Error Performance Evaluation of Wireless Communication Systems Using Maximal Ratio Combining with Multiple Interferers

In this paper we evaluate the error performance of wireless communication systems using M-branch maximal ratio combining (MRC) with multiple cochannel interference. Three cochannel interference models are considered: (A) L independent identically distributed (i.i.d.) Nakagami-m cochannel interferers; (B) L independent cochannel interferers consisting of L-N Nakagami-m interferers and N Rayleigh interferers; (C) L independent cochannel interferers in which each interferer follows Nakagami-m distribution for a fraction of time and Rayleigh distribution for the remaining time. In addition, the desired signal assumes Nakagami-m fading. This paper considers that an exponential correlation model is assumed for the desired signals received on each branch, while the interferers are assumed independent. Closed-form expressions are derived for the probability density functions (PDFs) of the instantaneous signal-to-interference power ratio (SIR) at the output of the MRC for the three interference models. Using these SIR PDFs, further closed-form expressions to evaluate the outage probability (OTP) and the average bit error probability (BEP) of differential phase-shift keying (DPSK) are derived. Numerical results showing the impacts of the system parameters on the OTP and the average BEP are then presented.     

Finite-State Markov Chain Models for the Intensity of Nakagami Fading

For the design, analysis, and simulation of communication systems with Nakagami-m fading channels, it is very convenient to model the fading by finite-state Markov chains in which the states represent fade levels or signal-to-noise ratios in decibels. Our approach to the development of such Markov chain models is to work with the intensity of the fading process, which is proportional to the logarithm of squared envelope of the faded signal. We demonstrate that all the parameters of the Markov chains can be determined from the bivariate distribution of the intensity of the Nakagami-m fading process. Several analytical results are derived from the bivariate distribution of the intensity, including expressions for the chain’s transition probabilities for both adjacent and nonadjacent states and the asymptotic distribution of the intensity for deep fades. For several values of m, we verify the accuracy of our Markov chain models as simulation tools by comparisons of the state probabilities and level-crossing rates obtained from simulations of the Markov chain with those obtained from our analytical expressions.     

Reliability of a jammed binary transmission over a Nakagami channel

This study presents a mathematic and numerical analysis of the probability of error in a binary transmission over a fading radio channel described by Nakagami-m distribution and its special cases. The transmission is jammed by a signal occupying the entire (or comparable) band before detection.     

Composite Phase PDF in Gamma Shadowed Nakagami Fading Channel

This paper presents a new Fourier series form probability density function (PDF) for the phase of the received signal over gamma shadowed Nakagami-m fading channel with additive Gaussian noise. This PDF is further used to evaluate the average symbol-error probability of M-ary CPSK. An alternative new closed-form expression for bit error-rate of binary CPSK is also derived and numerically compared with the corresponding result based on the Fourier series form phase PDF. We show that the two expressions are indeed numerically equivalent.     

Multivariate Nakagami-m distribution with constant correlation model

In this paper, a multivariate Nakagami-m distribution is derived using Royen's gamma distributions of one-factorial accompanying matrices for a constant correlation model. The cumulative distribution function, the probability density function and the covariances are obtained in infinite series form. From these results, we derive outage probabilities of selection combiners in both interference- and noise-limited scenarios with a constant correlation model over Nakagami-m fading assuming arbitrary average powers at each input of the combiner.     

Evaluation of Nakagami fading behaviour based on measurements in urban scenarios

It is well known that the short-term fading conditions of the received envelope in wireless communications channels can be modelled by means of the Nakagami distribution. The value of the m parameter, also called shape factor, indicates the severity of multipath fading, and is a measure of channel quality, making its estimation necessary in many applications. In this letter, a range of possible values of the m parameter based on the analysis of a measurements campaign in urban scenarios is presented.     

