In this paper, we focus on large intelligent reflecting surfaces (IRSs) and propose a new codebook construction method to obtain a set of predesigned phase-shift configurations for the IRS unit cells. Since the overhead for channel estimation and the complexity of online optimization for IRS-assisted communications scale with the size of the phase-shift codebook, the design of small codebooks is of high importance. We show that there exists a fundamental tradeoff between power efficiency and the size of the codebook. We first analyze this tradeoff for baseline designs that employ a linear phase-shift across the IRS. Subsequently, we show that an efficient design for small codebooks mandates higher-order phase-shift variations across the IRS. Consequently, we propose a quadratic phase-shift design, derive its coefficients as a function of the codebook size, and analyze its performance. Our simulation results show that the proposed design yields a higher power efficiency for small codebooks than the linear baseline designs.

中文翻译：

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IRS 辅助通信中的功率效率、开销和复杂性权衡——二次相移设计

在本文中，我们专注于大型智能反射面 (IRS)，并提出了一种新的码本构造方法，以获得一组预先设计的 IRS 单元的相移配置。由于信道估计的开销和 IRS 辅助通信的在线优化的复杂性随相移码本的大小而变化，因此小码本的设计非常重要。我们表明在功率效率和码本大小之间存在基本的权衡。我们首先分析在 IRS 上采用线性相移的基线设计的这种权衡。随后，我们展示了小型码本的有效设计要求整个 IRS 进行高阶相移变化。因此，我们提出了二次相移设计，推导出其系数作为码本大小的函数，并分析其性能。我们的仿真结果表明，与线性基线设计相比，所提出的设计为小码本产生了更高的功率效率。