Performance Analysis of Generic Amplify-and-Forward Cooperative Networks over Asymmetric Fading Channels

In this paper, we analyze the performance of multi-hop multi-branch amplify-and-forward (AF) networks over generalized fading channels. Using the moment generating function (MGF)-based approach, we develop general expressions for the outage probability and symbol-error rate (SER) performance of the system with maximal ratio combining (MRC) receiver. The MGF-based approach relies on numerical integration. To gain insights into system performance, we therefore investigate the asymptotic outage and SER performance of the system with MRC and selection combining (SC) receiver at the destination. In particular, we develop the asymptotic statistics of the end-to-end signal-to-noise ratio (SNR) of an AF multi-hop link. We further derive the cumulative density function of the sum of the individual end-to-end SNRs, received from different diversity paths for MRC receiver. We also study the power allocation problem in a multi-hop multi-branch system with MRC receiver. In generalized Gamma fading environments, we seek to find the power allocation strategy that maximizes the SNR at the destination subject to a total power constraint. By means of simulations, we validate our theoretical developments and verify the efficiency of our proposed power allocation in improving the received SNR compared to a generic cooperative system with no power allocation. We also conclude that our asymptotic expressions for the outage probability and SER match the simulations very well in medium-to-high-SNR regime.     

选择性放大传送协同通信在Nakagami信道中的性能分析

该文根据两个统计独立非负随机变量的调和平均值的概率密度函数在零点的变化特性,分析了选择性放大传送协同协议在Nakagami衰落信道中的性能,得出了高信噪比时系统误符号率的闭合表达式。理论分析和数值仿真结果表明,在Nakagami信道中选择性放大传送协同协议可获得和传统放大传送协同协议一样的分集阶数,并且具有更优的误符号率性能。     

Performance Analysis of Joint Adaptive Modulation and Diversity Combining Over Fading Channels

Both adaptive modulation and diversity combining represent important enabling techniques for future generations of wireless communication systems. In this paper, capitalizing on recent developments in adaptive combining, we propose three joint adaptive modulation and diversity combining (AMDC) schemes. With these schemes, the modulation mode and diversity combiner structure are adaptively determined based on the fading channel condition and error-rate requirement. We accurately analyze these three AMDC schemes in terms of processing power consumption, spectral efficiency, and error-rate performance. Selected numerical examples show that the proposed AMDC systems meet the target error-rate requirement while achieving high spectral efficiency with low processing power consumption     

SER Analysis of QAM with Space Diversity in Rayleigh Fading Channels

This paper derives the symbol error probability for quadrature amplitude modulation(QAM) with L-fold space diversity in Rayleigh fading channels. Two combining techniques, maximal ratio combining(MRC) and selection combining(SC), are considered. The formula for MRC space diversity is obtained by averaging the symbol error probability of M-ary QAM in an additive white Gaussian noise(AWGN) channel over a chi-square distribution with 2L degrees of freedom. The obtained formula overcomes the limitations of the earlier work, which has been limited only to deriving the symbol error rate(SER) of QAM with two branch MRC space diversity. The formula for SC space diversity is obtained by averaging the symbol error probability of M-ary QAM in an AWGN channel over the distribution of the maximum signal-to-noise ratio among all of the diversity channels for SC space diversity. No analysis for QAM with SC space diversity has been reported yet. Analytical results show that the probability of error decreases with the order of diversity. We can also see that the incremental diversity gain per additional branch decreases as the number of branches becomes larger. On the other hand, the performance of 16 QAM with MRC becomes much better than that of SC as the number of branches becomes larger. By giving the order of diversity, L, and the number of signal points, M, we have been able to obtain the SER performance of QAM with general space diversity. These results can be used to determine the order of diversity to achieve the desired SER in land mobile communication system employing QAM modulation.     

Packet Radio Performance Over Slow Rayleigh Fading Channels

Expressions for the throughput and average packet delay for a Pure-ALOHA single-hop packet radio system operating in slow Rayleigh fading are derived. For noncoherent frequency-shift-keying (NCFSK), an exact closed form expression is presented. For coherent phase-shift-keying (CPSK) an excellent approximation for large packet sizes is derived. This approximation technique is valid in general for other modulation schemes and for other fading channel statistical characterizations. The packet length which maximizes the useful data throughput in slow Rayleigh fading is found. The results of this investigation indicate that a packet radio system can be designed with a modest link margin for fading and achieve identical throughput performance over a nonfading channel and a fading channel with only a small increase in average packet delay for the fading channel.     

