Low SNR Asymptotic Rates of Vector Channels with One-Bit Outputs

We analyze the performance of multiple-input multiple-output (MIMO) links with one-bit output quantization in terms of achievable rates and characterize their performance loss compared to unquantized systems for general channel statistical models and general channel state information (CSI) at the receiver. One-bit ADCs are particularly suitable for large-scale millimeter wave MIMO Communications (massive MIMO) to reduce the hardware complexity. In such applications, the signal-to-noise ratio per antenna is rather low due to the propagation loss. Thus, it is crucial to analyze the performance of MIMO systems in this regime by means of information theoretical methods. Since an exact and general information-theoretic analysis is not possible, we resort to the derivation of a general asymptotic expression for the mutual information in terms of a second order expansion around zero SNR. We show that up to second order in the SNR, the mutual information of a system with two-level (sign) output signals incorporates only a power penalty factor of pi/2 (1.96 dB) compared to system with infinite resolution for all channels of practical interest with perfect or statistical CSI. An essential aspect of the derivation is that we do not rely on the common pseudo-quantization noise model.