Turbo Code with Modified LLR and Performance Analysis for Bluetooth Packets in Indoor Environments

Wireless Pers Commun (2010) 54:277–287DOI 10.1007/s11277-009-9725-0

Turbo Code with Modified LLR and PerformanceAnalysis for Bluetooth Packets in Indoor Environments

Salim Kahveci · Ismail Kaya

Published online: 23 April 2009© Springer Science+Business Media, LLC. 2009

Abstract Most of the restrictions in indoor environments do not exist for outdoor sites. Themain limitations for indoors are the attenuation of walls and the multipath fading effects. Thesignal propagation is limited by the standard free space path loss in outdoor environmentsor free space. The loss in free space is usually equal to the range squared whereas the lossexponent for indoors is more like the 4th power. This study investigates the performance ofturbo codes with modified Maximum-A-Posteriori (MAP) decoding algorithm for Bluetoothdata packets in indoor environments over the frequency selective Rayleigh fading channels;which are also called as indoor wireless communication channels. In order to reduce thecomputational complexity of turbo decoders, MAP algorithm is modified in this study. Biterror rate (BER) versus energy of bit-to-noise ratio (Eb/No) of modified MAP algorithms forBluetooth data packets at 2.4 GHz industrial-scientific-medical (ISM) band are evaluated bymeans of computer simulations. Thus, modified logarithmic likelihood ratio (LLR) methodcan significantly reduce the computational complexity of the MAP algorithm. Furthermore,the performances of different types of forward error correction (FEC) coding for Bluetoothdata packets are compared in the study.

Keywords Bluetooth · FEC · Turbo codes · MAP algorithm

1 Introduction

Bandwidth and transmission power are critical parameters in digital communication systems.Digital wireless communication is one of the particularly promising areas for the applicationof various Turbo codes. It is well known that a wireless communication channel is charac-terized by the multipath propagation of signals. The received signal suffers phase variationsand amplitude fluctuations as a result of this process. This in turn adversely affects bit error

S. Kahveci (B) · I. KayaDepartment of Electrical and Electronics Engineering, Karadeniz Technical University,61080 Trabzon, Turkeye-mail: [email protected]

123

278 S. Kahveci, I. Kaya

performance as compared to the transmission over an additive white Gaussian noise (AWGN)channel.

The development of novel powerful wireless indoor communication systems can beexpected according to already introduced standards, i.e. IEEE 802.11 (1…2 Mbits/s) andHIPERLAN (20 Mbits/s) or taking account of specific normalization activities performedwithin the frame of European Universal Mobile Telecommunication Systems (UMTS), dur-ing the upcoming decade. Indoor communication systems have to cope with the frequency andtime selective channel characteristics mainly because of multipath propagation and move-ments of the terminals, and reflectors or scatters, respectively [1,2]. Hence, the detailedknowledge of the radio wave propagation effects within buildings is inevitable for the devel-opment, performance assessment, and design of such wireless transmission systems. Globalchannel parameters such as delay spread, coherence bandwidth, coherence time, number ofdominant paths, and path loss are required to achieve a first approach of optimum parameters.On the other hand, the relationship between delay spread τrms and the symbol time Ts can beviewed in terms of two different degradation categories. The first one is the frequency non-selective or flat fading category; which is the model assumed for the wireless radio channelif Ts is much greater than τrms [3]. The second category is the frequency selective fadingthat is assumed when the coherent bandwidth of the channel is not very high compared tothe signal bandwidth. A simulation of the while system including a channel model, whichaccurately imitates the transmission constellation by means of synthesized channel impulseresponse in accordance with the real environment, in the design phase allows the necessaryperformance evaluation.

The indoor channel is typically modeled as a Rician channel. Rayleigh fading becomes anappropriate model when the line-of-sight (LOS) is blocked. Rayleigh fading is considered asa suitable indoor communication model in this study. In order to mitigate the effects of fadingand to reduce the penalty in signal-to-noise ratio (SNR), the channel coding is employed.Channel coding allows to reduce the transmission power by maintaining the quality of service,or vice versa, to improve the quality of service for given transmission power. Performancesof the Turbo codes in multipath fading channels were studied by many researchers; and thecomprehensive overviews of the research results are given in [4,5]. It can be observed fromthese studies that the analysis of Turbo codes in fading channels the maximum posteriori-decoding algorithm for recursive systematic convolution (RSC) codes was generally used.Turbo decoding is very complex and also belongs to the most computationally intensivebaseband tasks performed by the receiver. Turbo decoding algorithms may be impractical forimplementation in many wireless communication systems [5]. This study examines the biterror rate (BER) performance of Turbo codes with modified Maximum-A-Posteriori (MAP)decoding algorithm in Rayleigh fading channels with additive noise for the different typesof Bluetooth data packets.

