Compressed sampling using structurally mixed cyclic measurement matrices

The measurement matrix plays an important role in the hardware implementation of wideband sub-Nyquist sampling. In modulated wideband converter (MWC), the measurement sequences are derived from binary measurement matrix, e.g., random Bernoulli matrix, which can be easily implemented by M ×N shift registers. Utilizing the special cyclic structure, partial circulant measurement matrix only needs N shift registers, which greatly reduces the hardware complexity of the measurement circuits. However, the diminishment of randomness makes it sensitive to the signal noise and not universal to all the sparse position. In this paper, we propose the structurally mixed cyclic matrices to enhance the randomness of cyclic measurement structure. They have two parts of randomness: randomness in the generating sequence and randomness in the fixed mixture circuits. Especially, logically mixed cyclic matrix has the similar compressive performance, noisy robustness and universality with Bernoulli matrix. It is more suitable for compressed sampling of arbitrary-dimensionality spectrally sparse signal.