Low-Complexity Decoding Scheme for $1\times K$ Differential Space-Time Line Coded System With $M$-PSK Modulation

This study considers a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1\times K$</tex-math></inline-formula> differential space-time line coded system with one transmit antenna and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> receive antennas. A conventional joint maximum likelihood (ML) detection method requires a computational complexity order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(KM^{2})$</tex-math></inline-formula> for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula>-phase-shift keying symbols. By decomposing the joint ML into two individual ML detections and bounding the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> search constellation points by three regardless of modulation size, the proposed bounded ML detection can significantly reduce computational complexity to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(K)$</tex-math></inline-formula>. The numerical results verify that the complexity reduction of the proposed detection method can be obtained without compromising any bit-error-rate performance.