LENST

1. Università degli Studi di Firenze Dipartimento di Elettronica e Telecomunicazioni 12° MCM of the COST 289 October 30-31 – Firenze, Italy Pulse Repetition and Cyclic Prefix Communication Techniques in Impulse Radio UWB Systems Simone Morosi and Tiziano Bianchi Electronics and Telecommunications Department, University of Florence Via di Santa Marta 3, 50139 Firenze, ITALY Tel: +39 055 4796485 – Fax: +39 055 472858 e-mail: {morosi, bianchi}@lenst.det.unifi.it This work has been supported by Italian Research Program (PRIN 2005): Situation and location aware design solutions over heterogeneous wireless networks”. • LENST Laboratorio di Elaborazione Numerica dei Segnali e Telematica

2. Outline • Motivation • System model • Frequency Domain Detection • Comparison Criteria • Simulation Results • Conclusions

3. Motivation Our goal • The comparison of two techniques for Impulse Radio UWB systems which are based on the pulse repetition according to the spreading factor value and the Cyclic Prefix insertion. • Both techniques cause a throughput loss and have to be compared both in terms of performance and capacity, i.e. the maximum data rate which is afforded. • The redundancy due to the CP approach is not considered as an overhead, but as an alternative to the processing gain Nf . Our tool: Frequency Domain Detection (FDD) • FDD has been proposed for UWB single user systems in [Bia04] and [Ishi04] and extended to high data-rate multiuser systems in [Mor05] • This approach is based on both the introduction of the cyclic prefix and the use of a frequency domain detector. This approach is well suited for the applications which are based on data-rate scalability and rely on data gathering. [Bia04] T. Bianchi and S. Morosi, “Frequency domain detection for ultra-wideband communications in the indoor environment,” in Proc. of the IEEE Eighth International Symposium on Spread Spectrum Techniques and Applications, 2004, Aug.-Sept 2004. [Ishi04] Y. Ishiyama and T. Ohtsuki, “Performance evaluation of UWB-IR and DS-UWB with MMSE-frequency domain equalization (FDE),” in Proc. of the IEEE GLOBECOM ’04, vol. 5, Nov.-Dec. 2004. [Mor05] S. Morosi and T. Bianchi, “Frequency Domain Multiuser Detectors for Ultra-Wideband Short-Range Communications”, in Proc. of ICASSP 2005, Philadelphia, PA, USA, Mar. 2005.

4. Signal Structure (I) • tl indicates the delay of the l-th user with respect to the access point time reference • t(b) indicates the pulse shift that implements binary PPM • Tf and Tc are the frame and the chip periods • bl(i) = ±1 is the i-th binary symbol transmitted to the l-th user. The same bit is transmitted over Nf consecutive frame periods (Tb=NfTf ). • Nc chips fit exactly in one frame period (Tf = NcTc ). • Each active user is associated with a time-hopping pseudo-random periodic pattern cl(m) 0 1 2 3 TH code = [0,1,2,3]

5. 0 1 2 3 1/2 pl(k) -1/2 1/2 ql(k) Signal Structure (II) • The transmitted signal can be represented more conveniently as: • The discrete sequences pl(k) and ql(k) are periodic with period Nw = 2Nc Nf .

6. Downlink Model (I) • We consider a base station transmitting Nu signals synchronously to a set of Nu users Iu = {1, 2, . . . , Nu} • The Received Signal can be expressed as: • The function f(t) takes into account the effects of the channel, of the antennas, and of the matched filters of both transmitter and receiver. • The signal x(k) represents the digital counterpart of the UWB-IR TH-SS signal: • The signal h(t) models thermal noise.

7. Downlink Model (II) • By assuming that channel characteristics are constant over the entire block of samples and by sampling r(t) with period Tw , the following digital transmission model is obtained: • h(n) = f(nTw) represents the equivalent discrete channel impulse response of the UWB-IR system. • e(n) = h(nTw) represents a discrete time noise process.

8. Block Representation • The discrete signal xl(n) is divided in blocks of M samples • Low Data Rate scenario: • MNM= Nw , we need exactly NMblocks to transmit a single bit • High Data Rate scenario: • M = NbNw a group of Nb bits is transmitted over a block of M samples • Each block is extended by means of a cyclic prefix of length K. • If K ≥ Lc (Delay Spread), the channel does not cause any interference between adjacent blocks.

9. Frequency Domain Detection (I) • Any circulant matrix can be diagonalized by using a DFT. • We can express the channel matrix as: • WM is an M×M Fourier transform matrix and ΛH is a M×M diagonal matrix whose entries represent the channel frequency response. • The received vector after cyclic prefix removal can be expressed as a function of the bits of all active users, the TH sequences, and the channel frequency responses.

