  In this paper, the optimal spectral efficiency (data rate divided by the
message bandwidth) that minimizes the probability of causing disruptive
interference for ad hoc wireless networks or cognitive radios is investigated.
Two basic problem constraints are considered: a given message size, or fixed
data rate. Implicitly, the trade being optimized is between longer transmit
duration and wider bandwidth versus higher transmit power. Both single-input
single-output (SISO) and multiple-input multiple-output (MIMO) links are
considered. Here, a link optimizes its spectral efficiency to be a "good
neighbor." The probability of interference is characterized by the probability
that the signal power received by a hidden node in a wireless network exceeds
some threshold. The optimized spectral efficiency is a function of the
transmitter-to-hidden-node channel exponent, exclusively. It is shown that for
typical channel exponents a spectral efficiency of slightly greater than
1~b/s/Hz per antenna is optimal. It is also shown that the optimal spectral
efficiency is valid in the environment with multiple hidden nodes. Also
explicit evaluations of the probability of collisions is presented as a
function of spectral efficiency.
