This letter investigates a non-uniform activation aided distributed generalized spatial modulation (DGSM) scheme in a downlink distributed multiple-input multiple-output (DMIMO) system formed by geographically separated transmission reception points (TRPs). Unlike conventional uniform-activation DGSM, the proposed scheme assigns adaptive activation probabilities to different TRP subsets, thereby jointly exploiting the data-domain transmission capability and the index-domain information carried by cooperative subset selection. We derive a mutual-information upper bound under non-uniform activation and formulate a joint activation-probability and power allocation problem subject to a long-term average power constraint. To solve this problem, we develop a semi-closed-form joint probability and power optimization (SC-JPPO) algorithm, where the optimal activation probabilities are shown to follow a Softmax function of the effective utilities. Simulation results demonstrate that the proposed scheme improves spectral efficiency under the same activation scale and power budget compared with existing benchmarks.

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