Sparse Grassmannian Design for Noncoherent Codes via Schubert Cell Decomposition
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910004277149696 |
|---|---|
| author | Asano, Joe Hama, Yuto Iimori, Hiroki Pradhan, Chandan Malomsoky, Szabolcs Ishikawa, Naoki |
| author_facet | Asano, Joe Hama, Yuto Iimori, Hiroki Pradhan, Chandan Malomsoky, Szabolcs Ishikawa, Naoki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21009 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sparse Grassmannian Design for Noncoherent Codes via Schubert Cell Decomposition Asano, Joe Hama, Yuto Iimori, Hiroki Pradhan, Chandan Malomsoky, Szabolcs Ishikawa, Naoki Signal Processing Information Theory 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. |
| title | Sparse Grassmannian Design for Noncoherent Codes via Schubert Cell Decomposition |
| topic | Signal Processing Information Theory |
| url | https://arxiv.org/abs/2601.21009 |