Performance Analysis of DF Cooperative Diversity System With OSTBC Over Spatially Correlated Nakagami-$m$ Fading Channels

Abstract

In this paper, we investigate the performance of a cooperative decode-and-forward (DF) multiple-input–multiple-output (MIMO) relaying system with orthogonal space–time block code (OSTBC) transmissions over spatially correlated Nakagami- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$m$</tex></formula> fading channels for integer values of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$m$</tex></formula> . We consider both the opportunistic maximal-ratio combining (O-MRC) and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\lambda$</tex></formula> -MRC receivers at the destination. For the former MRC, we give the closed-form expression for the cumulative distribution function (cdf) of the instantaneous end-to-end signal-to-noise ratio (SNR); relying on this, the exact analytical and asymptotic expressions are also derived for outage probability (OP) and symbol error rate (SER), whereas for the latter MRC, the closed-form expressions are derived for the exact and asymptotic bit error rate (BER) of binary phase-shift keying (BPSK) signals. The optimal value of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\lambda$</tex></formula> that minimizes the BER is also provided by using Newton's method. It is shown that O-MRC outperforms <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\lambda$</tex></formula> -MRC since the former MRC takes the relay decoding results into account. For <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\lambda$</tex></formula> -MRC, the optimal <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\lambda$</tex></formula> decreases with the increase in the SNR and spatial correlation since increasing the SNR and spatial correlation could increase the confidence of the source–destination link and decrease the confidence of the source–relay link, respectively.