MMSE Optimal Algebraic Space-Time Codes

TL;DR

This paper investigates algebraic space-time codes that are optimized for MMSE reception, identifying classes of codes from crossed product and cyclic division algebras that achieve minimal SER and full diversity.

Contribution

It characterizes algebraic space-time codes that are MMSE optimal, including new classes from crossed product and cyclic division algebras, enhancing suboptimal decoding performance.

Findings

Certain high rate STBCs from crossed product algebras are MMSE optimal.

Codes from cyclic division algebras are also MMSE optimal.

These codes achieve minimal SER with MMSE and full diversity with ML.

Abstract

Design of Space-Time Block Codes (STBCs) for Maximum Likelihood (ML) reception has been predominantly the main focus of researchers. However, the ML decoding complexity of STBCs becomes prohibitive large as the number of transmit and receive antennas increase. Hence it is natural to resort to a suboptimal reception technique like linear Minimum Mean Squared Error (MMSE) receiver. Barbarossa et al and Liu et al have independently derived necessary and sufficient conditions for a full rate linear STBC to be MMSE optimal, i.e achieve least Symbol Error Rate (SER). Motivated by this problem, certain existing high rate STBC constructions from crossed product algebras are identified to be MMSE optimal. Also, it is shown that a certain class of codes from cyclic division algebras which are special cases of crossed product algebras are MMSE optimal. Hence, these STBCs achieve least SER when MMSE reception is employed and are fully diverse when ML reception is employed.