This letter proposes highly accurate closed-form approximations to channel distributions of two different reconfigurable intelligent surface (RIS)-based wireless system setups, namely, dual-hop RIS-aided (RIS-DH) scheme and RIS-aided transmit (RIS-T) scheme. Differently from previous works, the proposed approximations reveal to be very tight for arbitrary number ${N}$ of reflecting metasurface’s elements. Our findings are then applied to the performance analysis of the considered systems, in which the outage probability, bit error rate, and average channel capacity are derived. Results show that the achievable diversity orders $G_{d}$ for RIS-DH and RIS-T schemes are $N-1< G_{d}< N$ and ${N}$ , respectively. Furthermore, it is revealed that both schemes can not provide the multiplexing gain and only diversity gains are achieved. For the RIS-DH scheme, the channels are similar to the keyhole multiple-input multiple-output (MIMO) channels with only one degree of freedom, while the RIS-T scheme is like the transmit diversity structure.

中文翻译：

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RIS 辅助无线系统信道分布的精确闭式近似

这封信对两种不同的基于可重构智能表面 (RIS) 的无线系统设置的信道分布提出了高度准确的封闭形式近似，即双跳 RIS 辅助 (RIS-DH) 方案和 RIS 辅助传输 (RIS-T) ） 方案。与以前的工作不同，所提出的近似值显示对于任意数字非常紧 ${N}$ 反射超表面的元素。然后将我们的发现应用于所考虑系统的性能分析，其中推导出中断概率、误码率和平均信道容量。结果表明，可实现的多样性阶数 $G_{d}$ 对于 RIS-DH 和 RIS-T 方案是 $N-1< G_{d}< N$ 和 ${N}$ ， 分别。此外，揭示了两种方案都不能提供复用增益，只能实现分集增益。对于RIS-DH方案，信道类似于锁孔多输入多输出(MIMO)信道，只有一个自由度，而RIS-T方案则类似于发射分集结构。