Compressed Sensing via Dimension Spread in Dimension-Restricted Systems

Compressed sensing (CS) is applied to capture signals at sub-Nyquist rate when the sensing matrix satisfies the restricted isometry property (RIP). When in a dimension-restricted system which has small row dimension and not so good coherence, the RIP and measurement bound will not be satisfied, and compressed sensing can not be applied directly. In this letter, we propose the dimension spread CS to the dimension-restricted system by directed dimension spread and diversity dimension spread, which make the compressed sensing applicable. The spread dimension bounds for the proposed algorithms are deduced to guarantee exact recovery which are also proved by simulations. Meanwhile, the experimental comparisons for the directed dimension spread CS and diversity dimension spread CS are given and different CS recovery algorithms are carried out to show the effectiveness of the proposed algorithms in the dimension-restricted system. The diversity dimension spread CS outperforms the directed dimension spread CS for its effective dimension spread and diversity. The proposed algorithms can be directly applied in channel estimation and multiuser detection in overload system.