Decoder- Assisted Channel Estimation and Frame Synchronization of Turbo Coded Systems

M. Mostofa K. Howlader

Wireless Communications Research Group (WCRG) Department of Electrical and Computer Engineering

University of Tennessee, Knoxville, TN 37996 howlader@utk.edu

Abstract-Some previous research has demonstrated the feasibility of decoder-assisted frame synchro- nization [l] and channel estimation [2] as separate processes for coded systems. Here a joint decoder- assisted process of channel estimation and frame syn- chronization using the same sync word (SW) is pro- posed. In brief, the method entails using a S W em- bedded in the mid-packet for both channel estimation and frame synchronization. The method is based on a list-synchronization scheme, where a correlation-based frame synchronizer passes a list of possible delays to the turbo decoder. The turbo decoder makes the fi- nal decision about frame synchronization. The turbo decoder is draw upon pilot symbol assisted modula- tion (PSAM) techniques for channel estimation using the coded SW of frame synchronization. The perfor- mance of channel estimation technique using the SW is presented via simulation.

I. INTRODUCTION

Advanced decoding schemes are revolutionary in- novations for advancement of digital wireless commu- nications. These techniques achieved significant per- formance improvements over the conventional met h- ods of detection. Traditionally, the performances of these techniques have been evaluated under the as- sumption that perfect synchronizations and channel estimations have been obtained. Consequently, this unprecedented improvement necessitates better syn- chronization and channel estimation as a prerequi- site. Turbo codes offer very low error correction per- formance when used with perfect channel informa- tion, or side information (SI) that consists of channel noise variance, fading amplitude, and fading phase. For optimal results in a fading channel, turbo codes need to have perfect channel information. However, in real systems perfect SI is not achievable and the performance suffers as a result. In lieu of unrealizable perfect SI, methods have been devised to estimate the channel information. One proven method em- ploys pilot-symbol-assisted modulation (PSAM) [3], [2]. For fading, the degradation depends on the fad- ing channel parameters.

In this article, a joint method of frame syncbroniza- tion and channel estimation is proposed. The method uses a mid-packet SW for both frame synchronization

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and channel estimation. For frame synchronization, first a list of possible delays is generated from the re- ceived codeword using the a pp-ion knowledge of the coded SW. Then a decoder-assisted process is em- ployed that jointly estimates the best delay choice while generating channel estimates. If properly de- signed, the joint process can be shown to achieve the same results as independent frame synchroniza- tion and channel estimation but with less bandwidth. This is due to using the existing SW for channel es- timation rather than adding in pilot symbols. Here, the decoder assists the synchronization and channel estimation; the process is iterative rather than suc- cessive. The purpose of this proposed scheme LS to use the power of the decoding technique in chaanel estimation and kame synchronization using the :sitme SW without sacrificing the performance of the sys- tem. The PSAM technique is used for channel esti- mation because of its superior performance [3]. The assumption is that, at least, the SW will be reused as the required pilot symbols for channel estimation or portion of the pilot symbols as needed.

The SW can be transmitted with the coded bits as an uncoded or coded sequence. Our approach exploits the power of the error correction code to improve the synchronization performance. Although the decoder- assisted frame synchronization schemes is reported in [l], we will explain the basics briefly in Section 11. The remainder of the paper is organized as follows. The system model for channel estimation is presented in Section 111. Section IV presents the channel esti- mation principle using the SW. Section V shows simu- lation results of channel estimations considering w- ious schemes. Finally, conclusions and possible im- provements of the proposed scheme are given in Sec- tion VI.

11. DECODER-ASSISTED FRAME SYNCHRONIZATION We illustrate this concept with a simple example,

using a data packet in which information bit:s have been encoded using a rate 1/2, constraint length 3, convolutional code. The trellis diagram for this code is illustrated in Fig. l(a). We assume that the packet

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contains N information bits, as well as m = 2 termi- nation bits, so that the trellis of Fig. l(a) has four states and ( N + m + 1) stages, starting from time t = 0 and terminating at time t = N + m.

