Systems and methods in accordance with embodiments of the invention utilize a CS architecture based on a sub-linear time recovery process (with reduced memory requirements). In several embodiments, a novel structured measurement matrix is exploited during signal acquisition allowing the use of a recovery process based on relatively simple computational primitives making it more amenable to implementation in a fully-integrated form. One embodiment of the invention includes an analog front end configured to receive an analog input signal, and CS sampling circuitry connected to an output of the analog front end and configured to generate a plurality of measurements using a structured measurement matrix, where each row of the structured measurement matrix is generated using a different predetermined check node. In addition, the CS sampling circuitry is configured to generate the plurality of measurements at a rate that is less than the Nyquist rate of the analog input signal.