16-08-2012, 02:48 PM
Application of Compressive Sensing to Sparse Channel Estimation
[attachment=31691]
Abstract
Compressive sensing is a topic that has recently
gained much attention in the applied mathematics and signal
processing communities. It has been applied in various areas,
such as imaging, radar, speech recognition, and data acquisition.
In communications, compressive sensing is largely accepted for
sparse channel estimation and its variants. In this paper we highlight
the fundamental concepts of compressive sensing and give an
overview of its application to pilot aided channel estimation. We
point out that a popular assumption – that multipath channels are
sparse in their equivalent baseband representation – has pitfalls.
There are overcomplete dictionaries that lead to much sparser
channel representations and better estimation performance.
INTRODUCTION
What is Compressive Sensing
Since the term compressive sensing was coined a few years
ago [1], [2], this subject has been under intensive investigation
[3]–[5]. It has found broad application in imaging, data
compression, radar, and data acquisition to name a few (see
overview in [4], [5]).
In a nutshell, compressive sensing is a novel paradigm
where a signal that is sparse in a known transform domain can
be acquired with much fewer samples than usually required
by the dimensions of this domain. The only condition is that
the sampling process is “incoherent” with the transform that
achieves the sparse representation and “sparse” means that
most weighting coefficients of the signal representation in
the transform domain are zero. While it is obvious that a
signal that is sparse in a certain basis can be fully represented
by an index specifying the basis vectors corresponding
to non-zero weighting coefficients plus the coefficients –
determining which coefficients are non-zero would usually
involve calculating all coefficients.
Underwater Acoustic Channel
UWA channels are different from radio channels, due to
the fundamental differences between acoustic waves and radio
waves. For once, the practical bandwidths in UWA channels
are limited, due to the absorption of acoustic energy at high
frequencies. Also, the speed of sound is only about 1500 m/s
in water, while electromagnetic waves propagate at the speed
of light in air (3 × 108 m/s). As a result, UWA channels
usually have a long delay spread, even in relation to their (low)
sampling rate, for example about 20 ms in typical shallow
water environments along with a 10 kHz bandwidth, leading
to 200 taps in the baseband channel. While channel variations
happen at a similar rate to urban radio environments (tens
or hundreds of milliseconds), the symbol duration in UWA
systems is orders of magnitudes larger than that in radio
systems.
CONCLUSION
Compressive sensing has made a lasting impression in the
signal processing community, where besides an intriguing
theory it offers versatile applicability to many challenging
problems. In the communications community the application
of compressive sensing has been mainly on sparse channel
estimation for various types of channels, with extensions to
multiuser and cognitive radio systems. In this paper, we illustrated
the application of the compressive sensing techniques
using a concrete example of multicarrier underwater acoustic
communications. We showed that an overcomplete dictionary
leads to much sparser representation of a multipath channel
relative to the baseband tap-based channel model.
[attachment=31691]
Abstract
Compressive sensing is a topic that has recently
gained much attention in the applied mathematics and signal
processing communities. It has been applied in various areas,
such as imaging, radar, speech recognition, and data acquisition.
In communications, compressive sensing is largely accepted for
sparse channel estimation and its variants. In this paper we highlight
the fundamental concepts of compressive sensing and give an
overview of its application to pilot aided channel estimation. We
point out that a popular assumption – that multipath channels are
sparse in their equivalent baseband representation – has pitfalls.
There are overcomplete dictionaries that lead to much sparser
channel representations and better estimation performance.
INTRODUCTION
What is Compressive Sensing
Since the term compressive sensing was coined a few years
ago [1], [2], this subject has been under intensive investigation
[3]–[5]. It has found broad application in imaging, data
compression, radar, and data acquisition to name a few (see
overview in [4], [5]).
In a nutshell, compressive sensing is a novel paradigm
where a signal that is sparse in a known transform domain can
be acquired with much fewer samples than usually required
by the dimensions of this domain. The only condition is that
the sampling process is “incoherent” with the transform that
achieves the sparse representation and “sparse” means that
most weighting coefficients of the signal representation in
the transform domain are zero. While it is obvious that a
signal that is sparse in a certain basis can be fully represented
by an index specifying the basis vectors corresponding
to non-zero weighting coefficients plus the coefficients –
determining which coefficients are non-zero would usually
involve calculating all coefficients.
Underwater Acoustic Channel
UWA channels are different from radio channels, due to
the fundamental differences between acoustic waves and radio
waves. For once, the practical bandwidths in UWA channels
are limited, due to the absorption of acoustic energy at high
frequencies. Also, the speed of sound is only about 1500 m/s
in water, while electromagnetic waves propagate at the speed
of light in air (3 × 108 m/s). As a result, UWA channels
usually have a long delay spread, even in relation to their (low)
sampling rate, for example about 20 ms in typical shallow
water environments along with a 10 kHz bandwidth, leading
to 200 taps in the baseband channel. While channel variations
happen at a similar rate to urban radio environments (tens
or hundreds of milliseconds), the symbol duration in UWA
systems is orders of magnitudes larger than that in radio
systems.
CONCLUSION
Compressive sensing has made a lasting impression in the
signal processing community, where besides an intriguing
theory it offers versatile applicability to many challenging
problems. In the communications community the application
of compressive sensing has been mainly on sparse channel
estimation for various types of channels, with extensions to
multiuser and cognitive radio systems. In this paper, we illustrated
the application of the compressive sensing techniques
using a concrete example of multicarrier underwater acoustic
communications. We showed that an overcomplete dictionary
leads to much sparser representation of a multipath channel
relative to the baseband tap-based channel model.