Rome January 19-th, 2007

1. Wireless Mesh Networks:First part:Point to point links ofwireless mesh nodes based on MIMO UWB-IR technology 3-rd Workshop of WOMEN Project University of Rome “Sapienza”, INFOCOM Dept. (Faculty of Engineering) Rome January 19-th, 2007

2. Outline System model: main characteristics Derivation of the MIMO UWB-IR Co-Decoder Performance of the MIMO UWB-IR Co-Decoder Main aspects of the MIMO UWB-IR Synchronizer Conclusions

3. SPACE-TIME CODED PACKET TRANSMITTER ADOPTING OPPM MODULATION FORMAT NON-COHERENT ML DECODER MIMO UWB-IR System Model(with Poisson distributed multipath fading) PILOT SIGNAL GENERATOR FOR SYNCHRONISM RECOVERY NON-COHERENT ML SYNCHRONIZER

4. The MIMO UWB-IR channel model Multiple Cluster SISO channel responses with Poisson distributed arrivals and clusters and Log-Normally distributed path gains. ( It has been adopted for describing different indoor and outdoor propagation environments) A. Molish, D. Cassioli, et alii, “A Comprehensive Standardized Models for UltraWideband Propagation Channels”, IEEE Tr. On antennas and Propagation, Vol.54, No.11, pp.3151-3166, Nov.2006.

5. UWB-IR channel models

6. Main assumptions on the channel model A.1) According to J.H.Reed, An introduction to Ultra Wideband Communication Systems, Prentice Hall 2005 we may approximate each Multiple Cluster SISO channel response to single cluster one, by considering only the first cluster. A.2) In order to derive the co-decoder block we consider three different path gains’ ddp: 1) Gaussian 2) Log-Normal 3) Nakagami A.3) In order to derive the co-decoder block we assume the number V of arrivals and their values to be perfectly estimated A.4) The path gains are supposed to be spatially uncorrelated A.5) We consider slow-variant fading

7. The Co-Decoder block

8. ML Decoder Block Scheme NON-COHERENT ML SYNCHRONIZER Banks of Filters matched to M-OPPM symbols and their V+1 replicas . . . Decision Statistics Processing and selector of maximum

9. Setting of the pulse width TP to mitigate theInter-Pulse-Interference (IPI) Given the following positions : a) , temporal pulse width (monocycle) used by each transmit antennas b) M, the OPPM constellation cardinality of the symbols used for Space-Time coding of the L-ary Source Symbols. c) , the exponentially distributed inter-arrivals with arrival mean frequency equal to Let us set , to meet the following condition: for a fraction h of the service time, that is Such choice allows us to mitigate the IPI effect due to the Poisson distributed arrivals

10. stands for the (NtX (Nr (V+1)) ) multipath channel matrix The outputs of matched filters (matrix representation) stands for unitary (MxNt ) Space-Time codeword matrix corresponding to the M-OPPM coded symbols, that is denotes Unitary (MX1) vector. It is function of the uncoded L-ary source symbol “l”, and biunivocally associated to the M-ary OPPM coded symbol radiated by the i-th transmit antenna stands for (MxNr (V+1 ) ) Additive Gaussian noise matrix is the signal to noise ratio per each transmitted bit Nfis the number of frame per each symbol period Ts

11. Decision Statistics processing and selector of maximum • The ML Decoder works according to the following criterium:

12. Space Time Orthogonal Pulse Position Modulation (STOPPM) codes Definition 1) The unitary codeword matrices are composed by M rows and Nt columns. The number M (that is, the OPPM constellation cardinality) is given by product LNt 2) Any two distinctive codeword matrices are composed by 2Nt different columns Property of the STOPPM codes The spectral efficiency of the STOPPM codes is equal to Es: L=Nt=2 M=4

13. The Union-Chenoff upper bound retained STOPPM codes • “Log-Normal” frustraction integral. It cannot be expressed in closed form . • S.M.Hass, J.H.Shapiro, “Space-Time Codes for Wireless Optical Communications”, Eurasip Journal on Applied Signal Processing, pp. 211-220, no.3, 2002.

