NOMA Empowered Integrated Sensing and Communication.

Model

Dual-functional base station (BS) equipped with an $N$-antennas uniform linear array (ULA).

Communication Model

• K = { 1 , … , K } \mathcal{K}=\{1,\ldots,K\} K={1,…,K}: $K$ single-antenna users indexed.
• M = { 1 , … , M } \mathcal{M}=\{1,\ldots,M\} M={1,…,M}: $M$ radar targets indexed.
• ${\mathbf{w}}_i{s}_i\text{ for }\forall i\in \mathcal{K}$: where ${\mathbf{w}}_i\in {\mathbb{C}}^{N\times 1}$ are beamformers for delivering the information symbol $s_i$ to user $i$. BS transmits the superimposed signals to all users in downlink.
• $y_k={\mathrm{h}}_k^H{\sum }_{i\in \mathcal{K}}{\mathrm{w}}_i{s}_i+n_k={\sum }_{i\in \mathcal{K}}{\mathrm{h}}_k^H{\mathrm{w}}_i{s}_i+n_k$: the received signal $y_k$ at user $k$. where ${\mathrm{h}}_k={\Lambda }_k^{-1/2}{\tilde{\mathsf{h}}}_k,\forall k\in \mathcal{K}$ denotes the BS-user channel, ${\Lambda }_k^{-1/2}$ and ${\tilde{\mathbf{h}}}_k\in {\mathbb{C}}^{N\times 1}$ denote the large and small scale fading, respectively, and $n_k$ denotes the circularly symmetric complex Gaussian noise with variance ${\sigma }_n^2.$
• ${\Lambda }_1^{-1}\le {\Lambda }_2^{-1}\le \cdots \le$ ${\Lambda }_K^{-1}.$ We assume that the users’ indexes are in an increasing order with respect to their large-scale channel strength.
• R k → k = log ⁡ 2 ( 1 + ∣ h k H w k ∣ 2 ∑ i ∈ K , i > k ∣ h k H w i ∣ 2 + σ n 2 ) R_{k\to k}=\log_2\left(1+\frac{|\mathrm{h}_k^H\mathrm{w}_k|^2}{\sum_{i\in\mathcal{K},i>k}|\mathrm{h}_k^H\mathrm{w}_i|^2+\sigma_n^2}\right) R