Binary Sequence Set Design for Interferer Rejection in Multi-Branch Modulation

Dian Mo, Marco F. Duarte

Abstract: Wideband communication is often expected to deal with a very wide spectrum, thus receivers for the wideband communication systems often need to mitigate interferers to reduce the distortion caused by the amplifier nonlinearity and noise. Recently, the random modulation mixes a signal with different pseudorandom sequences using multiple branches of channels before sampling. In previous work, we introduced the design of a single spectrally shaped binary sequence that mitigates interferers to replace the pseudorandom sequence in a channel. However, the designed sequences cannot provide a stable recovery achieved by pseudorandom sequence approaches. In this paper, we extend our previous sequence design to guarantee stable recovery by designing a set of spectrally shaped sequences to be orthogonal to each other. We show that it is difficult to find the necessary number of sequences (equal to the sequence length) featuring mutual orthogonality and introduce oversampling to the sequence set design to improve the recovery performance of the designed sequences. We propose an algorithm for multibranch sequence design as a binary optimization problem, which is solved using a semidefinite program relaxation and randomized projection. In addition, while it is common to model narrowband interferers as a subspace spanned by a subset of elements from the Fourier basis, we show that the Slepian basis provides an alternative and more suitable compact representation for signals with components contained in narrow spectrum bands. Numerical experiments using the proposed sequence sets show their advantages against pseudorandom sequences and our previous work.