Computation over multiple access channels (CoMAC) has been proposed to solve the problem of spectrum scarcity in wireless networks, which combines communication and computation efficiently using the superposition property of wireless channels. In this paper, we consider a multi-cluster CoMAC network, whose performance is affected by the inter-cluster interference and the non-uniform fading. To minimize the sum mean squared error of signals aggregated at different fusion centers (FCs), we propose a transceiver design for multi-cluster CoMAC. Specifically, we adopt a uniform-forcing transmitter design to formulate the receiver design as a quadratic sum-of-ratios problem with nonconvex quadratic constraints. Then, we propose a branch-and-bound algorithm to find its optimal solution with a given error tolerance. To solve the problem in a decentralized way, we develop a distributed algorithm based on the primal decomposition theory. Each subproblem is solved by using the successive convex approximation method. Further combining Lagrange duality, we derive the optimal solution structure of each subproblem, based on which we can find the solution with lower complexity. Simulation results demonstrate the effectiveness of the proposed distributed transceiver design.

中文翻译：

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多集群网络中模拟函数计算的干扰管理


为了解决无线网络中频谱稀缺的问题，提出了多址信道计算（CoMAC），它利用无线信道的叠加特性将通信和计算有效地结合起来。在本文中，我们考虑多簇CoMAC网络，其性能受到簇间干扰和非均匀衰落的影响。为了最小化在不同融合中心（FC）聚合的信号的总均方误差，我们提出了一种用于多集群 CoMAC 的收发器设计。具体来说，我们采用均匀强迫发射机设计将接收机设计表示为具有非凸二次约束的二次比和问题。然后，我们提出了一种分支定界算法，以在给定的容错范围内找到其最优解。为了以分散的方式解决问题，我们开发了一种基于原始分解理论的分布式算法。每个子问题均采用逐次凸逼近法求解。进一步结合拉格朗日对偶性，推导出每个子问题的最优解结构，在此基础上找到复杂度较低的解。仿真结果证明了所提出的分布式收发器设计的有效性。