1. Bandwidth Scaling in UWB Communications Dana Porrat and David Tse University of California, Berkeley

2. Capacity of Fading Channels UWB over Multipath channel Combine Duty Cycle and spreading modulations? Theory –Kennedy, Gallager 1968 FSK + Duty Cycle achieves Spreading Modulations –DSSS no Duty Cycle  zero capacity Telatar & Tse, Médard & Gallager, Subramanian & Hajek

3. The UWB Channel Delay [nsec] [Volt] Measurement Bandwidth ~1 GHz

4. Multipath Channel Model Block constant: coherence time Delay spread L independent paths

5. How many paths in channel? Antennas separation up to 10 m, LOS and NLOS Strong paths counted: 60-90% of power Number of paths increases with Bandwidth

6. DSSS Capacity in Multipath Channel No Duty Cycle Telater & Tse: With Duty Cycle: Capacity depends on scaling of number of paths with W

7. Direct Sequence Spread Spectrum

8. DSSS Capacity with Duty Cycle Theorem 1: DSSS systems with duty cycle achieve for if Theorem 2: DSSS systems with duty cycle, where the receiver knows the path delays achieve for if

9. Parameters: W=10 GHz Tc=0.1 msec Td=200 nsec Why does duty cycle make a difference? Because of the channel uncertainty penalty Number of Paths Data Rate [bits/sec] C(AWGN) DSSS with Coherence Time Duty Cycle (LB) DSSS with No Duty Cycle (UB)

10. Parameters: W=10 GHz Tc=0.1 msec Td=200 nsec L=100 Duty Cycle for Spread Spectrum Duty Cycle Extremely Bursty: Infrequent Transmission Not so Bursty: Transmit on 1 coherence time of 500 C(AWGN) Data Rate [bits/sec] DSSS Capacity (LB)

11. Duty Cycle for Spread Spectrum Gain Uncertainty Penalty (UB) C(AWGN) Delay Uncertainty Penalty (UB) Extremely Bursty: Infrequent Transmission Not so Bursty: Transmit on 1 coherence time of 500 Duty Cycle DSSS Capacity (LB) Data Rate [bits/sec] Parameters: W=10 GHz Tc=0.1 msec Td=200 nsec L=100

12. Duty Cycle for Spread Spectrum DSSS with Perfect Channel Knowledge Extremely Bursty: Infrequent Transmission Not so Bursty: Transmit on 1 coherence time of 500 Gain Uncertainty Penalty (UB) C(AWGN) DSSS Capacity (LB) Delay Uncertainty Penalty (UB) Duty Cycle Data Rate [bits/sec] Parameters: W=10 GHz Tc=0.1 msec Td=200 nsec L=100

13. Pulse Position Modulation - PPM

14. DS Spread Spectrum vs. PPM Parameters: W=10 GHz Tc=0.1 msec Td=200 nsec Number of Paths Data Rate [bits/sec] PPM with Coherence Time Duty Cycle (UB) C(AWGN) DSSS with Coherence Time Duty Cycle (LB)

15. Duty Cycle for Two Modulations Duty Cycle Data Rate [bits/sec] C(AWGN) Extremely Bursty: Infrequent Transmission Not so Bursty: Transmit on 1 coherence time of 100 PPM (UB) DSSS (LB) DS Spread Spectrum allows a lower duty cycle because it is more efficient spectrally. Parameters: W=10 GHz Tc=0.1 msec Ts=Td=200 nsec L=100

16. DS Spread Spectrum vs. PPM PPM: Low data rate per Tc  has to transmit often  Large Penalty DSSS: High data rate per Tc  Infrequent transmission  Small Penalty

17. PPM Capacity with Duty Cycle Theorem 3: PPM systems with duty cycle, where the receiver knows the path delays achieve for if Theorem 4 (inverse): PPM systems with duty cycle, where the receiver knows the path delays have for if

18. DS Spread Spectrum vs. PPM 0 ? DS Spread SpectrumPPM W W L L Spectral efficiency determines max number of paths that can be handled by system Delays known, gains unknown

19. The Message Direct sequence spread spectrum and PPM achieve the channel capacity for if there are not too many channel paths, because duty cycle reduces the channel uncertainty penalty In situations that require low duty cycle spectral efficiency is key

20. Extra Slides

21. How Often to Transmit? Duty Cycle Extremely Bursty: Infrequent Transmission Not so Bursty: Transmit on 1 coherence time of 500 Calculated With L=100 Paths C(AWGN) Data Rate [bits/sec]