In this paper, we examine how to minimize the total energy consumption of a user equipment (UE) when it transmits a finite-sized data payload of a given length. The receiving base station (BS) controls a reconfigurable intelligent surface (RIS) that can be utilized to improve the channel conditions, but only if additional pilot signals are transmitted to configure the RIS. The challenge is that the pilot resources spent on configuring the RIS increase the energy consumption, especially when small payloads are transmitted, so it must be balanced against the energy savings during data transmission. We derive a formula for the energy consumption, taking both the pilot and data transmission power into account. It also includes the effects of imperfect channel state information, the use of phase-shifts with finite resolution at the RIS, and the passive circuit energy consumption. We also consider how dividing the RIS into subarrays consisting of multiple RIS elements using the same reflection coefficient can shorten the pilot length. In particular, the pilot power and subarray size are tuned to the payload length to minimize the energy consumption while maintaining parts of the aperture gain. Our analytical results show that, for a given geometry and transmission payload length, there exists a unique energy-minimizing subarray size and pilot power. For small payloads and when the channel conditions between the BS and UE are favorable compared to the path to the RIS, the energy consumption is minimized using subarrays with many elements and low pilot transmission power. On the other hand, when the channel conditions to the RIS are better and the data payloads are large, it is preferable to use fewer elements per subarray, potentially configuring each element individually and transmitting the pilot signals with additional power.

翻译：本文研究了用户设备（UE）在传输给定长度的有限数据负载时，如何最小化其总能耗。接收基站（BS）控制一个可重构智能表面（RIS），该表面可用于改善信道条件，但前提是需传输额外的导频信号来配置RIS。挑战在于，配置RIS所消耗的导频资源会增加能耗（尤其是在传输小负载时），因此必须在导频开销与数据传输节能之间进行权衡。我们推导了能耗公式，同时考虑了导频和数据传输功率，并包含了非完美信道状态信息、RIS有限分辨率相移的使用以及无源电路能耗的影响。此外，我们还探讨了将RIS划分为由多个单元组成的子阵（采用相同反射系数）以缩短导频长度的方法。具体而言，我们针对负载长度调整导频功率和子阵尺寸，以在保持部分孔径增益的同时最小化能耗。分析结果表明，在给定几何构型和传输负载长度下，存在唯一使能耗最小化的子阵尺寸和导频功率。当传输小负载且BS与UE之间的信道条件优于至RIS的路径时，采用多单元子阵和低导频发射功率可使能耗最小化；反之，当至RIS的信道条件较好且数据负载较大时，应减少每子阵的单元数（可能单独配置每个单元）并增强导频信号的发射功率。