Channel Division Multiple Access Based on High UWB Channel Temporal Resolution

Transcription

1 Channe Division Mutipe Access Based on High UWB Channe Tempora Resoution Rau L. de Lacerda Neto, Aawatif Menouni Hayar and Mérouane Debbah Institut Eurecom B.P Sophia-Antipois Cedex - France Emai: {Rau.de-Lacerda,Menouni,Debbah}@eurecom.fr Abstract Utra-WideBand (UWB) has been recenty presented as a promising radio technoogy due to the arge bandwidth avaiabe. This feature enabes point to point high data rates at short range as we as high tempora resoution with ong Channe Impuse Responses (CIR). Due to the their arge bandwidth, UWB systems enabes high tempora resoution with ong CIR. In this paper, we evauate an origina mutipe access scheme caed Channe Division Mutipe Access (ChDMA), where we use the CIR as a user signature. The signature code is given by the channe and the users are separated by their position: this signature is uniquey determined by the user s position, which changes from one position to another. This signature ocationdependent property provides decentraized fexibe mutipe access as the codes are naturay generated by the radio channe. The framework is anayzed and vaidated by capacity assessments using UWB measurements performed at Eurecom and compared with cassica CDMA schemes with random spreading codes. The anaysis is focused on the impact of the user s asynchronism and the period of symbo on system performance. Two structures are considered at the receiver: singe-user matched fiter and MMSE receiver with Gaussian and BPSK signaing schemes. Index Terms Mutipe access schemes, muti-user systems, channe signatures, channe division mutipe access, code division mutipe access, channe capacity, fading channes, noisy channes, spectra efficiency, mutiuser detection, mutiuser information theory, spread spectrum, wideband regime. I. INTRODUCTION Unti recenty, the main focus of Utra-WideBand (UWB) studies has been on the anaysis of point to point communications. Hence, in [], Kennedy showed that the infinite bandwidth capacity of a Rayeigh fading mutipath channe with perfect channe knowedge at the receiver is the same as the infinite bandwidth capacity of the non-fading Additive White Gaussian Noise (AWGN) channe with the same average received power. An interesting feature is that this capacity can be achieved with any kind of orthogona code set. In [], [3], [4], these resuts are generaized to the case where the channe is not known at the receiver with different constraints on the input signa. In [], ( the infinite ) bandwidth capacity is shown to be equa to : T d P T c, where T d and T c are respectivey the deay spread and the coherence time interva in the case of no inter-symbo interference (ISI). Surprisingy, the resut in this case is not vaid for any code set, but it depends This work is part of the European Network of Exceence NEWCOM, Contract IST NoE cruciay on the type of the orthogona signaing. In particuar, by transmitting at very ow duty cyce, capacity of the infinitebandwidth AWGN channe can be achieved independenty of the number of paths and code sets, which is not the case for spread spectrum signas. Spread spectrum signas (which is an interesting candidate for muti-user communications) were shown to suffer a dramatic oss in terms of mutua information uness the channe varies very sowy amost in a quasistatic way. The basic guidance behind this fact is that as the bandwidth increases, the power avaiabe to estimate each path is too sma for accurate channe detection techniques to work we. This effect degrades significanty the signa to noise ratio (SNR). As consequence, ow duty cyce signas are empoyed to mitigate the penaty factor due to channe estimation [5]. In mutiuser setting, however, there has not been proposed any mutipe access scheme abe to provide benefits of using ow duty cyce transmissions. For this reason, in this work, a signaing scheme for muti-user communications is proposed using ow duty cyce transmissions, which we ca it Channe Division Mutipe Access (ChDMA). Benefiting from the fact that the coherence time T c of UWB systems is arge (typicay about µs) whereas the deay spread T d is very sma (typicay from 5-4 ns, depending on the user environment), each user sends a very moduating peaky signa every T s. The resuting impuse response moduates the signa of interest and is decorreated of any other user sending information at the same time and in the same band. The system is equivaent to an upink code division mutipe access (CDMA) with random spreading codes for which the capacity region is known [6]. Due to the fact that the power dedicated to the channe estimation is imited the channe estimation efficiency when the bandwidth increases is bounded. Moreover, the high number of degrees of freedom of the channe provide enough uncorreated random spreading codes to separate the users. Note finay that the ow spectra efficiency typica of wideband systems does not impy that the communication is wastefu of channe resources or that the system operates far from channe capacity. This paper is organized as foows. In Section II presents the system mode, which incudes a briefy description of the We suppose, for simpicity sake, that T s is the same for a users and it is function of the maximum deay spread T (max) d. It is important to note that T s is strongy reated with the user s synchronism.

