A CMF-DFE-Based Turbo Equalization For Wireless Communication Systems

©BEYKENT UNIVERSITY

A CMF-DFE-BASED TURBO EQUALIZATION

FOR WIRELESS COMMUNICATION SYSTEMS

Salim KAHVECİ and İsmail KAYA

KTU, Department of Electrical & Electronics Engineering, 61080, Trabzon, Turkey, salim@ktu.edu.tr

ABSTRACT

In this paper, a new approach to the turbo equalization to reduce the channel effects for indoor wireless communication systems has been studied. The proposed turbo equalizer was simulated with a rate 1/3 turbo code, consisting of two components constraint length 3 RSC (Recursive Systematic Code) and a random interleaver size of the same input sequence. Channel reliability factor is an important parameter in the decoding process. On conventional approaches, it is assumed that this factor is known at receiver side. But, we assumed that receiver doesn't know the channel reliability factor in our study. At receiver input, we have to redefine the channel reliability factor used by the MAP (Maximum A Posteriori) decoding algorithm. Thus, we obtain then this factor by using received data sequence.

Simulation results show that the proposed turbo equalizer provided better BER (Bit Error Rate) performance than that of a conventional turbo equalizer scheme at low SNR (Signal-to-Noise Ratios).

Key Words: Bluetooth, CMF-DFE, MAP algorithm, Turbo codes, ISI Channel

ÖZET

Bu makalede, bina içi kablosuz haberleşme sistemlerinde kanal etkilerini azaltmak için yeni bir Turbo denkleştiriri üzerinde çalışılmıştır. Önerilen Turbo denkleştiriri iki adet öz yinelemeli sistematik konvolüsyonel (RSC) yapıdan oluşan 1/3 oranlı kodlayıcı ve aynı giriş dizisi boyutuna sahip bir rasgele serpiştirici için benzetim çalışması yapıldı. Kod çözücü işleminde kanal güvenirlilik faktörü önemli bir parametredir. Geleneksel yaklaşımda; bu parametrenin alıcı tarafından bilindiği kabul edilir. Ancak, buradaki çalışmamızda alıcının kanal güvenirlilik faktörünü bilmediği kabul edilir. Alıcı girişinde MAP kod çözücü algoritması kullanılarak kanal güvenirlilik

faktörünü yeniden tanımlamak zorundayız. Böylece, alınan veri kümesi kullanılarak bu faktör elde edilebilir.

Benzetim çalışması sonuçları, düşük işaret gürültü oranlarında (SNR) önerilen Turbo denkleştiririnin geleneksel Turbo denkleştiriciden daha iyi bit hata oranı (BER) başarımı sağladığını gösterir.

1 INTRODUCTION

High bit rate wireless communication systems such as Bluetooth and ZigBee suffer from intersymbol interference (ISI) in addition to noise during transmission over fading-frequency selective channels. General approaches separate the equalization and decoding functions. The concept of turbo equalization has been introduced in [1, 2] where equalization and decoding functions are jointly carried out. In turbo equalization, a soft-input soft-output (SISO) linear equalizer and a SISO decoder exchange soft information as iterative.

The optimisation criterion presented in this paper, called minimum mean log likelihood ratio (LLR) square error, is used for determining the coefficients of the equalizer. The equalizer coefficient gains are functions of the channel impulse response, extrinsic information and SNR. For each channel, the equalizer coefficient gains are determined for different SNRs and extrinsic LLR information variance.

The new turbo equalizer was simulated for Bluetooth system. Bluetooth is currently one of the most successful standards for low-power, low-cost and short-range wireless personal area networks (WPAN). A typical bluetooth system is composed of a small number of devices that form a wireless network called a "piconet". Connections are established ad hoc by a Bluetooth unit that becomes a master so that the other units called "slaves" synchronize with it. The bluetooth channel is divided into slots of length 625 |is so that time slots are alternatively used by master and slaves [3].

Low complexity turbo equalization schemes were proposed in the literature. For example, in [4] a turbo equalization scheme based on SISO linear equalization is proposed. However, it requires the use of a more reliable SISO algorithm such as the BCJR algorithm during the first iteration to obtain a reasonable performance.

Here, firstly channel reliability coefficient is determined at receiver input. Then conventional MAP algorithm is modified. Finally, the proposed

combined turbo decoder and equalizer structure is performed and BER performance results are showed for Bluetooth data packet.

