In a reconfigurable intelligent surface (RIS)-aided downlink, channel estimation errors due to noise during training lead to a sub-optimal RIS phase-shift configuration. This degrades the RIS beamforming gain. Furthermore, the errors lead to an imperfect estimate of the degraded beamforming gain itself. We analyze the cumulative impact of these errors on the achievable rate. We present two innovations that make our analysis tractable and insightful. First, we present a novel approximation for the effective downlink channel gain in the presence of estimation errors. Second, we prove that the central limit theorem applies to the effective downlink channel gain even in the presence of estimation errors and correlated cascaded channels due to closely-spaced RIS elements. Our analysis leads to insightful closed-form expressions for the optimal pilot and data powers that maximize the rate. The optimal power allocation achieves a significantly higher rate than the conventional approach that assigns equal power to pilots and data.

A fundamental trade-off exists between the time and energy allocated to pilots and data, accuracy of channel estimates, and data rate in a reconfigurable intelligent surface (RIS)-aided system. We optimize the above trade-off for a two-phase training scheme. In the first phase, the base station (BS) estimates the channel from the uplink pilots and configures the RIS. In the second phase, the user equipment estimates the channel from the downlink pilots and coherently demodulates the data. We derive an expression for the achievable rate that accounts for the impact of the channel estimation errors on the RIS phase-shift configuration and data demodulation. Our analysis uses a novel tractable approximation for the effective downlink channel gain and a novel proof that it is asymptotically Gaussian even in the presence of spatial correlation. Our analysis applies to the scenario where enough pilots are sent to estimate the cascaded channels and the cascaded channel grouping scenario that uses fewer pilots. We also study two channel models that depend on the location of the RIS relative to the BS. We derive insightful, closed-form expressions for the optimal powers and training durations. The optimal solution highlights the importance of boosting the pilot powers.

Underlay spectrum sharing addresses spectrum scarcity but imposes constraints on the interference the secondary system causes to the primary receiver. For a secondary transmitter that is subject to the stochastic and general interference-outage constraint and the peak transmit power constraint, we present a novel joint antenna selection and power adaptation rule. It addresses the twin goals of improving the spectral efficiency and reducing the power consumed of an underlay secondary system with low hardware complexity and cost. We prove that the rule maximizes the energy-efficiency (EE) of the secondary system. Its form differs from all other rules considered in the literature. We then present an insightful geometrical characterization of the optimal power of the selected antenna in terms of the channel gains within the secondary system and between the secondary and primary systems. Our approach leads to several special cases, which are themselves novel, and novel analytical insights about the performance and structure of the optimal rule. We also present an iterative subgradient-based algorithm and a simpler non-iterative bound-based algorithm to compute the rule’s parameters. The rule achieves a markedly higher EE compared to conventional approaches, and serves as a new fundamental benchmark for antenna selection in underlay spectrum sharing.

We propose a novel joint antenna selection and power adaptation rule that maximizes the energy-efficiency (EE) of an underlay spectrum sharing system. In an underlay system, a secondary user shares the spectrum with a higher priority primary user, but is subject to tight constraints on the interference it generates. Our approach exploits the spatial diversity benefits of multiple antennas to improve the secondary user’s performance, but with a hardware complexity and cost comparable to a single antenna system. We prove that the proposed rule is EE-optimal for a secondary transmitter that is subject to the interference-outage constraint, which generalizes the widely used peak interference constraint, and the peak transmit power constraint. It has a novel form different from the conventional rules considered in the literature. We present an insightful geometrical characterization that brings out the dependence of the optimal power on the channel gains within the secondary system and between the secondary and primary systems. The proposed rule achieves a markedly higher EE compared to conventional rules.