On the Impact of Fading and Inter-piconet Interference on Bluetooth Performance

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1 On the Impact o Fading and Inter-piconet Intererence on Bluetooth Perormance Andrea Zanella Dept. o Inormation Engineering University o Padova, Padova, Italy zanella@dei.unipd.it Andrea Tonello Bell Labs, Lucent Technologies Whippany, NJ, USA tonello@lucent.com Silvano Pupolin Dept. o Inormation Engineering University o Padova, Padova, Italy pupolin@dei.unipd.it Abstract In this paper we propose a simple method to evaluate the impact o ading and inter-piconet intererence on Bluetooth perormance. We consider in detail the joint eect, on packet error statistics, o intererence produced by adjacent Bluetooth piconets and ading. Hence, we illustrate the proposed method by investigating the potential perormance tradeo among the dierent radio packet ormats supplied by Bluetooth, as a unction o the radio channel conditions and intererence levels. Keywords Bluetooth perormance, ading, inter-piconet intererence. INTRODUCTION Bluetooth is an emerging radio interace that operates in the.4 GHz ISM unlicensed band, providing a raw bit rate o 1Mb/s by using a binary Gaussian shaped FSK modulation [1], []. To reduce intererence with other devices operating in the ISM band, Bluetooth adopts a requency hopping (FH spread spectrum technique, spanning 79 RF carriers, 1 MHz wide each. In order to communicate, two up to eight Bluetooth units may connect in a small network, called piconet. In each piconet, a unit acts as master, controlling the channel access by means o a simple polling scheme. Time is divided into consecutive slots o 65µs each, that are used or downlink (master-to-slave and uplink (slave-to-master transmissions, alternatively, in a time division duplex (TDD ashion. Namely, each time-slot is associated to a hop in the hopping sequence, resulting in a nominal hop rate o 16 hop/s. Dierent piconets are associated to independent FH channels. This allows more piconets to share the same physical space and spectrum without increasing excessively the mutual intererence. However, since the requency hopping sequences are not orthogonal and the channels are asynchronous, intererence among dierent piconets may occur. With the perspective o having Bluetooth integrated in almost every electronic device, in the near uture, the inter-piconet intererence issue becomes o high importance. Furthermore, the standard provides up to six packet ormats or asynchronous data traic that dier or time duration, data capacity and error protection. Thereore, the perormance yielded by such dierent packet ormats may show a tradeo as the radio channel conditions and intererence levels vary. AC HEAD. ms =.65 ms PAYL T Dxn= n; n=1,3,5 Figure 1. Bluetooth packet ormat In this paper we propose a general method to evaluate the impact o ading and inter-piconet intererence on Bluetooth perormance. Although some analysis o the eect o inter-piconet intererence has been done in literature, most o the work is either based on simulations only [3], [4] or it makes restrictive assumptions as ixed length packets, destructive intererence, absence o ading, [5], [6]. Our approach relaxes most o these assumptions. In particular, we take into account the statistic o the received signal and intererence power, number o potential intererers, probability o packets collision and type o packets used. We analytically derive the distribution o the intererence power along the desired packet. Then, we derive the distribution o both the desired signal and intererence power. From the above statistics, we can derive the bit error rate distribution along the packet, and consequently, the packet error This rate. approach allows us to remove the restriction o destructive intererence, i.e., even a single bit collision is suicient to declare the packet loss. An analysis that overcomes this restriction was already presented in [7]. However, the model was very complicated and its application to the case with more than 3 interering piconets was unpractical. On the contrary, the method we propose can be easily applied to the case o many intereres. Furthermore, we evaluate the perormance yielded by all the dierent packet ormats provided by Bluetooth, considering the eect o orward error correction (FEC and dierent packet lengths. To conclude the paper, we report a comprehensive set o perormance curves that illustrates the behavior o the Bluetooth network as a unction o its parameters, such as number o piconets, channel propagation conditions and packet ormat considered. Proc. o IEEE Wireless Personal Multimedia Communications Symposium, WPMC Honolulu, Hawaii October 7-3, //$17 IEEE 18