An Analytical Approach to Outage Analysis and Critical Cooperation Ratio in Coded Cooperation

In this paper, we analyze the performance of a coded cooperation based communication system using independent flat Nakagami-m fading channels. We examine the outage behavior of the cooperative system constrained on instantaneous received power which follows the Gamma distribution. The expression for outage probability of the coded cooperative communication system is derived which is applicable for arbitrary value of parameter m and contains single integral terms only. Finally, we present an analytical approach to evaluate the critical cooperation ratio that minimizes the total outage probability of the cooperative system.     

Performance modeling of finite state Markov chains for Nakagami-q and α–μ distributions over adaptive modulation and coding schemes

In this paper, performance modeling of finite state Markov chain (FSMC) for Nakagami-q and α–μ fading distributions over adaptive modulation and coding (AMC) schemes at the physical layer are discussed in detail, assuming that sufficient data is present to be transmitted continuously during the adaptive transmission period. However, this assumption is not always valid when queuing effects are taken into account at the data link layer. The received SNR obtained from a coded multiuser wireless system in the presence of a heavily shadowed environment is assumed to undergo a Nakagami-q (Hoyt distribution. Performance measures like level crossing rate, steady state probability, state transition probability and state time duration for Nakagami-q distribution and α–μ distribution are derived, plotted and analyzed. The BER for non-coherent FSK is shown to be much better than coherent FSK and PSK in the presence of Nakagami-q fading.     

How significant is the assumption of the uniform channel phase distribution on the performance of spatial multiplexing MIMO system?

Spatial multiplexing (SMX) multiple-input multiple-output (MIMO) systems are promising candidates to enhance the achievable throughput and the overall spectral efficiency in future wireless systems. Performance studies of these systems over different channel conditions assume simplified models for the channel phase distribution. This paper highlights the impact of the channel phase distribution assumption on the performance of SMX MIMO systems. The Nakagami-m and the \(\eta -\mu\) fading channels are considered in this study. In existing literature, performance studies of SMX MIMO systems over Nakagami-m fading channel assume uniform phase distribution. Though, it has been reported recently that the Nakagami-m channel phase distribution is not uniform. In this article, we show that the assumption of the channel phase distribution has a major impact on the performance of SMX MIMO systems. The obtained results demonstrate that the performance of SMX MIMO systems significantly varies with different channel phase distributions. Furthermore, it is shown that uniform assumption of channel phase distribution is incorrect and leads to erroneous conclusions. Detailed performance analysis for more accurate channel models are provided and results are sustained through Monte-Carlo simulations.     

Second‐order statistics of system with N‐branch microdiversity and L‐branch macrodiversity operating over gamma shadowed Nakagami‐m fading channels

The problem concerning short‐term fading and long‐term fading (shadowing) and their deleterious effects on wireless systems performance has been in focus for a long time. In this paper, motivated by the results of propagation measurements in land‐mobile and indoor‐mobile systems, and by the fact that gamma distribution can describe shadowing reliably, Nakagami‐m distribution is used to model the signal envelope and gamma distribution is used to model the average signal power. Receive diversity with maximal‐ratio combining and selection combining is implemented at the microlevel and macrolevel, respectively. The general case is explored, which assumes that microdiversity and macrodiversity are provided through arbitrary number of channels. Because shadowing has larger correlation distance than short‐term fading, correlated macrodiversity channels are studied. This paper investigates the dynamics of the received signal. A novel rapidly converging infinite‐series expression for average level crossing rate and average fade duration are obtained. Numerical results are graphically presented to examine the impact of fading severity, shadowing severity, number of diversity branches at the microlevel, number of base stations and correlation between base stations to the system's performance. Computer simulations are also performed to verify the validity and the accuracy of proposed theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Distributed differential space-time coding for asynchronous two-way relaying networks with Nakagami-m fading

