This paper considers a multipair amplify-and-forward massive MIMO relaying system with one-bit ADCs and one-bit DACs at the relay. The channel state information is estimated via pilot training, and then utilized by the relay to perform simple maximum-ratio combining/maximum-ratio transmission processing. Leveraging on the Bussgang decomposition, an exact achievable rate is derived for the system with correlated quantization noise. Based on this, a closed-form asymptotic approximation for the achievable rate is presented, thereby enabling efficient evaluation of the impact of key parameters on the system performance. Furthermore, power scaling laws are characterized to study the potential energy efficiency associated with deploying massive one-bit antenna arrays at the relay. In addition, a power allocation strategy is designed to compensate for the rate degradation caused by the coarse quantization. Our results suggest that the quality of the channel estimates depends on the specific orthogonal pilot sequences that are used, contrary to unquantized systems where any set of orthogonal pilot sequences gives the same result. Moreover, the sum rate gap between the double-quantized relay system and an ideal non-quantized system is a moderate factor of $4/pi^2$ in the low power regime.
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