Suppose that the SW is embedded in the informa- tion sequence, as a mid-amble at time t = P, rather than as a separate header. Just like the other data in the information sequence, the SW will be encoded by the decoder and will influence the path followed through the convolutional code trellis. For example, if the SW ‘00110’ is inserted into the data stream, then in the four time intervals leaving up to time t = P, the trellis will visit the states ‘OO’, ‘O17, ‘l17, and ‘lo’ in sequence, as shown in Fig. l(a).

Now suppose that there is uncertainty as to the pre cise time that the data packet arrives at the receiver. For example, in Fig. l(b), the four packets A, B, C, and D arrive at the receiver with a relative delay of 0, 1, 2, and 3 information bits respectively. The re- ceiver can easily distinguish between these 4 relative delays by observing the state of the Viterbi decoder at time t = P, because we have designed the SW to force the code into a sequence of known states. If we observe that the decoder state is ‘10’ at time t = P, then we know that the relative delay of packet A is 0 information bits. Similarly, if we know that the de- coder state is ‘11’ at time t = P, then we know that the relative delay of packet B is 1 information bit. In a similar fashion, we can obtain a one-teone corre- spondence between the decoder state at time t = P, and the relative delays of the other packets. As a re sult, the frame synchronization problem for the coded system may be directly related to the decoding oper- ation. Although this simple example resolves only four possible delays, reference [l] illustrates how this approach may be significantly generalized.

111. SYSTEM MODEL

Transmitter We assume that the data is BPSK modulated and perfect symbol and carrier synchro- nization has already been achieved. The data is transmitted in N-symbol frames, of which L sym- bols comprise the known SW s = (so, SI,. . + , SL-I) E {17-l}L7 and the remaining ( N - L) symbols represent data sequence d = (&, &+I, . , &-I) E (1, -l}(N-L). Then the data is encoded using a turbo encoder of 113 rate, constraint length kc = 3. The encoded data is subsequently channel interleaved in such a way to evenly distribute the coded SW across the entire packet for optimal channel estima- tion. This will be elaborated upon in a subsequent section.

Channel: The channel consists of a complex mul- tiplicative distortion with AWGN and Ftayleigh flat

t=N+m

,....

0 . . stage-

(a) Trellis representation of a 4-state convolutional encoder. The trellis terminares m an arbitrary state, depending on the arbitmy delay of the observation window.

1 2 0 t = P t=N+m

D+ I dam a r n ~ J 1 obscnationwin&w=N d & m

3

@)Atthetm”itter,SW ‘00110’isembeddedmthemid- amble of a packet and at the receiver, 4 observation windows A, B, C and D arrive with 0-3 bits delay respectively.

Fig. 1 . Tkellii diagram of the decoder-assisted synchroniza- tion scheme; Packet arrivals at the receiver for different delays are also shown for the proposed scheme of frame synchronization.

fading. The fading model has the autocorrelation ac- cording to Jake’s isotropic scattering model [4]

Rc (T) = c2 JO (2rfd7) 7 (1)

where f d is the relative Doppler between transmitter and receiver and JO is the zero order Bessel function. Note that the power of the fading is normalized to one. The system model is shown in Fig. 2 and is similar in nature to that shown in [2].

Receiver The receiver is shown in Fig. 2. As indi- cated in the channel section, the fading is slow with respect to the symbol period and 0at with no inter- symbol interference. Also, perfect carrier and symbol timing is assumed. The complex baseband received signal, sampled at symbol intervals t = kT, is given bY

r k = c k ( s k ) + nk7 (2)

where Ck is the fading described above, s k denotes the transmitted encoded bit sequence and n k is a sample of complex AWGN with two-sided power spec- tral density No12 for both real and imaginary compe nents. Here k is an integer and T is the symbol period. The receiver operates on the sequence r = ( r o , r 1 , - - . . , r ~ - 1 ) of N demodulated symbols. The frame synchronization problem is to estimate the relative delay f i E [0, M - 11 of the arriving packet, where M is the number of resolvable delays and M 5 N. The sequence r k is initially used to estimate the channel

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sw

' turbo xi channel st encoder ' interleaver

- n

I I

Frame Synchronizer

"bo decoder or interleav w [ a i , (c) Receiver

Fig. 2. System model for the proposed decoder-assisted joint frame synchronization and channel estimation scheme us- ing the same SW for both purposes.

information (fading amplitude and phase, and vari- ance of the noise), then sent through a channel dein- terleaver before being passed to a turbo decoder im- plemented using a log-MAP decoder. The channel estimation is further refined upon additional itera- tions [2]. Where 121 implements the refined channel estimation using inserted pilot symbols, we estimate the channel using the available coded SW.

