Motivated by the vision of making sixth-generation (6G) networks sustainable, we study the sparse antenna/array activation problems in uplink cell-free massive multiple-input multiple-output (CF mMIMO) networks. We first develop an antenna-level optimal bilinear equalizer (OBE) weighting framework, in which each access point-user equipment (AP-UE) pair is assigned a matrix-valued long-term weight to shape the contribution of individual antenna elements, thereby generalizing the conventional large-scale fading decoding (LSFD) strategy from scalar coefficients to antenna-element-aware weighting. Building on this structure, we formulate sparse antenna activation as structured sparsity-inducing mean square error (MSE) minimization problems, and design four activation schemes at two granularities: antenna-level and array-level, each with UE-specific and network-wide (all-UEs) variants. The resulting convex problems are solved efficiently via the proximal method with closed-form group-wise updates, while the network-wide schemes are modeled through hierarchical sparsity and handled by a tree-structured proximal operator. Numerical results under correlated Rician channels and a detailed power consumption model demonstrate that the OBE weighting scheme consistently improves spectral efficiency over the LSFD, with gains increasing with the number of antennas. Meanwhile, the studied sparse activation schemes can achieve substantial energy efficiency improvement and power reduction with controllable spectral efficiency loss.

翻译：受第六代(6G)网络可持续发展愿景的驱动，我们研究了上行无蜂窝大规模多输入多输出(CF mMIMO)网络中的稀疏天线/阵列激活问题。首先，我们开发了一种天线级最优双线性均衡器(OBE)加权框架，其中每个接入点-用户设备(AP-UE)对被分配一个矩阵值长期权重，以塑造单个天线单元的贡献，从而将传统的大尺度衰落解码(LSFD)策略从标量系数推广到天线单元感知加权。基于此结构，我们将稀疏天线激活建模为结构化稀疏诱导均方误差(MSE)最小化问题，并设计了两种粒度下的四种激活方案：天线级和阵列级，每种方案均包含用户特定和全网(所有用户)两种变体。由此产生的凸问题通过近端方法高效求解，具有闭式分组更新，而全网方案通过分层稀疏性建模，并由树结构近端算子处理。在相关莱斯信道和详细功耗模型下的数值结果表明：OBE加权方案相较于LSFD能持续提升频谱效率，且增益随天线数量增加而增大；同时，所研究的稀疏激活方案可在可控的频谱效率损失下实现显著的能效提升和功耗降低。