Design of spectrally shaped binary sequences via randomized convex relaxations

In wideband communication one often aims to detect a weak signal received together with a strong interferer. One can design a spectrally shaped sequence to be convolved with the received signal featuring a bandpass for the message and a notch for the interferer. Unfortunately, when the sequence must be quantized, commonly used constrained optimization schemes (e.g., semidefinite programs) are not amenable due to the spectrum distortion from quantization. We explore an alternative method that applies random projections on the solution of the semidefinite program. Our experimental evidence shows that our proposed method succeeds in finding suitable spectrally shaped sequences.