An 8×8 Quasi-Orthogonal STBC form for transmissions over eight or four antennas

Abstract

Abstract-An 8 × 8 two-symbol decodable quasi-orthogonal space-time block code (QO-STBC) is presented which can be transmitted across either 8 or 4 antennas with full rate and the same full diversity order. For the 8-transmit-antenna system, a new expression is developed to identify rotation angles that maximize the diversity (eigenvalue) product. In addition, it is shown that the previously proposed sum-eigenvalue maximization criterion for the design of rotation angles is not relevant/applicable and an alternative minimum eigenvalue maximization criterion is suggested. Finally, new optimal rotation angles are obtained by working directly with a pairwise-error-probability (PEP) upperbound expression. For 4-transmit-antenna systems and correlated channel fading conditions, the PEP-upper-bound is modified accordingly to take into account the channel correlation. Using the new PEP-upper-bound we obtain rotation angles that maximize the diversity product and find, contrary to previous results, that the optimized angles are independent of the correlation coefficient. Simulation studies initiated herein demonstrate the advantage of using the proposed codeword across 4 transmit antennas when compared with other 4×4 QO-STBC transmission schemes. For 8 transmit antennas, the studies compare the three selected rotation angle optimization criteria (diversity product, minimum eigenvalue, PEP-upper-bound).Index Terms-Constellation rotation, diversity product, MIMO systems, pairwise-error-probability (PEP), quasi-orthogonal space-time block codes (QO-STBC), sum or minimum eigenvalue maximization.

Orthogonal space-time block codes with sphere packing

“…2 for : the orthogonal design with 16-QAM has a better performance than the diagonal algebraic code , the high rate code , and the Golden code . The reason for this is that the diversity product can only characterize the worst-case pair-wise error probability, while the actual performance is governed by the whole spectrum of the determinants of the code difference matrices [27].…”

“…Defining as (26) in order to show , it is sufficient to prove that for any . For any pair of vectors and from the -dimensional lattice , the difference vector can be represented as (27) for some integers . According to the definition of the lattice , we know that is even.…”

“…The sum of these integers is also even. Substituting (27) and (28) In the following, we will prove that it is impossible to have the case that all of are zeros under the constraint that , i.e., and cannot be zero at the same time. Finally, if there is only one nonzero , i.e., and for all , we will show that , which also implies that .…”

Design of quasi-orthogonal STBCs with delay optimality

“…Introduction: Quasi-orthogonal space-time block codes (QO-STBCs) [1][2][3][4] have been greatly preferable since an independent joint maximum-likelihood (ML) detection of two complex [1 -3] or four real symbols [4] is available at a receiver. However to reduce decoding complexity, it is more critical to minimise codeword length.…”

“…This implies that under a condition of full diversity, the time length of a codeword matrix should be identical to the number of transmit antennas, which is called as delay-optimal [5]. However, the existing QO-STBCs [2][3][4] are delay-optimal only when N = 2 n transmit antennas. For other antennas, the codes are constructed by deleting certain columns from these delay-optimal codes.…”