Closed-form expressions for outage probability of decode-and-forward relaying over Nakagami-m fading channels

In this article, an exact closed-form expression is derived for outage probability of decode-and-forward (DF) cooperative communications over independent identically distributed Nakagami-m fading channels. Simulation results verify that the theoretical expressions for the outage probability are correct. The optimal power allocation based on the derived outage probability is also studied.     

Outage probability of opportunistic decode-and-forward relaying over Nakagami-m fading channels

In this article, the outage probability behavior of a relay network over Nakagami-m fading channels is analyzed. Both reactive and proactive opportunistic decode-and-forward (DAF) strategies are considered. The closed-form solutions to the outage probabilities on both opportunistic DAF strategies are derived. Simulation results conf'Lrrn the presented mathematical analysis.     

On the probability density functions of outage and inter-outage durations of the capacity of Rayleigh fading channels

Approximations for the probability density functions (PDFs) of the capacity outage and inter-outage durations over Rayleigh fading channels are studied. Exact closed form expressions for the Rice probability functions of the level-crossing intervals of the capacity process are derived, assuming a symmetrical Doppler power spectral density (PSD). These probability functions, which are obtained by applying the classical level-crossing theory, are known to describe the PDFs of outage and inter-outage durations only over their initial behavior. Additionally, the derived quantities are used to calculate approximate solutions for the considered PDFs based on the assumption of statistical independence between the level-crossing intervals. Numerical examples, considering Rayleigh mobile-tomobile fading channels, are presented together with simulation results to illustrate the analysis and examine the validity of the derived expressions. Particularly, it is shown that the theoretical results obtained provide accurate approximations for the PDFs of outage and inter-outage durations at low and high outage levels, respectively.     

Exact outage probability for equal gain combining with cochannel interference in Rayleigh fading

Equal gain combining (EGC) diversity has performance close to that of maximal ratio combining but at lower implementation complexity. We present a new outage performance analysis for EGC in mobile cellular radio systems that are limited by cochannel interference and undergo Rayleigh fading. We utilize a new model where interfering signals add in amplitude and phase across antenna array elements. In addition, the interfering signals may each have a different power. In comparing our analysis to an existing method, we find that: 1) as much as 1.5 dB difference in signal-to-interference ratio may exist at the same probability of outage; 2) the existing method can lead to overly optimistic outage performance prediction in certain situations.     

A closed-form expression for the symbol-error rate of M-ary DPSK in fast Rayleigh fading

The error performance of M-ary differential phase-shift keying on Rayleigh fading channels is widely analyzed in the framework originated by Pawula, and the results usually take the form of an integral. In this letter, we formulate the same problem in a different framework, and solve it by using a linear prediction-based technique resulting in a simple solution in closed form.     

Multi-layer coding strategy for multi-hop block fading channels with outage probability

This paper considers communication over a multi-hop Rayleigh block-fading channel, where there is no direct link between the transmission ends, and communication is carried out through the use of multiple cascaded relays, employing the Decode and Forward (DF) strategy. It is assumed that the relays cannot do buffering or apply coding over consecutive transmission blocks, and they can merely re-encode the retried information and forward an encoded version of information to the next hop. In this case, assuming the channel information of each hop is not available at the corresponding transmitter and considering the destination either receives a minimum rate R₀ or declare an outage event, a multi-layer coding strategy in addition to a single-layer code of the minimum rate R₀ are employed, where the optimal power allocation policy across code layers is derived, leading to the maximum average achievable rate for a given outage probability.     

Performance analysis of amplify-and-forward relaying with hybrid-ARQ in Rayleigh fading channels

Hybrid automatic repeat request (HARQ) is a well-known technique for improving system throughput and link performance of wireless communication systems, including cooperative communication systems. The amplify-and-forward (AF) relaying method is one of the most attractive cooperative diversity schemes because of its low complexity. In this article, the end-to-end performance in terms of block error rate (BLER) and normalized throughput of AF relaying with HARQ transmission under the Rayleigh fading channel is analyzed. Numerical results validate the proposed analysis and demonstrate the gain of HARQ schemes in AF relaying systems. This analytical method can be extended to the systems with other HARQ protocols and other cooperative relaying schemes.     

Information outage probability of distributed STBCs over Nakagami fading channels

Space-time block codes (STBCs) allow utilising the diversity provided by multiple-input-multiple-output (MIMO) communication channels, thereby decreasing the outage probability for a given communication rate. The contribution of this letter is the derivation of a closed-form expression of the outage probability of distributed STBCs deployed over Nakagami flat fading channels with different channel gains and fading parameters.     

Performance analysis of serial cooperative communications with decode-and-forward relaying and blind-EGC reception under nakagami fading channels

We analyze a serial cooperative transmission system with DF relaying over Nakagami fading channels. We consider a system in which the simple receivers will not estimate the amplitude of the received signals. Hence, signals are combined with equal gain before decoding. Moreover, the relays use a simple protocol when relaying the messages ? they re-transmit the message if they can decode the received message correctly; otherwise, they do not transmit anything and remain idle. We will derive an exact expression for the asymptotic symbol error rate of the system and evaluate the diversity properties.     

