On orthogonal designs and space-time codes

Abstract

Orthogonal-design-based space-time (ODST) codes of size (n x n) offer maximum diversity gain advantage and a simple yet optimal decoding algorithm under an arbitrary signal alphabet or constellation A However, these designs only exist for n = 2, 4, 8 when A is real and for n = 2 when A is complex. In this letter, we address the question of the existence of ODST codes of other sizes when A is restricted to be a proper. subset of either real or complex numbers. We refer to these as restricted-alphabet ODST (RA-ODST) codes. We show that real RA-ODST codes of size greater than 8 that also guarantee maximum diversity advantage do hot exist. Without the diversity requirement, RA-ODST codes exist only when A = {a, -a}, 0 < a is an element of R. Examples of such codes are provided, In the complex case, under the added requirement of maximum diversity advantage, we prove the nonexistence of complex RA-ODST codes under fairly simple assumptions regarding the signal alphabet.