Construction and Analysis of Quaternion MIMO-OFDM Communications Systems

Abstract

Abstract-Wireless communications systems with progressively higher spectral efficiency have been investigated in past decades. A promising area of research is the use of hypercomplex algebras, notably, the use of the quaternion algebra. This paper considers the construction of multiple-input-multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) using the algebra of quaternions. Several construction techniques for quaternion orthogonal code designs have been proposed in recent years, which offer the possibility to explore diversities in various domains, such as space, time, frequency, and polarization, in addition to combinations thereof. This paper presents a formulation for quaternion MIMO-OFDM in matrix form as an extension of the classical formulation that uses complex variables. Quaternions allow elegant representation of pairs of radiant elements in physical antennas configured for crosspolarized propagation. Several simulations validate the proposed method in diverse scenarios for wireless communications, in which combined diversities have been exploited.

Improved time and frequency synchronization for dual‐polarization OFDM systems

“…where z n,1 and z n,2 are complex additive noise with identical variances and H Â m is the baseband equivalent cross-polarized link model. Some link models for (11) may be found in literature [4,5]. This can be easily extended to more elaborated frequency-selective models using matrix notation in the frequency domain, as shown in literature [5].…”

“…DP antennas can be represented with quaternion algebra [3] by simple models that allow the accommodation of any polarization twist between transmit and receive antennas. The design of hypercomplex orthogonal frequency division multiplex (OFDM) modulation schemes using quaternions and hypercomplex algebras has been proposed by Meloni [4], and its extension to MIMO-OFDM has been recently proposed by Meloni et al [5]. These designs allow the exploration of a flexible quaternion OFDM communication system using combined diversities by quaternion orthogonal space-time block codes, with additional types of diversity, such as frequency and/or polarization diversity.…”

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

“…where 6). Please note that in the above code, both ends of a dual-polarized antenna will be used at each time slot.…”

“…as a seed matrix to generate the required QOD using (6). Thus, for a massive MIMO comprising of an 8 × 1 system, we have a QOD which has code rate 1/2 and is given in Equation (11).…”

“…The quaternion orthogonal designs (QODs) are under rigorous research, for instance, see [ 6 , 7 , 8 , 9 , 10 , 11 , 12 ]. However, an important construction technique in these previous designs is that they were either extensions of complex orthogonal designs (CODs) with some necessary properties to be applicable as QODs, or they were constructed from quasi-complex space time block codes (STBCs).…”