  Wideband communication is often expected to deal with a very wide spectrum,
which in many environments of interest includes strong interferers. Thus
receivers for the wideband communication systems often need to mitigate
interferers to reduce the distortion caused by the amplifier nonlinearity and
noise. Recently, a new architecture for communication receivers known as random
modulation mixes a signal with different pseudorandom sequences using multiple
branches of channels before sampling. While random modulation is used in these
receivers to acquire the signal at low sampling rates, the modulation sequences
used lack the ability to suppress interferers due to their flat spectra. 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 the 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
sequences to be orthogonal to each other. We show that it is difficult to find
the necessary number of sequences featuring mutual orthogonality and introduce
oversampling to the sequence set design to improve the recovery performance. We
propose an algorithm for multi-branch sequence design as a binary optimization
problem, which is solved using a semidefinite program relaxation and randomized
projection. 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.
