In our software-defined radio project, we aim at combining two standards luetooth and HIPERLAN/2. The HIPERLAN/2 receiver requires more computational power than Bluetooth. We choose to use this computational power also for Bluetooth and look for more advanced demodulation algorithms such as a maximum a posteriori probability (MAP) receiver. The paper discusses a simplified MAP receiver for Bluetooth GFSK signals. Laurent decomposition provides an orthogonal vector space for the MAP receiver. As the first Laurent waveform contains the most energy, we have used only this waveform for our (simplified) MAP receiver. This receiver requires a E/sub b//N/sub 0/ of about 11 dB for a BER of 10/sup -3/, required by the Bluetooth standard. This value is about 6 dB better than single bit demodulators. This performance is only met if the receiver has exact knowledge of the modulation index

Hoeksema, F.W.

Schiphorst, R.

Slump, C.H.

English

Schiphorst, Roelof

Slump, Cornelis H.

University of Twente Research Information

2003 4th IEEE Workshop on Signal Processing Advances in Wireless Communications A (SIMPLIFIED) BLUETOOTH MAXIMUM A POSTERIORI PROBABILITY (MAP) RECEIVER R. Schiphorst, E W Hoeksema and C.H. Slump Department of Electrical Engineering, Mathematics and Computer Science (EEMCS), University of Twente, Enschede, The Netherlands, Phone: (+31) (0)53 489 2770, email: [ r .schiphorst ,  f .w.hoeksema, c.h.slump]@utwente.nl ABSTRACT In our software-defined radio project we aim at combin- ing two standards: Bluetooth and HiperLANI2. The Hiper- LAN12 receiverrequires the most computation power in com- parison with Bluetooth. We choose to use this computa- tional power also for Bluetooth and look for more advanced demodulation algorithms such as a Maximum A posteriori Probability (MAP) receiver. This paper discusses a simpli- fied MAP receiver for Bluetooth GFSK signals. The Lau- rent decomposition provides an orthogonal vector space for the MAP receiver. As the first Laurent waveform contains the most energy we have used only this waveform for our (simplified) MAP receiver. This receiver requires a 2 of about 11 dB for a BER of required by the Bluetooth standard. This value is about 6 dB better than single hit demodulators. This performance will only be met if the re- ceiver has exact knowledge of the modulation index. 1. INTRODUCTION Since the introduction of second generation mobile com- munication systems such as GSM, the mobile communi- cation business has become a major business. Nowadays also other types of wireless communication such as wireless LAN or cordless telephone become popular. Furthermore there are not only different types of wireless communica- tions but there is also an excess of standards for each type of wireless communication. For example for wireless LAN standards, the following standards exists: IEEE 802.11b, IEEE 802.11a, HiperLANIl, HiperLAN/2, IEEE 802.11g, HomeRF etc. [I], [2]. In digital communication the trend is, due to Moore’s law, that more functionality of the radio transceiver is im- plemented digital, because the analog part of the transceiver remains the same in every fabrication technology whereas the digital part is scaled down. So the transceiver is more and more digitized. It is for these two reasons, the digi- talization of the transceiver and the abundance of standards which enables software (defined) radio 1.1. Outline The outline of this paper is as follows. First an introduction will he given on software (defined) radio and the software defined radio (SDR) project at the University of Twente. Then we discuss a Maximum A posteriori Probability (MAP) receiver which has two requirements; an orthogonal vec- tor space and an efficient search algorithm. The orthogo- nal vector space is provided by the Laurent decomposition which will be discussed first. Then, the MAP receiver and its search algorithm will be described. Finally BER versus EblNo plots are shown and compared with a single bit de- tector and conclusions are drawn. 1.2. Software radio The abundance of digital communication standards in not only disadvantageous for consumers but also for manufac- turers because they have to develop a new product for each standard. It is for that reason that the software-radio con- cept is emerging as a potential pragmatic solution: a soft- ware implementation of the user terminal able to dynami- cally adapt to the radio environment in which the terminal is located [3]. For manufacturers this could result in shorter development time, cheaper production due to higher vol- umes. Furthermore SDR has advantages for consumers be- cause it enables only software updates for new functionality without new hardware. Because of the analog nature of the air