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Uplink-downlink duality refers to the fact that under a sum-power constraint,the capacity regions of a Gaussian multiple-access channel and a Gaussianbroadcast channel with Hermitian transposed channel matrices are identical.This paper generalizes this result to a cooperative cellular network, in whichremote access-points are deployed as relays in serving the users under thecoordination of a central processor (CP). In this model, the users and therelays are connected over noisy wireless links, while the relays and the CP areconnected over noiseless but rate-limited fronthaul links. Based on aLagrangian technique, this paper establishes a duality relationship betweensuch a multiple-access relay channel and broadcast relay channel, under theassumption that the relays use compression-based strategies. Specifically, weshow that under the same total transmit power constraint and individualfronthaul rate constraints, the achievable rate regions of the Gaussianmultiple-access and broadcast relay channels are identical, when eitherindependent compression or Wyner-Ziv and multivariate compression strategiesare used. The key observations are that if the beamforming vectors at therelays are fixed, the sum-power minimization problems under the achievable rateand fronthaul constraints in both the uplink and the downlink can betransformed into either a linear programming or a semidefinite programmingproblem depending on the compression technique, and that the uplink anddownlink problems are Lagrangian duals of each other. Moreover, the dualvariables corresponding to the downlink rate constraints become the uplinkpowers; the dual variables corresponding to the downlink fronthaul constraintsbecome the uplink quantization noises. This duality relationship enables anefficient algorithm for optimizing the downlink transmission and relayingstrategies based on the uplink.

Uplink-Downlink Duality Between Multiple-Access and Broadcast Channels with Compressing Relays