Space-Time Focusing Transmission in Ultra-wideband Cooperative Relay Networks

Transcription

1 ICUWB 2009 (September 9-11, 2009) 1 Space-Time Focusing Transmission in Utra-wideband Cooperative Reay Networks Yafei Tian and Chenyang Yang Schoo of Eectronics and Information Engineering, Beihang University 37 Xueyuan Road, Haidian District, Beijing, P. R. China Emai: ytian@buaa.edu.cn, cyyang@buaa.edu.cn Abstract Space-time focusing transmission is a generaized form of beamforming in utra-wideband (UWB) systems by expoiting the unique feature of UWB signas. It can obtain energy gain and can reduce interference to coexisting users, thus can extend the distance and increase the capacity of UWB communications. Cooperative reay can further extend the coverage of UWB systems. In this paper, we first propose ZF and MMSE prefitering agorithms for space-time focusing transmission, and then propose a space-time focusing based cooperative reay scheme. The throughputs of broadcast mode and mutipe access mode in the reay networks are derived, whie their dependency on various system parameters is obtained. Numerica resuts show how many cooperative nodes are necessary to maximize the network throughput, and when the proposed prefitering agorithms perform we. I. INTRODUCTION Impuse radio utra-wideband (IR-UWB) technoogy is promising in miitary communication systems and wireess sensor networks due to its superior capabiity for providing security and coexistence. However, more widespread appications to onger range communications are restricted by the hard constraint of the power spectrum density imposed on UWB systems. UWB systems are different from narrow-band systems in its impuse nature and strict transmit power constraint. The impuse signa provides fine tempora and spatia resovabiity, which can be expoited for designing the space-time focusing transmission [1], [2]. The focused signa can ony be received at specific ocations and times. This eads to very ow eakage interference to coexisting users. As a generaized form of beamforming, space-time focusing can improve the ink performance in two ways. For a given transmission power, the transmission range can be extended by focusing the signa to a far away node. For a given transmission range, the transmission power can be reduced. As a resut, the interference to other coexisting users wi decrease and the network capacity wi increase. The we studied time-reversa (TR) technique [3] [8] can be appied for space-time focusing transmission in UWB systems. In the transmit side, the time-reversed and phaseconjugated channe response is used as a prefiter, where the physica channe serves as a tempora and spatia matched fiter (MF). However, the output SINR of TR scheme is imited by the imperfect auto-correation and cross-correation characteristics of UWB channes. To improve the spacetime focusing performance, we wi propose in this paper advanced prefitering agorithms based on zero-forcing (ZF) and minimum-mean-square-error (MMSE) criterions. Even when we use advanced prefitering agorithms for space-time focusing transmission, point-to-point ink can ony reach a imited distance. To further extend the coverage, we design a cooperative reay network where each node transmits with the space-time focusing prefitering. Considering that the source information can not arrive at the destination directy, we study the parae reay network, which consists of a broadcast (BC) mode and a mutipe-access (MA) mode transmissions [9] [11]. Since joint synchronization among reay nodes is hard to be impemented, especiay in UWB systems, joint space-time energy focusing is impossibe if we use the beamforming concept straightforwardy. It is we known that in energyimited systems, the mutua information accumuation is the same as the energy accumuation due to the inear growth of the capacity on the power [12]. Thus we propose to transmit independent streams from different reays to the destination. We can obtain the same throughput with the joint energy focusing scheme when the focused puses from different reays do no coide. In order to