2 Communication System Model

The Turbo coded transmission system studied in this study is depicted in Fig. 1. The informa-tion bits uk are grouped into Bluetooth data blocks of N bits; and these blocks are then fedinto the rate-R Turbo encoder. The systematic and parity bits of the resulting output block ofthe Turbo encoder are mapped onto binary phase shift keying (BPSK) signaling as the finalstep of the process.

The communication channel is a frequency selective Rayleigh fading channel with addi-tive white Gaussian noise. This channel model is presented in Fig. 2. Functions a(t) and θ(t)

123

Turbo Code with Modified LLR and Performance Analysis for Bluetooth Packets 279

Bluetoothpacket

Turboencoder

BPSKmodulator

Frequencyselectivechannel

CMFDemodulatorMAP

decoder

ku

uk AWGN

Fig. 1 Turbo-coded communication model

Fig. 2 A Rayleigh fadingchannel system

x(t)

a(t)exp(j (t))

(t)

y(t)

represent channel gain and channel phase, respectively; and η(t) is additive white Gaussiannoise with zero mean and two-sided power spectral density N0/2. Assuming coherent BPSKdetection implies that the phase θ(t) is known at the receiver, the discrete representation ofthe channel output signal is expressed as;

yk = ak xk + ηk (1)

where xk is a BPSK symbol amplitude having values of ±√Es . The channel gain ak is

Rayleigh distributed and has a mean-square value of Ea[a2

] = 1. The channel output isyk whereas ηk is AWGN noise. At the receiving side, the output symbols are passed to theTurbo decoder, which uses a modified MAP algorithm, following coherent BPSK detection.Channel matched filter (CMF) structure fully exploits the multipath activity in the channeland represents an optimum filter in the presence of noise. The CMF is commonly used tomaximize the received SNR in a technique sometimes referred as “maximal ratio combining”[6]. Previous implementations of this technique, however, have assumed the correction of thechannel effects. This is generally realized because of the need for time and phase tracking.Applying this approach, the signal component from each path is weighted by the complexconjugate of the channel gain of the corresponding path. The sum of these weighted com-ponents has the optimum SNR, and this sum is then passed to the remaining portion of thereceiver, i.e. the decoder.

3 Structure of the Bluetooth Packets

Bluetooth is a low-power-consumption and short-range wireless technology for creating per-sonal networks operating in the 2.4 GHz unlicensed ISM band with up to range of 100 meters.Wireless networks are usually formed ad-hoc from portable devices such as cellular phones,handhelds, and laptops. Bluetooth network arrangements can be either point-to-point or point-to-multipoint to provide correction links among a plurality of electronic devices. Two to eightdevices can be operatively connected into a piconet; wherein one of the devices serves as themaster while the others are the slaves at a given period.

123


Table 1 A summary of packettypes for synchronous andasynchronous logical transports[8]

Type code Slot SCO Link (1 Mbps) ACL Link (1 Mbps)

0011 1 DM1 DM1

0101 1 HV1 −0110 1 HV2 −0111 1 HV3 −1000 1 DV −1001 1 − AUX1

1010 3 − DM3

1011 3 − DH3

1110 5 − DM5

1111 5 DH5

Access code (68/72 bits)

Header(54 bits)

Payload(0-2744 bits)

Fig. 3 The basic packet format in the Bluetooth standard [7]

Two logical transports with distinct packet types are defined for the Bluetooth system;the SCO (Synchronous Connection Oriented) logical transport and the ACL (AsynchronousConnectionless Link) logical transport. 10 different packet types for each of these logicaltransports can be seen in Table 1. Only DM1, DM3, and DM5 Bluetooth data packets wereused in this study. With an ACL link, data can be carried in DH (Data High rate) packetsor DM (Data Medium rate) packets. The DM packets, on the other hand, carry less data butprovide extra error protection. The standard Bluetooth packet format is depicted in Fig. 3.Each packet consists of three parts: Access code, Header, and Payload [7]. The Access code(68 or 72 bits) is used to detect the presence of a packet and to address the packet to a spe-cific device. The header (54 bits) contains all the control information involved with packettypes and links. The payload (0–2744 bits) contains the actual message. The transmitted datacan be organized in two different packet types, as can be seen in Table 1, when using ACLlinks; the DM and DH packets. The DH packets do not include Forward Error Correction(FEC) information; hence, their induced transmission overheads are lower. Three DM andDH packets are defined, termed as DM1, DM3, DM5 and DH1, DH3, DH5, respectively[7,8]. A DM1 packet is sent during a single transmission slot while a DM3 packet employsthree times slot.

