Molecular Type Permutation Shift Keying in Molecular MIMO Communications for IoBNT

Molecular communication (MC) is a bio-inspired communication paradigm, which lays the foundation for the Internet of Bio-NanoThings (IoBNT) in the medical field. As a high energy-efficient information transfer method, MC via diffusion (MCvD) is envisioned as a promising candidate for IoBNT but suffers from low date rates due to the long tail of the channel impulse response (CIR). To this end, the multiple-input multiple-output (MIMO) technique has been introduced to MCvD. However, the inter-symbol interference (ISI) and inter-link interference (ILI) deteriorate the bit error rate (BER) performance of MIMO MCvD systems. In this paper, molecular type permutation shift keying in the space domain (MTPSK-SD) and time-interleaved MTPSK-SD are proposed for MIMO MCvD systems to improve the BER performance by reducing ILI. The principle of MTPSK-SD is further generalized to the spatio-temporal domain, yielding three spatio-temporal modulation schemes, which can provide desirable BER performance without requiring any CIR information in the communication scenarios affected by different levels of ISI and ILI. Two low-complexity detectors are proposed to obtain different trade-offs between anti-ILI and anti-ISI performance. Furthermore, a complementary coding scheme, which can effectively reduce the ILI under the considered symmetrical system topology, is designed and applied to all the proposed modulation schemes. Additionally, the BER upper bound is analyzed. Numerical simulations on BER corroborate the analysis and show that the proposed schemes are promising multi-molecule modulation alternatives, which outperform the existing MIMO MCvD modulation schemes.