Performance analysis of partial segmented compressed sampling

Recently, a segmented AIC (S-AIC) structure that measures the analog signal by K parallel branches of mixers and integrators (BMIs) was proposed by Taheri and Vorobyov (2011). Each branch is characterized by a random sampling waveform and implements integration in several continuous and non-overlapping time segments. By permuting the subsamples collected by each segment at different BMIs, more than K samples can be generated. To reduce the complexity of the S-AIC, in this paper we propose a partial segmented AIC (PS-AIC) structure, where K branches are divided into J groups and each group, acting as an independent S-AIC, only works within a partial period that is nonoverlapping in time. Our structure is inspired by the recent validation that block diagonal matrices satisfy the restricted isometry property (RIP). Using this fact, we prove that the equivalent measurement matrix of the PS-AIC satisfies the RIP when the number of samples exceeds a certain threshold. Furthermore, the recovery performance of the proposed scheme is developed, where the analytical results show its performance gain when compared with the conventional AIC. Simulations verify the effectiveness of the PS-AIC and the validity of our theoretical results. & 2013 Elsevier B.V. All rights reserved.