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| Format: | Preprint |
| Published: |
2023
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| Online Access: | https://arxiv.org/abs/2308.05078 |
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| _version_ | 1866913229214580736 |
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| author | Singh, Kamal |
| author_facet | Singh, Kamal |
| contents | We characterize the capacity of a low-rank wireless channel with varying fading severity at low signal-to-noise ratios (SNRs). The channel rank deficiency is achieved by incorporating pinhole condition. The capacity degradation with fading severity at high SNRs is well known: the probability of deep fades increases significantly with higher fading severity resulting in poor performance. Our analysis of the dyadic pinhole channel at low-SNR shows a very counter-intuitive result that - \emph{higher fading severity enables higher capacity at sufficiently low SNR}. The underlying reason is that at low SNRs, ergodic capacity depends crucially on the probability distribution of channel peaks (tail distribution); for the pinhole channel, the tail distribution improves with fading severity. This allows a transmitter operating at low SNR to exploit channel peaks `more efficiently' and hence improves spectral efficiency. We derive a new key result quantifying the above dependence for the double-Nakagami-$m$ fading pinhole channel - the capacity ${C} \propto (m_T m_R)^{-1}$ at low SNR, where $m_T m_R$ is the severity parameters (product) of the fadings involved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05078 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On The Capacity of Low-Rank Dyadic Fading Channels in the Low-SNR Regime Singh, Kamal Information Theory We characterize the capacity of a low-rank wireless channel with varying fading severity at low signal-to-noise ratios (SNRs). The channel rank deficiency is achieved by incorporating pinhole condition. The capacity degradation with fading severity at high SNRs is well known: the probability of deep fades increases significantly with higher fading severity resulting in poor performance. Our analysis of the dyadic pinhole channel at low-SNR shows a very counter-intuitive result that - \emph{higher fading severity enables higher capacity at sufficiently low SNR}. The underlying reason is that at low SNRs, ergodic capacity depends crucially on the probability distribution of channel peaks (tail distribution); for the pinhole channel, the tail distribution improves with fading severity. This allows a transmitter operating at low SNR to exploit channel peaks `more efficiently' and hence improves spectral efficiency. We derive a new key result quantifying the above dependence for the double-Nakagami-$m$ fading pinhole channel - the capacity ${C} \propto (m_T m_R)^{-1}$ at low SNR, where $m_T m_R$ is the severity parameters (product) of the fadings involved. |
| title | On The Capacity of Low-Rank Dyadic Fading Channels in the Low-SNR Regime |
| topic | Information Theory |
| url | https://arxiv.org/abs/2308.05078 |