10. Frequency Domain Detection (II) • The decision variables can be expressed as • Low Data Rate • High Data Rate • Minimum Mean Square Error (MMSE) detection has been considered, due its good tradeoff between performance and complexity. • where σ2e is the noise variance and σ2b indicates the power of transmitted symbols. This solution avoids noise amplification at the detector when the SNR is low.

11. RAKE Nf CP Nf/2 FDD How to compare the systems • If we assume that the CP size K has been fixed, the minimum block size required by FDD is M ≥ K. • Since UWB allows for redundancy in terms of pulse repetition, we set the block size as small as possible and compensate for the loss of throughput by shortening the pulse repetition factor Nf. • The block size is set to M = K. In order to have the same rate of the original system, the repetition factor of the FD system is set to NCPf = Nf/2. • This choice does not impose any relationship between M and the number of samples NCPw = 2Nc NCPf that are associated with a single bit.

12. Complexity considerations • Choosing K = Lc − 1 (classical FD receiver) gives optimum performance at a cost of a high complexity, i.e., too long CP. • Also the rake has to face an analogous inconvenient with suboptimum implementation (partial RAKE, selective Rake, ..) • We proposed also a reduced complexity FD receiver, in which only a subset of the total channel paths is taken into account: in this system K (and hence M) is reduced. • This solution is the FD counterpart of the partial RAKE and permits a smaller length of the CP and, therefore, a smaller size FFT. The drawback of this solution is the introduction of an increased ISI term (due to the last replicas of the channel which are no more contained into a single block of samples). • Nonetheless the MMSE detector can be redisegned by considering the increased ISI: this solution is defined partial-FD (P-FD) receiver.

13. Channel Model • The channel model has been simulated relying on the model proposed by Cassioli et al… in: • “Dajana Cassioli, Moe Z.Win, and Andreas F.Molisch,“The ultra-wide bandwidth indoor channel: From statistical model to simulations,” IEEE J. Select. Areas Commun., vol. 20, no. 6, pp. 1247–1257, Aug. 2002.” • A slow fading scenario has been assumed, so that the channel coefficients could be approximated as constant over a single block of samples. • Only the small scale fading statistics have been considered, assuming no shadowing and a reference pathloss of 0 dB. A constant power delay profile has been assumed, setting the power ratio between the line-of-sight replica and the reflected ones as 0.4 and choosing a decaying constant corresponding to a rms delay spread of about 50 ns, a typical value for indoor environments.

14. Working Conditions • The considered an UWB-IR scenario consists of an Access Point (AP) transmitting to a variable number of Mobile Terminals (MTs). • All the communications from the AP have been assumed synchronous. • The information bits are modulated (2-PPM) with Tw = 2 ns pulse duration • High Data-Rate (HR) system: • Nf = 4, Nc = 4; 15.6 Mbit/s. • Medium Data-Rate (HR) system: • Nf = 16, Nc = 4; 3.9 Mbit/s. • Low Data-Rate (LR) system: • Nf = 128, Nc = 32; 243.6 kbit/s. • The digital channel model has LRAKE = 100 sample-spaced resolvable replicas.

15. LR: Single User Both receivers achieve good performance unless a very low number of fingers or a very short CP is considered. Nf = 64, Nc = 16, single data flow

16. LR: 100% load It is important to consider an enough long CP in order to prevent from ISI detrimental effects. In particular, for high values of Eb/N0 the MMSE is not able to suppress the effects of the ISI caused by short CP and its performance tend to converge to the values of the RAKE receiver error floor. Nf = 64, Nc = 16, 16 data flows

17. MR: 50% load Nf = 16, Nc = 4, Eb/N0 =15 dB Nf = 16, Nc = 4, 2 data flows The same trend can be seen for a half loaded high rate system. Note that the PFDMMSE Equalizer has interesting results: the definition of the new equalization law permits to avoid the degradation caused by the ISI.

18. HR: Single User Nf = 4, Nc = 4, single data flow If an enough long CP is used the FD MMSE equalizer greatly overcomes the system based on the pulse repetition and the use of the RAKE receiver.

19. Conclusions • We compared UWB-IR systems based on the pulse repetition according to the spreading Factor value and the use of the RAKE receiver and on the Cyclic Prefix insertion and Frequency Domain MMSE Equalization. • Both systems admit sub-optimal implementation. • Both systems have been considered in different scenarios characterized by services with different rate and system with variable load. • The simulation results show that the system which is based on the Cyclic Prefix insertion and the adoption of the Frequency Domain MMSE is more suitable for high data rate highly loaded systems.