Two complex orthogonal space-time codes for eight transmit antennas

Two new constructions of complex orthogonal space-time block codes of order 8 based on the theory of amicable orthogonal designs are presented and their performance compared with that of the standard code of order 8. These new codes are suitable for multi-modulation schemes where the performance can be sacrificed for a higher throughput

Amicable T-matrices and applications

iii, 49 leaves ; 29 cmOur main aim in this thesis is to produce new T-matrices from the set of existing T-matrices. In Theorem 4.3 a multiplication method is introduced to generate new T-matrices of order st, provided that there are some specially structured T-matrices of orders s and t. A class of properly amicable and double disjoint T-matrices are introduced. A number of properly amicable T-matrices are constructed which includes 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 18, 22. To keep the new matrices disjoint an extra condition is imposed on one set of T-matrices and named double disjoint T-matrices. It is shown that there are some T-matrices that are both double disjoint and properly amicable. Using these matrices an infinite family of new T-matrices are constructed. We then turn our attention to the application of T-matrices to construct orthogonal designs and complex Hadamard matrices. Using T-matrices some orthogonal designs constructed from 16 circulant matrices are constructed. It is known that having T-matrices of order t and orthogonal designs constructible from 16 circulant matrices lead to an infinite family of orthogonal designs. Using amicable T-matrices some complex Hadamard matrices are shown to exist

Amicable Orthogonal Designs of Order 8 for Complex Space-Time Block Codes

New amicable orthogonal designs AODs(8; 1; 1; 1; 2; 2; 2), AODs(8; 1; 1; 4; 1; 2; 2), AODs(8; 1; 2;2; 2; 2; 4), AODs(8; 1; 2; 2; 1; 2; 4), AODs(8; 1; 1; 2; 1; 2; 4), AODs(8; 1; 2; 4; 2; 2; 2), AODs(8; 1; 1; 4; 1; 1; 2; 2), AODs(8; 2; 2; 2; 2; 2; 2; 2; 2) and AODs(8; 1; 1; 1; 2; 1; 2; 2; 2) are found by applying a new theorem or by an exhaustive search. Also some previously undecided cases of amicable pairs are demonstrated to be non-existent after a complete search of the equivalence classes for orthogonal designs

Constructions for orthogonal designs using signed group orthogonal designs

Craigen introduced and studied signed group Hadamard matrices extensively and eventually provided an asymptotic existence result for Hadamard matrices. Following his lead, Ghaderpour introduced signed group orthogonal designs and showed an asymptotic existence result for orthogonal designs and consequently Hadamard matrices. In this paper, we construct some interesting families of orthogonal designs using signed group orthogonal designs to show the capability of signed group orthogonal designs in generation of different types of orthogonal designs.Comment: To appear in Discrete Mathematics (Elsevier). No figure

Some Constructions for Amicable Orthogonal Designs

Hadamard matrices, orthogonal designs and amicable orthogonal designs have a number of applications in coding theory, cryptography, wireless network communication and so on. Product designs were introduced by Robinson in order to construct orthogonal designs especially full orthogonal designs (no zero entries) with maximum number of variables for some orders. He constructed product designs of orders $4$, $8$ and $12$ and types $\big(1_{(3)}; 1_{(3)}; 1\big),$ $\big(1_{(3)}; 1_{(3)}; 5\big)$ and $\big(1_{(3)}; 1_{(3)}; 9\big)$, respectively. In this paper, we first show that there does not exist any product design of order $n\neq 4$, $8$, $12$ and type $\big(1_{(3)}; 1_{(3)}; n-3\big),$ where the notation $u_{(k)}$ is used to show that $u$ repeats $k$ times. Then, following the Holzmann and Kharaghani's methods, we construct some classes of disjoint and some classes of full amicable orthogonal designs, and we obtain an infinite class of full amicable orthogonal designs. Moreover, a full amicable orthogonal design of order $2^9$ and type $\big(2^6_{(8)}; 2^6_{(8)}\big)$ is constructed.Comment: 12 pages, To appear in the Australasian Journal of Combinatoric

Square Complex Orthogonal Designs with Low PAPR and Signaling Complexity

Space-Time Block Codes from square complex orthogonal designs (SCOD) have been extensively studied and most of the existing SCODs contain large number of zero. The zeros in the designs result in high peak-to-average power ratio (PAPR) and also impose a severe constraint on hardware implementation of the code when turning off some of the transmitting antennas whenever a zero is transmitted. Recently, rate 1/2 SCODs with no zero entry have been reported for 8 transmit antennas. In this paper, SCODs with no zero entry for $2^a$ transmit antennas whenever $a+1$ is a power of 2, are constructed which includes the 8 transmit antennas case as a special case. More generally, for arbitrary values of $a$, explicit construction of $2^a\times 2^a$ rate $\frac{a+1}{2^a}$ SCODs with the ratio of number of zero entries to the total number of entries equal to $1-\frac{a+1}{2^a}2^{\lfloor log_2(\frac{2^a}{a+1}) \rfloor}$ is reported, whereas for standard known constructions, the ratio is $1-\frac{a+1}{2^a}$. The codes presented do not result in increased signaling complexity. Simulation results show that the codes constructed in this paper outperform the codes using the standard construction under peak power constraint while performing the same under average power constraint.Comment: Accepted for publication in IEEE Transactions on Wireless Communication. 10 pages, 6 figure

Code diversity in multiple antenna wireless communication

The standard approach to the design of individual space-time codes is based on optimizing diversity and coding gains. This geometric approach leads to remarkable examples, such as perfect space-time block codes, for which the complexity of Maximum Likelihood (ML) decoding is considerable. Code diversity is an alternative and complementary approach where a small number of feedback bits are used to select from a family of space-time codes. Different codes lead to different induced channels at the receiver, where Channel State Information (CSI) is used to instruct the transmitter how to choose the code. This method of feedback provides gains associated with beamforming while minimizing the number of feedback bits. It complements the standard approach to code design by taking advantage of different (possibly equivalent) realizations of a particular code design. Feedback can be combined with sub-optimal low complexity decoding of the component codes to match ML decoding performance of any individual code in the family. It can also be combined with ML decoding of the component codes to improve performance beyond ML decoding performance of any individual code. One method of implementing code diversity is the use of feedback to adapt the phase of a transmitted signal as shown for 4 by 4 Quasi-Orthogonal Space-Time Block Code (QOSTBC) and multi-user detection using the Alamouti code. Code diversity implemented by selecting from equivalent variants is used to improve ML decoding performance of the Golden code. This paper introduces a family of full rate circulant codes which can be linearly decoded by fourier decomposition of circulant matrices within the code diversity framework. A 3 by 3 circulant code is shown to outperform the Alamouti code at the same transmission rate.Comment: 9 page