interface, a soft- ware radio will always have an analog front end. In an ideal software radio, the analog-to-digital converter (ADC) and the digital-to-analog converter (DAC) are positioned di- rectly after the antenna. Such an implementation is not fea- sible due to the power that such device would consume and other physical limitations [4][5]. It is therefore a challenge to design a system that preserves most properties of the ideal software radio while being realizable with current-day tech- 0-7803-785&W03/$17.00 02003 IEEE 160 nology. Such a system is called a software-defined radio (SDR). There exists different points of views on software (de- fined) radio: The first line of thinking is to make current radio sys- tems flexible in order to be able to correct design flaws as current designs become more complex e.g. a parchable radio. So a manufacturer can patch its products afterwards. The second point of view is to add flexibility and re- configurability to radio hardware platforms to enable multi-standard receivers. This can be seen as a real- ization of the software defined radio concept. The third line of thinking is to implement radio algo- rithms using a general purpose processor (GPP). This can be seen as a realization of the software radio con- cept. The fourth point of view is to implement radio sys- tems which dynamically adapt to the radio environ- ment, communication needs and available resources. This can be seen as the realization of an adaptive ra- dio. 1.3. The Bluetooth HiperLAN12 SDR receiver project In our SDR project [6]  we aim at combining two different types of standards, Bluetooth [ l ]  and HiperLAN/2 [2] on one common flexible hardware platform whereas our focus is on the physical layer of the receiver: from antenna output to raw bits. The research is carried out by two chairs of the University of Twente: the IC-Design group which focusses on the analog part and the chair Signals and Systems on the digital part. Table 1 shows some characteristics of the physical layer of both standards. HiperLAN/Z is a high-speed Wireless LAN (WLAN) standard using Orthogonal Frequency Divi- sion Multiplexing (OFDM). Its physical layer is very simi- lar to the 802.11a standard. Bluetooth on the other hand is a low cost, low speed standard, designed for replacing fixed cables. Bluetooth uses Gaussian Frequency Shift Keying (GFSK) which is also used by other standards such as IEEE 802.11bandDECT. For OUT project we follow the second (and third line) of thinking of SDR: the HiperLAN/2 hardware is that complex to the Bluetooth hardware that the Bluetooth receiver may be added to the HiperLAN/2 at limited costs. In order to gain knowledge about Bluetooth and HiperLAN12 receivers we have built a test-bed with two separate receivers [7]. The functional architecture is depicted in figure 1. parameter I Bluetooth 1 HiperLAN/2 band \ 2.4 - 2.48 GHz 1 5.15 - 5.725 GHz ch. spacing 20 MHz modulation OFDM + BPSW nom. bitrate 1 MbitJs 12 - 72 MbitJs QPSW16-QM64-QAM Table 1. Some physical layer characteristics of Bluetooth and HiperLAN/2 Receiver Anam P m a r , W  ADC meld C b n m l  LI RF *gal Ch-l $gal Srnmbd s m m  Fig. 1. Functional architecture of the SDR test bed 2. LAURENT DECOMPOSITION The function of the channel-selection function (see figure I )  is to select one channel and to remove all others. Optimal demodulation is provided by a so-called Maximum A pos- teriori Probability (MAP) receiver. This receiver requires an orthogonal vector space which is given by the Laurent decomposition. This Laurent decomposition describes the GFSK signal by a sum of linear, orthogonal, Pulse Amplitude- Modulated (PAM) waveforms. 2.1. CPM signals Bluetooth uses Gaussian Frequency Shift Keying (GFSK) which belongs to the class of Continuous Phase Modulation (CPM) signals. A complex envelope of a CPM signal can be written as follows [SI: with +(t, a)  = h?r a,q(t - nT) (2) n In the equation above, h is the modulation index; a, the symbol sequence belonging to the transmitted binary sym- bols (cy, = {-1,l)) and q( t )  is denoted as the phase re- sponse. For frequency modulation the relation between the phase and frequency response g( t )  is given by: The phase response q(t) has the following properties: q( t )  = 0 t 5 0 (4) 161 q( t )  = 1 t 2 LT ( 5 )  with T is the bit duration and L is an integer value, which indicates the duration of the phase transition. 