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Future wearable and portable devices with multiple transmit antennas operating below 6 GHz are constrained by regulatory limitations on the level of electromagnetic radiation a user can be exposed to, measured using the specific absorption rate (SAR). Signaling designs that are optimized to include SAR constraints can improve the performance of uplink transmission. These signaling schemes could include closed-loop beamforming, closed-loop precoding, and space-time coding, which have all been shown to achieve increased rates when optimized as a function of SAR. Previous research addressed SAR constrained optimization only within a single coherence time block. In this paper, we present transmit policies that dynamically allocate user electromagnetic radiation exposure over time. We propose three exposure allocation methods - optimal, uniform, and asymptotic - in the practical case with causal channel state information (CSI), and an on-off transmission approach for the low SAR-to-noise ratio regime. Our results demonstrate that the performance of SAR-aware transmission can be further improved by exploiting frequency and time diversity.
multiple antenna array; specific absorption rate; convex optimization; dynamic programming