2 A CODE RATE 1/3 TURBO CODER

Turbo codes, a parallel concatenated error correcting scheme is obtained by transmitting together, the message sequence x called the systematic bit c0 and

the two parity sequences c and c2, which are obtained by encoding the

message sequence and the interleaved message information. Figure 1 depicts the general encoding structure for a turbo encoding scheme where n represents the interleaving, which is obtained by permuting the message bits in a random order. Here, we consider a turbo encoded sequence through an independent Rayleigh fading channel with imperfect channel estimate using antipodal binary phase shift keying modulation. The discrete time system model with c k £ + ^ / E " and 1<k<(N+2)/R, is the BPSK (Binary Phase Shift Key) transmitted symbol, where N and R represent the information sequence size and the code rate, respectively. For this case, the relationship between the symbol energy and bit energy can be stated as Es=R.Eb.

Figure 1. Encoding structure for (1, 5/7, 5/7)8 parallel turbo code

The discrete output at the receiving end obtained from the matched filter assuming perfect synchronization at any time instant k is given by;

rk = £ hk - ick + nk ( i )

where hk = ak + vk . In the above expression rk represents the received signal, hk is the Rayleigh distributed noisy fading channel coefficients, ak is the ideal Rayleigh fading coefficients, uk models the error in the fading

coefficient and rjk represents zero-mean additive white Gaussian noise (AWGN).

3 MODIFIED MAP ALGORITHM

The RSC decoders in Fig. 2 are each executed using a version of the classic MAP algorithm implemented in the log-domain. The MAP algorithm was first introduced to the coding community in 1974 by Bahl, Cocke, Jelinik and Raviv [5]. It is an algorithm for estimating random parameters with prior distributions. The MAP algorithm is considerably more complex than the Viterbi algorithm. Recently, the introduction of turbo codes have brought about an increased interest about this algorithm because of its superior performance under low Eb/N0's and high BERs.

A. The classical MAP algorithm

First of all, the MAP algorithm finds the probability P[sr>s1+11 r ] of each valid state transition (in the Trellis diagram) given the noisy observation vector r. The properties of the Markov process can be used to partition the numerator as;

P[sr>sM, r ]=a(si).y(sr>si+i).p(si+i) ( 2 ) We can give an intuitive explanation about the meanings of these components.

First, consider the term "a";

a ( s , ) = P[st , ( r o , r i , . . . , r ^ ) ] (3)

This represents the probability that the current state is s(i) given the noisy observation vector r(0), r(1), ..., r(L-1). This is because the current state doesn't depend on the future values of the observation vector. The final state si+1 is not at all considered here.

Ks, ~> s,+i) = P [ s, + ir, I s,] (4) This represents the probability of the state transition from si to si+1, given the

current state is s(i) [5, 6]. The "y" is also called the Branch Metric associated with the state transition si->si+1.

p (

S

=

(r

,...,r

) | s

] (5)

not considered at all here. The probability "a" can be found using the following recursion,

a ( si ) = Y ja ( Sr - 1)Y( Si - 1 - > S ) ( 6 )

Si-¡GA

Here the "A" implies the set of states S1-1, which are calculated to the state S1. The probability "P" can be calculated using the following recursion,

P ( si ) = Zp ( si + 1)Y( si - > S+1) (7)

si + 1g B

Here the "B" implies the set of states S1+1 that are connected to the state S1. Once the posterior probability of each possible state transition, P[s1->s1+1|r] is calculated, the message bit probabilities at each time instant "i" are calculated as;

P[x = 1| r] = £ P [ S i -> s

| r],

^ (8)

P[x = 0| r] = 2 P [ S i - > Si+1 | r]

Where si represents the set of all state transitions for which the input message bit is "1" and s0 represents all the state transitions for which the input message bit is "0". The Log-Likelihood Ratio (LLR) now becomes.

P i s , - > s

i | r]^

LLR, = ln

2P[s

-> s

\r]

v so

(9)

B. Modified MAP structure

In Eq. (9) LLR calculation at MAP algorithm, the channel reliability Lc value is required in order to Lc's evaluation, SNR at receiver have to be known. Estimation of the SNR at receiver as follows;

The LLR value is related with Lc in reference [7],

LLR = L

.a.rN

s 0

In Eq. (10), Lc is the channel reliability factor, a represents the amplitude of fading and r^ is the received sequence at the decoder.

