Effect of Interfering Users on the Moduation Order and Code Rate for UWB Impuse-Radio Bit-Intereaved Coded M-ary PPM Ruben Merz and Jean-Yves Le Boudec EPFL, Schoo of Computer and Communication Sciences CH-115 Lausanne, Switzerand phone: +41 1 69 6616, fax: +41 1 69 661 {ruben.merz,ean-yves.eboudec}@epf.ch Abstract We consider the impact of muti-user interference on a bitintereaved coded-moduation system with M-ary PPM BIC M- ary PPM in an impuse-radio utra-wideband physica ayer. In a reaistic scenario such as an ad hoc network, the interference is inherenty variabe. This ustifies the need for a physica ayer that can optimay adapt its transmission parameters to the interference eve. We use puncturing on the channe code so that we can not ony change the moduation order M but aso the channe code rate. We study by simuation how the optima combination of moduation order M and channe code rate behaves with various degrees of interference. The resuts show that BIC M-ary PPM can be successfuy adapted to various eves of interference conditions. It aso shows the benefit of both rate and moduation adaptation, especiay in the presence of muti-user interference. I. INTRODUCTION Recent resuts [1, [ in the fied of medium-access contro MAC for UWB time-hopping impuse-radio ad-hoc networks have demonstrated the advantages of rate adaptation. With rate adaptation, nodes do not attempt to contro the interference they create for concurrent users. Instead, they adapt their transmission rate to the current eve of interference. In [1 and [ a transmitter adapts its rate by dynamicay changing the channe code rate based on feedback from its destination. This scheme is very efficient in the presence of a high eve of interference. However, when the network is ighty oaded, the possibiity of augmenting the moduation order woud permit for a great increase in spectra efficiency. This motivates us to study the performance of a physica ayer that can not ony adapt its channe code rate, but aso increase the moduation order. We seected bit-intereaved coded-moduation BICM [. It has a ow compexity and can be easiy used with any type of binary channe code. We use it with M-ary puse position moduation M-ary PPM. In this paper, we are not interested in optimizing the channe code or intereaver design. Rather, we want to study The work presented in this paper was supported in part by the Nationa Competence Center in Research on Mobie Information and Communication Systems NCCR-MICS, a center supported by the Swiss Nationa Science Foundation under grant number 55-67, and by CTI contract No719.;1 ESPP-ES the interaction between the moduation order M and the channe code rate R c. Furthermore, we want to show how this reativey simpe design can yied to substantia performance improvements. Bit-intereaved coded moduation BICM was proposed in [ and [4 and M-ary PPM for UWB was anayzed in [5. Previous work on combined moduation and channe coding can be found in [6, [7, [8 and [9; they a consider signa consteations in two dimensiona spaces. Hence, they do not take advantage of the infrequent puse transmission characteristics of puse based physica ayers. Instead of changing the moduation order to increase the spectra efficiency, it is possibe to make the puse transmission period PTP variabe as in [1 and [11. However, makes the average transmitted power on the channe variabe if the power used to send a singe puse is fixed. Note that [1 considers M-ary PPM but without channe coding and muti-user interference MUI. Since we consider the effect of muti-user interference, we cannot use the Gaussian approximation on the interference [1. Hence, we anayze by simuation the performance of the BIC M-ary PPM physica ayer. We consider a mutipath channe and severa concurrent