Hybrid Digital-Analog Relaying for Cooperative Transmission Over Slow Fading Channels

Hybrid digital-analog coding schemes have been proposed in source-channel coding to increase the robustness toward channel mismatch, in the absence of transmitter channel state information (CSIT). Recognizing that the same kind of robustness is needed at the relay in a three-node relay network, we propose several novel relaying protocols based on hybrid digital-analog transmission. We compare the performance of the new schemes with traditional digital-only (decode-and-forward or compress-and-forward) or analog-only (amplify-and-forward) relaying, as well as to performance bounds corresponding to genie-aided compress-and-forward relaying. Our new protocols achieve significant gains in terms of achievable expected rates, and they are able to close in on the performance bounds. In particular, we conclude that the best overall performance is obtained by an adaptive combination of decode-and-forward and hybrid digital-analog relaying.      

Digital Transmission Performance on Fading Dispersive Diversity Channels

The reception and detection of a single digit under known channel conditions are investigated. The probability of error for an optimum one-shot receiver instantaneously matched to the channel state is averaged over an ensemble of dispersive diversity channels. The average probability of error as a function of energy to noise ratio is found to be solely dependent on the ratio of rms dispersion width to data symbol width. For these dispersive channels an implicit diversity effect is qualitatively explained in terms of eigenvalues that depend on the ensemble statistic. The one-shot receiver performance provides a bound for practical receivers. In a comparison with a decision feedback equalizer, it is shown that on moderately dispersive channels the equalizer nearly achieves optimum one-shot performance. Since an adaptive version of this equalizer exists, this means data transmission on slowly fading channels is possible at rates above the natural rate suggested by the channel dispersion spread without bandwidth expansion and with small intersymbol interference penalty. The use of one-shot receiver performance curves can also be used as estimates of equalizer performance in situations where computation of the latter is impractical.     

Performance Analysis of Blind-Adaptive-Subspace Multiuser Detectors Over Multipath Fading Channels

Perturbation analyses for various kinds of blind-adaptive-subspace multiuser detectors are presented in this paper. Closed-form expressions are derived for the minimum-mean-square-error detector, zero-forcing detector, and group-blind detector in terms of output signal-to-interference-plus-noise ratio and bit-error rate over a multipath fading channel. Numerical results show that the analytical results match well with the simulation results for both static and dynamic environments. Furthermore, the proposed analytical results can be treated as performance bounds for other blind-adaptive singular-value-decomposition-based subspace multiuser detectors     

Secure Communication Over Fading Channels

The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The broadcast channel from the source node to receivers 1 and 2 is corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The parallel BCC with independent subchannels is first studied, which serves as an information-theoretic model for the fading BCC. The secrecy capacity region of the parallel BCC is established, which gives the secrecy capacity region of the parallel BCC with degraded subchannels. The secrecy capacity region is then established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived. In particular, the secrecy capacity region is established for the basic Gaussian BCC. The secrecy capacity results are then applied to study the fading BCC. The ergodic performance is first studied. The ergodic secrecy capacity region and the optimal power allocations that achieve the boundary of this region are derived. The outage performance is then studied, where a long-term power constraint is assumed. The power allocation is derived that minimizes the outage probability where either the target rate of the common message or the target rate of the confidential message is not achieved. The power allocation is also derived that minimizes the outage probability where the target rate of the confidential message is not achieved subject to the constraint that the target rate of the common message must be achieved for all channel states.     

On the Performance of Energy-Division Multiple Access Over Fading Channels

In this paper we consider a multiple-access scheme in which different users share the same bandwidth and the same pulse, and are discriminated at the receiver on the basis of the received energy using successive decoding. More specifically, we extend the performance analysis from the case of additive white Gaussian noise channels (presented in a previous work Salvo Rossi in Wirel Pers Commun, in press) to the case of fading channels. The presence of channel coefficients introduces a new degree of freedom in the transceiver design: unlike the AWGN case, different ordering among the users provides different transmitted energy, thus different overall system performance. Optimal ordering, in terms of minimum transmitted energy, is derived analytically. Analytical and numerical results, in terms of bit error rate and normalized throughput, are derived for performance evaluation in fading environments with optimal ordering exhibiting significant gains w.r.t. static ordering.     