Bluetooth transmission with the 1/3-FEC and 2/3-FEC coded DM packet types are alsoresearched in this study. The strongest, which is 1/3-FEC encoding, involves simply repeat-ing each bit three times and is then decoded by carrying out a majority function on thereceiving side [9]. This process is sufficient to detect two in every three bits input and tocorrect one in every three. The packet header uses 1/3-FEC encoding as the link informationcontained therein is the most critical part of the packet. The (15, 10) Hamming code, alsoknown as 2/3-FEC, is a cyclic and systematic codes according to the Bluetooth standard[10]. The 10 binary data symbols and the 15 binary code symbols of one code word can beshown by u = [u0, u1, u2, . . . , u9] and c = [c0, c1, c2, . . . , c14], respectively; where ui andci ∈ {0, 1}. Thus, there are 15 bits output for every 10 bits input. This protection is suffi-cient to detect 2 bits in the 10 bits input and to correct 1 bit in every 10 bits. The binary code

123


symbols ci are then mapped to binary modulation symbols as {±1}. Apart from the ACLlinks, Bluetooth also uses SCO links for realizing point-to-point wireless paths between amaster and a specific slave mode.

4 The Map Algorithm with Modified LLR

The Turbo decoder calls for two identical MAP decoders and operates in an iterative manner;where the log domain extrinsic probabilities output LLR(Pout (uk |Y )) from one MAP decoderwill be passed to another as the priori probabilities of received codeword. Each decoder real-izing MAP decision rule calculates the log-likelihood ratio for each information bit in thereceived block Y in this iterative decoding of Turbo codes. The log-likelihood ratio for theinput symbol uk is defined as;

LLR(uk) = lnP(uk = 1|Y )

P(uk = 0|Y )(2)

LLR can also be written in a different form;

LLR(uk) = LLRc(ysk |uk) + LLRa(uk) + LLRe(uk) (3)

where LLRc(ysk |uk) is the channel value; LLRa(uk) is the a priori information; and LLRe

(uk) is the extrinsic information. The channel value LLRc(ysk |uk) is given as;

LLRc(ysk |uk) = ln

P(ysk |uk = 1)

P(ysk |uk = 0)

(4)

The extrinsic information LLRe(uk) is an expression including quantities of αk(s), βk(s), andγi (yk, s′, s). The quantity αk(s) represents a state likelihood at time k based on a forwardsweep through the trellis; and βk(s) represents a state likelihood based on a backward sweepthrough the trellis. The γi (yk, s′, s) is the transitional probability that can be expressed as in[11]:

γi (yk, s′, s) = P(ysk |uk = i)P(uk = i) (5)

Simplification of the calculations in the MAP decoding can be obtained by using loga-rithms of αk(s), βk(s), and γi (yk, s′, s).αk(s) and βk−1(s′) are then substituted as seen in[12];

ln[αk(s)] = ln[∑s−1

s′=0

∑1i=0 e(ln αk−1(s′)+ln γi (yk ,s′,s))

]

ln[βk−1(s′)] = ln[∑s−1

s′=0

∑1i=0 e(ln βk (s)+ln γi (yk ,s′,s))

] (6)

The Max-Log-MAP algorithm is based on the application of the following approximation;

ln(ex1 + ex2 + ex3 + · · · + exN ) ≈ max(x1, x2, x3, . . . , xN ) (7)

which significantly reduces the computational effort in the calculation of ln[αk(s)] andln[βk−1(s′)]. Using approximation (7) in Equation 6 the approximation below is obtained;

ln[αk(s)] ≈ max(s′,i)

{ln αk−1(s′) + ln γi (yk, s′, s)}

ln[βk−1(s′)] ≈ max(s′,i)

{ln βk(s) + ln γi (yk, s′, s)} (8)

123


The LLR can then be expressed as in [13],

LLR(uk) ≈ max(s′,s)

{ln αk−1(s′) + ln γ1(y p

k , s′, s)

+ ln βk(s)} + ln(P(ysk |uk = 1)) + ln(P(uk = 1))

− max(s′,s)