A signal detection scheme was proposed for two-way relaying networks (TWRNs) using distributed differential space-time coding (DDSTC) under imperfect synchronization. Unlike most existing work perfect with synchronization assumed, a relative delay between the signals transmitted from both sources to the relay was considered. Since perfect channel state information (CSI) is difficult to be acquired in fast fading, the scenarios and computation complexity will be increased especially when there appear multiple relays, CSI is assumed unavailable at all nodes. Therefore, the article proposes a differential signal detection scheme based on estimating and cancelling the imperfect synchronization component in the received signal at the two source nodes, followed by a least square (LS) decoder. Simulations, using the Nakagami-m fading channel due to its versatile statistical distribution property, show that the proposed scheme for both source nodes are effective in suppressing the inter-symbol interference (ISI) caused by imperfect synchronization while neither the source nodes nor the relay nodes have any knowledge of CSI.     

On the application of the sum of generalized Gaussian random variables: maximal ratio combining

In most wireless communication systems, the additive noise is assumed to be Gaussian. However, there are many practical applications where non-Gaussian noise impairs the received signal. Examples include co-channel and adjacent channel interference in mobile cellular systems, impulsive noise in wireless and power-line communications, ultra-wide-band interference and multi-user interference in wireless systems, and spectrum sensing. To cover this issue, we consider in this paper the application of the sum of generalized Gaussian (GG) random variables (RVs). To this end, we consider single-input multiple-output (SIMO) systems that operate over Nakagami-m fading channels in the presence of an additive white generalized Gaussian noise (AWGGN). Specifically, we derive a closed-form expression for the bit error rate (BER) of several coherent digital modulation schemes using maximal ratio combining diversity in the Nakagami-m fading channels subject to an AWGGN. The derived expression is obtained based on the fact that the sum of L GG RVs can be approximated by a single GG RV with a suitable shaping parameter. In addition, the obtained BER expression is valid for integer and non-integer value of the fading parameter m. Analytical results are supported by Monte-Carlo simulations to validate the analysis.     

Energy harvesting cognitive radio networks: security analysis for Nakagami-m fading

Energy harvesting has lately been of particular attention to researchers. In addition, cognitive radio networks (CRNs) are recognized as an attainable measure for the problem of radio spectrum shortage in next generation radio access. A combination of these two technologies, which forms energy harvesting CRNs (EHCRNs), allows wireless communication terminals to prolong their operation time in limited spectrum scenarios. Nonetheless, that CRNs create opportunities for secondary users to access primary users’ spectrum induces vulnerability of message security. So far, security capability analysis of EHCRNs has been limited to Rayleigh fading whilst Nakagami-m fading is more common than Rayleigh fading and better reflects distinct fading severity degrees in practical scenarios. Accordingly, this paper firstly offers the precise security capability analysis of EHCRNs under interference power constraint, Nakagami-m fading, maximum transmit power constraint, and primary interference. Then, the offered analysis is ratified by computer simulations. Ultimately, multiple results reveal that the security capability is considerably improved with smaller primary interference and lower required security threshold. Moreover, the security capability is significantly impacted by channel severity and is optimized with appropriate selection of time percentage.

     

Exact BER Analysis of Differential Chaos Shift Keying Communication System in Fading Channels

An exact method is employed to analyze the bit error rate (BER) performances of differential chaos shift keying (DCSK) communication system over fading channels. The exact BER performances of DCSK in Nakagami-m Rayleigh and Rician fading channels are derived, respectively. The Gaussian approximation (GA) method is compared with the exact method. The numerical results and simulation results for the two methods are presented and are compared in the fading channels, respectively. These results support our theoretical analysis.     