14. Performance of the STOPPM codes Nk- fading G-fading • Nr=3 • Nf=6 Lg-N fading CM3’s Multipath Intense Profile

15. Coverage Ranges and Troughput(1/2) • BER target: • Transmit Power: 2.5mW (Typically adopted for outdoor systems) • Each parameter of SISO links is according to CM1: • 4) The baseband monocycle is equal to the Gaussian pulse second derivative • M.Z.Win, R.A.Scholtz, ''Ultra-Wide Banbwidth Time-Hopping Spread Spectrum • Impulse Radio for Wireless Multiple Access Communications'', IEEE Tr. on Comm., • vol.48, pp.679-691, Apr.2002. • 5) The path loss model is according to the Siviak-Petroff one • K.Siwiak, A.Petroff, ''A Path link model for Ultra Wide Band • Pulse Transmissions'', IEEE VTC2001, Rhodes, Greek, May 2001. • 6) Throughput: 136.0Mbps • 7) The Log-Normal fading is considered

16. Coverage Ranges and Troughput(2/2) Table of coverage Ranges reached by the proposed MIMO UWB-IR co-decoder , equipped with the STOPPM codes. Any SISO link is according to CM1.

17. The IPI effect CM3’s Multipath Intense Profile G fading Nt=2, Nr=1, Nf=4

18. Channel Impairments – Spatially correllated Fading (1/2) A.Paulray, R.Nabar, D.Gore, Introduction to Space-Time Wireless Communications, Cambridge university Press, 2003. Spatial Covariance Matrix.

19. Channel Impariments- Spatially Correlated Fading (2/2) Lg-N fading Nt=Nr=2, Nf=12 CM3’s Multipath Intense Profile

20. Channel Impairments- Cross-Polarization A.Paulray, R.Nabar, D.Gore, Introduction to Space-Time Wireless Communications, Cambridge university Press, 2003. Channel Model Nakagami Fading Nt=Nr=2, Nf=15 CM3’s Multipath Intense Profile

21. Synchronism RecoveryThe ML Synchronizer block

22. SNR losses due to Asynchronism • Let us assume that any time arrival estimate is affected by some error , that is

23. SPACE-TIME CODED PACKET TRANSMITTER ADOPTING OPPM MODULATION FORMAT NON-COHERENT ML DECODER MIMO UWB-IR System Model(with Poisson distributed multipath fading) PILOT SIGNAL GENERATOR FOR SYNCHRONISM RECOVERY NON-COHERENT ML SYNCHRONIZER

24. NON Coherent ML Synchronizer- Main Aspects (1/2) • It jointly estimates the number V of arrivals and their values , according to the ML criterium, without any knowledge on the magnitude of the channel coefficients • Such estimation is asymptotically exact • It is pilot-aided • From Cramer-Rao bound point of view, the SIMO version is to prefer to a MIMO version with orthogonal signaling • E.Baccarelli, M.Biagi, C.Pelizzoni, N.Cordeschi, “Multi-Antenna Noncoherent ML Synchronization for UWB-IR faded channels ”, Journal of Communications and Networks (JCN), vol. 8, No.2, pp.194-204, Giugno 2006

25. Joint ML estimation of V and Prop.1: Let us indicate the arrival times’ and channel coefficients vectors, and let be a received signal G.S. representation, then the following joint ML estimation can be equivalently effected by only estimanting the arrivals times and their number V, that is with

26. The ML equations’ system Properties of the resulting ML equation system : • The i-th equation is function only on the corespondent time arrival. The (V+1) equations are independent each other • Any solution can be admitted only when : Serial implementation

27. The expression of Cramer Rao Bound with

28. ML Synchronizer (Early-Late Gate serial version) yNr(t) LNr “late”output X dt blocco Lj + y1(t) yj(t) L1 X (1) dt Tw Late  X Tw (2) - Template Signal Generator LOOP FILTER + + Early  (1+Ns) Tw E1 + “early”output ENr +

29. Performance of the ML synchronizer

30. Conclusions • The proposed MIMO UWB-IR co-decoder is optimized to work under different path gains pdfs • It works in non-coherent mode • The proposed STOPPM codes can minimize the Union-Chernoff upper bounds • The resulting solution allows to extend the (typically) low coverage of the SISO UWB-IR systems • The proposed ML synchronizer can be simply implemented as serial version of early-late gate.