Nakagami衰落信道下多跳合作分集系统的中断率

该文在Nakagami衰落信道下研究了多跳无线网络中合作分集系统的中断性能。根据单节点和多节点中继的情况导出了合作系统再生中继时中断率的数学闭式解,并在高平均信噪比下给出了系统的分集度。理论分析和仿真研究的结果表明多跳合作系统在一定条件下可实现全路由分集,其分集度为所有路由的分集度之和,不是所有合作节点的和,但每支路由的分集度取决于该路由两跳中较小的值。     

Exact Outage Probability of Underlay Cognitive Cooperative Networks Over Rayleigh Fading Channels

Our contribution in this paper is the derivation of an exact closed-form outage probability formula for underlay cognitive cooperative networks operated over Rayleigh fading channels. The derivation considers the correlation among received signal-to-noise ratios, two critical constraints (interference power constraint and maximum transmit power constraint), and non identically distributed (i.d.) channels. The derived formula is corroborated by Monte Carlo simulations and is served as an useful and effective tool to evaluate the performance behavior of underlay cognitive cooperative networks without time-consuming simulations under different operation parameters. Numerical results illustrate that underlay cognitive cooperative networks suffer the outage saturation phenomenon for a given maximum interference power level.     

Performance Analysis of Amplify-and-Forward Relay Systems with Interference-Limited Destination in Various Rician Fading Channels

In this paper, we investigate the performance of a dual-hop fixed-gain amplify-and-forward relay system in the presence of co-channel interference at the destination node. Different fading scenarios for the desired user and interferers’ channels are assumed in this study. We consider the Rician/Nakagami- \(m\) , the Rician/Rician, and the Nakagami- \(m\) /Rician fading environments. In our analysis, we derive accurate approximations for the outage probability and symbol error probability (SEP) of the considered scenarios. The generic independent non-identically distributed (i.n.d.) case of interferers’ channels is considered for the Rician/Nakagami- \(m\) scenario; whereas, the independent identically distributed (i.i.d.) case is studied for the Rician/Rician and the Nakagami- \(m\) /Rician environments. Furthermore, to get more insights on the considered systems, high signal-to-noise ratio (SNR) asymptotic analysis of the outage probability and SEP is derived for special cases of the considered fading scenarios. Monte-Carlo simulations and numerical examples are presented in order to validate the analytical and asymptotic results and to illustrate the effect of interference and other system parameters on the system performance. Results show that the different fading models of interferers’ channels have the same diversity order and that the interference degrades the system performance by only reducing the coding gain. Furthermore, findings show that the case where the fading parameter of the desired user first hop channel is better than that of the second hop gives better performance compared to the vise versa case, especially, at low SNR values; whereas, both cases almost behave the same at high SNR values where the performance of the system is dominated by the interference affecting the worst link. Finally, results show the big gap in system performance due to approximating the Rician fading distribution with the Nakagami- \(m\) distribution which is an indication on the inaccuracy of making such approximations in systems like the considered.     

Target Tracking Over Fading Channels

The problem of tracking a target in a multitarget environment when the observations are received over a fading channel is considered. The optimal Bayes solution to the tracking problem in such cases involves growing memory and hence is not feasible. A particularly effective suboptimal scheme uses a probabilistic judgment at each stage of the observations to overcome this problem. This concise paper presents an evaluation of the scheme in terms of mean-square error performance when the observations are received over fading channels.     

Secure Broadcasting Over Fading Channels

We study a problem of broadcasting confidential messages to multiple receivers under an information-theoretic secrecy constraint. Two scenarios are considered: 1) all receivers are to obtain a common message; and 2) each receiver is to obtain an independent message. Moreover, two models are considered: parallel channels and fast-fading channels. For the case of reversely degraded parallel channels, one eavesdropper, and an arbitrary number of legitimate receivers, we determine the secrecy capacity for transmitting a common message, and the secrecy sum-capacity for transmitting independent messages. For the case of fast-fading channels, we assume that the channel state information of the legitimate receivers is known to all the terminals, while that of the eavesdropper is known only to itself. We show that, using a suitable binning strategy, a common message can be reliably and securely transmitted at a rate independent of the number of receivers. We also show that a simple opportunistic transmission strategy is optimal for the reliable and secure transmission of independent messages in the limit of large number of receivers.     

