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UWB Channels – Capacity and Signaling Department 1, Cluster 4 Meeting Vienna, 1 April 2005 Erdal Ar ı kan Bilkent University. Outline. UWB Channels Definition Energy, power constraints Capacity estimates Conclusions Suggestions for future research Time Reversal: A signaling scheme for UWB

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  1. UWB Channels – Capacity and SignalingDepartment 1, Cluster 4 Meeting Vienna, 1 April 2005Erdal ArıkanBilkent University

  2. Outline • UWB Channels • Definition • Energy, power constraints • Capacity estimates • Conclusions • Suggestions for future research • Time Reversal: A signaling scheme for UWB • Definition • TR-UWB research problems • Further issues and related research problems

  3. Definition of the UWB Channel • Defined by an FCC ruling (2002). • Bandwidth: 3.1–10.6 GHz • Radiated power limited to -41.3 dBm/MHz in any 1 MHz bandwidth • Minimum 500 MHz bandwidth

  4. UWB Channel Indoor Emissions Limit

  5. UWB Energy At full transmitted power of –41.3 dBm/MHz over the entire 7.5 GHz, the total transmitted energy is 0.56 mW.  UWB systems are not energy limited. Should one use the entire available bandwidth?

  6. To spread or not to spread? • If transmitter energy is fixed, spreading the energy uniformly across all available degrees of freedom of a wideband fading channel leads to collapse of achievable rates, due to deterioration of channel estimates. (Médard- Gallager, 2002; Telatar-Tse, 2000; Subramanian- Hajek, 2002) • In the UWB channel model, transmitter’s available energy is allowed to increase as more degrees of freedom are used, so there is no collapse of achievable rates. • Spreading in UWB channels is beneficial. Other considerations such as interference to and from other users may dictate the actual bandwidth usage.

  7. UWB Range and Interference • Thermal noise power at room temperature is N0= -114 dBm/MHz. • UWB emissions are allowed to be at PT = - 41.3 dBm/MHz. • Assuming isotropic antennas, received power at distance d is where  is the wavelength, 2.8 cm <  < 9.7 cm. • For PR = N0, d = 343 , which is 9.6 – 33.3 m.

  8. IEEE UWB Channel Model z(t) y(t) s(t) x(t) + h(t) • The channel is modeled as an linear filter with additive white Gaussian noise. • Measurements show coherence times of Tc = 200 s and delay spreads of Td = 200 ns.

  9. Saleh-Valenzula Model

  10. IEEE UWB Model: Parameter sets CM1-4

  11. Sample CM1 realization (resolution 167 ps)

  12. Sample CM4 realization (resolution 167 ps)

  13. Frequency Domain Channel Model • A number of parallel correlated channels where Gi is the channel coefficient at frequency i, Zi~CN(0,No). • The number of channels is given by the time-bandwidth product K=TW where W is the RF bandwidth and T is the signaling period.

  14. A lower bound on UWB capacity • Use the inequality and take Xi~CN(0,s). Then, where gi is the inverse DFT of Gi . • Telatar and Tse (2000) bound is similar with the restriction |gi|= const., but without the factor of 2.

  15. Case study • Channel model: CM4 • Range: 10 m • SNR at receiver: –3.88 dB • Coherence time: Tc = 200s • RF bandwidth: W=0.5 to 6 GHz in steps of 0.5 • Sampling period: Ts = 1/W • Carrier frequency: fc = 5.092 GHz • Long frame length: T=200s • Short frame length: T=1s

  16. Rate vs. Bandwidth, Long packets (T=200s)

  17. Rate vs. Bandwidth, Short Packets (T=1s)

  18. Conclusions • “Peaky” signaling is not required for UWB communications since only the power-spectral density is constrained, not the total power. • Achievable rates by Gaussian inputs come close to channel capacity if the frame length is comparable to channel coherence time of 200s. Penalty for not knowing the channel is negligible. • On the other hand, for short packets, training overhead is very significant.  What are good signaling schemes for short frames?

  19. Time Reversal and UWB • By reversibility, hAB(t) = hBA(t). • B receives hAB(-t)hAB(t), which is likely to be peaky. • C receives hAB(-t)hAC(t), which is unlikely to be peaky if C is sufficiently far away from B. • hXY(t) likely to have low coherence in time and space for high delay-bandwidth product channels, such as the UWB channel. B sends an impulse, A measures channel response hBA(t) A B A transmits data using pulses hBA(-t)

  20. UWB-TR Research Topics • Achievable rates by the TR signaling • Effect of noisy measurements on TR signaling • Combining MIMO and TR • TR signaling with multiple transmitter-receiver pairs, each within ‘hearing’ distance of each other, and the sum of achievable rates

  21. Further UWB Research Topics • Interference problems • How to deal with narrowband interference to a UWB system. An interference signal of bandwidth10 MHz reduces the UWB channel coherence time to 10 ns from 200 s. • Co-existence of UWB with other systems such as 802.11.a. • Issues related to RF front-end • Front-end amplifier saturation due to a strong interfering signal • Signal design taking into consideration the amplifier nonlinearities

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