Asymptotic Capacity of Non-Coherent One-Bit MIMO Channels with Block Fading

Sheng Yang, Richard Combes

Abstract: In this work, we investigate the capacity of a block fading one-bit multi-antenna channel without a priori channel state information. We consider the asymptotic regime with a large number of receive antennas. We show that the capacity scales as $\frac{1}{2}\begin{pmatrix}T\\ 2\end{pmatrix}\log(\alpha_{\text{snr},T}n_{\mathrm{r}})$ under the peak power constraint $\mathsf{snr}$ and with coherence block size $T$. In particular, we derive the exact form of $\alpha_{\text{snr},T}$ for $T=2$ and $T=3$. Furthermore, for an arbitrary value of $T$, we derive a lower bound of $\alpha_{\text{snr},T}$ by proposing a low-complexity signaling scheme. We also obtain a closed-form expression of $\alpha_{\text{snr},T}$ when $\mathsf{snr}$ is small.