All-spectrum Digital Waveform Design via Bit Flipping

We consider the problem of interference avoidance via all-spectrum digital waveform design in wireless communication links that operate in multipath fading environments. Specifically, we select a square-root raised cosine pulse-shaping signal that occupies all-hardware accessible frequency bandwidth. We propose an algorithm that optimizes a sequence of $L$ sign/phase-shifted repeats of the basic shaping pulse to form the all-spectrum digital waveform that will carry our information symbols. The sequence can take values from either binary or quaternary alphabets. We propose to optimize the specific values of the sign/phase shift sequence via bit flipping such that the signal-to-interference-plus-noise ratio (SINR) at the output of the max-SINR linear receiver is maximized at any given time. The complexity of the proposed algorithm is O($L$3) and is independent of the alphabet size. Simulation studies demonstrate that the proposed digital waveform designs achieve practically the same SINR post-filtering performance with max-SINR optimal waveforms designed via exhaustive search.