  The paper presents an analysis of the time reversal in multi-path
Rayleigh-fading channels with $N$ inputs (transmitters) and $M$ outputs
(receivers).
  The main issues addressed are the condition of statistical stability, the
rate of information transfer and the effect of pinholes. The stability
condition is proved to be $MC\ll N_{\rm eff}B$ for broadband channels and $M\ll
N_{\rm eff}$ for narrowband channels where $C$ is the symbol rate, $B$ is the
bandwidth and $N_{\rm eff}$ is the {\em effective} number of transmitters. It
is shown that when the number of layers, $n-1$, is relatively low compared to
the logarithm of numbers of pinholes $N_{\rm eff}$ is given by $n^{-1}$ times
the harmonic mean of the number of transmitters and the numbers of pinholes at
all layers. On the other hand, when the number of layers is relatively large
the effective number of pinholes diminishes exponentially. The energy
efficiency is shown to be optimal when the power supply is set to the noise
level times $BN_{\rm eff}$ and that the maximal information rate is roughly
$BN_{\rm eff}$ when the stability condition is violated.
