Average SEP of AF Relaying in Nakagami-m Fading Environments release_vwaeisl6pzctnjedx7grhufk4y

Abstract

This paper is devoted to an investigation of an exact average symbol error probability (SEP) for amplify and forward (AF) relaying in independent Nakagami-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:math> fading environments with a nonnegative integer plus one-half <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:math>, which covers many actual scenarios, such as one-side Gaussian distribution (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mi>m</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:math>). Using moment generating function approach, the closed-form SEP is expressed in the form of Lauricella multivariate hypergeometric function. Four modulation modes are considered: rectangular quadrature amplitude modulation (QAM), <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mrow><mml:mi>M</mml:mi></mml:mrow></mml:math>-ary phase shift keying (MPSK), <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mrow><mml:mi>M</mml:mi></mml:mrow></mml:math>-ary differential phase shift keying (MDPSK), and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:mrow><mml:mi>π</mml:mi></mml:mrow></mml:math>/4 differential quaternary phase shift keying (DQPSK). The result is very simple and general for a nonnegative integer plus one-half <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:math>, which covers the same range as integer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M9"><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:math>. The tightness of theoretical analysis is confirmed by computer simulation results.
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