AI 中文总结
本文刻画了无先验CSI的稀疏MIMO信道自由度，提出精确DoF公式，并应用于ISAC权衡分析。
AI 中文摘要
我们刻画了无先验信道状态信息（CSI）的点对点块状无记忆信道的自由度（DoF），该信道具有固定数量的$K$条传播路径，其中发射端（Tx）和接收端（Rx）分别配备具有$N_t$和$N_r$个天线的非均匀线性阵列（NULA）。阵列元素的位置是固定的、已知的、两两不同的，且不需要等间距。均匀线性阵列（ULA）是一个特例。在每个长度为$T$的块中，到达角（AoA）、离开角（AoD）以及独立的复高斯路径增益被重新抽取。Tx和Rx都知道状态分布，但在传输前不知道当前实现。接收端可以从参考信号估计信道，或在不进行显式信道估计的情况下解码，参考符号计入$T$中，其能量计入功率约束。在上述模型下，我们证明当$N_r\ge K+1$、$N_t\ge\max\{K,2\}$且$T\ge K$时，对于$K=1$，DoF为$1-\frac{1}{T}$；对于$K\geq 2$，DoF为$K(1-\frac{3}{2T})$。分析结果进一步通过其在集成感知与通信（ISAC）中的DoF权衡分析应用得到展示。对于更一般的阵列结构，建立了可达性结果，而逆命题在一般情况下仍然开放。
英文摘要
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.
