CSEM Scientific and Technical Report 2008

Compressed Sensing: Multi-user Impulse Radio Ultra-wideband Time of Arrival
Estimation
H. Zhan, J. Ayadi , J. Y. Le Boudec • , J. Farserotu
This study considers the application of Compressed Sensing (CS) for Time of Arrival (ToA) estimation with Impulse Radio (IR) Ultra-WideBand
(UWB) radio [1] is considered. The fine time resolution of IR UWB signals has created a vision of novel ranging and positioning applications to
augment existing narrowband systems operating in dense multipath environments. ToA estimation is used in range-based localization to help
determine the distance between the transmitter and receiver from the propagation time of the signal.
For many years, signal acquisition systems have been based
on the Nyquist-Shannon sampling theorem that states that the
number of samples needed to recover a signal without error is
twice the bandwidth. Recently, the emerging field of CS has
let to a fresh look at data acquisition: the number of required
measurements needed to reconstruct signal without error
depends on its sparsity and not on its bandwidth. Hence, if the
signal has a very sparse representation on some basis, or
more generally on some dictionary, it is possible to sample it
using very few, linear measurements.
CS theory always has two steps. (1) First step is measuring
(sampling) process. In this step, a few random measurements
(samples) are generated by projecting the sparse signal onto
a random basis. For continuous signals, CS suggests a new
framework for Analog-to-Information (A/I) conversion which
offers a promising approach to the Analog-to-Digital (A/D)
conversion bottleneck that enables sampling at a rate
comparable to the sparse signal information rate rather than
Nyquist rate. Wideband signals in many RF applications often
have a large bandwidth but only low information rate (relative
to sparsity). However, the extremely large bandwidth of the
received IR UWB signal requires very high-speed A/D
converters. The required sampling rate of A/D converters in
UWB receiver may be beyond what is feasible with state- ofthe-art
technology today. CS theory shows promise for
decreasing the required sampling rate, lowering costs and
reducing complexity. (2) The second step is the recovery
process. The sparse signal can be recovered by the random
measurements in this step.
However, most CS recovery algorithms work only under
Gaussian noise environments. To recover IR UWB signals
under Non-Gaussian noise (multi-user interference)
environments, a novel CS recovery algorithm that can be used
to estimate ToA with IR UWB radios was developed. First, a
new optimization criterion which is based on CS and Akaike
Information Criterion (AIC) was proposed. To solve this
optimization algorithm, a new iterative algorithm which is
based on the Expectation Maximization (EM) algorithm was
developed.
The CS ToA algorithm shows good performance under the
IEEE 802.15.4a channel model. Rs as the ratio of the ampling
rate to Nyquist sampling rate is defined. Figure 1 illustrates
the ranging error versus the number of iteration at different
number of users. It can be noted that there is a significant
performance improvement. To obtain good estimation, only
5 iterations are needed. When the sampling rate decreases by
20%, the ranging error is less than 0.3 meters. The ranging
error versus the different values of Rs and number of users is
shown in Figure 2, from which it can be seen that the ranging
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error decreases as the sampling rate increases. The
increasing Rs which means that the number of random
measurements increase and so the ranging error should
decrease.
Figure 1: Ranging error versus the number of iterations at different
number of users
Figure 2: Ranging error versus the different values of Rs at different
number of users.
•
LCA2, School of Computer and Communication Sciences, EPFL
[1] This project was supported (in part) by National Competence
Center in Research on Mobile Information and Communication
Systems (NCCR-MICS), a center supported by the Swiss
National Science Foundation; www.mics.org