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

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

3. NON-COHERENTMLSYNCHRONIZER PILOT SIGNAL GENERATOR GENERATORFOR SYNCHRONISM SYNCHRONISM RECOVERY RECOVERY MIMO UWB-IR System Model (with Poisson distributed multipath fading) SPACE-TIME CODED SPACE-TIME CODED PACKET TRANSMITTER ADOPTING OPPM MODULATION FORMAT NON-COHERENTMLDECODER

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 SISO UWB-IR channel Cluster mean frequency Ray mean frequency Cluster decay factor Ray decay factor Multipath Spread CM 1 (LOS) 0.02332.57.14.35.05 CM 2 (NLOS) 0.40.55.56.710.38 CM 3 (NLOS) 0.06672.1147.914.18 CM 4 (ENLOS) 0.06672.1241230.1

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 Banks of Filters matched to M-OPPM symbols and their V+1 replicas. Decision Statistics Processing and selector of maximum.. NON-COHERENTMLSYNCHRONIZER

9. Setting of the pulse width T P to mitigate the Inter-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  of the service time, that is Such choice allows us to mitigate the IPI effect due to the Poisson distributed arrivals

10. The outputs of matched filters (matrix representation) stands for unitary (MxN t ) 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 the (N t X (N r (V+1)) ) multipath channel matrix is the signal to noise ratio per each transmitted bit stands for (MxN r (V+1 ) ) Additive Gaussian noise matrix N f is the number of frame per each symbol period T s

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

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

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 Lg-N fading Nk- fading G-fading Multipath Intense Profile Nr=3 N f =6 CM3’s

15. 1)BER target: 2)Transmit Power: 2.5mW (Typically adopted for outdoor systems) 3)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 Coverage Ranges and Troughput (1/2)

16. Coverage Ranges and Troughput (2/2) NtNt NrNr R(mt) 1112 1226 2232 2347 3355 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) Spatial Covariance Matrix. A.Paulray, R.Nabar, D.Gore, Introduction to Space-Time Wireless Communications, Cambridge university Press, 2003.

19. Channel Impariments- Spatially Correlated Fading (2/2) Lg-N fading N t =N r =2, N f =12 CM3’s Multipath Intense Profile

20. Channel Impairments- Cross-Polarization Nakagami Fading N t =N r =2, Nf=15 Channel Model A.Paulray, R.Nabar, D.Gore, Introduction to Space-Time Wireless Communications, Cambridge university Press, 2003. CM3’s Multipath Intense Profile

21. Synchronism Recovery The ML Synchronizer block

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

23. NON-COHERENTMLSYNCHRONIZER PILOT SIGNAL GENERATOR GENERATORFOR SYNCHRONISM SYNCHRONISM RECOVERY RECOVERY MIMO UWB-IR System Model (with Poisson distributed multipath fading) SPACE-TIME CODED SPACE-TIME CODED PACKET TRANSMITTER ADOPTING OPPM MODULATION FORMAT NON-COHERENTMLDECODER

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. 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 Joint ML estimation of V and Prop.1: can be equivalently effected by only estimanting the arrivals times and their number V, that is with

26. 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 : The ML equations’ system Serial implementation

27. The expression of Cramer Rao Bound with

28. + - + Late  L Nr + (1+Ns) “early”output (1) (2) LOOP FILTER Template Signal Generator TwTw “late”output E1E1 E Nr Early  + TwTw + L1L1 T w y Nr (t) y 1 (t) X X X y j (t) dt blocco L j ML Synchronizer (Early-Late Gate serial version)

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.