IV. CHANNEL ESTIMATION USING SW

The channel estimation technique in conjunction with turbo PSAM has been shown to achieve favor- able results depending on the channel parameters [2]. The channel estimation algorithm for PSAM can be directly applied to the coded SW in what we will re- fer to as SW assisted modulation (SWAM). The turbo channel estimation algorithm for SWAM is described in the following. Note that it is a variant of the turbo PSAM proposed in [2].

For the first iteration, the decoder-assisted channel estimation does not have a priori symbol estimates and estimation is accomplished using only the coded SW. An approximation of the best minimum mean square estimate for the fist pass is described by

(3) i = - N ,

where w i is the set of filter coefficients according to Wiener-Hopf equations, up is a transmitted coded SW symbol and y?Ji is the received value of closest SW symbol to Y k - i . After the initial estimation, the chan- nel estimation uses a priori symbol estimates gener- ated from the turbo decoder and is described by

(4)

where V k - i is the turbo symbol estimates and Y k - - i is the received symbols. Here, the channel gain is found using all of the received symbols in conjunction with the symbol estimates of the turbo decoder after the first iteration.

Note that for sufficiently small filter lengths relakive to the fade rate, (N , << l/fdTs), the filter coefficients are approximately equal. The filter is then a moving average that is simpler than the Wiener filter and achieves the same results. Our simulations use the moving average approximations.

The most accurate estimation is achieved if the coded SW is completely and evenly distributed across the transmitted packet. If the SW is clustered in the middle of a packet, then the channel estimates at the edges of the packet will not be as optimal leading to degradation of performance and likewise if the SW is clustered at any other location. To distribute the SW across the channel, a balance has to be achieved be- tween the packet size, block channel interleaver struc- ture, the exact placement of the SW, and the channel demands. Fig. 3 illustrates the encoding process and the resulting distribution. Note that for turbo encod- ing which employs recursive systematic convolutional encoding, a portion of the parity symbols is unknown due to the intrinsic pseuderandom interleaver. One option is to ignore the unknowns which will drop the number of coded SW symbols by a 1/3. Another op- tion is to puncture and replace with a known symbol. The tradeoff is illustrated in the Simulation section.

The design methodology for distributing the coded SW symbols across the packet would follow along these general steps: (i) find typical fade rate of chan- nel; (ii) derive ideal spacing for estimation symbols; (iii) determine packet size based on spacing require- ments and given SW; (iv) design block interleaver ac- cording to spacing; (v) find placement of SW in data bits, that in conjunction with block interleaver, would evenly and completely distribute coded symbols.

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Fig. 3. Flowchart of encoding process affecting coded SW distribution.

V. SIMULATION RESULTS

We assume that the fade rate f d T s is 0.005 and the spacing between 2 consecutive SW bit is 16 for chan- nel estimation,which is found as a good choice in [2]. For a turbo encoder with constraint length, kc = 3, the SW is xx100. The 'xx' in the SW refers to encoder state dependent bits that adaptively force the encoder state to zero. The SW bits are encoded at 1/3 rate leading to 9 coded SW for channel estimations. For a spacing of 16, the packet size can be 144 with the appropriate block interleaver being 9x16. Placement of the SW in the original data stream is important for a balanced distribution. The 2nd parity bits are unknown due to the turbo encoder pseuderandom interleaver and random data stream. As a result, the effective number of coded symbols for estimation pur- poses in our example drops from 9 to 6. Two possible options are either to ignore the 2nd symbol bits, or puncture and replace with a known symbol. Fig. 4 il- lustrates the performance difference in relation to use of the unknown parity symbols using the parameters specified above. The packet length L = 48 including SW xx100, SW placement 22, a [8 181 block inter- leaver, and a resultant coded SW spacing of 18. The decoder employed 8 iterations. Simulations indicated that the puncturing method results in a 0.5 dB per- formance improvement.