understand the potentia of space-time focusing transmission in UWB systems, we study the performance of TR and the two proposed prefitering agorithms in the cooperative reay network with simpe but typica topoogies. The impact of reay number and channe deay spread is anayzed, and the coision probabiity is obtained in MA mode transmissions. The rest of the paper is organized as foows. Section II and III describes the proposed space-time focusing prefitering agorithms and the cooperative reay scheme. Section IV anayzes the network throughput and the optima cooperative reay number. Numerica resuts are given in section V to compare the TR prefitering with the ZF and MMSE prefiterings in various scenarios, and concusions are provided in the ast section. II. SPACE-TIME FOCUSING TRANSMISSION In free space, we must use mutipe antennas for spacetime focusing transmission [13] [15]. In mutipath channes, however, one antenna is enough since the deays of mutipe transmitted puses can be controed to arrive at the receiver at the same time /09/$ IEEE 353

2 2 We can use prefitering to adjust the transmit time and ampitude of the puses. The simpest space-time focusing prefitering scheme is time-reversa, but its performance is degraded by the imperfect auto-correation and cross-correation characteristics of UWB channes. It is we known that ZF and MMSE criterions are better than MF criterion in terms of maximizing the signa to interference and noise ratio (SINR). In the seque, we wi design the prefiters based on these two criterions for BC and MA modes transmission (these modes wi be described in more detais in Section III). In IR-UWB mutiuser systems, the transmitted signa of the k-th user using puse ampitude moduation (PAM) before prefitering is s (k) (t) = N s 1 n=0 x (k) n p(t nt s ), (1) where N s is the symbo number in a packet, x (k) n is the moduated ampitude of the n-th transmitted symbo for the k- th user, p(t) is the UWB puse with width T p, T s is the symbo duration, and T s = NT p. For the brevity of descriptions, spreading is not considered, and the energy of each symbo is normaized. In practica UWB channes, the arriva time of the mutipath components is not equay spaced. Nevertheess, after the puse matched fiter and samping, the equivaent channe mode is equay spaced [16], whie some channe coefficients are weak or even zero. Assume that the channe response of the kth user is L (k) c 1 h (k) (t) = h (k) δ(t T p ), (2) h (k) =0 where L (k) c is the number of resovabe paths in the kth ink, is the channe fading coefficient, max k {L(k) c } = L. Empoying prefiter with coefficients g (k) the transmitted signa wi be s (k) (t) = N s 1 n=0 x (k) n L (k) p 1 =0 and ength L (k) p, g (k) p(t nt s T p ). (3) When TR technique is considered, g (k) = h (k) (L (k) c ), no matter in BC or in MA modes. When L (k) c > N, i.e., ISI exists, the prefiter ength L (k) p wi aso be arger than N. To suppress the intersymbo interference (ISI) and mutiuser interference (MUI), ZF or MMSE criterion can be used to design the prefiter. Then the focusing peak in tempora and the focusing area in spatia wi be sharper. In BC modes, a the K users are synchronous, the transmitted signa is a summation of K prefitered signas, s(t) = k=0 The received signa of the kth user is s (k) (t). (4) r (k) (t) = s(t) h (k) (t) + z(t), (5) where the operator denotes inear convoution, and z(t) is the additive white Gaussian noise (AWGN) with zero mean and power spectrum density N 0. The received signa is ony samped at the focused peak positions, y n (k) = r (k) (t) p(t) t=nts. (6) Define the sampes at time nt s of a K users as a vector y = [y n (1), y n (2),, y n (K) ] T. Then we can rewritten the discrete received signa as y = H Gx + z, (7) where H is the channe matrix, the symbo ( ) denotes matrix conjugate transpose, G is the prefitering matrix, x is the transmitted ampitude vector, and z is the noise vector. The channe matrix is composed by each user s channe vector h (k), i.e., where, H = [h (1), h (2),, h (K) ], h (k) = [h (k) 0, h(k) 1,, h(k) L 1 ]T. The expressions of the