Abstract
Energy efficiency (EE) is one of the main design criterion for the current and next generation of communication systems. Whereas, reflective intelligent surface (RIS) is foreseen to be a key enabler of the next generation of communication systems by facilitating the propagation of radio frequency signals, and in turn, possibly improving its spectral efficiency (SE) and/or EE. This paper investigates both the EE and SE of a multi-hop multi-antenna RIS-aided communication system through its fundamental trade-off. To this end, we first provide a generic and accurate closed-form approximation (CFA) of the SE (ergodic capacity) for multi-hop multi-antenna RIS-aided systems and verify its accuracy through simulations for various numbers of antennas/phase shifters and hops. Based on this expression, we then derive a novel and accurate CFA of the fundamental EE-SE trade-off for multi-hop multi-antenna RIS-aided systems. We subsequently use our CFA to analyse the variations of the EE as a function of the number of antennas/phase shifters and hops when considering a realistic power consumption model. It turns out that increasing the number of hops is more energy efficient than increasing the number of antennas/phase shifters and that multi-hop communication with RIS is not necessarily always more energy efficient than classic multi-antenna communication, as it is for instance the case in a simple device-to-device communication scenario.