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SUMMARY Due to the sparse structure of ultra‐wideband (UWB) multipath channels, there has been a considerable amount of interest in applying the compressive sensing (CS) theory to UWB channel estimation. The main consideration of the related studies is to propose different implementations of the CS theory for the estimation of UWB channels, which are assumed to be sparse. In this study, we investigate the suitability of standardized UWB channel models to be used with the CS theory. In other words, we question the sparsity assumption of realistic UWB multipath channels. For that, we particularly investigate the effects of IEEE 802.15.4a UWB channel models and the selection of channel resolution both on channel estimation and system performances from a practical implementation point of view. In addition, we compare the channel estimation performance with the Cramer‐Rao lower bound for various channel models and number of measurements. The study shows that although UWB channel models for residential environments (e.g., channel models CM1 and CM2) exhibit a sparse structure yielding a reasonable channel estimation performance, channel models for industrial environments (e.g., CM8) may not be treated as having a sparse structure due to multipaths arriving densely. Furthermore, it is shown that the sparsity increased by channel resolution can improve the channel estimation performance significantly at the expense of increased receiver processing. Copyright © 2013 John Wiley & Sons, Ltd.

In wideband spectrum sensing, compressive sensing approaches have been used at the receiver side to decrease the sampling rate, if the wideband signal can be represented as sparse in a given domain. While most studies consider the reconstruction of primary user's signal accurately, it is indeed more important to analyze the presence or absence of the signal correctly. Furthermore, these studies do not consider the achievable lower bounds of reconstruction error and how well the selected method performs correspondingly. Motivated by these issues, we investigate in detail the primary user detection performance of Bayesian compressive sensing (BCS) approach in this paper. Accordingly, we (i) determine the BCS signal reconstruction performance in terms of mean-square error (MSE), compression ratio and signal-to-noise ratio (SNR), and compare it with the conventionally used basis pursuit approach, (ii) determine how well BCS performs compared with the Bayesian Cramer-Rao lower bound (BCRLB) of the signal reconstruction error, and (iii) assess the probability of detection performance of BCS for various SNR and compression ratio values. The results of this study are important for determining the achievable performance of BCS based spectrum sensing.