transmitters. We do not consider narrowband interference. We show the packet error rate in various topoogies and interference conditions. We aso anayze the best combination M, R c of moduation order M and channe code rate R c in the presence of mutiuser interference. II. SYSTEM MODEL AND ASSUMPTIONS We consider a bit-intereaved coded-moduation system BICM as described in [. We use M-ary puse position moduation PPM with time-hopping [5 and a binary ratecompatibe punctured convoutiona RCPC code of rate R c [1. We assume a mutipath propagation channe and a coherent, singe user, Rake receiver. From the channe encoder and the moduator, BICM is obtained by concatenating the output of the convoutiona encoder with the M-ary PPM moduator through a bit intereaver Π. In this paper, we assume a perfect random intereaver. Foowing the terminoogy of [, we denote with X = {, 1,..., M 1} the so caed signa
PSfrag repacements set of size X = M = k. We aso define the binary abeing map µ M : {c 1,..., c k } {, 1} k x X 1 The binary abeing map µ modes the moduator. In the case of M-ary PPM, the set X corresponds to the set of avaiabe puse positions. The convoutiona encoder produces coded bocks c = [c, c,..., c k K 1 of k K coded bits. Each coded bock c is intereaved. The output Πc of the intereaver is broken into sub-bocks of k bits. Then, these sub-bocks are mapped into one of the M signas in X. An iustration of the transmitter and receiver chain is given in Figure 1. From the moduator, the signa transmitted by the i th source is { where s i t = x i } K 1 K 1 = p t T f c i T c x i T m is the symbo sequence with x i X, K = is the bock or packet ength T c is the chip width, T f is the frame ength, T m is the puse position offset and c i is the Time-Hopping Sequence THS. The THS is a sequence of integers uniformy distributed in [, P T P M + 1 where P T P = T f T c is the Puse Transmission Period. We assume that there is no inter-symbo interference or intra-symbo interference ISI. The constraint on the inter-symbo interference can be enforced by having a guard time T g at the end of each frame, or by constraining the THS such that the minimum spacing between two consecutive chips is arger than T g. The constraint on the intra-symbo interference can be enforced by choosing a sufficienty arge T m. The puse pt has unit energy i.e. pt dt = 1. The channe impuse response between the i th transmitter and the receiver is = L 1 h i t = α i δt ν i where δ is a Dirac function, ν i is the deay induced by the th path and L the maximum number of paths. We denote by A i = L 1 = the tota energy of the channe. The α i channe is considered to be static for the duration of a packet transmission. At the receiver side, we consider a coherent, singe user, Rake receiver. However, the number of branches of the Rake receiver is assumed to be imited to L L. The received signa is rt = U h i t s i t φ i + nt 4 i=1 where is the convoution operator, U is the number of transmitters present in the system, φ i [, T f is the deay between the i th transmitter and the receiver, and nt is zero mean white Gaussian noise with two-sided power spectra density N. User 1 =n 1 Interferer i φ i T c T f T m T m =n c 1 T c =n =n+1 Fig.. Iustration of the definitions. φ i is the deay between interferer i and the source, T f is the frame ength, T c is the chip width and T m is the puse position offset. The dashed curve foowing the puses represents the mutipath propagation. Note that the puse position offset T m is not necessary equa to the chip width T c. The autocorreation Θτ of the puse pt is Θτ = ptpt τdt The puse shape of pt at the receiver is the second derivative of a Gaussian puse, i.e. t t pt = C E 1 4π exp π 5 where is a time normaization factor and C E an energy