2 h User user (athough the tota spectra efficiency decreases) as the number of users decreases. In a the foowing, we assume that for any i, E( h i ) =. h Tc User User Channe () h 3 c c c c User 3 User Channe () Fig.. Channe Impuse Division Mutipe Access Scheme with three users. c c c c User 3 Channe (3) channe mode and the capacity equations. The simuation characteristics are detaied in Section III. After that, some performance resuts are shown in Section IV. Finay, in Section V, the concusion and some perspectives are presented. II. SYSTEM MODEL To buid the system mode, we consider a fading channe with additive white gaussian noise, ike typica utra-wideband wireess environments. Furthermore, considering the upink case, we assume that the system empoys K users and each user transmits a ow duty moduating signa every T s. In this case, the symbo received at the access point is given by: y = Hs + n, () where y is a N vector with N = T s T r, which represents the reation between the deay between the transmission of symbos and the samping rate at the receiver. H = [h,..., h K ] is a N K matrix which contains the time response vector h i of each user i. s is a K vector which contains the transmitted symbos of the various users, typicay {+, } due to the ow spectra efficiency of wideband signas. n is a N additive white gaussian noise vector of variance σ. In the system empoyment, the ISI is avoided due to the fact that users transmit ony every T s, which is greater than T d. As a consequence, we can consider that the channe impuse responses works as users signatures to access the environment, ike a mutipe access scheme as CDMA. It is important to note that the impuse radio has ong been seen as a moduation scheme and never as a mutipe access scheme. Note that each user has a particuar channe h i, and we suppose that each channe is independent from the others 3. Because of this assumption, it is possibe to use the channe signature to separate the signas that come from different users. The system can achieve very good spectra efficiency as ong as the number of users is high compared to the deay spread and the coherence time is quite ong. Moreover, the system is fexibe in the sense that the spectra efficiency of the system depends mainy on the number of users and increases for each is the frequency resoution and is the bandwidth aocated for the T s T r utra-wideband signa 3 See section II-A for a discussion on this issue. Fig.. Channe Division Mutipe Access signaing. A. Mutipath Channe c3 c3 c3 c3 We consider a time invariant channe c (k) of user k given by: c (k) (τ) = L (k) = λ (k) δ(τ τ (k) ), () where λ and τ represent respectivey the gain and the deay of the -th mutipath. For simpicity sake, we suppose that a users are in the same environment, operating at the same bandwidth, and the number of paths is the same (L (k) = L). Furthermore, because of the puse signa g empoyed for the transmission of the symbos on the environment, the channe h (k) (τ) of the k-th user is given by h (k) (τ) = L = λ (k) g(τ τ (k) ), (3) where g is the transmit fiter. As consequence, the discrete channe matrix H is given by the concatenation of the discrete channe vector of each user as show in the foowing: H = [h () h ()... h (K) ]. (4) where the channe vector ength is given by the ratio between the tempora resoution (T r ) and the symbo period (T s ). B. expressions Assuming Gaussian signaing, the instantaneous spectra efficiency is given by: For the optimum receiver: γ opt = N og det (I N + σ ) HHH For the matched fiter (MF) and the MMSE receivers: γ = K og N ( + SINR i ) i=

