Exact Degrees of Freedom of Spatially Sparse MIMO Channels Without Prior CSI
Abstract
We characterize the degree of freedom (DoF) of a point-to-point blockwise memoryless channel without prior channel state information (CSI), with a fixed number K of propagation paths, where the transmitter (Tx) and the receiver (Rx) are equipped with nonuniform linear arrays (NULAs) of Nt and Nr antennas, respectively. The positions of array elements are fixed, known, pairwise distinct, and need not be equally spaced. The uniform linear array (ULA) is a special case. In each block of length T, the continuous angles of arrival (AoAs), angles of departure (AoDs), and independent complex Gaussian path gains are redrawn. Both Tx and Rx know the state distributions but are not given the current realizations before transmission. The receiver may estimate the channel from reference signals or decode without explicit channel estimation, with reference symbols counted in T and their energy counted against the power constraint. Under the aforementioned model, we show that the DoF is 1−1/T for K=1, and K(1−3/2T) for K ≥ 2, when Nr≥ K+1, Nt≥max{K,2}, and T≥ K. The analytical results are further demonstrated by their applications to the DoF tradeoff analysis in integrated sensing and communication (ISAC). For more general array structures, an achievability result is established, while the converse remains open in general.
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BibTeX
@misc{xiong2026exact,
title = {{Exact Degrees of Freedom of Spatially Sparse MIMO Channels Without Prior CSI}},
author = {Yifeng Xiong and Weijiang Zhao and Fan Liu and Shi Jin and Jianhua Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07926},
eprint = {2609.07926},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07926},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Exact Degrees of Freedom of Spatially Sparse MIMO Channels Without Prior CSI
AU - Yifeng Xiong
AU - Weijiang Zhao
AU - Fan Liu
AU - Shi Jin
AU - Jianhua Zhang
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.07926
UR - https://arxiv.org/abs/2609.07926
AB - We characterize the degree of freedom (DoF) of a point-to-point blockwise memoryless channel without prior channel state information (CSI), with a fixed number K of propagation paths, where the transmitter (Tx) and the receiver (Rx) are equipped with nonuniform linear arrays (NULAs) of N_t and N_r antennas, respectively. The positions of array elements are fixed, known, pairwise distinct, and need not be equally spaced. The uniform linear array (ULA) is a special case. In each block of length T, the continuous angles of arrival (AoAs), angles of departure (AoDs), and independent complex Gaussian path gains are redrawn. Both Tx and Rx know the state distributions but are not given the current realizations before transmission. The receiver may estimate the channel from reference signals or decode without explicit channel estimation, with reference symbols counted in T and their energy counted against the power constraint. Under the aforementioned model, we show that the DoF is 1−1/T for K=1, and K(1−3/2T) for K ≥ 2, when N_r≥ K+1, N_t≥max{K,2}, and T≥ K. The analytical results are further demonstrated by their applications to the DoF tradeoff analysis in integrated sensing and communication (ISAC). For more general array structures, an achievability result is established, while the converse remains open in general.
ER -