Theoretical analysis and measurement results of vegetation effectson path loss for mobile cellular communication systems

This paper reports on studies of propagation in an urban forested park area to investigate the statistical nature of the time fading for frequencies ranging from 0.9 GHz to 1.8 GHz, as well as to examine the range dependence and the base station height gain. Measurements of the received signal over 30 s intervals for a stationary mobile were used to construct the distribution functions for the fading. In most cases, the distribution could be approximated by a Rician distribution, whose K-factor was found to depend on transmitter height     

New closed-form expressions for SNR estimates of Nakagami fading channels by the method of moments

Method of moments has been a parameter estimation technique appropriate to calculate signal-to-noise ratio (SNR) estimates in fading channel models in which an optimal technique like maximum likelihood estimation is not mathematically tractable. In this article, the ratio of the second moment squared to the fourth moment of the received signal envelope is considered to calculate an exact expression for the SNR estimate in Nakagami-m fading channel for M-QAM and \(\theta \)-MQAM modulations as well as expressions to evaluate the variance and the mean of the estimate. The paper presents two useful contributions for SNR estimation theory on Nakagami fading. Besides the exact algebraic expression for the estimate for a generalized QAM modulation scheme, its performance is evaluated through a statistical linearization argument.     

Outage Performance of OFDM-Based Selective Decode-and-Forward Cooperative Networks Over Nakagami-<Emphasis Type="Italic">m</Emphasis> Fading Channels

In this paper, we investigate the outage performance of OFDM-based selective decode-and-forward cooperative networks over independent but not necessarily identically distributed (i.n.i.d.) Nakagami-m fading channels, with integer values of parameter m. A unified closed-form expression for the outage probability is derived for three selective relaying schemes. The effect of the coherence bandwidth on the proposed scheme is also investigated. Monte Carlo simulations are carried out to validate our analysis.     

Mobile Communications Using Source-Selected Multi-Antenna AF Relays Over Dual-Hop Nakagami-{\varvec{m}} Channels

This paper presents a scheme for dual-hop amplify-and-forward multi-antenna, multi-relay selection over Nakagami-m fading channels. A source-selected best relay performs maximal ratio combining on received data, applies variable gain, and then uses beamforming to transmit to a destination device. Such a configuration is beneficial for end-to-end communication using single antenna mobile terminals with a multi-antenna relay infrastructure. Closed form expressions for performance metrics are derived that cater for arbitrary number of relays, arbitrary number of receive and transmit antennas and different fading parameters. Results are verified through simulation. Furthermore, the influence of multiple antennas, the effects of fading, power imbalance between hops, and the beneficial impact of additional relays are explored.     

Performance analysis of a convolutional coded DS/CDMA system in Nakagami fading channels

In this paper, we investigate the performance of convolutional coded DS/CDMA with noncoherent M-ary orthogonal modulation operating in a multi-user environment over a slow and frequency nonselective Nakagami-m fading channel with additive white Gaussian noise (AWGN). An expression for the pairwise error probability that can be used to compute the upper bound of coded system is first derived. Performance of the DS/CDMA system with and without the convolutional codes is then presented. We have observed that convolutional codes can compensate for the degradation quite well in multi-user situations over Nakagami fading channels with AWGN. For the case of an extreme fading, however, it has been seen that the convolutional code reaches its limit to improve the overall system performance as the number of users increase. This revised version was published online in August 2006 with corrections to the Cover Date.     

A comprehensive performance analysis of relay-aided CDMA communications over dissimilar fading channels

In this paper, bit error probability (BEP), outage probability (OP) and channel capacity (CC) of direct-sequence code-division multiple access systems with amplify-and-forward relaying are presented for different fading scenarios. In the first scenario, the source-destination link is assumed to experience Rayleigh fading while it is subject to Nakagami-m fading in the second scenario. The source-relay and relay-destination channels are considered to have Nakagami-m fading conditions in two scenarios. First, analytical expressions for the end-to-end probability density function (PDF) are derived by using the convolution integral. Then, BEP, OP and CC are obtained based on these PDFs in terms of infinite series. Truncation error analyses are presented for different parameter values in order to show that truncation error arising from the infinite series is negligible. Simple and easy-to-compute asymptotic expressions are also introduced for BEP and OP in order to simplify the performance analysis in high signal-to-noise ratio region. Simulation results are provided to show the accuracy of the proposed approximate and asymptotic expressions.