Sock Oh is with Samsung Electronics CO., LTD., Suwon 443-742, Korea and Dong Seog Han is with the School of Electrical Engineering and Computer Science, Kyungpook National University, Daegu 702-701, Korea (e-mail: [email protected], [email protected]). Manuscript received January 15, 2007
A bidirectional DFE without channel estimation is proposed in this paper. Most of communication systems, like IEEE 802.11x, DMB, and ATSC 8-VSB, use a convolutional coding to reduce the error rate in the received signal, and the Viterbi decoder is used as the decoder. The output of the Viterbi decoder is fed back to the feedback filter (FB) to reduce the error propagation effect and to enhance the equalizer output SNR [5]. The proposed bidirectional DFE uses the Viterbi decoder path metrics to select the outputs between the F-DFE and RDFE without any channel estimation. The bidirectional DFE and the selection algorithm are proposed with the Viterbi decoder path metrics. The proposed system is analyzed and compared with the conventional BAD in the typical urban 6 (TU6) channel [6] which is a typical channel model for the performance evaluation in the mobile communication systems. II. PROPOSED BIDIRECTIONAL DFE The conventional BAD [3] goes through the received signal reconstruction stage with the estimated channel filter and the arbitration stage that selects the output between the F-DFE and the R-DFE. The exact channel estimation is not easy work with a short training sequence in fading channel conditions. Moreover, the arbitration process of the conventional BAD could be inaccurate in dynamic channel conditions. Therefore, a robust bidirectional DFE should be developed that is independent of the channel estimation and has a symbol-bysymbol arbitration process. The proposed bidirectional DFE arbitrated by Viterbi path metrics (BI-VI) is shown in Fig. 1. In the symbol arbitration process in Fig. 1, the proposed bidirectional DFE uses path metrics of resulting parameters of Viterbi decoding. Since path metrics in the Viterbi decoder are used for the maximumlikelihood symbol detection [5, 7], the proposed bidirectional DFE selects the outputs between the F-DFE and the R-DFE by monitoring the path metrics for the two DFEs. In addition, the Viterbi decoder operates every output symbol of the F-DFE and the R-DFE, the symbol arbitration can be a symbol-bysymbol process. The symbol-by-symbol process guarantees the robustness of the proposed bidirectional system to the channel variation in dynamic channels. In this section, we explain channel estimation and the algorithm for adaptive weight activation using a data-recycling algorithm. Then, the operation of the proposed sparse equalizer is described with the application of the results obtained from the aforementioned processes.
0098 3063/07/$20.00 © 2007 IEEE
H.-S. Oh and D. S. Han: Bidirectional Equalizer Arbitrated by Viterbi Decoder Path Metrics
Received sequence
r [n ]
Feedforward Transversal Filter w ff [n ]
DT R
61
DT R
z fwd [n ] Decision
FB2
FB1
Viterbi Decoder l min.fwd [n ]
bˆfwd [n ] bˆdec.fwd [n ] in
TR Feedforward Transversal Filter w ff [n ]
TR
z rvs [n ]
r [n ]
Decision
FB2
FB1
Recovered sequence
bˆBI-VI [n ]
control
bˆrvs [n ]
Reverse Viterbi Decoder
AB
out
l min.rvs [n ] TR: Time Reverse AB: Arbitrator FB: Feedback Transversal fb [n ] Filter w fb [n ] w DT R: Time reverse delay
brvs [n ]
bˆdec.rvs [n ]
Fig. 1. The proposed bidirectional DFE arbitrated by the Viterbi decoder path metrics.