For example, it is assumed that channel has two coefficients. At receiver input rk is rewritten;

rk = ho ck + hick - i + n ( i i )

*

The complex conjugate of the rk is rk *

''k ,

rk

=

+ K

+

n*

*

The multiplication of the rk and rk is as follows;

rkr* = ho ho ckc* + ho h!ckck - i + ho hick - ic* + hi h*c k-ick + nknk = ( ho h'k + hihl)CkCk + nkr tk

= d 0 + a

(13)

2

In Eq. (13), <j is the variance of noise, d0 is the sum of all branch energy and E{.} is the expectation value of the received signal. Thus, the noise variance is formulated in Eq. (14).

<

= E{r

r* } - d o (14)

2

After < is estimated, the channel reliability Lc factor is calculated for LLR. This approach is more important than conventional solutions for SNR unknown at receiver.

4 PROPOSED TURBO EQUALIZATION

Channel matched filter (CMF)-decision feedback equalizer (DFE) is one of the most important pseudo-linear equalizers, and is discussed in [8]. Figure 3 shows its block diagram that has two linear transversal filter, the Feed Forward filter (FF) and the Feed Back filter (FB). Least mean square (LMS) algorithm is a very attractive adaptation algorithm for CMF-DFE, both in the decision directed adaptation mode and the blind adaptation mode [9]. In LMS adaptation, the filter coefficients wi are adapted as;

w

[k +1] = w

[k ] - ju.x[k - i].e* [k ] (15)

Figure 2. The proposed combining CMF-DFE-turbo equalizer structure.

In Figure 3, x[k] is the feed forward filter inputs and e[n] is the error signal. In the decision directed adaptation the error signal e[n] is obtained by subtraction of input and output of "decision" block.

e[k] = d[k] - z[k]

In new combined CMF-DFE and turbo decoder introduced, the turbo decoding process is used instead of the decision block as shown in Figure 2. In Figure 2, the CMF-DFE equalizer output zk is formulated as follows,

= z f f

X,,

Where, ffi and fbj are the FF filter coefficients and FB filter coefficients,

respectively. At the first iteration, zk is applied the FB filter input. After the

1-th iteration, 1-the inverse iteration output is applied to 1-the FB filter input. The decoding algorithm is based on Log-Likelihood ratios or L-values, which are defined as;

f

nh

i) ^

L ( r

k

= l°g

P ( f k =

0)

(18)

where rk represents the estimate of the user bit rk. The demodulator generates

the log likelihood ratios L(zk) of the channel symbol zk. These zk are the

received values of the ck bits. A priori L-values of the user bits are called

Lpnori( rk). These two kinds of log likelihood ratios are the inputs of the MAP module. Based on these inputs, L(zk) and Lpriori( rk) and on knowledge of the

component code, updates of the L-values of the user bit estimates are produced which are called extrinsic values Lext( rk ).

Figure 3. The CMF-DFE equalizer structure.

The L-values of the estimated user bits can be obtained [10];

L ( rk ) = L ( z k ) + LPnon(rk) + LeXt ( rk) (19)

Based on this Log-Likelihood ratio, the estimate of user bit rk is obtained.

r

= sign(LLR(r

)) (20)

The turbo decoding is performed by applying these MAP modules in an iterative way for each of the component codes where MAP-1 corresponds to RSC-1. The extrinsic information of each module is used as a priori information for the other module. The application of this procedure first for MAP-1 and then for MAP-2 is called one iteration. After a certain number of iterations the solution has converged closely to the ideal maximum likelihood decoding.

Here, a total of 79 hopping channels are changed in a pseudo-random sequence up to 1600 times per second. If necessary, faulty data telegrams are resent using another channel without a notable time delay. Frequency hopping method of Bluetooth, channels that are occupied by other wireless systems or those that are frequently subject to interference are detected automatically and removed from the hopping sequence. This increases reliability and ensures interference-free coexistence with a WLAN (Wireless Local Area Networks) 802.11b/g system. Bluetooth can use -and reuse- the available frequency band efficiently because of the FHSS (Frequency Hopping Spread Spectrum) modulation method.

