New formulas reveal exact data limits for sparse mimo channels
Exact Degrees of Freedom of Spatially Sparse MIMO Channels Without Prior CSI
Information Theory
Summary
This paper finds exact limits on how much information can be sent over wireless channels with multiple antennas when the channel paths are few and unknown beforehand. The researchers figured out formulas for these limits based on the number of signal paths, antennas, and transmission time without knowing the channel details in advance. Their results help understand communication capabilities in realistic situations where both the sender and receiver have only statistical knowledge of the channel environment. They also show how these findings could affect systems that combine radar sensing and data communication.
What this means in practice
- •For wireless system designers: Calculate precise data capacity limits for sparse multipath MIMO channels without prior channel knowledge in various antenna configurations.
- •For communication system engineers: Analyze tradeoffs between sensing and communication performance in integrated systems given channel sparsity and unknown channel states.
Authors
Yifeng Xiong, Weijiang Zhao, Fan Liu, Shi Jin, Jianhua Zhang
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 $N_t$ 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 $1-\frac{1}{T}$ for $K=1$, and $K(1-\frac{3}{2T})$ for $K \geq 2$, when $N_r\ge K+1$, $N_t\ge\max\{K,2\}$, and $T\ge K$. 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.