2 BLUETOOTH PACKET FORMATS Bluetooth provides both Synchronous Connection Oriented (SCO and Asynchronous Connection Less (ACL links, or coded voice and best-eort data traic (symmetric and asymmetric, respectively. In the ollowing, we will ocus on ACL links only. Figure 1 depicts a generic Bluetooth data packet ormat. Each packet contains three main ields: the access code (AC, the packet header (HEAD and, optionally, the payload ield (PAYL. The 7-bit AC ield is used or synchronization and piconet identiication. The receiver correlates the incoming signal against the expected AC. I the correlator output does not exceed a given threshold, the packet is discarded. The AC is ollowed by an 18-bit packet header ield (HEAD. The HEAD is coded with a 1/3 orward error correction (FEC code, which is obtained by two-time repetition o every bit, resulting in a total ield length o 54 bits. Finally, the packet is trailed by the PAYL ield, whose length can vary rom up to 78 bits, depending on the packet type. The PAYL can be unprotected or protected by a /3 block code or FEC able to correct a single error in each codeword o 15 bits. ACL packets can extend over one, three or ive consecutive time slots. When a multi-slot packet is used, the transmitter requency remains unchanged or the entire packet duration, thus reducing the loss o capacity due to the guard time o. ms that is required at each requency hop. ACL packets are usually denoted by Dxk, where x stands or M and H and distinguishes between protected Medium-capacity and unprotected High-capacity packets, while k denotes the number o slots occupied by the packet (k=1,3 or 5. SYSTEM MODEL We ocus on the perormance o a target receiver (TR, which is positioned r meters apart rom the corresponding transmitter. We consider the joint eect o noise, path loss, ading and intererence rom adjacent Bluetooth piconets, while, at this phase o the work, the shadowing eect is neglected. Intererence may be produced by each terminal in the coverage area. However, the number o potential intereres is given by the total number o adjacent piconets, since only one terminal at a time is allowed to transmit in each piconet. A potential intererer becomes an eective intererer when it transmits a packet on the same carrier requency o the target packet. Radio Propagation and Intererence Models In the typical scenario deined or Bluetooth, the ading process can be assumed lat on the 1 MHz bandwidth and constant or the entire duration o a data packet. Furthermore, signals rom dierent transmitters incur in independent ading and, because o the FH mechanism, even successive packets rom the same transmitter are interested by independent ading. The perormance o the GFSK receiver depends on the instantaneous signal to noise/intererence ratio. However, the eect o the noise and intererence power on the bit error rate (BER is, in general, dierent. Following the approach proposed in [3], we consider a gross bit error rate unction given by Prx BER = β P R + N R, (1 I I where β( is the receiver perormance curve, Prx is the instantaneous signal power at the receiver, P I is the total instantaneous intererence power and N is the white noise power [3]. The weight actors R I and R correspond to the signal-to-intererence (SIR and signal-to-noise (SNR power ratios, respectively, which are required to have a raw BER o 1-3 or the corresponding type o intererence. The instantaneous signal power at a distance r rom the transmitter is given by γ=p T Ar -η α, where P T is the nominal transmitted power, Ar -η accounts or the deterministic path loss, and α represents the normalized ading envelope, which may be Rice or Rayleigh distributed. The values o P T, A and η are assumed constant and equal or all the users in the system, so that the statistic o γ is determined by the statistic o the normalized power =α r -η. The total power o n interering signals is assumed to be given by the sum o the power o each intererer [3], [7], i.e., P I =P T AΛ n, where Λ n = i i, i=1,,,n, is the total normalized power. Since the random variables i are assumed to be independent and identically distributed (iid, the probability density unction (pd o Λ n is given by ( n ( Λ Λ = ( Λ n, where ( is the pd o and (n ( denotes the n-old convolution o ( with itsel. The pd o can be expressed in terms o the pd o α and r, i.e., D = r α. ( η η ( dr ( r r ( r By assuming the interering piconets to be uniormly distributed around the TR, within a circle o ray D, the distance r rom the TR is a random variable with pd r i (r =r/d, r [,D]. The pd o the square envelope α is ound to be ( ρ K ( ρ ( ( K + 1 ρ = + K e e I 4K( K 1 1 α + i where K is the Rice actor, and I ( is the zero-order modiied Bessel unction o the irst kind [8]. For K=, we obtain the pd or a Rayleigh ading model, which turns out to be exponential, ( ρ = exp( ρ, ρ. αi In this case, ( turns out to be given by ( ( + η η + η = Γi, D ηd η η,, (3 19

3 where Γ i (a,b is the incomplete gamma unction as deined in [9]. For η=, (3 can be urther simpliied as ollows D 1 e ( ( 1+ D = D. (4 Packet Error Probability The exact perormance analysis o the system, which takes into account, in particular, the time shits among piconets, turns out to be very complex in terms o computational resources and elaboration time required. Hence, we relax this constraint by assuming that all the piconets are synchronized to the time slot. Furthermore, we assume that interering piconets use single-slot packets only. Under these hypotheses, a packet rom an adjacent piconet can be a potential danger to only one packet in the target piconet [6]. Hence, the model we consider is somewhat optimistic and yields to an upper bound or the actual system perormance. The packet error probability depends on the distribution o the signal and intererence power along the target packet. η Let = α r be the normalized signal power, which is assumed to be constant or the entire packet duration. Then, the average packet error probability or the generic Dxk target packet is given by η η ( r ( r PERxk = d PEPxk, (5 α where PEP xk ( is the packet error probability given that the signal power is. Under the hypothesis o synchronous piconets, the number N e o eective intererers and their power may change slot by slot in an independent way, as depicted in Figure or a multi-slot target packet and two eective intererers. 