An Introduction to Compressed Sensing

Conventional signal sampling is that the sampling rate must be at least twice the maximum frequency presented in the signal. In the field of signal sampling or compressed, Shannon theorem plays an implicit role. However, the signal is uniformly sampled at or above the Nyquist rate. Thus, this sampling is not a effective approach. Fortunately, Candes and Tao, Donoho have introduced a new sampling theory: Compressed sensing, which was beyond Nyquist sampling theory. CS theory asserts that one can recover certain signals and images from far fewer samples or measurments than traditional methods use. To make this possible, CS relies on two priciples: signal sparsity and incoherence of measurment matrix.

On channel estimation problem, we can introduce CS theory. In general, there always exist a large delay spread and only has a few dominant taps in high data rate wireless communication. that is to say, this multipath channel has sparsity. In the process of channel estimation, training matrix can be designed Toeplitz structre which satisfies Restrict Isometry property (RIP).

How to exploit the channel prior information

Today, my supervisor dicussed with me about the channel estimation problem by exploiting channel prior information.
Accoding to our experiment of wireless communication, we find that channel nature property can be discribed as two part: the first part is overall zero taps and the second is dominant by a few nonzero taps. Thus, we can employ this information on channel estimation. If we search a proper length of overall zero, we will model channel impluse response properly. If you have some interest, we can discuss it in detail or refer to my paper: partial sparse channel estimation by expoiting prior information. My email is gui@uestc.edu.cn.

An promising theory: Matrix completion

Matrix completion, which was proposed by Candes and Tao, is a new matrix recovery technqiue which is come from compressed sensing (CS) theory. In general, Matrix reconstruction from few entries is impossiple. However, there exist recovery possiblity, if we know the Matrix has low-rank perpety. As Candes said, matrix completion will become a hot topic which can be employed many areas such as GPS and MIMO channel estimation.

MIMO channel estimation is a challenge task, especially in frequency-selective fading channel. Thus, MIMO channel estimation employ matrix completion which based on CS theory is a new idea. But, how we can do it? This is my research at present. If you have some suggestion about it, don't forget tell me. Waiting for your commances. Many thanks.

One of my reseach topics: MIMO Channel Estimation

The importance of wireless channel estimation and understanding channel knowledge for successful design of communication systems can never be overstated. In eariler of channel estimation, the wireless medium was viewed as an obstacle or challenge in designing reliable communication links. However, decades of research and subsequent insights have change this paradigm. Modern day communcation systems rather tend to exploit the channel knowledge for increasing system reliablity and thoughtput by employing techniques such as MIMO, which is the key for extending the limits of existing communication systems. Thus, MIMO channel estimation become a most important challenge because it must be to overcome the highly frequency selective of the fading channel.