Optimal Current Control for MISO-OFDM Based Through-the-Earth Communications with Magnetic Induction

Magnetic induction (MI) communications are widely used to realize through-the-earth transmissions due to the advantages of high penetration efficiency, stable channel, and small antenna size. However, traditional MI communications are mainly based on single or multiple carriers with resonant frequencies, which makes the achievable rate much less than the capacity of frequency-selective MI channel. To approach the capacity of frequency-selective MI channel, we formulate the orthogonal-frequency-division-multiplexing (OFDM) based MI communication framework, where resonant frequency and nonresonant frequencies are comprehensively utilized. Also, multiple transmit coils are equipped for the aboveground user to enhance the receive power of the underground user with single coil. We propose the optimal current control scheme in closed-form, which aims at maximizing the achievable rate under the constraint of transmit power. Based on the proposed current control scheme, the approximate expression for the capacity of frequency-selective multiple-input-single-output MI (MISO-MI) channel is given. Numerical results verify our theoretical analyses and show that MISO-OFDM based MI communication system can significantly increase the achievable rate. It is also shown that the proposed current control scheme can achieve larger achievable rate as compared with other schemes.