normaization factor. Hence, with 5, the autocorreation Θτ is [ [ 4 τ Θτ = 1 4π + 4π τ τ exp π If T p is the width of the puse, the autocorreation Θτ is equa to zero outside the interva [ T p, T p. III. BIT-INTERLEAVED CODED M-ARY PPM In this section, we first compute the outputs of the matched fiters of the M-ary PPM demoduator. We then show how these outputs are used in the decision rue of [ for the channe decoder. A. Output of the M-ary PPM matched fiters We et i = 1 be the user of interest. We assume perfect channe knowedge and perfect synchronization between the transmitter 1 and the receiver i.e. φ 1 =. Since we have M matched fiter outputs, we have M tempate waveform w m t, m =, 1,..., M 1, matched on the signa from the first transmitter where = w m t = K 1 = L 1 = K 1 = α 1 h 1 t p t T f c 1 T c mt m p t T f c 1 T c mt m ν 1 Then, the th output r,m of the m th matched fiter is r,m = +1Tf 6 T f rtw m tdt 7
Encoder Π Moduator MUI N Demoduator Π 1 Decoder R c M Fig. 1. Bock diagram of the BIC MPPM physica ayer. The bit intereaver is denoted by Π, R c denotes the code rate and M is the moduation order. The channe, where muti-user interference MUI and noise N is added, is depicted with the dashed box. Using equations,4 and 6, the right-hand side of 7 becomes r,m = U L 1 i=1 = α i L 1 α 1 = p t T f c i p +1Tf T f T c x i T m φ i ν i t T f c 1 T c mt m ν 1 dt After a few manipuations, the previous expression can be rewritten as I r,m = s,m + I i,m + n,m 8 i= The contribution s,m of the user of interest at the output of the m th matched fiter is s,m = = L 1 = L 1 = α 1 α 1 Θ [ m x 1 T m 9 1{x 1 =m} 1 In a simiar way, we can obtain the contribution of the i th, i > 1, interferer is L 1 L 1 I i,m = α 1 = = where see Figure [ α i Θ i,m + ν 1 ν i φ i 11 i,m = c 1 c i + m x i T m, if c 1 T c > φ i and c 1 c i 1 + m x i 1 T m T f, otherwise 1 Finay, the fitered white noise n,m N, σn with σ N = N With equation 8, the origina continuous time channe of equation 4 is transformed into M parae discrete time channes. In other words, the continuous time channe is mapped with an equivaent vector channe py x of dimension M. B. BIC M-ary PPM decoder We first reca the resuts from [ and then describe how they are used in our case. We define Xb i as the subset of a signas x X whose abe has the vaue b {, 1} in position i. For instance, with k =, the subset X 1 is {1, 11, 11, 111}. The channe decoder makes decisions according to the maximum ikeihood ML rue ĉ = arg max c C for i = 1,..., k where for b {, 1} λ i y, b = og λ i y, c x X i b 1 p y x 14 is the ML bit metric. The decision rue 1 is easiy impemented with a Viterbi decoder. This is a very attractive feature from an impementation point of view. For M >, the decision metric in 1 can be computationay too compex. Aso, it necessitates the knowedge of σn. Hence for M >, the og-sum approximation og z max og z see [4 can be used to obtain the foowing simpified bit metrics λ i y, b = max og p y x 15 x Xb i Exampe 1: With M = 4, the binary abeing map µ is µ : {, 1, 11, 1} {x 1, x, x, x 4 } 16 Hence, for i = 1 and b =, the bit metrics 14 and 15 are λ 1 y, = og [ py x 1 + py x 17 λ 1 y, = max [ og py x 1, og py x 18 Now in the case of a singe user receiver, we can express the suboptima bit metric 18 as a function of the matched fiter outputs. It is straightforward to show that Simiary, λ 1 y, = max [ r,1, r, λ 1 y, 1 = max [ r,, r,4 λ y, = max [ r,1, r,4 λ y, 1 = max [ r,, r,