prefitering matrix and the transmitted ampitude vector are, however, depended on whether ISI exists. When there is no ISI, x = [x (1) n, x (2) n,, x (K) n ] T, G = [g (1), g (2),, g (K) ], g (k) = [g (k) 0, g(k) 1,, g(k) L 1 ]T. Using the reciprocity of wireess channes, the transmitter can obtain the channe matrix H. Then the prefiter matrix can be obtained with ZF and MMSE criterions respectivey as G ZF = H(H H) 1, (8) G MMSE = H(H H + σ 2 I) 1. (9) When there is ISI, i.e., L/N = M > 1, the consecutive transmitted symbos x (k) n M+1 to x(k) n+m 1 wi a have contributions to the received symbo y n (k), then x = [a (1) n, a (2) n a (k) n = [x (k),, a (K) n ] T, n M+1,, x(k) n G = [P (1), P (2),, P (K) ],,, x (k) n+m 1 ], P (k) = [g (k) M+1,, g(k) 0,, g(k) M 1 ]T, where g (k) m is a vector down-shifted from g k by mn eements, and the upper mn eements are fied by zeros. Simiary, g (k) m is a vector up-shifted from g k by mn eements, and the ower mn eements are fied by zeros. The reative shifting between adjacent g (k) m is N eements. In this case, G can not be obtained from (8) or (9) directy, since its dimension is arger than H s. Considering that there exists shifting reations among the coumns of G, we can sove this probem by using a equivaence formua. Since both the prefiter and the channe can serve as inear fiters, the received signa wi be identica if we swap the two matrices, that means H G = G H, (10) 354

3 3 (a) Fig. 1. (a) Singe-source mutipe-reay cooperative network topoogy. (b) Mutipe-source singe-reay cooperative network topoogy. where G = [g (1), g (2),, g (K) ], H = [Q (1), Q (2),, Q (K) ], (b) Q (k) = [h (k) M+1,, h(k) 0,, h(k) M 1 ]T. G can then be obtained from H with ZF and MMSE criterions, and the prefiter coefficients of each user are the coumns of G. In MA modes, each user transmit its own prefitered signa without joint synchronization. The received signa is a summation of a K signas each with a random deay τ k, r(t) = k=0 s (k) (t τ k ) h (k) (t) + z(t). (11) To demoduate the information of a K users, we need K sampes in one symbo duration. The sampe for the kth user is y (k) n = r(t) p(t) t=nts+τ k. (12) It is different in designing the prefiter in MA modes from that in BC modes. In BC modes, we assume that the transmitter knows the data and channe information of a K users, thus the pre-mud can be used. In MA modes, however, each transmitter ony knows its own data and channe information, thus the pre-equ is appied. The pre-equ for each transmitter can be designed as conventiona channe-inverse ZF or MMSE pre-equaizers. Since there is no joint synchronization, the focused peak of other inks may appear at any time, thus a the sideobes shoud be suppressed. III. COOPERATIVE RELAY UWB NETWORKS To further extend the coverage of UWB communications, we consider to use parae reay networks where each node transmits with prefitering. As shown in Fig. 1(a), the source information can not arrive the destination directy. The deveoped schemes and anaysis resuts can be easiy extended to other network topoogies, such as the mutipe-source singereay topoogy, as shown in Fig. 1(b). In parae reay networks, a source node tries to transmit information to a destination node through mutipe reays. There are two stages in this transmission procedure. The first stage is the BC mode transmission, where the source node distributes information to the reays. The second stage is the MA mode transmission, where mutipe reays transmit their information to the destination. There has been intensive studies on the reaying schemes in narrow-band systems, such as ampify-and-forward, decodeand-forward, distributed space-time coding, and distributed beamforming (DBF) [17] [19], etc. However, UWB systems differ in nature from the narrow-band systems since they are impuse-based and power-imited. UWB systems can resove a arge number of mutipath components in densey scattered channes, therefore can obtain abundant diversity gain from each ink. As a consequence, we do not need to combine the mutipe inks to obtain more diversity gain, what we require is the