{ln αk−1(s′) + ln γ0(y p

k , s′, s) + ln βk(s)}+ ln(P(ys

k |uk = 0)) + ln(P(uk = 0)) (9)

The soft output, LLR(uk), is computed with the aid of the forward, backward, and branchmetrics as a difference of two maximums. In the following calculations, the minuend max-imum corresponds to the state transitions with transmitted systematic bit ys

k = 0; and thesubtrahend corresponds to the state transitions with ys

k = 1 [14]. The hard bit estimate u′k is

obtained merely by the signum function, sgn(.) of the LLR(uk). It is necessary in the MAPalgorithm to modify calculation of conditional probabilities P(yk |uk)for the Rayleigh fadingchannel as compared to the AWGN channel.

The LLR(uk) value is related with channel reliability factor, represented by Lc, as follows;

LLR(uk) = LcakY Nk (10)

In Eq. 10, Lc = 4 EsN0

is the channel reliability factor for AWGN channel; ak represents

the amplitude of fading channel coefficients; and Y Nk is the received sequence at the MAP

decoder. Es is the symbol power; and N0 is the power spectral density of noise. The channelreliability factor, represented by Lc, is very significant for calculation of the LLR(uk). It isassumed in literature that Lc is to be known at receiver side. In this study, however, it isconsidered that Lc is not known at the side of receiver. It is proposed that it must be esti-mated by using received data sequence from the channel output. The ways of obtainment hasbeen examined by an example. For instance, it is assumed that channel has a0 coefficient. Atreceiver input of yk is then rewritten;

yk = a0xk + ηk (11)

The complex conjugate of the yk is y∗k ;

y∗k = a∗

0 x∗k + η∗

k (12)

Lastly, the multiplication of the yk and y∗k is as follows;

yk y∗k = a0a∗

0 xk x∗k + a0xkη

∗k + a∗

0 x∗k ηk + ηkη

∗k

= (a0a∗0 )xk x∗

k + ηkη∗k

= d0 + σ 2 (13)

In a wireless communication system, the channel must be estimated for equalization. Theestimated channel impulse response (CIR) is normally affected by additive noise. The prob-lem of estimating the CIR is more difficult to solve for time-varying channels. The differencebetween the statistical characteristics of the additive noise and the multipath channel is thatthe CIR coefficients are located only in the window of the CIR length whereas the additivenoise per channel tap is uniformly distributed over the whole length of the estimated CIR.The estimated CIR and noise variance are very useful in many areas; such as channel coding,data equalization and adaptive filter implementations.

In Eq. 13, σ 2 is the variance of noise and d0 represents the branch energy. Thus, the noisevariance is formulated in Eq. 14;

σ 2 = E{yk y∗k } − d0 (14)

123


where E{.} is the expectation value of the received signal. The channel reliability factor Lc iscalculated without difficulty for LLR(uk)following the estimation of the σ 2. This approachis more important than conventional solutions for unknown SNR at receiver side [15]. TheLog-MAP, Max-Log-MAP, and Constant-Log-MAP algorithms have been simulated underthe estimated Lc condition in this study.

Log-MAP algorithm is MAP process implemented in log-domain. Nevertheless, the imple-mentation of the Log-MAP algorithm described above is not easy. Aside from the Max-Log-MAP algorithm, there are some techniques to simplify the Log-MAP algorithm by invokingan approximation for the sake of reducing the associated implementation complexity of max∗function. Assuming that δ1 and δ2 are real numbers:

4.1 Linear-Log-MAP Algorithm

The Linear-Log-MAP algorithm uses the following linear approximation;

max∗ = max(δ1, δ2) +{

0, if |δ2 − δ1| > Ta (|δ2 − δ1| − T) , if |δ2 − δ1| ≤ T

(15)

In Valenti’s work [16], a solution is found by minimizing the total squared error betweenthe exact correction function and its linear approximation; where “a” and “T” are constantvalues as a = −0.249 and T = 2.506.

4.2 Constant-Log-MAP Algorithm

In Constant-Log-MAP algorithm, the max∗ operation can be evaluated by;

max∗ = max(δ1, δ2) +{

0, if |δ2 − δ1| > TC, if |δ2 − δ1| ≤ T

(16)

where C is a constant. The best parameters are C = 0.5 and T = 1.5 as shown in [16]. The max∗can be computed by in [16] in the Constant-Log-MAP algorithm. The linear-Log-MAP algo-rithm, first introduced in [17], uses the linear approximation. In the Max-Log approximation,however, max∗(.) is computed by using max∗(δ1, δ2) = max(δ1, δ2). Thus, the complexityof the Log-MAP algorithm can be further reduced by using the max-Log approximation. Thecomparison for performances of these approximations is given in Sect. 5.