T f T c T m K 5 ns 1 ns 5 ns 14 bits L E p N 4.877.818 mw -8 dbm TABLE I NUMERICAL VALUES OF THE PARAMETERS OF THE PHYSICAL LAYER Average SNR [db with 4 paths 5 15 1 5 SNR with fu Rake Avg. SNR with 4 best fingers 5 Fig.. Comparison of the average SNR obtained with a 4 fingers Rake receiver and the theoretica maximum SNR. The maximum SNR coud be obtained with a fu Rake receiver. This figure aso provides the correspondence between the ink distance and the SNR. IV. FORMANCE EVALUATION In this section, we evauate the performance of the BIC M- ary PPM physica ayer in various conditions, most notaby in the presence of muti-user interference. Our two main performance metrics are the rate and the packet error rate. The numerica vaues of the parameters of the physica ayer are given in Tabe I. We do not use a perfect Rake receiver. Instead, we use a seective Rake receiver S-Rake [14 with L = 4. With L = 4, the performance oss is around or db in terms of SNR [14. This is confirmed by simuation; on Figure, we dispay the average SNR with respect to the theoretica SNR that woud be obtained with a fu Rake receiver. Even tough we gather ony L paths of the channe impuse response, a arge enough vaue of T m is necessary in order to accommodate for the deay spread of the mutipath channe. This ensures the orthogonaity of the moduation. We seected the RCPC codes from [15; the mother code has rate 1 4. Aong with the uncoded case R c = 1, they provide the foowing set of avaiabe rates R = {R, R 1,..., R 4 } = {1, 8/9, 8/1, 8/11,..., 8/} of size R = 5. The bock or packet ength is K = 14 bits. We consider M =, 4, 8. The maximum vaue of the moduation order is imited by the frame ength T f. Foowing [, we use a Gray mapping for the moduation map µ. For M = 4 µ 4 : {, 1, 11, 1} {, 1,, } 19 and for M = 8 µ 8 : {, 1, 11, 1, 11, 111, 11, 1} {, 1,,, 4, 5, 6, 7} The channe parameters are chosen according to the IEEE 8.15.4a CM1 channe mode [16. The path oss attenuation is computed according to [17. A the simuations have been performed using Matab. We consider three interference scenarios. A first scenario with no muti-user interference U = 1, a second scenario with one interferer at one meter from the receiver U = and a third scenario with five interferers at one meter from the receiver U = 6. We present the resuts as a function of the ink distance between the transmitter of interest and the receiver. The correspondence between the average received SNR and the ink distance is given by Figure. A. Effect of the Muti-User Interference on the Packet Error Rate On Figure 4a we show the with no MUI for R c = 4 5, R c = 1 and R c = 1 4 for M =, 4, 8. Simiary, on Figure 4b we show the for for the same set of moduation order and channe code rate in the presence of five interferers. On Figure 5a and Figure 5b, we fix M = and compare the with R c = 1 uncoded, R c = 4 5 and R c = 1. Aready with R c = 4 5 we can observe a significant decrease of the with respect to the uncoded case. A traditiona way to compute the if ony the bit error rate BER is avaiabe is to use P ER = 1 1 BER K 1 This assumes that a the bits of the packet are independent and identicay distributed i.i.d. Since we can aso obtain the BER from our simuations, we compare 1 with the we obtained by simuations. As can be observed on Figure 4 with M =, equation 1 is ony vaid in the uncoded case without MUI. In the other cases, using 1 aways overestimates the. Resuts are simiar with M = 4, 8. Indeed, the MUI breaks the i.i.d assumption. B. Effect of the Muti-User Interference on the Best Combination of Moduation and Channe Code For each of the scenarios, we computed for each ink distance the for each moduation order and a subset of the avaiabe channe code rate 1. Then for each moduation order, we ooked for the best rate, i.e. the maximum channe code rate assuming a maximum of 1%. From these curves, we can infer the best combination of moduation order and channe code rate. The resuts are presented on Figure 6 and the best 1 Every two channe codes starting from R c = 1. Hence there are 1 avaiabe rates.