2.2. Laurent decomposition In [9] it has been shown that equation 1 can he written as a sum of PAM waveforms (this is also deduced in the ap- pendix of [IO]): Q-1 S(t,a) = C b k + C k ( t  - nT) (6) k 0  n with Q = aL-' 7 and the PAM waveform c k ( t )  in equation 9. . The so-calledpseudo symbols bk., are given in equation with cy, the mth data bit and P k , i  is the ith bit of the so-called radix-2 representation of k (, so ,&,< bas a value 0 or 1): L-1 k = 2a-'Pk,i  1 5 k 5 Q - 1 (8) i=l c k ( t )  is a product of functions u(t): L-1 c k ( t )  = u(t)  n u(t + iT + LT&() 1 5 k 5 Q - 1 (9) i=l where the function u(t) is defined as follows: U ( t )  = sin(haq(t))/sin(ha) 0 5 t 5 LT u(t)  = u(2LT - t )  LT 5 t 5 2LT (10) u(t)  = 0 elsewhere From equation 10 it can be seen that the function u(rj is symmetric around t = LT and has a duration of 2LT. In many cases the signal power is concentrated in the first pulse, Q. So, the CPM signal can be approximated by using only this pulse (which simplifies the construction of the MAP receiver): S(t,  a)  TS bo,,co(t - 0) (11) n 2.3. Laurent decomposition of Bluetooth GFSK This section derives the Laurent decomposition for Blue- tooth GFSK modulation. The frequency response function g ( t )  is equal to the response of "one bit" to a Gaussian filter: LL (b) cz and CJ (c) ea. CS. % and t i  Fig. 2. Signal components of GFSK with BT = 0.5 and L = 4  with and with the BT product, BT = 0.5 The modulation index can vary between 0.28 and 0.35 according [I]. As the smallest modulation index gives the worst performance (at the same noise power), we used this modulation index for the Laurent decomposition. The re- sulting PAM waveforms (with L = 4) are shown in figure 2 for a modulation index h of 0.2.3. From the figure, it can be seen that the 6rst waveform co is the most important pulse. Figure 3 shows the phase of an example GFSK signal and its Laurent approximation. Note that the approxima- tion, using only the first Laurent term, and neglecting tran- sients effects, already equals the original GFSK signal. Zoom- ing in (figure 4) reveals that there are some small differ- ences. 162 Fig. 3. Phase plot of an example GFSK signal and its Lau- rent decompositions I I i-. ~ .~ ," ~ - - - - -I_ Fig. 4. A zoomed-in version of figure 3 3. A MAXIMUM A POSTERIORI PROBABILITY (MAP) RECEIVER In the previous section an orthogonal vector space has been derived that can be used in a MAP receiver. Only the first Laurent waveform is important, other waveforms can be ne- glected, especially if the noise power is high. Following the GramSchmidt procedure we have to normalize and mirror the first Laurent waveform: H d i )  = I lco(t)l l  (14) The M A P  receiver is shown in figure 5 .  Recall that the Laurent approximation of the GFSK Bluetooth signal is (eq. 1 I): i.(t, a )  En ho.nco(t - Q) (15) So, the filter Ho(t )  is a matched filter for the first Lau- rent waveform. Therefore the output of the filter is an (opti- mal) estimation of bo,%. This estimation has an optimal 2 but suffer also from Inter-Symbol Interference (ISI). So an - /algorithm I Fig. 5. MAP receiver - o(n)=-I  _.___= (") , sr, = S k . d 4  Fig. 6. Viterbi algorithm efficient search algorithm will he needed which determines the optimal path through the trellis diagram. For our MAP receiver we used the Viterbi algorithm. As the Gaussian filter has an filter length of about 3 bit times, a Viterhi algorithm with maximal 2 state variables should he sufficient; (cyn-? and on-l). The states and their branches to the next states are shown in figure 6. 3.0.1. Steps in the Viterbi algorithm Every sample the Viterhi algorithm must: calculate all 8 the branch metrics (, see equation 16) as two paths enter each state, save only the path with the highest state, the otber can be discarded. determine the state with the highest value and then de- cide the value of a n - ~ ,  and update the state variables (Y,-z. an-i and bn-3 The Viterbi algorithm can be initialized by setting the first sample to hn-3 and setting all states to zero. Then the algorithm starts at the qth sample for decoding the first bit. The branch metric is defined as follows: Bhl = b 0 , ~ - 3 e x p ( j h ~ c y ~ - ~  + jh?ra,-l+ jhmn)i&, (16) where go,,, is the output of filter Ho(t) 3.1. Results In Figure I the performance of the MAP receiver is depicted for several modulation indexes and for several Viterbi algo- rithms. For each 2 value 500000 bits have been simulated. Furthermore we used 80 samples per symbol in our simula- tion model. After the Ha filter, the sample stream was deci- mated with a factor 10, so 8 samples per symbol were used for synchronization and bit detection. A f (for the small- est modulation index) of about 11 dB is required for a BER of (required by the Bluetooth standard). 