In this paper, the uplink performance of Multi-User Multiple Input Multiple Output (MU-MIMO) Zero Forcing (ZF) receiver is investigated over correlated Rayleigh fading channels with channel estimation error. A mathematical expression for the sub-streams' output Signal to Noise Ratio (SNR) with transmit and receive-correlation is derived in the presence of erroneous channel estimates. Besides, an approximate and accurate expression for the Bit Error Rate (BER) of ZF receiver for 16-Quadrature Amplitude Modulation (QAM) with transmit-correlation is deduced in terms of the hypergeometric function. Subsequently, the developed analytical BER is verified by Monte-Carlo trails accounting various system parameters. The simulation results indicate that ZF receiver's BER relies solely on the transmit-correlation for the same number of transmit and receive-antennas at higher average SNR values per transmitted symbol (Es/N0). Also, a logarithmic and exponential growth in the BER is observed with an increase in the Mean Square estimation Error (MSE) and correlation coefficient, respectively.

In this paper, we show exact bit error rates (BERs) for orthogonal space-time block code (OSTBC) decoded-and-forward (DF) relaying networks over independent and non-identically distributed (INID) Rayleigh fading channels. We consider both non-adaptive DF (non-ADF) and adaptive DF (ADF) schemes for OSTBC relay networks with arbitrary multiple-input multiple-output (MIMO) relay antenna configurations. For each scheme, we derive the probability density functions (PDFs) of indirect link and combined links, respectively. Based on the derived PDFs, we express exact BERs and then, their accuracy is verified by the comparison with simulation results. It is confirmed that the transmit diversity gain of the relay node can be obtained when the relay is close to the source and then, the receive diversity gain of the relay node as well as ADF gain over non-ADF can be obtained when the relay is close to the destination.

In recent years, since Turbo and LDPC codes are very close to the Shannon limit, a great deal of attention has been placed on the capacity of AWGN and fading channels with arbitrary inputs. However, no closed-form solution has been developed due to the complicated Gaussian integrations. In this paper, we investigate the capacity of AWGN and fading channels with BPSK/QPSK modulation. First, a simple series representation with fast-convergence for the capacity of AWGN is developed. Further, based on the series expression, the capacity of fading channels including Rayleigh, Nakagami and Rice fading can be obtained through some special functions. Numerical results verify the accuracy and convergence speed of the proposed expressions for the capacity of AWGN and fading channels.

In this paper, we propose an analytical approach for adaptive decode-and-forward (ADF) relaying schemes consisting of burst data transmission based on pilot symbol assisted-channel estimation (PSA-CE) methods over quasi-static Rayleigh fading channels. At first, we focus on the error-event at relay nodes in which the transmission mode switching is carried out burst by burst, whereas previous studies assumed the transmission mode switching symbol-by-symbol, thus showing lower error rate bound. Under consideration of burst transmission for ADF relay systems, we derive exact error rate expressions which better estimate the performance of actual systems. Then, the average bit and burst error rates are derived in approximated expressions for an arbitrary link signal-to-noise ratio (SNR) related with channel estimation errors. Their accuracy is confirmed by comparison with simulation results. Furthermore, ADF relay systems with PSA-CE schemes are confirmed to select correctly decoded relay nodes without additional signaling between relay nodes and the destination node and it is verified to achieve the performance at a cost of negligible SNR loss.

The performance of multiuser multiple-input single-output (MU-MISO) systems is not only affected by small-scale multipath fading but also by large-scale fading (i.e., shadowing) and path loss. In this paper, we concentrate on the sum rate distribution of MU-MISO systems employing linear zero-forcing beamforming, accounting for both multipath fading and shadowing effects, as well as spatial correlation at the transmit and receiver sides. In particular, we consider the classical spatially correlated lognormal model and propose closed-form bounds on the distribution of the achievable sum rates in MU-MISO systems. With the help of these bounds, we derive a relationship between the interuser distance and sum rate corresponding to 10% of the cumulative distribution function under different environmental conditions. A practical conclusion from our results based on the considered system is that the effect of spatially correlated shadowing can be considered to be independent when the interuser distance is approximately five times the shadowing correlation distance. Furthermore, a detailed analysis of the effects of composite channel attenuation consisting of multipath fading and shadowing is also provided.

