**6. Conclusion**

In this chapter, we proposed a pre-filtering method for UWB channel estimation based on the theory of CS, whose measurement matrix is just a Toeplitz matrix, and the channel estimation accuracy is improved. The method proposed in this paper avoided the magnification to the noise. Thus when the reconstructed signal is used as a referent template at the receiver in the noise realization, a better BER performance can be achieved.

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The correlation detector for UWB communication discussed in this paper employs the channel estimates to the conventional correlation detection directly, while the design of the whole system combining the channel estimation and signals detection will be a further research. Moreover, it is the key point of improving the BER performance of the correlation detector to search for a CS reconstruction method, which can successfully recover the referent template under the noise realization and fewer measurements with overwhelming probability. In addition, we analyze the choices of reconstruction algorithms using several simulations. Both the OMP and the BPDN algorithms are compared to the Dantzig selector for different signal noise ratio to give the opinions for choosing suitable reconstruction algorithms.

Admittedly, there are several other theoretical and practical aspects of UWB channel estimation methods based on compressed sensing that need discussing in future. Below, however, we briefly comment on some of these aspects. First, the different types of measurement matrix according to the UWB channels should be in further study. In this paper, we do some attempts to construct the quasi-Toeplitz matrix developing the model of UWB channel estimator. Somewhat similar theoretical arguments can be made to argue the other type of measurement matrix to get better estimation performance. Second, extensive numerical simulations carried out in literatures for a number of CS estimators have established that the performance of CS estimation methods is markedly superior to that of traditional methods based on LS criterion. However, the nontraditional methods based on MUSIC and ESPRIT algorithms are not optimal for estimating sparse channels. This is because it is possible for a channel to have a small number of resolvable paths but still have a very large number of underlying physical paths, especially in the case of diffuse scattering. So the two algorithms can be employed combining with the compressed sensing framework. Third, one expects the representation of real-world multipath channels in certain bases to be only effectively sparse. The channel model and channel parameters are localized with the perfect channel model in this paper. Finally, and perhaps most importantly for the success of the envisioned wireless systems, the CS can be leveraged to design efficient overcomplete dictionary for estimating sparse UWB channels.