energy gain. Space-time focusing transmission can provide such an energy gain in each ink. To reaize the joint space-time focusing in an anaogous way of DBF, joint synchronization among the mutipe reay nodes is necessary. However, joint synchronization is hard to be impemented in distributive networks, especiay in IR- UWB reay networks. Noting that in energy-imited systems the mutua information accumuation is the same as the energy accumuation, we can transmit independent streams from different reays to the destination without the need of joint synchronization. The accumuated throughput wi be the same with the joint energy focusing scheme when the randomy arrived signas do not coide at the destination, thanks to the impuse nature of the signas. In BC mode, the source transmits independent streams to different reays using pre-mud agorithms. In MA mode, each reay forwards its stream to the destination empoying pre- EQU agorithms. In this way, the receiver in reays and in the destination are very simpe, where ony samping and decision are required. With the growing of the number of reays, there wi be increased interference among BC inks and increased coision among MA inks. To avoid compicated retransmission mechanisms in the network, an advanced error contro scheme, rateess code [20] [24], can be used. With the hep of the rateess code, the reays and destination can directy discard the error packets, and can recover the source information after coecting enough number of packets without considering their arriva sequence. IV. PERFORMANCE ANALYSIS In this section, we wi anayze the throughput of the proposed UWB cooperative reay network. Its dependency on system parameters, such as reay number, mutipath deay, and puse repetition frequency (PRF), wi be studied. A. Broadcast Mode In BC mode, the same transmit power P t are used for a users. We assume that the signa of a users have the same PRF, and the received power of the desired user at a given node is P r. We first study the received SINR when TR prefitering is used. Assume that every mutipath component is a zero mean independent random variabe with average power i (τ), where subscript i represents the ith user. When τ max < T f, 355

4 4 i.e., no ISI exists, the interference signa in the ith user from other users is I(t) = k=0,k i Pr h k( t) h i (t). (13) Since the signas are synchronous in BC mode, the desired focusing peak is ony impacted by the interference at that time. The peak is focused at t = 0, therefore the average interference power is the mean square of I(0), i.e., P I = E { I(0) 2} = P r E = P r k=0,k i =0 k=0,k i =0 = P r k=0,k i =0 L 1 2 h k()h i () L 1 E{ h k () 2 }E{ h i () 2 } L 1 k () i (). (14) In the derivation, we have used the discrete form expression of the UWB channe response, where L = τ max /T p is the number of resovabe paths. To gain more insight, we consider a specia case that the channe has fat power deay profie and its tota power is normaized, then k () = 1 L and P I = K 1 L P r = αp r, (15) where α = (K 1)/L, it wi converge to K/L when both K and L approach infinity. The mutipath components can be viewed as random spreading sequences when the channe power deay profie is fat, where L refects the spreading gain, α refects the network oad. In genera cases, UWB channe power deay profies are not fat, and the mutipath channe ength L may not exacty refect the spreading gain. However, some approximations can be made to evauate the impact of mutipath channe ength. For exampe, the ength of RMS deay spread can be used to refect the spreading gain. Due to the ack of space, we skip the detaied anaysis in this paper. The output SINR at BC mode is β = P r P r σ 2 = + P I σ 2, (16) + αp r where σ 2 = R b N 0. Given a required SINR β, the achievabe data rate can be cacuated as R b = P ( ) r 1 N 0 β α. (17) It shows that if TR prefitering is used, α < 1 β is required, i.e., the user number K shoud be ess than L β + 1. When there exists ISI, i.e., τ max > T f, we can anayze the output SINR in an anaogous way by regarding the ISI as a specia kind of MUI. The number