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.

中文翻译：

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多分支调制中干扰抑制的二进制序列集设计

宽带通信通常需要处理非常宽的频谱，因此宽带通信系统的接收机通常需要减轻干扰以减少放大器非线性和噪声引起的失真。最近，随机调制在采样前使用多个信道分支将信号与不同的伪随机序列混合。在之前的工作中，我们引入了单个频谱形状二进制序列的设计，该序列可以减轻干扰以替换信道中的伪随机序列。然而，设计的序列不能提供通过伪随机序列方法实现的稳定恢复。在本文中，我们扩展了我们之前的序列设计，通过设计一组彼此正交的频谱形状序列来保证稳定的恢复。我们表明很难找到具有相互正交性的必要数量的序列（等于序列长度），并在序列集设计中引入过采样以提高设计序列的恢复性能。我们提出了一种将多分支序列设计作为二元优化问题的算法，该算法使用半定程序松弛和随机投影来解决。此外，虽然通常将窄带干扰建模为由来自傅立叶基的元素子集跨越的子空间，但我们表明，Slepian 基为具有包含在窄频带中的分量的信号提供了一种替代且更合适的紧凑表示。使用所提出的序列集的数值实验显示了它们相对于伪随机序列和我们以前的工作的优势。