STBCs using capacity achieving designs from crossed-product division algebras

V Shashidhar,B.A Sethuraman,B Sundar Rajan

doi:10.1109/icc.2004.1312617

V Shashidhar, B.A Sethuraman + Show 1 more

Open Access

https://doi.org/10.1109/icc.2004.1312617

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Abstract

We construct full-rank, rate-n space-time block codes (STBC), over any a priori specified signal set for n-transmit antennas using crossed-product division algebras and give a sufficient condition for these STBCs to be information lossless. A class of division algebras for which this sufficient condition is satisfied is identified. Simulation results are presented to show that STBCs constructed in this paper perform better than the best known codes, including those constructed from cyclic division algebras and also to show that they are very close to the capacity of the channel with QAM input.

Highlights

AND PRELIMINARIESA Space-Time Block Code (STBC) C over a complex signal set S, for n transmit antennas, is a finite set of n × l, (n ≤ l) matrices with entries from S or complex linear combinations of elements of S and their conjugates
We construct rate-n n × n designs over subfields of C from crossed-product division algebras and give a sufficient condition for these designs to be capacity achieving and the resulting STBCs to be information lossless for arbitrary number of transmit and receive antennas
The results presented in [7], [8] using cyclic division algebras follow as a special case of the results in this paper

Summary

INTRODUCTION

A Space-Time Block Code (STBC) C over a complex signal set S, for n transmit antennas, is a finite set of n × l, (n ≤ l) matrices with entries from S or complex linear combinations of elements of S and their conjugates. For an information lossless STBC C we call the design used to describe C, a capacity achieving design It was shown in [11], that Alamouti code is the only complex orthogonal design which achieves capacity for 2 transmit and 1 receive antenna. A rate-2, 2 × 2 design was given in [12], which achieves capacity for 2 transmit and arbitrary number of receive antennas. In [14], rate-n n×n designs are constructed using cyclic division algebras for 2, 3 and 4 transmit antennas. We construct rate-n n × n designs over subfields of C from crossed-product division algebras (defined in Section II) and give a sufficient condition for these designs to be capacity achieving and the resulting STBCs to be information lossless for arbitrary number of transmit and receive antennas.

STBC CONSTRUCTION

MUTUAL INFORMATION

SIMULATION RESULTS

DISCUSSION