High-Dimensional Hybrid Modulation (HDHM): Bridging Coherent and Noncoherent Transmissions

Design of advanced modulations needs to be revisited to cater for the diverse requirements of future 6th Generation (6G). While most existing modulation schemes operate coherently and need pronounced channel-tracking pilots to reach performance limits, noncoherent transmission offers a viable option by avoiding channel estimation. Noting that the noncoherent capacity-achieving input symbols are good sphere packing over Grassmannian field and each symbol is a subspace in Euclidean space, additional information can be embedded by further packing over the subspaces. In this paper, we propose a hybrid high-dimensional modulation scheme that bears both noncoherent and coherent components via multi-branch mapping. The packing problem is formulated into optimizing rotational angles of noncoherent codewords whose closed-form expressions are derived in this paper. A two-stage binary labeling as well as integration method with waveform are proposed to extend performance limits. Correspondingly, a channel-adjustable receiver is proposed to recover the noncoherent and coherent components sequentially. Simulations demonstrate that the proposed method yields Grassmannian most 2.4dB gain compared with pilot-based scheme under suitable coding pair of two branches.