5 Simulation Results

The use of Turbo coding for Bluetooth application in indoor environments is considered asa novel approach. Computer simulations are performed for various types of Bluetooth datapacket in order to investigate the performance of Turbo codes with modified MAP decodingalgorithm on frequency selective Rayleigh fading channels. The rate −1/3 Turbo codes basedon RSC component codes with generator polynomials (15/13)8 are studied; and the RSCcodes are found to have 8 states in typical indoor applications where the channel exhibitslow delay spread. Thus, a Rayleigh fading channel with BPSK modulation is assumed forthis study; and the information blocks are considered as DM1, DM3, and DM5 packets. Theresults of the performance analysis up to 5-iteration of the modified MAP algorithms andFEC codes for Bluetooth DM1, DM3, and DM5 packets are presented in Figs. 4, 5 and 6,respectively. These figures also depict clear comparisons with respect to the performance ofregular Bluetooth without Turbo coding.

123


(Code rate 1/3, DM1packet, 8-state and 5-iteration)

0 2 4 6 8 10 12 14 161E-7

1E-6

1E-5

1E-4

1E-3

1E-2

1E-1

1E+0

Eb/No (dB)

BER

Without Coding

1/3-FEC

(15,10) Hamming

Max-Log-MMAP

Constant-Log-MMAP

Linear-Log-MMAP

Log-MAP

Fig. 4 BER-Eb/No curves for the Bluetooth DM1 packet

(Code rate1/3, DM3 packet, 8-state and 5-iteration)

0 2 4 6 8 10 121E-6

1E-5

1E-4

1E-3

1E-2

1E-1

1E+0

Eb/No (dB)

BE

R

Without Coding

1/3-FEC

(15,10) Hamming

Max-Log-MMAP

Constant-Log-MMAP

Linear-Log-MMAP

Log-MAP

Fig. 5 BER-Eb/No curves for the Bluetooth DM3 packet

123


(Code rate1/3, DM5packet, 8-state and5-iteration)

0 2 4 6 8 101E-8

1E-7

1E-6

1E-5

1E-4

1E-3

1E-2

1E-1

1E+0

Eb/No (dB)

BE

R

Without Coding

1/3-FEC

(15,10) Hamming

Max-Log-MMAP

Constant-Log-MMAP

Log-MAP

Linear-Log-MMAP

Fig. 6 BER- Eb/No curves for the Bluetooth DM5 packet

The results of performances of the Modified Max-Log-MAP (Max-Log-MMAP), ModifiedConstant-Log-MAP (Constant-Log-MMAP), Log-MAP (Log-MAP) algorithms, and Blue-tooth DM1 packet without Turbo coding are depicted in Fig. 4. The best performance isobtained using the Log-MAP algorithm. On the other hand, the computational complex-ity is the maximum also for the Log-MAP algorithm. The results of the performance ofthe Bluetooth DM3 packet are shown in Fig. 5. The obtained BER-Eb/No curve for (15, 10)Hamming is better than that of the modified Max-Log-MMAP algorithm. BER performancesof the modified MAP algorithm can be seen for the Bluetooth DM5 packet in Fig. 6. 10−3 ofBER is obtained at 6 dB of Eb/No for the Max-Log-MMAP algorithm and at almost 4 dB ofEb/No for the other modified algorithms as seen in Fig. 6. Approximately 1.9 dB of perfor-mance difference occurs between the Max-Log-MMAP and Linear-Log-MMAP algorithmsat 10−3 of BER.

For all DM-rate Bluetooth data packets, it can also be observed that BER performance ofthe (15,10) Hamming coding is better than that of the 1/3-FEC coding for Bluetooth systemin indoor environment as illustrated in Figs. 4, 5 and 6.

6 Conclusion

This paper investigates the error performance characteristics of Turbo codes with themodified LLR for Bluetooth DM data packets over a frequency selective Rayleigh fadingchannel. This study is focused on different MAP decoding algorithms with modified channelreliability coefficient. Considerable improvements have been observed on coding gain onRayleigh channels by performing computer simulations. The performance curves of various

123


MAP algorithms have been provided so that the channel reliability factor Lc is estimated atreceiver and also compared with those of the cases with no Turbo and FEC coding schemes.

