A Randomized Projection Relaxed Method for Mixing Function Design to Enhance MWC Performance

In the Modulated Wideband Converter (MWC), a Sub-Nyquist sampling scheme for wideband signals, the binary mixing functions play a pivotal role in performance, particularly in challenging low SNR conditions. A major difficulty of MWC in this condition is the aggregation of noise from the whole spectrum at the baseband, caused by the aliasing process over spectrum slots, which is the result of multiplying the input signal with binary mixing functions. In this article, we present two methods for the calculation of these mixing functions based on convex optimization, but in a different way from previous research. Instead of randomized projection for dimension reduction to satisfy a built-in rank-1 matrix constraint, we aim to directly obtain the rank-1 matrix. This way, we get rid of the disadvantages of the randomized projection method, such as instability in regenerating an answer while repeating the algorithm, and infeasibility of the problem in an insufficient number of iterations. In comparison with the previous works, the experimental results indicate that applying the designed sequences to the MWC structure performs remarkably better in terms of lower recovery error and higher correlation of the recovered signal with the main one.