of equivaent interference users is then τmax T f (K 1), and the interference power becomes P I = R f τ max αp r. (18) The resut shown in (16) is the same as the average output SINR of the MF receiver deveoped in random spreading CDMA systems [25], where the asymptotic expressions of the output SINR of ZF and MMSE mutiuser detectors are aso deveoped. Without considering the transmit power constraints, the received SINR using a ZF or MMSE prefiter in the transmitter and that using a ZF or MMSE detector in the receiver shoud be equa. Athough the asymptotic resuts ony converge when both the spreading sequence ength and the user number approach infinity [25], these resuts are sti of practica significance for providing guideines in system design. The average output SINR of the ZF pre-mud is [25] { Pr(1 α) β = σ, α < 1 2 0, α 1, (19) where the impact of channe fading has been averaged. In the same way, given β, we can obtain the achievabe data rate R b when ZF prefiter is used, i.e., ( 1 α R b = P r N 0 β ). (20) The average output SINR of the MMSE pre-mud of the ith user is [25] where P r,i β = σ K L k=1,k i I(P r,k, P r,i, β), (21) I(P r,k, P r,i, β) = P r,kp r,i P r,i + P r,k β, (22) P r,i and P r,k are the received power of the ith and kth user. In BC modes, they are identica. The achievabe data rate can then be obtained as R b = P r N 0 ( 1 β α 1 + β ). (23) The throughput of the BC mode is the sum rate of K users, i.e., R t,bc = KR b. (24) From the expression shown in (17), (20), and (23), we know that increasing the user number wi reduce the singe user data rate due to the increased mutiuser interference. Meanwhie, more simutaneous transmission inks wi increase the network throughput given the singe ink transmission rate. Therefore, there shoud be an optima vaues of the ink number. Since R b is a inear function of α, and α = (K 1)/L, (24) is a quadratic function of K, we can obtain its maxima vaue at the point where its first derivative equas zero. Thus we can obtain the optima reay number K opt with three kinds of prefiters as foows, [ L 2β ], for TR prefiter K opt = ], for ZF prefiter, (25) [ L 2 [ L(1+β ) 2β where [ ] denotes round operator. ], for MMSE prefiter 356

5 5 B. Mutipe-Access Mode In MA modes, the transmit power of each node is assumed as the same, but the received power may be very different because of the propagation distance. In addition to the interference power, the coision among the focused peaks from mutipe users wi aso affect the throughput. We first assume that no coision happens. Then the received SINR with the TR prefiter is P r,i β i = σ K L k=1,k i P, (26) r,k and R b can be cacuated as before. When the ZF or MMSE pre-equ is used, the sideobe wi be very ow and the interference from other users can be ignored, so that β i = P r,i σ 2. (27) In MA modes, puse coision is one of the critica factors that degrade the throughput. To get a concise expression of the coision probabiity, we need an ideaized assumption that a puses arrive in uniform deay and in discrete interva, i.e., it must fa in one of the N = T f /T p time sots and can not span across two time sots. The coision probabiity can be derived as ( ) N 1 p c = 1. (28) N The proof comes from a cassic probabiity probem. Put K bas into N bins randomy one by one, each bin can have any number of bas, then in average how many bins have ony one ba? Since N bins have no difference, we first consider the probabiity that ony one ba fas in a given bin. There are N K possibe ways to put K bas into N bins. We can divide the procedure into two steps to consider the possibiity of ony one ba in a given bin. At first, we pick one from the K bas into this bin, there are CK 1 possibiities. Then we put the rest K 1 bas into the rest N 1 bins, there are (N 1) possibiities. Using the mutipication principe, there are totay CK 1 (N 1) possibiities, so that the probabiity that ony one ba fas in the given bin is C 1 K (N 1). Since there are N bins, the average number of N K the bins that have ony one ba is N C1 K (N 1) N K = K ( ) N 1. (29) The puse coision probem is the