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UWB Channels: Capacity and Signaling

This document discusses the definition of UWB channels, energy and power constraints, capacity estimates, and future research suggestions in UWB signaling. It also explores the concept of Time Reversal as a signaling scheme for UWB. Additionally, it highlights various research topics related to UWB, including interference problems, coexistence with other systems, and RF front-end issues.

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UWB Channels: Capacity and Signaling

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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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