Random circulant orthogonal matrix based Analog Compressed Sensing

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Conference Proceeding
GLOBECOM - IEEE Global Telecommunications Conference, 2012, pp. 3605 - 3609
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Analog Compressed Sensing (CS) has attracted considerable research interest in sampling area. One of the promising analog CS technique is the recently proposed Modulated Wideband Converter (MWC). However, MWC has a very high hardware complexity due to its parallel structure. To reduce the hardware complexity of MWC, this paper proposes a novel Random Circulant Orthogonal Matrix based Analog Compressed Sensing (RCOM-ACS) scheme. By circularly shifting the periodic mixing function, the RCOM-ACS scheme reduces the number of physical parallel channels from m to 1 at the cost of longer processing time, where m is in the order of several dozen to several hundred in MWC. It is proved that the m×M measurement matrix of RCOM-ACS scheme satisfies the Restricted Isometry Property (RIP) condition with probability 1-M-O(1)when m = O(rlog2Mlog3r), where M is the length of the periodic mixing function, r denotes the sparsity of the input signal. Furthermore, to make a good tradeoff between processing time and hardware complexity, a short processing time RCOM-ACS scheme is proposed in this paper. Simulation results show that, the proposed schemes outperform MWC in terms of recovery performance. © 2012 IEEE.
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