same as the bas-bins probem. Since the puse arrives randomy at uniform and discrete intervas, and there are N time sots and K arriva puses, the average number of puses that do not coide is (29), therefore the coision probabiity is (28). Without coision, the network throughput can increase with the number of cooperative nodes. However, the coision probabiity wi aso increase with the node number. In MA modes, since the received signa power and interference power are different for each user, the achievabe N rate is aso different even given the same required β. The throughtput of MA mode is R t,ma = K R b,k (1 p c ). (30) k=1 Like in BC modes, we want to see the baance of increased communication inks and the increased coision probabiity in terms of K, thus we consider a specia case that each ink has the same data rate and R b = R f, then N = 1/(R b T p ) and the coision probabiity p c = 1 (1 R b T p ). (31) The throughput of MA mode becomes R t,ma = KR b (1 R b T p ). (32) We wi see the impact of K in next section. V. NUMERICAL RESULTS In this section, we wi compare the throughput of the cooperative reay network using three kinds of prefiters, anayze the optima number of reay nodes and the impact of coision on the throughput through numerica resuts. Observe (17), (20), and (23), we can see that the data rate in BC modes is independent of the received power if R b is normaized by P r /N 0. This normaized data rate ony depends on the network oad α and the required SINR, β. Fig. 2 shows the numerica resuts of the normaized throughput in BC modes, i.e., R t,bc /(P r /N 0 ), versus the number of cooperative reay nodes K, where three kinds of prefiters are compared. The UWB puse width T p is assumed to be 1 ns, and the maxima channe deay τ max is 60 ns, such that the number of resovabe paths L = 60. For reiabe communication, the required SINR β is assumed to be 4.2 db. It is shown from the figure that there is no big difference of the normaized throughputs of the network with different prefiters when the number of reay nodes is ess than 5. The difference wi increase when more nodes participate in reaying. As expected, the MMSE prefiter performs the best, TR prefiter performs the worst. The optima reay numbers of the TR, ZF and MMSE prefitering schemes are 11, 30 and 41, respectivey. Using more reay nodes wi reduce the throughput. From (26) we know that, in MA modes the data rate of each user depends on the ink distances and path osses of a users, thus it is hard to show a possibe scenarios except for the equa distance case. It is shown from (32) that, when a the users have the same data rate, R b, and the puse width is given, the throughput, R t,ma, ony depends on R b and the reay node number K. The increasing of both R b and K wi increase the coision probabiity, athough the singe user data rate and the reay inks wi aso increase. Fig. 3 shows the network throughput in MA mode versus the singe user data rate and the reay number, where the puse width is 1 ns. In the upper part of the figure, R b is fixed as 50 Mbps, and in the ower part of the figure, K is fixed as 10. For comparison, the network throughput under the assumption of coision-free is aso shown. We can see that the impact of coision becomes 357

6 6 Normaized Throughput MMSE ZF TR Number of Reay Nodes Fig. 2. Normaized throughput versus the number of cooperative reay nodes in BC modes, where L = 60, β =4.2 db. The vertica ines indicate the optima reay numbers. Throughput (Mbps) Throughput (Mbps) Without coision With coision Number of Reay Nodes Without coision With coision Singe User Data Rate (Mbps) Fig. 3. Network throughput versus the number of cooperative reay nodes and singe user data rate in MA modes, where R b = 50 Mbps in the upper part and K = 10 in the ower part. apparent when K > 4 in the upper case and R b > 20 Mbps in the ower case. VI. CONCLUSION To appy UWB networks for ong-distance high-rate transmission, a cooperative reay scheme using space-time focusing transmission is proposed in this paper. Theoretica anaysis and numerica resuts on network throughput