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UWB Channels – Capacity and Signaling Department 1, Cluster 4 Meeting Vienna, 1 April 2005 Erdal Arıkan Bilkent University

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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

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

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4 UWB Channel Indoor Emissions Limit

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5 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? UWB Energy

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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, transmitters 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.

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7 UWB Range and Interference Thermal noise power at room temperature is N 0 = -114 dBm/MHz. UWB emissions are allowed to be at P T = dBm/MHz. Assuming isotropic antennas, received power at distance d is where is the wavelength, 2.8 cm < < 9.7 cm. For P R = N 0, d = 343, which is 9.6 – 33.3 m.

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

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9 Saleh-Valenzula Model

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10 IEEE UWB Model: Parameter sets CM1-4

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11 Sample CM1 realization (resolution 167 ps)

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12 Sample CM4 realization (resolution 167 ps)

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13 Frequency Domain Channel Model A number of parallel correlated channels where G i is the channel coefficient at frequency i, Z i ~ CN(0,N o ). 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.

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

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

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

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

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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?

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19 Time Reversal and UWB By reversibility, h AB (t) = h BA (t). B receives h AB (-t) h AB (t), which is likely to be peaky. C receives h AB (-t) h AC (t), which is unlikely to be peaky if C is sufficiently far away from B. h XY (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 h BA (t) A transmits data using pulses h BA (-t) AB

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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

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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 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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