3 3 which the SINR vaue is respectivey cacuated by h H i SINR MFi = h i σ (h H i h i) + K j=,j i hh i h j (5) SINR MMSEi = h H i ( H i HH i + σ I) h i, (6) where H i is N (K ) matrix which contains a time response vectors h j for a j i. For a receiver, the signa to noise ratio σ is reated to the spectra efficiency γ by: σ = N K γ Eb N. The spectra efficiency of these receivers with random spreading has been studied in [6]. The expression of the mutua information with BPSK signaing is given by: Sync. MF Sync. MMSE Assync. MF Assync. MMSE CDMA MF CDMA MMSE γ = K + e v og N ( ) + e SINRi SINR iv dv, i= π (7) where SINR i for MF and MMSE receivers are aready defined before. III. SIMULATION CHARACTERISTICS For the simuations, two different evauations are empoyed. First, we wi compare the performance of the ChDMA and the CDMA for synchronous and asynchronous users. In such simuations, we assume that the sampes are in tempora domain with a fixed number of sampes. The second kind of simuations are empoyed to estimate the impact of the symbo period (T s ) when the asynchronous case is empoyed by using a random deay retard 4 for a fixed bandwidth. To perform the simuation, some assumptions are considered: Assumption : The considered channe bandwidth is GHz with resoution of MHz, which gives a channe vector with ength equa to 5, due to the fact that the maximum deay spread of the indoor channe is imited on 5 ns. Assumption :. To compare the spectra efficiency of our proposa, we simuated a CDMA system where signature waveforms are assigned at random. In this case, each code word is chosen equay ike and independent for each user, where each chip corresponds to { 5, 5 }. Assumption 3: The asynchronous case are generated by the introduction of retards on the channe vectors. This retard (τ (k) i ) is given by a uniform variabe generated between [, T s ]. IV. CAPACITY PERFORMANCE AND COMPARISON OF RESULTS In Fig. 3, we show the spectra efficiency when synchronous and asynchronous modes are empoyed on a ChDMA system in terms of the reation between the number of the users and the resoution ( K N ). In the same figure, we show the performance of the CDMA system when pseudo random codes are used. As we can see, the effect of the asynchronism maximizes the spectra efficiency of the system, given amost 4 The deay retard is imited between zero and the symbo period (T s ) Fig. 3. db. Capacity anaysis on the impact of the asynchronism when E b = the same performance of the perfect CDMA capacity. This effect is generated by the fact that rea channes have a typica power deay profie which spread the energy over ony a few sampes. When the asynchronism between users is considered, the interference is spread on a considered sampes, avoiding the concentration of interference on the most important sampes. To evauate the impact of the symbo period, we show in Figs. 4 and 5 the spectra efficiency curves when we empoy asynchronous ChDMA and CDMA systems with matched fiter receivers. The first figure shows the performance when Gaussian signaing is used. As we can see, the impact with respect to the ratio K N is not significative, but we can confirm our intuition that when we increase the symbo period, we decrease the spectra efficiency. We can concude that the performance of the asynchronous ChDMA and the CDMA is the same when we empoy the same system characteristics. In the same direction, Fig. 5 shows the performance when BPSK signaing is empoyed, and we confirm that the greatest spectra efficiency period of symbo is given when the symbo period is equa to the atest significative deay. In Fig. 6 and 7, we show the spectra efficiency of the asynchronous ChDMA and CDMA when Gaussian and BPSK signaing are empoyed, respectivey. As for the matched fiter receiver, we see that the performance is amost the same, but as ong as we decrease the period of symbo, we increase the spectra efficiency. Another interesting effect that we can see in this figure is that the cassica peak found on the performance of the MMSE receiver in terms of the number of users is inversey reated with the period of symbo. Again, the performance of the asynchronous ChDMA and the CDMA is the same. The curves were simuated for a Eb No of db. As we can see, the performance of the CDMA-based case is equa to the resuts of the asynchronous ChDMA case.