1 interferers 1 5 interferers 1 1 1 1 1 1 1 4 M=8,R=4/5 M=4,R=4/5 M=,R=4/5 M=8,R=1/ M=4,R=1/ M=,R=1/ M=8,R=1/4 M=4,R=1/4 M=,R=1/4 1 1 1 4 M=8,R=4/5 M=4,R=4/5 M=,R=4/5 M=8,R=1/ M=4,R=1/ M=,R=1/ M=8,R=1/4 M=4,R=1/4 M=,R=1/4 a with no MUI b with 5 interferers Fig. 4. The curves correspond to the for R c = 4 5, Rc = 1 and Rc = 1 with M =, 4, 8. 4 1 interferers 1 5 interferers 1 1 1 1 1 1 1 1 4 R=1 R=4/5 R=1/ Approx, R=1 Approx, R=4/5 Approx, R=1/ 1 1 4 R=1 R=4/5 R=1/ Approx, R=1 Approx, R=4/5 Approx, R=1/ a M = and no interferers. With the channe code, the approximation is not vaid. b M = and 5 interferers. Note how even in the uncoded case the approximation is not vaid anymore due to the MUI. Fig. 5. From eft to right, the three pain curves correspond to the with no coding, R c = 4 5 and Rc = 1 and M =. The dashed curves are the approximation using the traditiona approximation 1 1 BER K. The approximation is vaid ony in the uncoded case without MUI. combination of moduation and channe code are given in Tabe II. It is interesting to observe in Tabe II that every time the moduation order changes, the coding rate either decreases or stays constant. There are no coding rates augmentation when the moduation order decreases. On Figure 6, we can ceary observe the rate decrease due to the MUI in near-far cases. When one interferer is present, the range is reduced by approximatey 4 meters. For 5 interferers, it is reduced by 8 meters. The sope of the rate curve increases with the eve of MUI. However, when the distance between the transmitter and the receiver is short reative to the distance between the interferers and the receiver, the MUI has practicay no impact. C. A Note about the Power Consumption The energy per data bit E d is defined as E d = EP kr c Hence E d decreases if either k increases or the code rate R c increases. However, when k is incremented, the number of matched fiter outputs at the receiver is doubed. Hence, when k is increased, the decrease of E d has to be compared with the
Link distance in meters 1 4 5 6 8 1 1 14 U = M 8 8 8 8 8 8 8 4 4 R id 4 6 1 16 4 U = 1 M 8 8 8 8 8 8 4 n/a n/a R id 4 1 1 4 n/a n/a U = 5 M 8 8 8 4 n/a n/a n/a n/a R id 8 8 1 16 n/a n/a n/a n/a TABLE II BEST COMBINATION OF MODULATION ORDER AND CHANNEL CODE interferers M=8, R max 1 interferer M=8, R max.5 M=4, R max M=, R max.5 M=4, R max M=, R max M=8, R 4 M=8, R 4 Rate with t =.1 1.5 1 M=4, R 4 M=, R 4 Rate with t =.1 1.5 1 M=4, R 4 M=, R 4.5.5 a Best rate versus ink distance obtained for each moduation without mutiuser interference. b Best rate versus ink distance obtained for each moduation in the presence of 1 interferer at a distance of 1m from the receiver. Rate with t =.1.5 1.5 1 5 interferers M=8, R max M=4, R max M=, R max M=8, R 4 M=4, R 4 M=, R 4.5 c Best rate versus ink distance obtained for each moduation in the presence of 5 interferers at a distance of 1m from the receiver. Fig. 6. For various interference conditions, the pain curves represent the best rates obtained for each moduation order M for M =, 4, 8. For a given M and ink distance, the best rate is obtained by ooking for the best channe code assuming a maximum. The dashed curves represent the rates obtained for each M with the channe code of owest rate. These figure ceary show the benefit of being abe to adapt the code rate and the moduation in various interference conditions, even in the presence of strong near-far interference.