are provided, which indicate that there exists an optima cooperative reay number to maximize the network throughput since more reay nodes wi cause undesirabe mutua interferences in BC modes and coisions in MA modes. The simpe TR scheme ony performs we in few reay nodes and ow-rate scenarios whie advanced prefitering agorithms become superior when more nodes participate in cooperation and when date rate is high. REFERENCES [1] T. Strohmer, M. Emami, J. Hansen, G. Papanicoaou, and A. J. Pauraj, Appication of time-reversa with MMSE equaizer to UWB communications, in GLOBECOM 2004, pp [2] M. Emami, M. Vu, J. Hansen, A. J. Pauraj, and G. Papanicoaou, Matched fitering with rate back-off for ow compexity communications in very arge deay spread channes, in Asiomar Conference on Signas, Systems and Computers, 2004, pp [3] H. T. Nguyen, J. B. Andersen, and G. F. Pedersen, The potentia use of time reversa techniques in mutipe eement antenna systems, IEEE Commun. Lett., vo. 9, pp , Jan [4] H. T. Nguyen, I. Z. Kovcs, and P. C. F. Eggers, A time reversa transmission approach for mutiuser UWB communications, IEEE Trans. Antennas Propagat., vo. 54, pp , Nov [5] N. Guo, R. C. Qiu, and B. M. Sader, A UWB radio network using mutipe deay capture enabed by time reversa, in MILCOM 2006, pp [6] R. C. Qiu, C. Zhou, N. Guo, and J. Q. Zhang, Time reversa with MISO for utrawideband communications: experimenta resuts, IEEE Antennas Wireess Propagat. Lett., vo. 5, pp , Dec [7] R. C. Qiu, A theory of time-reversed impuse mutipe-input mutipeoutput (MIMO) for utra-wideband (UWB) communications, in ICUWB 2006, pp [8] C. Zhou, N. Guo, B. Sader, and R. Qiu, Performance study on time reversed impuse MIMO for UWB communications based on measured spatia UWB channes, in MILCOM 2007, pp [9] F. H. P. Fitzek and M. D. Katz, Eds., Cooperation in Wireess Communications: Principes and Appications. Springer, [10] A. Scagione and Y.-W. Hong, Opportunistic arge arrays: cooperative transmission in wireess mutihop ad hoc networks to reach far distances, IEEE Trans. Signa Processing, vo. 51, pp , Aug [11] R. J. Barton, J. Chen, K. Huang, S. Perotta, and D. Wu, Optimaity properties and performance anaysis of co-operative time-reversa communication in wireess sensor networks, IET Proceedings on Communications, vo. 1, pp , Feb [12] T. M. Cover and J. A. Thomas, Eements of Information Theory. John Wiey & Sons, [13] J. L. Schwartz and B. D. Steinberg, Utrasparse, utrawideband arrays, IEEE Trans. Utrason., Ferroeect., Freq. Contr., pp , Mar [14] M. G. M. Hussain, Principes of space-time array processing for utrawide-band impuse radar and radio communications, IEEE Trans. Veh. Techno., vo. 51, pp , May [15] F. Dowa and A. Spiridon, Spotforming with an array of utra-wideband radio transmitters, in UWBST 2003, pp [16] Y. Tian and C. Yang, Noncoherent mutipe-symbo detection in coded utra-wideband communications, IEEE Trans. Wireess Commun., vo. 7, pp , June [17] A. Nosratinia, T. E. Hunter, and A. Hedayat, Cooperative communication in wireess networks, IEEE Commun. Mag., vo. 42, pp , Oct [18] T. Miyano, H. Murata, and M. Araki, Space time coded cooperative reaying technique for mutihop communications, in VTC2004-Fa, pp [19] H. Ochiai, P. Mitran, H. V. Poor, and V. Tarokh, Coaborative beamforming for distributed wireess ad hoc sensor networks, IEEE Trans. Signa Processing, vo. 53, pp , Nov [20] M. Luby, LT codes, in the 43rd Annua IEEE Symp. on Foundations of Computer Science, 2002, pp [21] D. J. C. MacKay, Fountain codes, IEE Proceedings on Communications, vo. 152, pp , Dec [22] A. Shokroahi, Raptor codes, IEEE Trans. Inform. Theory, vo. 52, pp , June [23] J. Castura and Y. Mao, Rateess coding and reay networks, IEEE Signa Processing Mag., vo. 24, pp , Sept [24] A. F. Moisch, N. B. Mehta, J. S. Yedidia, and J. Zhang, Performance of fountain codes in coaborative reay networks, IEEE Trans. Wireess Commun., vo. 6, pp , Nov [25] D. N. C. Tse and S. V. Hany, Linear mutiuser receivers: effective interference, effective bandwidth and user capacity, IEEE Trans. Inform. Theory, vo. 45, pp , Mar