Blind Deconvolution Demixing using Modulated Inputs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908834530852864 |
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| author | Hameed, Humera Ahmed, Ali |
| author_facet | Hameed, Humera Ahmed, Ali |
| contents | This paper focuses on solving a challenging problem of blind deconvolution demixing involving modulated inputs. Specifically, multiple input signals $s_n(t)$, each bandlimited to $B$ Hz, are modulated with known random sequences $r_n(t)$ that alter at rate $Q$. Each modulated signal is convolved with a different M tap channel of impulse response $h_n(t)$, and the outputs of each channel are added at a common receiver to give the observed signal $y(t)=\sum_{n=1}^N (r_n(t)\odot s_n(t))\circledast h_n(t)$, where $\odot$ is the point wise multiplication, and $\circledast$ is circular convolution. Given this observed signal $y(t)$, we are concerned with recovering $s_n(t)$ and $h_n(t)$. We employ deterministic subspace assumption for the input signal $s_n(t)$ and keep the channel impulse response $h_n(t)$ arbitrary. We show that if modulating sequence is altered at a rate $Q \geq N^2 (B+M)$ and sample complexity bound is obeyed then all the signals and the channels, $\{s_n(t),h_n(t)\}_{n=1}^N$, can be estimated from the observed mixture $y(t)$ using gradient descent algorithm. We have performed extensive simulations that show the robustness of our algorithm and used phase transitions to numerically investigate the theoretical guarantees provided by our algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13481 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Blind Deconvolution Demixing using Modulated Inputs Hameed, Humera Ahmed, Ali Signal Processing This paper focuses on solving a challenging problem of blind deconvolution demixing involving modulated inputs. Specifically, multiple input signals $s_n(t)$, each bandlimited to $B$ Hz, are modulated with known random sequences $r_n(t)$ that alter at rate $Q$. Each modulated signal is convolved with a different M tap channel of impulse response $h_n(t)$, and the outputs of each channel are added at a common receiver to give the observed signal $y(t)=\sum_{n=1}^N (r_n(t)\odot s_n(t))\circledast h_n(t)$, where $\odot$ is the point wise multiplication, and $\circledast$ is circular convolution. Given this observed signal $y(t)$, we are concerned with recovering $s_n(t)$ and $h_n(t)$. We employ deterministic subspace assumption for the input signal $s_n(t)$ and keep the channel impulse response $h_n(t)$ arbitrary. We show that if modulating sequence is altered at a rate $Q \geq N^2 (B+M)$ and sample complexity bound is obeyed then all the signals and the channels, $\{s_n(t),h_n(t)\}_{n=1}^N$, can be estimated from the observed mixture $y(t)$ using gradient descent algorithm. We have performed extensive simulations that show the robustness of our algorithm and used phase transitions to numerically investigate the theoretical guarantees provided by our algorithm. |
| title | Blind Deconvolution Demixing using Modulated Inputs |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2602.13481 |