1 (The shaded parts on the target packet indicate where collision occurs. Let us partition the Dxk target packet in k dierent parts, so that each part occupies a single slot. The irst part diers rom the others in that it contains the AC and HEAD ields, besides a raction o the i1 i i3 = T k1= T Target Packet ( T k Figure. Intererence in synchronized piconets 1 We neglect the possibility o multiple collisions o the target packet with packets rom the same terminal. This assumption is partially motivated by the time division duplex mechanism adopted in each piconet, which guarantees a minimum distance o one slot between consecutive packets rom the same terminal. PAYL ield. Furthermore, the irst. ms o the slot are not occupied by useul data. The other k-1 parts have the same structure: they contain an equal raction o the PAYL ield, which is extended over the entire slot. Hence, the conditioned packet error probability can be expressed as PER xk k 1 ( = P ( P (, (6 1 where P A ( denotes the conditioned probability that the irst part o the packet is correctly received, given that the normalized signal power is. Analogously, P B ( is the probability that any one o the other parts o the packet is correctly decoded. Such probabilities depend on the statistic o the number n e o eective intererers and the aggregated intererence power Λ n e. Hence, we can express the probability P A(B ( as ollows: P N A( B, ne = A p ( = PN ( n Λ ( ( Λ Λ ( Λ e e d n P e A B n e n e ne, where P A(B (, Λ n is the probability that the part A (res. B o the packet is correctly received, given that the normalized signal and intererence powers are and Λ n. I all the carrier requencies have the same probability to be chosen at each requency hop, then the statistic o n e is given by P Ne p ne ne ( n ( sp ( sp e B (7 N = F F n 1, (8 e where P F =s/n F, N F =79 is the total number o available channels and s is the probability that a packet is transmitted by an adjacent piconet in a given slot. To derive the expressions o P A (, Λ n and P B (, Λ n, we need to introduce the correct-reception probability o each one o the ields that compose the Bluetooth packet. Let β be the BER values obtained by (1 or P rx =P T A and PI=P T AΛ. The AC ield is recognized when the number o erroneous bits in the AC does not exceed a correlator threshold value, CT. Hence, the probability that the AC is accepted is given by AC ok CT 7 j 1 j= j j ( Λ = 7, β ( β. (9 The HEAD ield contains 18 code-words protected by a 1/3 FEC code. Consequently, the ield is well recognized provided that each one o the 18 code-words does not contain more than 1 erroneous bit. The probability o this event is ok 3 ( 18 (, Λ = 3β ( 1 β + ( β HEC. (1 1 Finally, let PL ok (h,, Λ be the probability that a block o h consecutive bits in the payload ield is correctly decoded. Then, or unprotected packet ormats, we have

4 (,, = ( β h PL Λ 1 ; (11 ok h while, or protected ormats, we have PL 15 ( h (,, = 15 β ( 1 β + ( β ok h Λ (1 1 where the symbol is used to indicate the ceiling unction. The probability P A (, Λ n is, then, given by A ( Λ = AC (, Λ HEC (, Λ PL ( L,,, P (13, ok ok ok A Λ where L A is the length o the raction o the payload ield that is contained in the irst part o the target packet. The probability P B (, Λ n is, instead, given by B ( Λ = PL (,, PL ( 45,, Λ P, (14, ok ok where we have considered that the irst. ms o each slot are let idle by the intererer packets and, then, the BER on this part o the packet is determined by the white noise power only. RESULTS In this section, we irst analyze the potential perormance tradeo between the dierent packet ormats supplied by Bluetooth. Then, we investigate the accuracy o the analytic model proposed, by comparing the theoretical results with some simulations. Table 1. Model parameters P T A η R I R N 1 mw dB +17dB -87 dbm The analysis that ollows has been carried out considering the values given in Table 1 or the system parameters [3]. In particular, the noise power N was chosen to have a BER o.1 or a received power o -7 dbm, as required by the Bluetooth speciications [1]. The interering piconets were scattered over an area o ray D=1 m around the TR. Perormance Analysis In the ollowing, we consider an asymmetric ACL link, where data lows in the orward direction, carried by D xk packets, while acknowledgments are returned in the backward direction by means o single slot packets. We disregard the error statistic o the eedback channel and ocus on the perormance o the orward link only. Beside the PEP xk, we consider the orward throughput, ν xk, which is deined as the average number o user data bits transmitted without errors in the orward direction, per unit o time. Please, note that the actual throughput perceived at the upper layers may be lower than ν xk, because o errors in the return link. Figure 3 shows the packet error probability (upper part and the throughput (lower part achieved by the six ACL