**Theory**

- Channel measurement and modelling
- ISI effect is dominant, compared to fading effect. Since the pulse is very short, the ISI or echoing effect (superposition of replicas) is very strong.
- Saleh-Valenzuela Model (S-V)
- For UWB channels, since the transmitted pulse is so short that every multipath is resolvable (i.e., different replicas/echoes do not collide in time), there is no need to use equalizer to remove ISI. Perfect equalization only gives less than 1 dB gain over the non-equalization case. (See Arjunan Rajeswaran's ICC 2003 paper)

For an ultra-wideband (UWB) system, since the signal bandwidth and the sampling rate are high, there are only a small number of paths that contribute to a resolvable tap/bin. So central limit theorem does not hold and we do not see uniformly distributed phase. It is observed in actual measurements that the phase only takes values of 0 or \pi.

Measurement results show that the amplitudes can be modeled as lognormal-distributed r.v.'s. The reason why the amplitude does not follow a Rayleigh distribution, is that central limit theorem does not hold due to a small number of paths associated with a resolvable bin. Two Poisson models are employed in the modeling of the arrival times of resolvable paths. The first Poisson model is for the first path of each path-cluster and the second Poisson model is for the paths (or rays) within each cluster. The power delay profile is modeled by a double exponential decay model; i.e., the average powers of the first paths of path-clusters follow an exponential-decaying law, and the average powers of the paths within each cluster also follow an exponential-decaying law.

- Modulation and detection
- Interference and capacity
- Regulatory issues
- Positioning services
- Receiver architectures
- In UWB system

- Integrated circuits and antennas
- Field trials and measurements

Since lognormal distribution is statistically better than Rayleigh distribution for the same SNR, i.e., lognormal has a larger tail than Rayleigh, we need fewer taps in the RAKE receiver to achieve the same BER performance.

**Applications**

- RADAR
- Positioning
- Ad-hoc networks
- Personal Area Networks
- RF tags
- Tools for system analysis
- Integrated circuit design and implementation