Degrees of freedom found for sparse MIMO channels without prior knowledge
Exact Degrees of Freedom of Spatially Sparse MIMO Channels Without Prior CSI
Information Theory
Summary
Communicating wireless signals often involves understanding the paths signals take between antennas. This paper studies how much information can be transmitted when the number of signal paths is limited and the sender and receiver do not know the channel conditions beforehand. The authors calculate exact limits on communication efficiency, called degrees of freedom, under certain antenna setups and channel conditions. Their results help better understand how to design wireless systems that transmit data and sense environments simultaneously. The findings apply to common antenna layouts and provide steps toward more general cases.
degrees of freedomMIMOchannel state informationnonuniform linear arrayangles of arrivalangles of departureblockwise memoryless channelintegrated sensing and communicationchannel estimationpath gains
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.