Space time block codes (STBCs) have been studied to exploit the spatial and temporal diversities in wireless systems. Orthogonal space time polarization block codes (OSTPBCs) designed using the quaternion algebra promise gains in terms of higher data rates, diversity and spectral efficiency. In this context, quaternion modulation has been proposed using the dual-polarized antennas to generate efficient selection of the polarization and optimal decoding at the receiver end. In this paper, the quaternion modulation technique has been evaluated considering the quaternionic channel using the dual-polarized antennas. The results show promising diversity gains with benefits in terms of spectral efficiency and data rates. An extension of this scheme for higher number of symbols and higher dual-polarized antenna dimensions has also been presented. The proposal includes linear decoupled decoding of the quaternion orthogonal codes (QODs) at the receiver end where the complexity stays independent of the number of transmitted symbols. The design of the quaternion modulation using the quaternionic channel fully exploits the polarization diversity in addition to unfolding its applicability for future massive multiple-input multiple-output (MIMO) wireless systems.

Over the past few decades, wireless communication aims to support high data rates and reliability and thus several techniques exploiting space, time, and polarization diversities have been used to achieve large diversity gains. Orthogonal space time block codes (OSTBC) in combination with polarization diversity promise optimal diversity gains. For dual-polarized antennas, we propose a new system model based on the quaternionic structure of the channel, which offers a way to exploit polarization diversity quite independently of other forms of diversities. Moreover, such OSTPBC achieve better throughput and provide a linear decoupled decoding solution at the receiver, which significantly reduces computational complexity.

Quaternion orthogonal designs (QODs) are considered the foundation of orthogonal space time polarization block codes (OSTPBCs). OSTPBCs benefit from orthogonal polarizations and orthogonal space and time block coding simultaneously to enhance the capacity of wireless communication systems. To exploit these advantages of OSTPBCs, this paper explores two generalized construction techniques of QODs, where the first one is based on symmetric-paired designs while the second technique maps the complex orthogonal designs (CODs) to QODs directly. With these schemes, QODs for any number of transmit antennas can be constructed. Moreover, a low-complexity maximum-likelihood (ML) decoder for the proposed construction techniques has been presented that provides optimal decoupled decoding with phenomenal complexity reduction. Simulation results show that the diversity order of the first QOD construction is higher than the second design given the number of transmit antennas are same.

In this paper, near-orthogonal random space-time block codes (STBCs) are used to design near-orthogonal channels to transmit information independently in a fully opportunistic multi-hop strip-shaped cooperative wireless network. This opportunistic large array (OLA) network is considered to have fixed hop boundaries having constant node density and operating on decode-and-forward (DF) relaying mode. To deal with random number of DF nodes, in each hop, directional statistical concepts are used for the randomization of underlying deterministic STBC letting each node to transmit linear combination of symbols or STBC columns. The transmissions are modeled stochastically with Markov chain. Network performance is evaluated on the basis of one-hop success probability and coverage for different number of nodes per hop, and dimensions of STBCs.