Orthogonal STBC Set Building and Physical Layer Security Application

Abstract

Given a selected complex orthogonal space-time block code (STBC), transformation algorithms are provided to build a set, S, of unique orthogonal STBCs with cardinality equal to $|{\mathbf{S}}| = {2^{r + c + k - 1}}\cdot r!\cdot c!$, where r, c, and k are the number of rows, columns, and data symbols in the STBC matrix, respectively. A communications link is discussed that encodes data symbols with a chosen STBC from the set known only to the transmitter and intended receiver as a means of providing physical layer security (PLS). Expected bit error rate (BER) and information-theoretic results for an eavesdropper with a priori knowledge of the communications link parameters with the exception of the chosen STBC are presented. Monte Carlo simulations are provided to confirm the possible BER results expected when decoding the communications link with alternative STBCs from the set. Application of the transformation algorithms provided herein are shown to significantly increase the brute force decoding complexity of an eavesdropper compared to a related work in the literature.