energy required to produce the M = k matched fiters. V. CONCLUSION BIC M-ary PPM appears to be perfecty suitabe for an adaptive system as in [1, [. In the case of a channe without mutiuser interference, the moduation coud be easiy adapted to the channe condition. Indeed, the receiver coud track one or severa channe metrics such as the bit metrics at the output of the decoder see 14, the received energy, or the M-ary PPM channe capacity. However, in the case of a channe with interfering users, the choice of an appropriate metric and adaptation agorithm remains open. It woud be interesting to study the performance of BIC M-ary PPM with an iterative decoder as is done with BICM- ID [18 as we as the performance with an energy detector instead of a Rake receiver. Aso, in the presence of nearfar interference, an interference mitigation [ scheme coud increase the performance. REFERENCES [1 J. Y. Le Boudec, R. Merz, B. Radunovic, and J. Widmer, DCC-MAC: A decentraized MAC protoco for 8.15.4a-ike UWB mobie adhoc networks based on dynamic channe coding, in Proceedings of Broadnets, San Jose, October 4. [ R. Merz, J. Widmer, J.-Y. Le Boudec, and B. Radunovic, A oint PHY/MAC architecture for ow-radiated power TH-UWB wireess adhoc networks, Wireess Communications and Mobie Computing Journa, Specia Issue on Utrawideband UWB Communications, vo. 5, no. 5, pp. 567 58, August 5. [ G. Caire, G. Taricco, and E. Bigieri, Bit-intereaved coded moduation, IEEE Transactions on Information Theory, vo. 44, no., pp. 97 946, May 1998. [4 E. Zehavi, 8-PSK treis codes for a rayeigh channe, IEEE Transactions on Communications, vo. 4, no. 5, pp. 87 884, May 199. [5 F. Ramirez-Mirees, Performance of utrawideband SSMA using time hopping and m-ary PPM, IEEE Journa on Seected Areas in Communications, vo. 19, no. 6, pp. 1186 1196, June 1. [6 A. Forouzan and M. Abtahi, Appication of convoutiona error correcting codes in utrawideband m-ary PPM signaing, IEEE Microwave and Wireess Components Letters, vo. 1, no. 8, pp. 8 1, August. [7 K. Takizawa and R. Kohno, Combined iterative demapping and decoding for coded UWB-IR systems, in IEEE Conference on Utra Wideband Systems and Technoogies, November, pp. 4 47. [8, Combined iterative demapping and decoding for coded m-ary BOK DS-UWB systems, in Joint IEEE Conference on Utra Wideband Systems and Technoogies & IWUWBS, May 4, pp. 7 11. [9 S. Yoshida and I. Ohtsuki, Performance evauation of adaptive internay turbo coded utra wideband-impuse radio aitc-uwb-ir in mutipath channes, in IEEE 6th Vehicuar Technoogy Conference, vo., September 4, pp. 1179 118. [1 N. August, R. Thirugnanam, and D. Ha, An adaptive UWB moduation scheme for optimization of energy, BER, and data rate, in UWBST, 4, pp. 18 186. [11 I. Guvenc, H. Arsan, S. Gezici, and H. Kobayashi, Adaptation of mutipe access parameters in time hopping UWB custer based wireess sensor networks, in IEEE Internationa Conference on Mobie Ad-hoc and Sensor Systems MASS, October 4, pp. 5 44. [1 R. Merz and J.-Y. Le Boudec, Conditiona bit error rate for an impuse radio UWB channe with interfering users, in IEEE Internationa Conference on Utrawideband ICU 5, September 5. [1 J. Hagenauer, Rate-compatibe punctured convoutiona codes RCPC codes and their appications, IEEE Transactions on Communications, vo. 6, no. 4, pp. 89 4, Apri 1988. [14 M. Win, G. Chrisikos, and N. Soenberger, Effects of chip rate on seective RAKE combining, IEEE Communications Letters, vo. 4, no. 7, pp. 5, Juy. [15 P. Frenger, P. Orten, T. Ottosson, and A. Svensson, Rate-compatibe convoutiona codes for mutirate DS-CDMA systems, IEEE Transactions on Communications, vo. 47, no. 6, pp. 88 86, June 1999. [16 A. F. Moisch, K. Baakrishnan, C.-C. Chong, S. Emami, A. Fort, J. Kareda, J. Kunisch, H. Schantz, U. Schuster, and K. Siwiak, IEEE 8.15.4a channe mode - fina report, document 4/66r, Avaiabe at http://www.ieee8.org/15/pub/tg4a.htm, November 4. [17 S. Ghassemzadeh, R. Jana, C. Rice, W. Turin, and V. Tarokh, Measurement and modeing of an utra-wide bandwidth indoor channe, IEEE Transactions on Communications, vo. 5, no. 1, pp. 1786 1796, October 4. [18 X. Li, A. Chindapo, and J. Ritcey, Bit-intereaved coded moduation with iterative decoding and 8 PSK signaing, IEEE Transactions on Communications, vo. 5, no. 8, pp. 15 157, August.