一种改进的差分空时协同分集方案及误码性能分析

提出了一种分布式差分空时分集方案，通过对差分编码方式的改进，可使用多种星座形状来进行调制。在采用了QAM星座调制时，比传统的PSK调制具有更好的性能，可以改善无线网络中的能量效率。在不考虑协同节点间误码的情况下，分析和推导了平坦衰落瑞利信道下该方案的SER性能上限的表达式。仿真结果表明采用QAM调制下的DSTBC性能优于PSK调制下的DSTBC。同时在慢衰落的条件下，仿真结果和理论分析的结果吻合较好，说明了方案的有效性。     

Performance Analysis of Relay-Assisted Cooperative Systems in Correlated Fading Channels

In this paper, the effect of fading correlation at the receiving elements of a linear antenna array in a relay-assisted cooperative single-input multiple-output (SIMO) system has been investigated over flat Rayleigh fading channels. Considering a model of local scatterer around the source and relay nodes and uniform angle of arrival (AOA) distribution, the spatial cross-correlation analysis is presented and extensive simulation studies are performed to determine the envelope correlation as a function of antenna spacing, mean AOA and angular spread. Error performance analysis for coherent binary and quaternary modulations are presented for fixed-gain amplify-and-forward (AF) and fixed decode-and-forward (DF) relaying with dual diversity maximal-ratio combiner (MRC) receiver array. Error probability in terms of bit error probability (BEP) and symbol error probability (SEP) is evaluated to study the effect of relevant parameters on the correlation performance. The presented results establish the fact that fixed DF relay network performs relatively well than fixed-gain AF relaying. Superior performance of dual-hop cooperative SIMO system over conventional single-hop SIMO system has also been observed.     

MIMO Cooperative Diversity with Scalar-Gain Amplify-and-Forward Relaying

We analyze diversity performance of scalar fixed- gain amplify-and-forward (AF) cooperation in multiple-input multiple-output (MIMO) relay channels with ns source antennas, nR relay antennas, and nD destination antennas. We first derive the exact symbol error probability (SEP) for maximum likelihood decoding of orthogonal space-time block codes with M-ary phase-shift keying modulation over such channels and then characterize the effect of MIMO cooperative diversity on SEP behavior in a high signal-to-noise ratio regime. We show that the simple scalar-gain AF cooperation can create the diversity order d_AF les n_Sn_D + n_Sn_Rn_D/max{n_S, n_R, n_D} with the equality if 2max{n_S, n_R,n_D} ges n_S + n_R + n_D - 1. This finding reveals that the number of relay antennas greater than or equal to n_S + n_D - 1 is required to achieve the additional diversity order n_Sn_D by scalar-gain AF relaying. We also present the asymptotic SEP as the number of relay antennas tends to infinity.     

Average LCR and AFD for SC Diversity Over Correlated Weibull Fading Channels

The analytic methods of average LCR (Level Crossing Rate) and AFD (Average Fading Duration) are applied in the analysis for the SC (Selection Combining) diversity, which works over the correlated Weibull statistics channel. The dual branch SC diversity was used to prove the accuracy of the derived theoretical formula in this paper. We adopt different probability density functions (pdf) and cumulate distribution functions (CDF) to show the Moreover, the numerical results obtained from computer are verified to the published researches.     

Spectral Efficiency Evaluation for MRC Diversity Schemes Over Generalized Rician Fading Channels

In this paper, closed-form expressions for the capacities per unit bandwidth for generalized Rician fading channels are derived for power and rate adaptation, constant transmit power, channel inversion with fixed rate, and truncated channel inversion adaptation policies. The closed-form solutions are derived for the single antenna reception (without diversity combining) and maximal-ratio combining (MRC) diversity cases. Truncated channel inversion adaptation policy is the best policy for the single antenna reception case, while the channel inversion with fixed rate policy is the best policy for the MRC diversity case. Constant transmit power policy provides the lowest spectral efficiency as compared to the other policies with and without diversity.