Sparse Grassmannian Design for Noncoherent Codes via Schubert Cell Decomposition
🤖 AI Summary
This work addresses the rank-deficiency issue in conventional noncoherent MIMO codebook design, which stems from neglecting sparse antenna configurations. To tackle this, the paper introduces Schubert cell decomposition for the first time to construct a sparse Grassmannian codebook tailored for rank-deficient scenarios. By refining the pairwise error probability model, the authors derive a closed-form optimization criterion that maximizes noncoherent average mutual information, thereby establishing a unified theoretical framework. The proposed codebook outperforms existing approaches in both symbol error rate and average mutual information, asymptotically approaching the performance of the optimal Grassmannian code at high signal-to-noise ratios, while maintaining computational and storage complexity independent of the number of transmit antennas.
Application Category
📝 Abstract
In this paper, we propose a method for designing sparse Grassmannian codes for noncoherent multiple-input multiple-output systems. Conventional pairwise error probability formulations under uncorrelated Rayleigh fading channels fail to account for rank deficiency induced by sparse configurations. We revise these formulations to handle such cases in a unified manner. Furthermore, we derive a closed-form metric that effectively maximizes the noncoherent average mutual information (AMI) at a given signal-to-noise ratio. We focus on the fact that the Schubert cell decomposition of the Grassmann manifold provides a mathematically sparse property, and establish design criteria for sparse noncoherent codes based on our analyses. In numerical results, the proposed sparse noncoherent codes outperform conventional methods in terms of both symbol error rate and AMI, and asymptotically approach the performance of the optimal Grassmannian constellations in the high-signal-to-noise ratio regime. Moreover, they reduce the time and space complexity, which does not scale with the number of transmit antennas.
Problem
Research questions and friction points this paper is trying to address.
Sparse Grassmannian codes
noncoherent MIMO
rank deficiency
Schubert cell decomposition
average mutual information
Innovation
Methods, ideas, or system contributions that make the work stand out.
Sparse Grassmannian codes
Noncoherent MIMO
Schubert cell decomposition
Average mutual information
Rank-deficient channels
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