To summarize, it can be observed that the proposed method achieves a performance gainof approximately 1.8 ∼ 2 dB with respect to the classical Log-MAP algorithm.

References

1. Rappaport, T. S. (1996). Wireless communications principles and practice. Englewood Cliffs, NJ:Prentice-Hall.

2. Medbo, J. (1998). Radio wave propagation characteristics at 5 GHz with modeling suggestions forHIPERLAN/2. ETSI BRAN 3 ERI074A.

3. Proakis, J. G. (2000). Digital communications (4th ed.). New York: McGraw-Hill, Inc.4. Vucetic, B., & Yuan, J. (2000). Turbo codes: Principles and applications. Boston, London: Kluwer

Academic Publishers.5. Hanzo, L., Liew, T. H., & Yeap, B. L. (2002). Turbo coding, turbo equalization and space-time coding

for transmission over fading channels. Chichester: John Wiley & Sons.6. Wang, S. Y., Chi, H. C., & Quek, C. C. (2005). A two-dimensional RAKE receiver architecture with an

FFT-based matched filtering. IEEE Transactions On Vehicular Technology, 54(1), 224–234.7. http://www.bluetooth.com.8. Bluetooth SIG, “Specification of the Bluetooth system”, Bluetooth core specification 2.0 EDR [Vol. 0],

November, 2004.9. Bray, J., & Sturman, C. F. (2001). Bluetooth connect without cables (pp. 59–60). NJ, USA: Prentice Hall

Inc.10. Chui, T. Y., Thaler, F., & Scanlon, W. G. (2002). A novel channel modeling technique for perfor-

mance analysis of Bluetooth baseband packets. In Proceedings of the IEEE International Conference OnCommunication. NY, USA (pp. 308–312).

11. Hall, E. K., & Wilson, S. G. (1998). Design and analysis of turbo codes on Rayleigh fading channels.IEEE Journal on Selected Areas in Communication, 16(2), 160–174.

12. Gambe, H., Tanaka, Y., Ohbuchi, K., Tshihana, T., & Li, J. (2005). An improved sliding window algo-rithm for max-log-map turbo decoder and its programmable LSI implementation. IEICE Transactions onElectronics, E88-C(3), 403–412.

13. Vogt, T., & Wehn, N. (2006). A reconfigurable application specific instruction set processor for viter-bi and log-MAP decoding. In Proceedings of IEEE Workshop Signal Proceesing Systems Design andImplementation. Banff, Canada (pp. 142–147).

14. Loo, T. A. K. K., & Jumaa, S. A. (2003). High performance parallelised 3GPP turbo decoder. In Proceed-ings of IEE European Personal Mobile Communication Conference. Glasgow, UK (pp. 337–342).

15. Ampeliotis, D., & Berberidis, K. (2006). Low complexity turbo equalization for high data rate wirelesscommunications. EURASIP Journal on Wireless Communications and Networking, 2006, 1–12.

16. Valenti, M. C., & Sun, J. (2001). The UMTS turbo code and an efficient decoder implementation suitablefor software-defined radios. International Journal of Wireless Information Networks, 8, 203–215.

17. Cheng, J. F., & Ottosson, T. (2000). Linearly approximated log-MAP algorithms for turbo coding. InProceedings of IEEE VTC. Tokyo, Japan.

123

http://www.bluetooth.com


Author Biographies

Salim Kahveci completed his Bachelor, Master and Ph.D. Degreesof Electrical & Electronics Engineering at the University of KaradenizTechnical, Trabzon, Turkey, in 1996, 1999, and 2006, respectively. Heis a Member of IEEE. His research interests include wireless commu-nications, Bluetooth system and Turbo Coding/Equalization.

Ismail Kaya received both the B.S. and M.S. degrees in electrical andelectronics engineering from Karadeniz Technical University, Trabzon,Turkey, in 1987 and 1990 respectively and the Ph.D. degree in TheCenter of Communications Research from University of Bristol, UnitedKingdom, in 1998. He is currently Assistant Professor of electricaland electronics engineering at Karadeniz Technical University. His cur-rent research interests include wireless communications and networksincluding MIMO, OFDM, CDMA, digital implementation of commu-nication systems, fast channel equalization and estimation techniques,information theory, and coding.

123

Turbo Code with Modified LLR and Performance Analysis for Bluetooth Packets in Indoor Environments

Documents

Transcript of Turbo Code with Modified LLR and Performance Analysis for Bluetooth Packets in Indoor Environments