In this paper, we analyze the performance of a dual-hop multiuser amplify-and-forward (AF) relay network with the effect of the feedback delay, where the source and each of the K destinations are equipped with Nt and Nr antennas respectively, and the relay is equipped with a single antenna. In the relay network, multi-antenna and multiuser diversities are guaranteed via beamforming and opportunistic scheduling, respectively. To examine the impact of delayed feedback, the new exact analytical expressions for the outage probability (OP) and symbol error rate (SER) are derived in closed-form over Rayleigh fading channel, which are useful for a large number of modulation schemes. In addition, we present the asymptotic expressions for OP and SER in the high signal-to-noise ratio (SNR) regime, from which we gain an insight into the system performance with deriving the diversity order and array gain. Moreover, based on the asymptotic expressions, we determine power allocation among the network nodes such that the OP is minimized. The analytical expressions are validated by Monte-Carlo simulations.

The fading channel model is seen as an important approach that can efficiently capture the basic time-varying properties of wireless channels, while physical layer security is a promising approach to providing a strong form of security. This paper focuses on the fundamental performance study of applying physical layer security to achieve secure and reliable information transmission over the fading wire-tap channel. For the practical scenario where the main channel is correlated with the eavesdropper channel but only the real time channel state information (CSI) of the main channel is known at the transmitter, we conduct a comprehensive study on the fundamental performance limits of this system by theoretically modeling its secrecy capacity, transmission outage probability and secrecy outage probability. With the help of these theoretical models, we then explore the inherent performance tradeoffs under fading wire-tap channel and also the potential impact of channel correlation on such tradeoffs.

The outage performance of a multiuser two-way amplify-and-forward (AF) relaying network, where N-th best selection scheme with the consideration to the feedback delay, is investigated. Specifically, the new closed-form expressions for cumulative distribution function (CDF) and outage probability (OP) are presented over time varying Rayleigh-fading channels. Furthermore, simple approximate OP is derived assessing the high signal-to-noise-ratio (SNR), which identifies the diversity behavior. Numerical results show excellent agreement with theoretical results.

The focus of this study is the performance of the relaying network with incremental selective decode-and-forward (ISDF) protocol in non-selective slow Nakagami-m fading channels. To enhance bandwidth efficiency, when the direct transmission is not successful the relay is used to retransmit a clean copy of the source signal. The proposed protocol achieves a significant reduction in the power consumption and an improvement in performance compared to the fixed decode-and-forward (DF). The exact symbol error rate (SER) of M-PSK modulation for the ISDF protocol over general fading channels is derived. However, as the exact SER analysis is very complicated, we provide an approximated SER expression. Based on this approximation, we provide an optimum power allocation coefficient where the aggregate transmit power constraint is imposed on the source and the relay. Our results show that at least 50% of total power must be used by the direct link, and the remaining may be used by the relay. Furthermore, power allocation in this protocol is independent of the quality of the source-destination channel and modulation constellation size. Numerical results show that the ISDF protocol can reduce the average transmit power with respect to the fixed DF protocol.

In this letter, an improved statistical simulation model with a new parameter computation method is proposed for Rayleigh fading channels. Compared with the existing simulators, the proposed model yields much higher simulation efficiency, while it can still obtain adequate approximations of the desired statistical properties.

In this letter, we provide an asymptotic error rate performance evaluation of space-time block codes from coordinate interleaved orthogonal designs (STBCs-CIODs), especially in shadowed Rayleigh fading channels. By evaluating a simplified probability density function (PDF) of Rayleigh and Rayleigh-lognormal channels affecting the STBC-CIOD system, we derive an accurate closed-form approximation for the tight upper and lower bounds on the symbol error rate (SER). We show that shadowing asymptotically affects coding gain only, and conclude that an increase in diversity order under shadowing causes slower convergence to asymptotic bound due to the relatively larger loss of coding gain. By comparing the derived formulas and Monte-Carlo simulations, we validate the accuracy of the theoretical results.

Underlay cognitive systems allow secondary users (SUs) to access the licensed band allocated to primary users (PUs) for better spectrum utilization with the power constraint imposed on SUs such that their operation does not harm the normal communication of PUs. This constraint, which limits the coverage range of SUs, can be offset by relaying techniques that take advantage of shorter range communication for lower path loss. Symbol error rate (SER) analysis of underlay cognitive relay systems over fading channel has not been reported in the literature. This paper fills this gap. The derived SER expressions are validated by simulations and show that underlay cognitive relay systems suffer a high error floor for any modulation level.

