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 电子与信息学报 , 2006, Abstract: This paper investigates the outage performance of the cooperative diversity systems for multi-hop wireless networks over Nakagami fading channels. Their closed-form expressions of the regenerative outage probability are derived, and the diversity orders are achieved at high Average Signal-to-Noise Ratio (ASNR) in terms of the single relaying node case and multiple relaying nodes case. The theoretical analysis and simulation results show that the cooperative systems can offer the full-route diversity at some given manners, and their diversity order is the sum of the full route diversities, not the sum of all cooperative nodes, however, the diversity order of each route is determined by the smaller one between that of the two hops.
 Mathematics , 2015, Abstract: This paper addresses the problem of rate selection for the cooperative hybrid automatic repeat request with chase combination (HARQ-CC) system, where time correlated Nakagami-m fading channels are considered. To deal with this problem, the closed-form cumulative distribution function (CDF) for the combine SNRs through maximal ratio combining (MRC) is first derived as a generalized Fox's $\bar H$ function. By using this result, outage probability and delay-limited throughput (DLT) are derived in closed forms, which then enables the rate selection for maximum DLT. These analytical results are validated via Monte Carlo simulations. The impacts of time correlation and channel fading-order parameter $m$ upon outage probability, DLT and the optimal rate are investigated thoroughly. It is found that the system can achieve more diversity gain from less correlated channels, and the outage probability of cooperative HARQ-CC system decreases with the increase of $m$, and etc. Furthermore, the optimal rate increases with the number of retransmissions, while it decreases with the increase of the channel time correlation.
 EURASIP Journal on Wireless Communications and Networking , 2007, Abstract: We analyze the exact average symbol error probability (SEP) of binary and -ary signals with spatial diversity in Nakagami- (Hoyt) fading channels. The maximal-ratio combining and orthogonal space-time block coding are considered as diversity techniques for single-input multiple-output and multiple-input multiple-output systems, respectively. We obtain the average SEP in terms of the Lauricella multivariate hypergeometric function . The analysis is verified by comparing with Monte Carlo simulations and we further show that our general SEP expressions particularize to the previously known results for Rayleigh ( = 1) and single-input single-output (SISO) Nakagami- cases.
 Mathematics , 2015, Abstract: Modeling and analysis of cooperative spectrum sensing is an important aspect in cognitive radio systems. In this paper, the problem of energy detection (ED) of an unknown signal over Nakagami-$m$ fading is revisited. Specifically, an analytical expression for the local probability of detection is derived, while using the approach of ED at the individual secondary user (SU), a new fusion rule, based on the likelihood ratio test, is presented. The channels between the primary user to SUs and SUs to fusion center are considered to be independent Nakagami-$m$. The proposed fusion rule uses the channel statistics, instead of the instantaneous channel state information, and is based on the Neyman-Pearson criteria. Closed-form solutions for the system-level probability of detection and probability of false alarm are also derived. Furthermore, a closed-form expression for the optimal number of cooperative SUs, needed to minimize the total error rate, is presented. The usefulness of factor graph and sum-product-algorithm models for computing likelihoods, is also discussed to highlight its advantage, in terms of computational cost. The performance of the proposed schemes have been evaluated both by analysis and simulations. Results show that the proposed rules perform well over a wide range of the signal-to-noise ratio.
 EURASIP Journal on Wireless Communications and Networking , 2007, DOI: 10.1155/2007/53742 Abstract: We analyze the exact average symbol error probability (SEP) of binary and M-ary signals with spatial diversity in Nakagami-q (Hoyt) fading channels. The maximal-ratio combining and orthogonal space-time block coding are considered as diversity techniques for single-input multiple-output and multiple-input multiple-output systems, respectively. We obtain the average SEP in terms of the Lauricella multivariate hypergeometric function FD(n). The analysis is verified by comparing with Monte Carlo simulations and we further show that our general SEP expressions particularize to the previously known results for Rayleigh (q = 1) and single-input single-output (SISO) Nakagami-q cases.
 EURASIP Journal on Wireless Communications and Networking , 2011, Abstract: We consider differential-pulse position modulation (DPPM) in an ultra wideband (UWB) communication system. A typical format for a DPPM signal in a UWB system is derived from that of a pulse position modulation (PPM) signal. The error probabilities of a UWB DPPM system with receive diversity over additive white Gaussian noise (AWGN) and Nakagami fading channels are derived. Both single-user and multiuser environments are considered. Performance results are presented which show that the frame error rate (FER) with DPPM is better than that with PPM, and the FER performance can be improved significantly by receive diversity.