Since the path metric reveals a similarity between the equalizer output and the transmitted symbol, the arbitration process could be performed by comparing the minimum path metrics between the F-DFE and the R-DFE without channel estimation. DTR in Fig. 1 is the required time for reversing the incoming order of a packet. The transmitted signal b[n] is passed through the channel h[n] and added by the additive white Gaussian noise
(AWGN) in the receiver. Therefore the received sequence { r[n]} at a time n in Fig. 1 is expressed as r[ n ] =
L2
∑
k =− L1
h [ k ] b [ n − k ] + w[n], 0 ≤ n ≤ N − 1
(1)
where h[n] is a discrete channel that has a length of L1 + L2 + 1 symbols, w[n] is AWGN with zero mean and a
noise variance of σ w2 and N means a packet size. The received sequence is transferred to the F-DFE and the R-DFE, respectively, where the sequence is reversed for the R-DFE. The F-DFE output zfwd [n] and the R-DFE output zrvs [n] are directly fed back to the FB1 and the FB2, respectively. The Viterbi decoder outputs bˆdec.fwd [n] and bˆdec.rvs [n] of the F-DFE and the R-DFE are fed back to the FB1 and the FB2 with a traceback delay time D of the Viterbi decoder, respectively. Consequently, the output of each DFE is expressed into three parts as zfwd [n] = +
K2
∑
k =− K1 M
∑
k = D +1
and
D
wff [ k ] r [ n − k ] + ∑ wfb [ k ] bˆfwd [ n − k ] k =1
wfb [ k ] bˆdec.fwd [ n − k ], 0 ≤ n ≤ N − 1
(2)
zrvs [n] = +
K2
D
∑
k =− K1
w% ff [ k ] r% [ n − k ] + ∑ w% fb [ k ] b%rvs [ n − k ]
M
∑
k = D +1
k =1
(3)
w% fb [ k ] bˆdec.rvs [ n − k ], 0 ≤ n ≤ N − 1
where r%[n] is the rearranged sequence form of the received sequence r[n] as r%[n] = r [ N − 1 − n ] , 0 ≤ n ≤ N − 1 (4) wff [ k ] , w% ff [ k ] , wfb [ k ] , w% fb [ k ] in eqs. (2) and (3) are the
feed forward filter (FF) and the FB tap weights of the F-DFE and the R-DFE, respectively, and expressed as w ff = { wff [ k ] , − K1 ≤ k ≤ K 2 } (5) % ff = { w% ff [ k ] , − K1 ≤ k ≤ K 2 } w
(6)
w fb = { wfb [ k ] , 1 ≤ k ≤ M }
(7)
% fb = { w% fb [ k ] , 1 ≤ k ≤ M } w
(8)
where K1 + K 2 + 1 and M are the length of the FF and the FB, respectively. bˆfwd [ n] and b%rvs [n] are the decided signal of the F-DFE and the R-DFE outputs and bˆ [n] and bˆ [ n] dec.fwd
dec.rvs
are the Viterbi decoder and the reverse Viterbi decoder outputs in eqs. (2) and (3). The weight adaptation algorithm considered in this paper is the least mean squares (LMS) algorithm [8] considering robustness and convenience of hardware implementation. The weight adaptations of the F-DFE and the R-DFE are expressed as wff [ k ] = wff [ k − 1 ] + μ1efwd [n]r [ n − k ] , − K1 ≤ k ≤ K 2 (9) wfb [ k ] = wfb [ k − 1 ] + μ 2 efwd [n]bˆfwd [ n − k ] ,1 ≤ k ≤ D wfb [ k ] = wfb [ k − 1 ] + μ 2 efwd [n]bˆdec.fwd [ n − k ] , D +1 ≤ k ≤ M (10)
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%ff [ k −1] + μ1ervs[n]r% [ n − k ] , −K1 ≤ k ≤ K2 (11) w%ff [ k ] = w w% fb [ k ] = w% fb [ k − 1] + μ2ervs [n]b%rvs [ n − k ] ,1 ≤ k ≤ D w% fb [ k ] = w% fb [ k − 1] + μ2ervs [n]bˆdec.rvs [ n − k ] , D+1 ≤ k ≤ M (12) where μ1 and μ2 are the step sizes of the FF and the FB, respectively. The error signals efwd [n] and ervs [n] in eqs. (9) to (12) are
efwd [n] = b[n] − zfwd [n] e [n] = b%[n] − z [n] rvs
b[n] = δ ( n mod 2 ) beven [n] + δ ( ( n mod 2 ) − 1 ) bodd [n], 0 ≤ n ≤ N − 1
(20)
where δ ( x ) is defined as ⎧ 1, when x = 0 ⎩ 0, otherwise
δ ( x) = ⎨
(21)
and N means a packet size. The state diagram of the convolutional encoder according to eqs. (18) and (19) is depicted in Fig. 2.
(13)
rvs
during the training sequence and
efwd [n] = bˆfwd [n] − zfwd [n] e [n] = b% [n] − z [n] rvs
rvs
(14)
rvs
during the payload data. b% [ n ] is the reversed sequence of the transmitted signal as
b%[n] = b[ N − 1 − n ] , 0 ≤ n ≤ N − 1
(15)
The decided output of the R-DFE is reversed to be the final output of the R-DFE as
bˆrvs[n] = b%rvs [ N −1 − n ] , 0 ≤ n ≤ N −1
(16)
At a symbol time n , the arbitrator of BI-VI in Fig. 1 selects the outputs between the F-DFE, bˆ [n] , and the R-DFE, fwd
bˆrvs [n] by comparing the minimum path metrics of each
Viterbi decoder, λmin.fwd [n] and λmin.rvs [n] . Because the minimum path metrics of the Viterbi decoders can be an indicator for the confidence of the decoded data, the BI-VI uses the minimum path metrics for path arbitration. The final selected output of BI-VI, bˆBI-VI [n] is
⎧⎪ bˆfwd [n], λmin.fwd [n] < λmin.rvs [n] bˆBI-VI [n] = ⎨ ⎪⎩ bˆrvs [n], λmin.fwd [n] > λmin.rvs [n]
(17)
Since another time reverse is required to the output of the R-DFE be put into the arbitrator in Fig. 1, the arbitrator can be operated after decoding a packet. Therefore, the delay time between the DFE outputs and the calculation of the minimum path metrics does not mattered. It is assumed that a convolutional encoder with a code rate of 1/2 and a constraint length of 3 for explaining the proposed BI-VI. The generated payload data brand [n] is encoded by two generator polynomials beven [n] for the even bit and bodd [n] for the odd bit defined as and
beven[n] = 1+ brand [ n −1] + brand [ n − 2]
(18)
bodd [n] = 1 + brand [ n − 2 ] ,
(19)
respectively. Therefore, the transmitted data b[n] is
Fig. 2. State diagram used for the forward Viterbi decoder.
