Uplink-downlink duality refers to the fact that under a sum-power constraint, the capacity regions of a Gaussian multiple-access channel and a Gaussian broadcast channel with Hermitian transposed channel matrices are identical. This paper generalizes this result to a cooperative cellular network, in which remote access-points are deployed as relays in serving the users under the coordination of a central processor (CP). In this model, the users and the relays are connected over noisy wireless links, while the relays and the CP are connected over noiseless but rate-limited fronthaul links. Based on a Lagrangian technique, this paper establishes a duality relationship between such a multiple-access relay channel and broadcast relay channel, under the assumption that the relays use compression-based strategies. Specifically, we show that under the same total transmit power constraint and individual fronthaul rate constraints, the achievable rate regions of the Gaussian multiple-access and broadcast relay channels are identical, when either independent compression or Wyner-Ziv and multivariate compression strategies are used. The key observations are that if the beamforming vectors at the relays are fixed, the sum-power minimization problems under the achievable rate and fronthaul constraints in both the uplink and the downlink can be transformed into either a linear programming or a semidefinite programming problem depending on the compression technique, and that the uplink and downlink problems are Lagrangian duals of each other. Moreover, the dual variables corresponding to the downlink rate constraints become the uplink powers; the dual variables corresponding to the downlink fronthaul constraints become the uplink quantization noises. This duality relationship enables an efficient algorithm for optimizing the downlink transmission and relaying strategies based on the uplink.
翻译:上下链接的双重性是指以下事实:在超强限制下,高斯多端接入频道和高斯广播频道的能力区域与埃米提亚转换频道矩阵相同。本文将这一结果概括为合作型蜂窝网络,在中央处理器(CP)的协调下,远程接入点作为中继器用于为用户服务。在这个模型中,用户和中继器通过无声无线连接连接,而中继器和中继器则通过无噪音但收费有限的前厅链接连接。根据拉格兰加技术,本文在多端接入中继频道和广播中继频道之间建立了双向关系。假设中继器使用压缩战略。具体地说,我们显示,在同一总传输电源限制和个人前导速率限制下传情况下,高斯多端接入和广播中继频道的可实现率区域是相同的,当独立压缩或Wyner-Ziv和多变式压缩压缩战略向下向下连接时,则使用双向下链接的双向下链接。关键观察是,如果在前端传输链路的每个向前端和直线链接中端约束中,则会使前端制约的机和直端制约的机变后变后端制约成为了。