Feedback outage correlated with CQI and its impact on multiuser diversity in Rayleigh fading channels

This letter addresses a feedback outage when the channel condition of the feedback channel is correlated with that of the traffic channel the quality information of which is being carried by the feedback, and its impact on the multiuser diversity in flat Rayleigh fading channels. The correlation is described by the time delay as well as the frequency separation between the traffic and the feedback channel. The average capacity is provided in terms of the time and the frequency factor. With numerical investigations, we show that the capacity degradation due to the feedback outage is generally saturated at the great frequency separation approximately over 45 MHz (e.g., in present IS-95 cellular systems), within which it fluctuates depending on the feedback delay     

Nakagami信道的中断容量分析

本文讨论了Nakagami-m衰落信道系统的中断容量性能,在发射端未知信道信息,接收端的信道估计存在误差时,给出了计算中断容量上界和下界的表达式,它们是接收端的估计误差和信道参数的函数,仿真结果表明随着估计误差的增大中断容量的上界和下界同时降低,但是中断容量的下界随着信道参数的增大而增大,上界随着信道参数的增大而减小。     

Tight bounds on the error probability of coded modulation schemesin Rayleigh fading channels

This paper presents a tight upper bound on the bit error performance of coded modulation schemes in Rayleigh fading channels. Upper and lower bounds on the pairwise error probability are first derived. The upper bound is then expressed in a product form to be used with the transfer function bounding technique. This upper bound has the same simplicity as the union-Chernoff bound while providing closer results to the exact expression. Examples for the case of four-state and eight-state TCM 8PSK schemes are also given to illustrate the tightness and the application of this upper bound     

Multi-branch DFE for Rayleigh fading multipath channels

Multipath Rayleigh fading channels which have very fast time variation can cause loss of tracking in equalisers, from which recovery without retraining is unlikely. A new multi-branch decision feedback equaliser is suggested to improve bit error rate performance while maintaining very low complexity. Simulation results demonstrate its suitability     

Finite-state Markov model for Rayleigh fading channels

We form a finite-state Markov channel model to represent Rayleigh fading channels. We develop and analyze a methodology to partition the received signal-to-noise ratio (SNR) into a finite number of states according to the time duration of each state. Each state corresponds to a different channel quality indicated by the bit-error rate (BER). The number of states and SNR partitions are determined by the fading speed of the channel. Computer simulations are performed to verify the accuracy of the model     

GQR models for multipath Rayleigh fading channels

In this paper, reduced complexity statistical models for the representation of wide sense stationary-uncorrelated scattering doubly selective fading channels are developed. Their derivation is based on the evaluation of Fourier integrals by means of Gaussian quadrature rules. The accuracy and the complexity of the proposed models is assessed, and is then compared to that provided by other modeling techniques available in the literature     

New closed-form bounds on the performance of coding in correlated Rayleigh fading

New, simple bounds are presented for the probability of error in a binary hypothesis test for communications using diversity signaling in correlated Rayleigh fading. The bounds are developed in the context of pairwise error-event probabilities in decoding an error-correction code. A long-standing conjecture regarding the form of worst-case error events in exponentially correlated Rayleigh fading is also proven. The utility of the results is illustrated by their application to transfer-function bounds on the probability of bit error for a system using a convolutional code. The closed-form transfer-function bounds are shown to be tighter than previously developed transfer-function bounds for communications in exponentially correlated Rayleigh fading.     

Average bit-error probability performance for optimum diversity combining of noncoherent FSK over Rayleigh fading channels

We derive the performance of the optimum noncoherent frequency-shift keying diversity combining receiver and compare it with that which implements the more traditional noncoherent postdetection equal gain combining scheme to reveal the degree of suboptimality of the latter.     

Efficient expression and bound for pairwise error probability in Rayleigh fading channels, with application to union bounds for turbo codes

This work provides a new exact expression for the pairwise error probability under perfect channel state information. Using this expression, the average union upper bounds for (1,7/5,7/5) and (1,5/7,5/7) turbo coding schemes are presented based on transfer function approach assuming fully interleaved Rayleigh fading channels. Derivation for the pairwise error probability leads to a compact approximation which overlaps with the exact expression. This new approximation is computationally more efficient than the existing ones, and leads to a much quicker general ion of union bounds for performance analysis.     

Effect of multiple antennas at the source on outage probability for amplify-and-forward relaying systems

The amplify-and-forward (AF) relaying system considered here consists of a source node with M transmit antennas, and relay and destination nodes with a single antenna each. The closed-form expressions for the outage probabilities for maximum-ratio-transmission (MRT) at the source are presented for some specific values of M. Numerical results show that increasing M from 1 to 2 can achieve roughly a 3dB SNR gain, guaranteeing the same outage probability. However, we discover that for M ≥ 3, the additional gain compared to M = 2 decreases quickly as the SNR increases. Therefore, increasing M above 3 does not achieve significantly greater gain over M = 2 at high SNR.