4 Measure Ts = Measure Ts =.5 Measure Ts = CDMA Ts = Measure Ts = Measure Ts =.5 Measure Ts = CDMA Ts = Fig. 4. Capacity anaysis on the impact of T s when a Match Fiter receiver is empoyed at E b = db with a Gaussian signaing. Fig. 6. Capacity anaysis on the impact of T s when a MMSE receiver is empoyed at E b = db with a gaussian signaing Rea Ch. Ts = Rea Ch. Ts =.5 Rea Ch. Ts = CDMA Ts = Rea Ch. Ts = Rea Ch. Ts =.5 Rea Ch. Ts = CDMA Ts = Fig. 5. Capacity anaysis on the impact of T s when a Match Fiter receiver is empoyed at E b = db with a BPSK signaing. Fig. 7. Capacity anaysis on the impact of T s when a MMSE receiver is empoyed at E b = db with a BPSK signaing. It is important to note that the resuts presented for the CDMA case is for a perfect channe, i.e., the channe does not have mutipaths, which is an unfair assumption when we consider rea channes. Actuay, when we empoy CDMA systems in rea channes, it is necessary to add some compex structures ike scrambing codes, which increases the code ength and the computationa compexity of the receiver. In this cases, the CDMA system needs to know the channe information to adapt the transceiver architecture with the objective to maximize the system capacity and to ameiorate the spectra efficiency to be abe to achieve high data rates. For the CDMA case, as the channe profie is constant, the asynchronism wi not change the performance. The ony assumption that we need to consider to empoy the ChDMA is the knowedge of the channe at the receiver. Moreover, the natura codes generated by the environment introduces a natura privacy, which can be expoited without additiona compexity. V. CONCLUSION For the synchronized case, the resuts are encouraging especiay if we take into account the fact that the codes in ChDMA system are naturay provided by the channe estimation, they are ocation dependent which wi increase the privacy. They aso benefit from code hopping at each new channe reaization which wi increase the resistance against

5 5 inter-codes interference. Despite the sowest performance of the MF receiver, when we empoy MMSE receivers, the ChDMA has amost the same performance as the CDMAbased case. This resut impies that, even in a synchronous system, it is possibe to buid receivers for the ChDMA that is abe to achieve a performance comparabe to the CDMA capacity. For the asynchronism case, it is possibe to achieve the CDMA capacity for both receivers. Thanks to the exponentia shape of the rea channe, ony a few paths wi interfere which improve significanty the performance as we can see from the figures. As future work, detaied anaysis on the optimization of the symbo period shoud be done by the use of theoretic information toos. Furthermore, we know that the degrees of freedom pays an important roe on the system modeing, and some studies are being conducted to anayze the impact of the degrees of freedom given by the channe mode when high correated channes are considered. REFERENCES [] R. S. Kennedy, Fading Dispersive Communication Channes. New York, USA: Wiey, 969. [] I. E. Teatar and D. N. C. Tse, Capacity and Mutua Information of Wideband Mutipath Fading Channes, IEEE Trans. on Information Theory, pp , Juy. [3] V. Subramanian and B. Hajek, Broad-band Fading Channes: Signa Burstiness and Capacity, IEEE Trans. on Information Theory, pp , Apr.. [4] M. Médard and R. G. Gaager, Bandwidth Scaing for Fading Mutipath Channes, IEEE Trans. on Information Theory, pp , Apr.. [5] D. Porrat, D. N. C. Tse, and S. Nacu, Channe uncertainty in utra wideband communication systems, IEEE Transactions on Information Theory, 5 (Submitted). [6] S. Verdu and S. Shamai, of CDMA with Random Spreading, IEEE Trans. on Information Theory, pp. 6 64, Mar. 999.