On an Orthogonal Space-Time-Polarization Block Code

Abstract

<p class="MsoNormal" style="text-align: left; margin: 0cm 0cm 0pt; layout-grid-mode: char;" align="left"><span class="text"><span style="font-family: ";Arial";,";sans-serif";; font-size: 9pt;">Over the past several years, diversity methods such as space, time, and polarization diversity have been successfully implemented in wireless communications systems. Orthogonal space-time block codes efficiently combine space and time diversity, and they have been studied in detail. Polarization diversity has also been studied, however it is usually considered in a simple concatenation with other coding methods. In this paper, an efficient method for incorporating polarization diversity with space and time diversity is studied. The simple yet highly efficient technique is based on extending orthogonal space-time block codes into the quaternion domain and utilizing a description of the dual-polarized signal by means of quaternions. The resulting orthogonal space-timepolarization block codes have given promising results in simulations. In the example described in this paper, the achievable performance gain for two transmit and one receive antennas is approximately 6 dB at a bit error rate of 10-4 when compared with the Alamouti code.</span></span><span style="font-family: ";Arial";,";sans-serif";; font-size: 9pt;"></span></p&gt

Channel equalization and beamforming for quaternion-valued wireless communication systems

“…Compared to the summary contribution in [13], in addition to the detailed analytical modeling steps, the main difference is the GCMA algorithm and the related simulations. Although quaternion-valued wireless communication employing multiple antennas has been studied before, such as the design of orthogonal space-time-polarization block code in [14], to our best knowledge, it is the first time to study the quaternion-valued equalization and interference suppression/beamforming problem in this context. Moreover, the dual-polarised antenna pair or an array of them has a similar structure to the well-studied vector sensors or sensor arrays [15,16,17,18], where they are used mainly for traditional array signal processing applications.…”

On the issue of decoupled decoding of codes derived from quaternion orthogonal designs

“…As such, these quaternion orthogonal designs (QODs) over quaternion variables can be used as building blocks for orthogonal space-time-polarization block codes (OSTBCs) [5][6][7][8][9]. By taking advantage of the view of a quaternion variable as a combination of complex variables, we have shown that it is possible to use QODs to increase the complex rate in a QOD beyond what is possible with a COSTBC.…”

“…1. Hence, each transmission channel is described by the channel gain matrix H (m) ; m = 1, 2, …, N, where In [7], we have utilized the representation of a quaternion variable s = z 1 + z 2 j as s = [z 1 , z 2 ], so that a quaternion matrix Q can be converted into a complex matrix with twice as many columns [6,7,9]. However, we have referred to the complex representation of Q again as Q It was possible to use the context (e.g., the implied size or domain) to determine which representation of Q was being utilized but ultimately lead to a confusion and an abuse of the notation.…”

“…This raised the question of whether it is possible to increase the ratio of the number of complex variables to the number of rows by sacrificing orthogonality or by other means. Recently, orthogonal designs over the quaternion domain were considered in part to address this question [5][6][7][8][9].…”

Fully Quaternion-Valued Adaptive Beamforming Based on Crossed-Dipole Arrays

“…Since the output of a quaternion-valued beamformer is also quaternion-valued, only two components of the quaternion are used to recover the SOI, which leads to redundancy in both calculation and data storage. However, with the development of quaternion-valued communications [14][15][16], it is very likely that in the future we will have quaternion-valued signals as the SOI, where two traditional complex-valued signals with different polarisations arrive at the antenna array with the same DOA. In such a case, a full quaternion-valued array model is needed to compactly represent the four-component desired signal and also make sure the four components of the quaternion-valued output of the beamformer are fully utilised.…”