Quaternion Codes in MIMO System of Dual-Polarized Antennas

The use of quaternion orthogonal designs (QODs) to describe point-to-point communication among dual-polarized antennas has the potential to provide higher rate orthogonal and quasi-orthogonal complex designs exploiting polarization diversity among space and time diversities. Furthermore, it is essential to have a space time block code (STBC) which offers a linear and decoupled decoder which quasi-orthogonal designs fail to attain. In this paper, we show how the realm of quaternions unexpectedly offers us a possible solution and codes obtained from quaternion designs mostly achieve both linear and decoupled decoders. This motivated us to perform an indispensable search for QODs such that the code rate is bounded below by 1/2 and does not sharply decrease as the number of transmit antennas increases. It is shown that three famous recursive techniques do not satisfy this criteria and their code rates decrease rather rapidly. Therefore, we propose another method of constructing quaternion designs suitable for any number of transmit antennas and verify that these attain linear and decoupled decoders with the system model based on quaternionic channel. It is shown that such designs outperform others in terms of transmit diversity, code rates and the optimality of the proposed decoder is validated through simulation results.

Linear and Decoupled Decoders for Dual-Polarized Antenna-Based MIMO Systems

Quaternion orthogonal designs (QODs) have been used to design STBCs that provide improved performance in terms of various design parameters. In this paper, we show that all QODs obtained from generic iterative construction techniques based on the Adams-Lax-Phillips approach have linear and decoupled decoders which significantly reduce the computational complexity at the receiver. Our result is based on the quaternionic description of communication channels among dual-polarized antennas. Another contribution of this work is the linear and decoupled decoder for quasi-orthogonal codes for non-square as well as square designs. The proposed solution promises diversity gains with the quaternionic channel model and the decoding solution is independent of the number of receive dual-polarized antennas. A brief comparison is presented at the end to demonstrate the effectiveness of quaternion designs in two dual-polarized antennas over available STBCs for four single-polarized antennas. Linear and decoupled decoding of two quasi-orthogonal designs is shown, which has failed to exit previously. In addition, a QOD for 2×1 dual-polarized antenna configuration using quaternionic channel model shows a 3 dB gain at 10−5 in comparison to the same code evaluated for 2×2 complex representation of the quaternionic channel. This gain is further enhanced when the received diversity for these the cases is matched i.e., 2×2. The code using the quaternionic channel model shows a further 13 dB improvement at 10−5 BER.

Efficient orthogonal functional magnetic resonance imaging designs in the presence of drift

To study brain activity, by measuring changes associated with the blood flow in the brain, functional magnetic resonance imaging techniques are employed. The design problem in event-related functional magnetic resonance imaging studies is to find the best sequence of stimuli to be shown to subjects for precise estimation of the brain activity. Previous analytical studies concerning optimal functional magnetic resonance imaging designs often assume a simplified model with independent errors over time. Optimal designs under this model are called g-lag orthogonal designs. Recently, it has been observed that g-lag orthogonal designs also perform well under simplified models with auto-regressive error structures. However, these models do not include drift. We investigate the performance of g-lag orthogonal designs for models that incorporate drift parameters. Identifying g-lag orthogonal designs that perform best in the presence of a drift is important because a drift is typically assumed for the analysis of event-related functional magnetic resonance imaging data.