Minimizing Hidden-Node Network Interference by Optimizing SISO and MIMO Spectral Efficiency

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.