163 1 BER “.n/Y* EWNO plot tor h = 0.28 I Fig. 7. BER versus E6/No plot 4. CONCLUSIONS AND RECOMMENDATIONS In this paper we have derived a (simplified) MAP receiver for Bluetooth signals. This receiver requires (for the small- est modulation index) a % of about 11  dB for a BER of 10V3 (required by the Bluetooth standard). From figure 7 it can seen, that the Viterbi algorithm with 2 states has only a small performance degradation compared with the 4-state algorithm. Other demodulators, such as single bit detectors have worse performance. In our simulation model we have also implemented an FM discriminator which requires about a 2 of 17 dB [ l l ] .  The value equals the one found in liter- ature [12]. We have seen in simulations that a direct con- version demodulator 1131, requires the same $. So the performance gain is 6 dB. A MAP receiver needs exact knowledge of the modula- tion index because the performance is very sensitive for the modulation index error. A possible solution to this problem is to estimate the modulation index from the fist, known, pan of the Bluetooth packet, the access code. Funher re- search will have to verify this. Another solution is the use of adaptive search algorithms, such as an Decision Feed- back Equalizer (DFE). Acknowledgment We thank our colleagues from the IC-Design group of the University of Twente for their work on the analog part. More- over we thank Kiwi Smit of Ericsson Eurolab Netherlands B.V. for his comments. This research is supported by the PROGram for Research on Embedded Systems & Software (PROGRESS) of the Dutch organization for Scientific Re- search NWO, the Dutch Ministry of Economic Affairs and the technology foundation STW. 5. REFERENCES [l] Bluetooth SIG, “Specification of the bluetooth system -core,” Technical Specification Version 1.1, Bluetooth SIG, February 2001. “Broadband radio access networks (bran); hiperlan type 2; physical (phy) layer,” Technical Spec- ification ETSI TS 101 475 V1.2.2 (2001-02), ETSI, 650 Route des Lucioles - Sophia Antipolis, ValhOMe - FRANCE, February 2001. [2 ]  ETSI, [3] J. Mitola, Sofrware Radio Architecture: Object- Oriented Approaches to Wireless Systems Engineer- ing, Wiley, 2000. [4] R.H. Walden, “Performance trends for analog-to- digital converters,” IEEE Communications Magazine, pp. 96101,  February 1999. [5] V.J. Arkesteijn, E.A.M. Klumperink, and B. Nauta, “An analogue front-end architecture for software de- fined radio,” 13th proRISC workshop, November 2002. [6] “The bluetooth-hiperlad2 sdr receiver project,” http://nt5.el.utwente.nl/sdr/. [7] V.J. Arkesteijn, R. Schiphorst, F.W. Hoeksema, E.A.M. Klumperink, B. Nauta, and C.H. Slump, “A software-defined radio test-bed for wlan front ends,” 3nd PROGRESS workshop on Embedded System and Sofrware, 2002. [SI U. Mengali, “Decomposition of m-ary cpm signals into pam waveforms,” IEEE transactions on informa- tion theory, vol. 41, no. 5, pp. 1265-1275, September 1995. [9] P.A. Laurent, “Exact and appropiate construction of digital phase modulateds by superposition of ampli- tude modulated pulses (amp),” IEEE transactions on communications, vol. 34, no. 2, pp. 15@160, February 1986. [lo] G. Kawas Kaleh, “Simple coherent receivers for par- tial response continous phase modulation,” IEEE Journal on Selected Areas in Communications, vol. 7, no. 9, pp. 1427-1436, December 1989. [ I l l  R. Schiphorst, F.W. Hoeksema, and C.H. Slump, “Bluetooth demodulation algorithms and their perfor- mance:’ Workshop on Sofrware Radios (WSR2002), Karlsrnhe (Gj, March 2002. [12] A. Soltanian and R.E. Van Dyck, “Performance of the bluetooth system in fading dispersive channels and in- terference,” Proceedings of IEEE Globecom, Novem- ber 2001. [I31 M.H.L. Kouwenhoven, High-Pelformance Frequen~-Demodulation Systems, Ph.D. thesis, Delft University of Technology, 1998. 164 

A (Simplified) Bluetooth Maximum a Posteriori Probability (MAP) Receiver

A software-deﬁned radio test-bed for wlan front ends,”

An analogue front-end architecture for software deﬁned radio,” 13th proRISC workshop,

Bluetooth demodulation algorithms and their performance,”

Decomposition of m-ary cpm signals into pam waveforms,”

Exact and appropiate construction of digital phase modulateds by superposition of amplitude modulated pulses (amp),”

High-Performance Frequency-Demodulation Systems,

Performance of the bluetooth system in fading dispersive channels and interference,”

Performance trends for analog-todigital converters,”

radio access networks (bran); hiperlan type 2; physical (phy) layer,”

Simple coherent receivers for partial response continous phase modulation,”

Software Radio Architecture: ObjectOriented Approaches to Wireless Systems Engineering,

Speciﬁcation of the bluetooth system -

https://ris.utwente.nl/ws/files/5364813/01318942.pdf

A (Simplified) Bluetooth Maximum a Posteriori Probability (Map) Receiver

A (Simplified) Bluetooth Maximum a Posteriori Probability (Map) Receiver

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