For the proposed BI-VI, it is proposed that the reverse Viterbi decoding structure for the R-DFE. The structure of the reverse Viterbi decoder is shown in Fig. 3. In the R-DFE, the input sequence to the Viterbi decoder is reversed comparing with the original sequence. To decode the reversed sequence, it should be done a ‘2-bit reverse’ operation at before and after the reverse Viterbi decoding. For the reverse Viterbi decoding in Fig. 3, the state diagram of Fig. 2 should be redrawn as in Fig. 4. As depicted in Fig. 4, all the four states a, b, c, and d, and the input-to-output relationship are the same as the original state diagram in Fig. 2. Consequently, the reverse Viterbi decoding can be operated by using the state diagram in Fig. 4.
Fig. 3. The reverse Viterbi decoding scheme.
III. SIMULATION RESULTS
Comparison among the F-DFE, BAD, and BI-VI is performed in the TU6 channel [6] with slight modification considering BPSK and QPSK modulations. The TU6 channel is proposed by the COST207 project, which investigates and analyzes channel characteristics. Three kinds of channels, TU, hilly terrain (HT), rural area (RA) are modeled in the COST207 project. The TU6 channel presented in Table 1 is a
H.-S. Oh and D. S. Han: Bidirectional Equalizer Arbitrated by Viterbi Decoder Path Metrics
suitable model of the urban area communication environments. Each path of the TU6 channel suffers the Rayleigh fading and has a Doppler frequency. In the simulation, the Doppler frequency is fixed at 22.2 Hz in the TU6 channel with a carrier frequency of 470 MHz when a vehicle moves by 60km/h.
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the R-DFE could have similar probability of error in the equalizer output. Therefore, the BI-VI makes a diversity effect. SERs in Fig. 5(b) are for QPSK modulation. The results are similar to the BPSK case of Fig. 5(a). The BI-VI shows about 0.5 dB SNR gain over the F-DFE and the BAD. -1
10
Symbol Error Rate
-2
10
-3
10
F-DFE BAD BI-VI
-4
10
3
4
5
6
Fig. 4. State diagram used for the reverse Viterbi decoder.
7 Eb/N0 [dB]
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11
8
9
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(a) BPSK case
0.0 0.2 0.5 1.6 2.3 5.0
-3 0 -2 -6 -8 -10
Rayleigh Rayleigh Rayleigh Rayleigh Rayleigh Rayleigh
For the DFE, the length of the FF and the FB taps is 300, respectively. The step size of the FF and the FB is set at 0.00005 considering the convergence of all the DFEs. Since the depth of the Viterbi decoder is usually set over 5 times the constraint length of the encoder [9], it is set at 20 in the simulations. The LMS algorithm is used in the training sequence and the direct decision is adopted in the payload data. The simulation time is set as 20,000 packet times and one packet is consisted by 500 symbols as [3]. The training sequence is 10 % per packet. The conventional BAD assumes perfect channel estimation in the static channel condition and the window size of the arbitrator is 30 symbols [3]. Comparison of the symbol error rate (SER) among the FDFE, BAD, and BI-VI is shown is Fig. 5 in the static TU6 channel with the Doppler frequency of 0 Hz. SERs in Fig. 5(a) are for BPSK modulation. The BAD shows similar performance to the F-DFE in Fig. 5(a). From the simulation results, since the rate of selecting the F-DFE in the BAD varied from 50 % to 90 % according to the input SNRs, the arbitrator of the BAD can not select correctly. The proposed BI-VI is superior to the BAD by an SNR of about 0.5 dB in Fig. 2(a) and the rate of selecting the F-DFE maintains about 50 %. Because the TU6 channel has several strong ghosts and one pre-ghost,
0
10
-1
10 Symbol Error Rate
Path 0 1 2 3 4 5
TABLE I TU6 CHANNEL PROFILE Delay [us] Amplitude [dB] Doppler frequency [Hz]
-2
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-3
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F-DFE BAD BI-VI
-4
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3
4
5
6
7 Eb/N0 [dB]
(b) QPSK case Fig. 5. Symbol error rate with static TU6 channel.
