  We analyze the channel capacity of a system with a large number of one-bit
transceivers in a classical Rayleigh environment with perfect channel
information at the receiver. With $M$ transmitters and $N=\alpha M$ receivers,
we derive an expression of the capacity per transmitter $\mathcal{C}$, where
$\mathcal{C}\leq\min(1,\alpha)$, as a function of $\alpha$ and signal-to-noise
ratio (SNR) $\rho$, when $M\to\infty$. We show that our expression is a good
approximation for small $M$, and provide simple approximations of $\mathcal{C}$
for various ranges of $\alpha$ and SNR $\rho$. We conclude that at high SNR,
$\mathcal{C}$ reaches its upper limit of one only if the ratio $\alpha>1.24$.
Expressions for determining when $\mathcal{C}$ "saturates" as a function of
$\alpha$ and $\rho$ are given.