packet ormats, or dierent numbers o potential intererers. The curves have been obtained in the case o Rayleigh ading and or a distance r o 8 meters between transmitter and receiver o the target piconet. A irst evidence rom the PEP xk ν xk (Kb/s N X ν (Kbit/s r =8 m, K T = in db Figure 3. Perormance o dierent packet ormats Figure 4. Perormance-crossing points DM5 DM3 DM r K T = in db & DM5 & DM r r igure is that the PEP curves or DMk and DHk packet ormats get close each other as the number o potential intererers increases. In other words, in the presence o inter-piconet intererence, the FEC code does not give any signiicant beneit to the packet error probability. The throughput curves in the bottom part o the igure, reveal the presence o a crossing point between the perormance curves achieved by Dx5 and Dx3 packet ormats, when the number o potential intererers is around 1. This was expected, since the collision probability is lower or shorter packet ormats than or longer ones, at the expense o the maximum packet capacity. N X ν (Kbit/s K T = 6 db & DM5 & DM r 1

5 Figure 4 is divided in ours parts. The graphs on the irst row show the throughput crossing point N X, i.e., the number o potential intererers or which ν x5 is approximately equal to ν x3. The graphs on the second row show the throughput value at the crossing point. Curves have been obtained by considering a Rayleigh ading model or the intererers and both a Rayleigh (irst column and a Rice (second column model, with K=6dB, or the desired signal. Curves are plotted against the distance r between the TR and its transmitter. We can note that the presence o Line o Sight (LOS between transmitter and receiver has a marginal impact on the throughput crossing point. However, in the case o Rice ading the throughput at the crossing point is higher and, hence, the system is less sensitive to inter-piconet intererence. (% = r Figure 5. Analysis accuracy Analysis Accuracy In order to estimate the accuracy o the results provided by the analytical model, we have compared the theoretical results with some simulations. The simulator computes the real throughput assuming not synchronized piconets. On the other hand, recall that in the theoretical analysis users are assumed to be slot-synchronous. Figure 5 shows the distance, in percentage, between the theoretical and the experimental throughput values. In the let-most graph, the error is evaluated or dierent values o r, while was ixed to 1. In the right-most graph, r was ixed to 5 meters, while varied rom to. We can note that the bound provided by the analysis is airly tight when the number o potential intererers is small and r is either small or close to the maximum coverage range. On the contrary, or values o r close to hal the coverage range and or higher number o intererers the bound becomes loose. CONCLUSIONS In this paper we have presented a simple and general method to evaluate the perormance o Bluetooth or various packet ormats, in the presence o ading and interpiconet intererence. (% r =5 m The analysis has revealed that protected packet ormats achieve very poor perormance in case o inter-piconet intererence, since the FEC code is not able to cope with the burst o errors produced by an interering signal. As expected, long and short packet ormats have shown a perormance tradeo as the number o potential intererers increases over a given threshold. The crossing point o the throughput curves is strictly related to the distance r and the presence o LOS between transmitter and receiver. Finally, we have analyzed the accuracy o the proposed model, by comparing theoretical and simulation results. The perormance bound provided by the theoretical analysis has proved to be airly tight when the number o potential intererers is small (less than 8 and the distance between transmitter and receiver is either small or large. On the contrary, when the distance between transmitter and receiver is around hal the coverage range, the statistic o the intererence along the packet becomes relevant or the packet error probability. REFERENCES [1] Speciication o Bluetooth System, ver. 1., July 1999 [] Haartsen, J.C. The Bluetooth radio system., IEEE Personal Communications, IEEE, Feb.. [3] Zürbes, S., Stahl, W., Matheus, K., and Haartsen, J., Radio Network Perormance o Bluetooth, in Proceedings o IEEE International Conerence on Communications,, (ICC, New Orleans, USA, June 18-,. [4] Zürbes, S., Considerations on link and system throughput o Bluetooth networks, Personal, Indoor and Mobile Radio Communications,, (PIMRC, London, UK, September 18-1,. [5] El-Hoiydi, A., Packet Error Rate due to Intererence Between Bluetooth Networks - Probabilistic Upper Bound and Simulation Results, 1 Virginia Tech MPRG Symposium on Wireless Personal Communication, Blacksburg, USA, pp. 3-3, June 1. [6] El-Hoiydi, A., Intererence Between Bluetooth Networks - Upper Bound on the Packet Error Rate, IEEE Communications Letters, vol. 5, issue 6, June 1, pp [7] Karnik, A., Kumar, A., Perormance Analysis o the Bluetooth Physical Layer, IEEE International Conerence on Personal Wireless Communications, (ICPWC, December, Hyderabad, India. [8] Linnartz, J.P., Narrowband Land-Mobile Radio Networks, Artech House [9] Gradshteyn, I.S., Ryzhik, I.M., Table o integrals, series and products, Academic Press, New York, 1965.