This letter presents a method for obtaining an exact average symbol error rate (ASER) of M-phase shift keying (M-PSK) transmission for the Nth best opportunistic amplify-and-forward (OAF) relay systems over Rayleigh fading channels. This approach begins with deriving the relay selection probability when a relay is selected as the Nth best one with respect to the received signal-to-noise ratio. We then derive the modified moment generating function (MGF) for the Nth best OAF relay systems by taking the given Nth best-relay selection probability into consideration. Based on the modified MGF, we derive the exact ASER which accurately explicates the Nth best OAF relay system characteristics. Simulation results confirm the exactness of the analysis results for M-PSK transmission with respect to the number of relays, the Nth best relay selection, and the relay position.

This study shows a fast simulation method of turbo codes over slow Rayleigh fading channels. The reduction of the simulation time is achieved by applying importance sampling (IS). The conventional IS method of turbo codes over Rayleigh fading channels focuses only on modification of additive white Gaussian noise (AWGN) sequences. The proposed IS method biases not only AWGNs but also channel gains of the Rayleigh fading channels. The computer runtime of the proposed method is about 1/5 of that of the conventional IS method on the evaluation of a frame error rate of 10-6. When we compare with the Monte Carlo simulation method, the proposed method needs only 1/100 simulation runtime under the condition of the same accuracy of the estimator.

In this letter, we derive another exact bit error rate (BER) for decode-and-forward (DF) relay systems over Rayleigh fading channels. At first, our focus is on fixed-DF (FDF) relay schemes in which the probability density function (PDF) is derived based on error-events at relay nodes. Some insight into how erroneous detection and transmission at relay nodes affect both the combined signal-to-noise ratio (SNR) and the averaged BER is obtained, and cooperative diversity is observed from the closed-form BER expression. In addition, the developed analytical method is extended to adaptive-DF (ADF) schemes and the exact BER expressions are derived. Simulation results are finally presented to validate the analysis.

In this letter, we investigate the Nth-best user selection scheme for amplify-and-forward cooperative systems over Rayleigh fading channels. We deduce the probability density function, the cumulative density function, and the moment generating function of the end-to-end signal-to-noise ratio of the system. Then, the respective closed-form expressions of the average symbol error probability and the outage probability at the destination are derived. The diversity order obtained in the scheme increases with user number but becomes less as the selection sequence number N increases. Simulation results verify the analytical results.

This paper gives statistical analysis of double fading channels which are typically found in keyhole MIMO(multiple input multiple output) models. First, to investigate the potential of identically distributed double Nakagami-Rice MIMO keyhole channels including LOS(line of sight) environment, the density function of SNR(signal to noise ratio) which corresponds to the only one non-zero eigenvalue of channel correlation matrix is presented. In addition to the exact expression with an infinite series form, an approximation formula with a simple monomial form derived by substituting Nakagami m formula for Rician distribution is also considered. Next, similar equations are introduced for double Rayleigh channels which have correlated branches in both the transmitter and receiver sides(independent but nonidentical case is included here). Through computer simulations, the effectiveness of the proposed formulae is verified, and in double Nakagami-Rice fading case, the advantage of the approximated formula particularly for large array size and/or large Rician factor is demonstrated.

Switch and stay combining (SSC) is an attractive diversity technique due to its low complexity and compatibility to resource-constrained wireless networks. This letter proposes a distributed SSC for partial relay selection networks in order to achieve spatial diversity as well as to improve spectral efficiency. Simulation results show that the performance loss (in terms of bit error probability) of the proposed networks relative to partial relay selection networks with selection combining is not substantial.

Generalized selection combining (GSC) was recently proposed as a low-complexity diversity combining technique for diversity-rich environments. This letter proposes a multi-hop Decode-and-Forward Relaying (MDFR) scheme in conjunction with GSC and describes its performance in terms of average bit error probability. We have shown that the proposed protocol offers a remarkable diversity advantage over direct transmission as well as the conventional decode-and-forward relaying (CDFR) scheme. Simulation results are also given to verify the analytical results.

This paper studies the optimum combining (OC) system with multiple arbitrary-power interferers and thermal noise in a flat Rayleigh fading environment. The main contribution of the paper is a concise performance analysis for the overload OC system where the number of interferers exceeds or is equal to the number of antennas elements. Simple closed-form formulas are derived for the moment generating function (m.g.f) of the output signal-to-interference-plus-noise ratio (SINR) and the symbol error rate (SER) with M-ary phase shift keying (M-PSK). These formulas are expressed as a finite sum involving polynomial, exponential and exponential integral terms. Based on the derived m.g.f, the closed-form explicit expressions for the moments of the output SINR are determined. Finally, asymptotic analysis illustrates that employing distinguished power control is an effective approach to combat the SER floor for the overload OC system.