5 SIMULATION RESULTS

Gaussian Noise. Channel coefficients are { 0.227, 0.46, 0.688, 0.46, 0.227 }. BER-SNR curves are obtained in order to 1000 Monte Carlo Simulations. In this paper, we have redefined the channel reliability factor used by the MAP algorithm. Although there are many Bluetooth packet types (DV, DHX, DMX), we only uses DM1 Bluetooth packet for ACL (Asynchronous Connectionless Link) link.

BER

SNR(dB)

Figure 4. Obtained BER-SNR curves for proposed turbo equalizer for bluetooth data

packet.

The classical turbo equalizer (TE) and proposed turbo equalizer performances are showed in Fig. 4 claret ret and wild grass green color lines, respectively. To combining and individual receiver systems, 1th iteration (l.iter), 3rd

iteration (3.iter), and 10th iteration (lO.iter) were performed. It is seen that the

proposed schemed is better than does the classical turbo equalizer. The turbo equalizer provides gain about 1 dB for 1th iteration at 10-3 bit error rate. As can

be find in Fig. 4, the greatest improvement in BER performance occurred mostly in the high SNR values.

Thus an additional benefit of proposed turbo equalizer is that it requires a fewer decoder iterations than classical one [11], which it can be seen in Fig. 5.

BER

SNR(dB)

Figure 5. Iteration saving with proposed equalizer for Bluetooth data packet

6 CONCLUSION

The bit error rate versus signal-to-noise performances of the proposed combining of the CMF-DFE and turbo decoder versus individual DFE and turbo decoder are examined. The provided improvement is considerable when the ISI is severe. On the contrary published studies [11, 12] until recent years, we implemented combining CMF-DFE-based Turbo equalizer with significant gain at lower iteration. We obtained also the channel reliability factor showed Lc at receiver side. This architecture was simulated for Bluetooth DM1 (Data

Medium 1-slot) data packets. As a consequence, the idea of combining equalizer and iterative decoding of turbo codes indicates interesting potential for usage in future short-range, low-cost and low-power indoor wireless communication systems (such as WiMAX and ZigBee).

REFERENCES

[1] Laot, C., Glavieux, A., and Labat, J.; Turbo Equalization : Adaptive

equalization and channel decoding jointly optimized, IEEE Journal of Selected Areas in Commun., vol.19, (September 2001), 1744-1752.

[2] Raphaeli, D., and Zarai, Y.; Combined turbo equalization and turbo

[3] Haartsen, J. C. ; The Bluetooth Radio System, IEEE Personal Communications (2000), 7-28, 36.

[4] Tuchler, M., Koetter, R., and Singer, A. C.; Turbo Equalization: principles and new results, IEEE Trans. Commun., 50, (May 2002), 754-767.

[5] Bahl, L., Jelinek, L., Raviv, J., and Raviv, F.; Optimal Decoding of Linear Codes for Minimising Symbol Error rate, IEEE Transactions on Information Theory, Vol. IT-20, (March 1974), 284-287.

[6] Vogelbrush, F., and Haar, S.; Improved soft ISI cancellation for turbo equalization using full soft output channel decoder's information, in Proceedings of IEEE Global Telecommunications Conference (GLOBECOM), 3, Francisco, USA, (December 2003), 1736-1740.

[7] Shin, H., and Hong, J.; Channel Reliability Estimation for Turbo Decoding in Rayleigh Fading Channels With Imperfect Channel Estimates, IEEE Commun. Letters, 6-11, (November 2002), 503-505.

[8] Proakis, J. G.; Digital Communications, McGraw-Hill, Third Edition, (1995).

[9] Baltaci, Y., Kaya, 1., Nix, A.; Implementation of a HiperLAN/1 compatible CMF-DFE equaliser, Proceedings of VTC, (2000), 1884.

[10] Benedetto, S., Divsalar, D., Montorsi, G., and Pollara, F.; A soft-Input Soft-Output APP Module for Iterative Decoding of Concatenated Codes, IEEE Commun. Letters, 1-1, (1997), 22-24.

[11] Jiang, S., Ping, L., Sun, H., and Leung, C. S.; Modified LMMSE turbo equalization, IEEE Communications Letters, 11-11, (2004), 891-894.

[12] Ampeliotis, D., Berberidis, K; Low Complexity Turbo Equalization for High Data Rate Wireless Communications, EURASIP Journal on Wireless Communications and Networking, (2006), 1-12.