Song, Y; Xu, H; Wan, K; Wong, KK; Caire, G; Shamai, S; (2025) Achievable Rates for a Primitive Gaussian Diamond Channel with Rayleigh Fading. In: IEEE International Symposium on Information Theory Proceedings. IEEE: Ann Arbor, MI, USA. (In press).

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Abstract

This paper studies the ergodic achievable rates of a primitive Gaussian diamond channel with Rayleigh fading. The system is modeled as a two-hop relay channel where a single user communicates with a central processor (CP) through two relays. These relays are agnostic to the user's codebooks and are considered 'primitive' because the fronthaul links are error-free but have limited capacity. In this setup, the channel state information (CSI) is assumed to be available only at the relays and not at the CP. Despite the simplicity of this configuration, deriving an accurate characterization of the ergodic capacity is surprisingly challenging. To address this, we first establish an analytical rate upper bound, assuming that the relays can cooperate and that the CP has access to the CSI as well. In order to obtain lower bounds, we resort to specific analytically/numerically tractable achievability strategies. When designing such strategies, we need to take into account that the CP has no CSI and that each relay has only statistical knowledge of the CSI other relay. Under these constraints, we propose two achievable schemes employing different estimation and compression methods at relays. Simulation results show that these schemes achieve performance close to the derived upper bound over a wide range of system parameters.

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