For comparison purposes, an equivalent PSAM simulation is performed. The only difference in setup is that 9 pilot symbols are inserted in the encoded data stream. The constraint length, length of data, block interleaver, code rate, and number of iterations remain the same. As seen in Fig. 5, the peffor- mance of the PSAM is identical to SWAM (punc- turing and replacing unknown parity symbols within) experimental error. For SWAM, the encoder is of con- straint length kc = 3, fade rate f d T s = 0.005, packet length L = 48 including SW xx100, SW placement

, , . . I , . . . . . . . - . . . . . . . . .

Fig. 4. SWAM performance using and not using the 2nd parity bit.

22, a [9 161 block interleaver, and a resultant coded SW spacing of 16. The decoder employed 8 iterations. The PSAM encoder and decoder is exactly the same with the exception of inserting 9 pilot symbols spaced every 16 symbols in the encoded data stream.

.... ...... .. . . 1111.1 ,--, 1""",11 .....* 1 1 . 1 4 1 1 , , ; .*"I . .

. . I

' I . . . . . . =. :

: . . . . . . . . - - .. .! .. - . . . . ."; . . . . In 7 . , I . . . . . . . . . . . . . . . . . . . . . . . , . . . .

. . . . . . . . . . . . . ...... . :

Fig. 5. PSAM versus SWAM puncturing and replacing un- known parity symbols.

Next, we compared the performance of the parti- tioned and joint synchronization-channel estimation schemes. In the partitioned scheme, we considered 8 iterations in synchronization for the list synchro- nizer, then one iteration for channel estimation on the synchronized data frame. In the joint scheme, we also chose 8 iterations for channel estimation and

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synchronization jointly, and decoded output is chosen according to the most probably synchronized frame position. Here, we selected different packet size. The packet is 64 bits long including the 2 tail bits and SW. The 4 unknown parity bits from the lower RSC are replaced by known bits, so 12 effective SW are used in frame synchronization and channel estimation. With spacing 16 and 12 SW, the coded packet size is 192. The block channel interleaver is chosen as [12 161, and SW placement is 29 in the uncoded packet.

Fig. 6 shows that the performance of the joint scheme is modestly better than the partitioned scheme. In the joint scheme, the refined channel es- timation improves the turbo decoding performance, which directly influences the synchronization and thus the overall performance. Although this scheme’s better performance is achieved at the expense of ad- ditional iterative channel estimation operation, which is less significant compared to the decoding operation.

SWAM Tumo Perlormawe CanparDon

lo-‘

................................. ................................... 104

................... , .......... ................................... ....................................................... 5 104

10-

................... .: ....... .: ..................... :... ................. : . . . . . . . . : .......... 1 0‘

............................................................................................. lo+

0 1 2 3 4 5 6 7 8 9 EMlo (6B)

Fig. 6. Performance comparison of separated and joint syn- chronization and channel estimation scheme.

VI. CONCLUSION The proposed SWAM method for decoder-assisted

channel estimation can achieve the same results as PSAM without the additional increase in bandwidth. The only drawback to SWAM is that it is not as scal- able as PSAM. For SWAM, the number of channel es- timation symbols is tied into the size of the SW. If the packet size increases but the SW remains the same, then the spacing is increased leading to degradation in performance. Future testing is needed to address the effect of SW puncturing on frame synchronization. Also, the performance link between block channel in- terleaver and SWAM needs to be further investigated. To properly distribute the coded SW, the block inter- leaver is modified and may not be ideal.

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REFERENCES [I] M. M. K. Howlader and B. D. Woerner, “Decoder-assisted

frame synchronization for packet transmission,” IEEE Journal on Selected Areas in Communications, pp. 2331- 45, vol. 19, no. 12, Dec. 2001.

(21 M. Valenti and B.D. Woerner, “Refined channel estirna- tion for coherent detection of turbo codes over flat fading channels,” Electronic Letters, vol. 34, pp. 1648-1649, Aug. 20 1998.

[3] J. K. Cavers, “An analysis of pilot symbol assisted modu- lation for Rayleigh fading channels,” IEEE Trans. Vehic. Technol., vol. 40, no. 4, pp. 686-693, Nov. 1991.

141 W.C. Jakes, Mobile Microwave Communication, New York, John Wiley & Sons, 1974.

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