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Today, wireless networks become the most popular way to communicate. However, information can be easily eavesdropped or extracted by eavesdroppers due to the broadcast nature of wireless communication. Multi-hop relay communication systems provide for higher secrecy performance than direct transmission techniques. In this paper, the physical layer secrecy performance of multi-hop decodeand-forward (DF) relay network is investigated in the presence of multiple passive eavesdroppers over Nakagami-m fading channels. To do so, we find out the exact closed-form expressions of existence probability of secrecy capacity and secrecy outage probability by using statistical characteristics of signal-to-noise ratio (SNR). Importantly, these expressions are in more general forms compared to other results in the literature. The proposed results show a quite agreement between numerical analysis and equivalent Monte-Carlo simulations.

Abstract-In this paper, we analyze the maximum likelihood decoding performance of non-regenerative cooperation employing Alamouti scheme. Specifically, we derive two closed-form expressions for average symbol error probability (SEP) when the relays are located near by the source or destination. The analytical results are obtained as a single integral with finite limits and an integrand composed solely of trigonometric functions. Assessing the asymptotic (high signal-to-noise ratio) behavior of SEP formulas, we show that the distributed-Alamouti codes achieves a full diversity order. We also perform Monte-Carlo simulations to validate the analysis.Index Terms-Alamouti, distributed space-time codes (DSTCs), non-regenerative relays, symbol error probability (SEP).

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