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

UWB Channels – Capacity and Signaling

Department 1, Cluster 4 Meeting Vienna, 1 April 2005

Erdal 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

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

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.

2

4

dPP

TR

8

IEEE UWB Channel Model

• 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.

+h(t)x(t) y(t)

z(t)

s(t)

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.

iiii ZXGY 1,...,0 Ki

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.

)|;()|;(

)|;();,();(

XYGIGYXI

XYGIYGXIYXI

15

Case study

• Channel model: CM4

• Range: 10 m

• SNR at receiver: –3.88 dB

• Coherence time: Tc = 200s

• 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=200s

• Short frame length: T=1s

16

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

17

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

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 200s. 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 transmits data using pulses hBA(-t)

A B

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