 International Journal of Wireless & Mobile Networks , 2012, Abstract: This article investigates the efficacy of a novel moment generating function (MGF) based analytical framework for calculating the ergodic channel capacities of cooperative dual-hop amplify-and-forward (CAF) relay networks under three distinct source-adaptive transmission policies in Rice and Nakagamim fading environments. The proposed analytical approach relies on a new exponential-type integral representation for the logarithmic function 1 2 20ln ( ) ( ) , 0,x xx e e dxγγ γ∞ = >∫ that facilitates the task of averaging it over the probability density function (PDF) of end-to-end signal-to-noise ratio (SNR) in a myriad of stochastic fading environments. We also resort to a well-known bounding technique to derive closed-form formulas for the upper and lower bounds for the MGF of dual-hop CAF relayed path SNR in Rice and Nakagami-m channels (since exact evaluation of the MGF of half-harmonic mean SNR in Rice fading is known to be very complicated and numerically unstable). These two attributes dramatically reduces the computational complexity of evaluating the ergodic capacities of CAF multi-relay networks with the optimal joint power-and-rate adaptation (when the channel side information is available at both the transmitter and the receiver) and the optimal rate-adaptation with a constant transmit power (whenchannel side information is available at the receiver only) policies.
 Computer Science , 2012, Abstract: A multi-access multiple-input multiple-output (MIMO) relay differential chaos shift keying cooperative diversity (DCSK-CD) system is proposed in this paper as a comprehensive cooperation scheme, in which the relay and destination both employ multiple antennas to strengthen the robustness against signal fading in a wireless network. It is shown that, with spatial diversity gains, the bit error rate (BER) performance of the proposed system is remarkably better than the conventional DCSK non-cooperation (DCSK-NC) and DCSK cooperative communication (DCSK-CC) systems. Moreover, the exact BER and close-form expressions of the proposed system are derived over Nakagami fading channels through the moment generating function (MGF), which is shown to be highly consistent with the simulation results. Meanwhile, this paper illustrates a trade-off between the performance and the complexity, and provides a threshold for the number of relay antennas keeping the user consumed energy constant. Due to the above-mentioned advantages, the proposed system stands out as a good candidate or alternative for energy-constrained wireless communications based on chaotic modulation, especially for low-power and low-cost wireless personal area networks (WPANs).
 EURASIP Journal on Advances in Signal Processing , 2008, DOI: 10.1155/2008/580368 Abstract: We consider an amplify-and-forward (AF) cooperative diversity system where a source node communicates with a destination node directly and indirectly (through multiple relays). In regular multiple-relay cooperative diversity systems, all relay nodes relay the source signal using orthogonal channels (time slots, carriers, or codes) to avoid cochannel interference. Hence, for a regular cooperative diversity network with M relays, we need M+1 channels (one for the direct link and M for the M indirect links). This means that the number of required channels increases linearly with the number of relays. In this paper, we investigate the performance of the best-relay selection scheme where the ￠ € best ￠ € relay only participates in the relaying. Therefore, two channels only are needed in this case (one for the direct link and the other one for the best indirect link) regardless of the number of relays (M). The best relay is selected as the relay node that can achieve the highest signal-to-noise ratio (SNR) at the destination node. We show that the best-relay selection not only reduces the amount of required resources but also maintains a full diversity order (which is achievable by the regular multiple-relay cooperative diversity system but with much more amount of resources). We derive closed form expressions for tight lower bounds of the symbol error probability and outage probability. Since it is hard to find a closed-form expression for the probability density function (PDF) of SNR of the relayed signal at the destination node, we use an approximate value instead. Then, we find a closed-form expression for the moment generating function (MGF) of the total SNR at the destination. This MGF is used to derive the closed-form expressions of the performance metrics such as the average symbol error probability, the outage probability, the average SNR, the amount of fading, and the SNR moments. Furthermore, we derive the asymptotic behavior of the symbol error probability. From this asymptotic behavior, the diversity order and its dependence on the number of relays (M) can be explicitly determined. Simulation results are also given to verify the analytical results.
 电子与信息学报 , 2009, Abstract: The behavior of the probability density function of the harmonic mean of two independent distributed non-negative random variables at the origin is analyzed. This result is then applied to study the performance of selection amplify-and-forward cooperation protocol in Nakagami fading channel and closed-form expression of the Symbol Error Rate (SER) in high SNR region is also provided. Both analytical and numeric results show that the selection amplify-and-forward cooperation protocol maintains the same diversity order as the conventional amplify-and-forward protocol, and has better SER performance.
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