Abstract
A time-diversity system is implemented in this work using a time-diversity encoder. The diversity encoder uses an orthogonal matrix to map vectors of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> modulated symbols to vectors of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> diversity symbols. Each modulated symbol is implicitly transmitted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> times in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> successive periods when the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> diversity symbols are transmitted. No changes in the symbols’ transmission rate occur due to the proposed time-diversity scheme. The diversity symbols are transmitted with the same transmission rate of modulated symbols in the systems with no signal diversity. The proposed system uses the same bandwidth of the system with no signal diversity too. In the receiver, the outputs of the matched filter are stored in a buffer of length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> during the diversity period. After filling the buffer, its contents are multiplied with the inverse of the fading matrix. A diversity detector remaps the diversity symbols to the modulated symbols. It also combines the corresponding modulated symbols in one decision variable. The noise samples in the decision variables are uncorrelated. A maximum-likelihood (ML) detector and a linear detector are used as diversity detectors in this work. The performance of the proposed system achieves the same performance as the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> diversity channels system with a unity-gain-combiner (UGC) receiver.
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