The SERs of the F-DFE, BAD, and BI-VI are shown in Fig. 6 in the TU6 channel shown in Table I. In Fig. 6(a) with the BPSK modulation, the BAD shows 1.5 dB SNR degradation over the F-DFE. It is because the possibility to select a more reliable output by the arbitrator is not guaranteed in the BAD by the lack of the training sequence and inaccurate channel estimation. The BI-VI is superior to the BAD by an SNR of about 2.3 dB in Fig. 6(a). In Fig. 6(b) with QPSK modulation, the BI-VI shows over 1.4 dB SNR gain against the BAD while the BAD is inferior to the F-DFE by 0.8 dB. From the simulation results, the proposed BI-VI using Viterbi decoder path metrics can operate correctly regardless of the channel variations.
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REFERENCES [1]
[2]
Symbol Error Rate
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[3] -2
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[4] F-DFE BAD BI-VI
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[5] 10
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(a) BPSK case
[6] [7] [8]
0
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[9]
Hae-Sock Oh was born in Daegu, Korea on August 8, 1975. He received the B.S., M.S, and Ph. D degrees from Kyungpook National University, Daegu, Korea, in 1999, 2001, and 2006, respectively. Since 2006, he has been with Samsung Electronics Co., LTD. His main research interests are spread-spectrum technique, adaptive array, digital communications, and DTV systems.
Symbol Error Rate
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-2
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-3
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S. Ariyavisitakul, “A decision feedback equalizer with time-reversed structure,” IEEE J. Select. Areas Commun., vol. 10, no. 3, pp. 599-613, Apr. 1992. J. Balakrishnan and C. R. Johnson, Jr., “Bidirectional decision feedback equalizer: infinite length results,” in Proc. Asilomar Conf. on Signals, Systems, and Computers, vol. 2, Pacific Grove, CA, USA, pp. 14501454, Nov. 2001. J. K. Nelson, A. C. Singer, U. Madhow, and C. S. McGahey, “BAD: Bidirectional Arbitrated Decision-Feedback Equalization,” IEEE Trans. Commun., vol. 53, no. 2, Feb. 2005. D. S. Han, “Serially connected bi-directional DFE suitable for 8-VSB modulation,” IEEE Trans. Broadcasting, vol. 52, no. 1, Mar. 2006. G. D. Forney, Jr., “Maximum likelihood sequence estimation of digital sequences in the presence of intersymbol interference,” IEEE Trans. Inform. Theory, vol. 18, no. 3, pp. 363-378, May 1972. TeamCast, DVB-H Validation Task Force – Final Report, Jan. 2005. G. D. Forney, Jr., “The Viterbi algorithm,” Proc. of the IEEE, vol. 61, no. 3, pp. 268-278, Mar. 1973. S. U. H. Qureshi, “Adaptive equalization,” Proc. of the IEEE, vol. 73, no. 9, pp. 1349-1387, Sep. 1985. I. A. Glover and P. M. Grant, Digital Communications, London, UK: Prentice Hall, 1998.
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(b) QPSK case Fig. 6. Symbol error rate with TU6 channel.
IV. CONCLUSIONS
The bidirectional DFE arbitrated by the Viterbi decoder path metrics has been presented in this paper. Without any channel information, the proposed BI-VI effectively selects the output between the F-DFE and the R-DFE by utilizing the Viterbi decoder path metrics. There fore, the proposed BI-VI can obtain the diversity gain to enhance the equalizer output performance. In the TU6 channel, the proposed BI-VI properly selected more exact outputs between the F-DFE and the R-DFE and showed robust performance regardless of the channel variations.
Dong Seog Han was born in Daegu, Korea on February 10, 1966. He received his B.S. degree in electronic engineering from Kyungpook National University (KNU), Daegu, Korea, in 1998, his M.S and Ph.D degrees in electrical engineering form the Korea Advanced Institute of Science and Technology (KAIST), Daejon, Korea, 1n 1989 and 1993, respectively. From October 1987 to August 1996, he was with Samsung Electronics, Co. Ltd., where he developed the transmission systems for QAM HDTV and Grand Alliance HDTV receivers. Since September 1996, he has been with the School of Electronic and Electrical Engineering, Kyungpook National University. Currently he is an Associate Professor in the school of Electronic and Electrical Engineering, KNU. He worked as a courtesy Associate Professor in the electrical and computer engineering, University of Florida in 2004. His main research interests are digital communications and array signal processing.
