Nakagami-m Fading Parameter Research Articles

Impact of Correlated Fading on Multi-Connectivity

Multi-connectivity (MC) is regarded as one of the key features that meet the requirements of ultra-reliable low-latency communications for 5th generation networks, as it provides multiple diversity branches. Recently, we evaluated the decoding reliability of various MC setups and different combining algorithms by analyzing the resulting outage probabilities. In this work, we are interested in how much the performance is affected by correlated fading. Specifically, we analyze the outage probability of MC systems with joint decoding reception operating over correlated quasi-static Rayleigh and Nakagami-m fading channels. Our main contributions are as follows: (i) deriving the exact outage probability in integral form and the asymptotic outage probability at high signal-to-noise ratio (SNR) in closed form; (ii) deriving the correlation loss, which quantifies the extra SNR required under correlated fading as compared with the independent scenario; and (iii) evaluating frame-error rates of quasi-cyclic low-density parity-check codes by Monte-Carlo simulations. Our results show that the correlation loss is marginal for a low to moderate level of correlation, whereas the diversity gain is not affected by correlation whatsoever. Furthermore, we find that the correlation loss is independent of the degrees of freedom encapsulated by the Nakagami-m fading parameter.

Bias Reduction in the Closed-Form Maximum Likelihood Estimator for the Nakagami-m Fading Parameter

In this letter, we discuss a corrective bias for the modified maximum likelihood estimator of the Nakagami-m fading parameter. The obtained corrected estimator has a closed-form expression, which plays an essential role in describing fading effects in wireless communication. Numerical results show that the bias-corrected estimator outperforms the existing methods and returns unbiased estimates for the fading parameter even for very small sample sizes.

On the Performance of LMS Communication With Hardware Impairments and Interference

This paper investigates the performance of a dual-hop decode-and-forward (DF) relaying-aided land mobile satellite communication over Shadowed-Rician (SR) fading channels. A practical model for the satellite relaying system is first developed, where the impacts of satellite multi-beam antenna, radio propagation loss, and random shadowing are taken into account. Next, by assuming that the multi-beam satellite suffers from hardware impairments (HIs) and is perturbed by interference signals, we derive an equivalent end-to-end signal-to-interference-plus-noise-and-distortion-ratio of the system, and justify that the maximum ratio transmission at the source and the maximum ratio combining at the destination are the optimal transmit-receive beamforming schemes on the proposed HIs model. Then, closed-form expressions for the probability density function (PDF) of the sum of independent and identically distributed (i.i.d) squared SR random variables in the case of integer and rational Nakagami-m fading parameters are derived. Based on the derived PDF, new analytical expressions for the outage probability (OP) and average throughput are obtained in the presence of HIs and interference. Moreover, the asymptotic OP and average throughput at high signal-to-noise ratio are investigated to reveal the achievable diversity order of the system. Finally, Monte Carlo simulation results are provided to corroborate the analytical results.

Outage Performance for Multiuser Threshold-Based DF Satellite Relaying

Satellite communication plays an important role in future seamless wireless network. In this paper, we investigate the system outage performance of a multiuser threshold-based decode-and-forward (DF) satellite relaying network, where the satellite employing spot beam technology is used as an aerial relay to assist the signal transmission between the terrestrial equipments with multi-antenna. Assuming that maximum ratio transmission (MRT) and maximum ratio combining (MRC) are utilized to achieve the optimal performance, we first obtain the equivalent output signal-to-noise ratio (SNR) expression of the considered system, where frequency division multiplexing access (FDMA) scheme is exploited in the uplink. Then, we derive the closed-form system outage probability (SOP) expression for the considered system, where both uplink and downlink are subject to shadowed-Rician (SR) fading with path loss and antenna gain being considered. The main advantage of our theoretical formula is that it can be used in the case of integer and rational Nakagami-m fading parameters. Furthermore, asymptotic SOP formula at high SNR is also presented to show the diversity order and coding gain of the considered system. Finally, simulation results are provided to verify the correctness of the exact and asymptotic SOP expressions and reveal the effects of representative parameters on the system outage performance of the satellite relaying system with threshold-based DF protocol.

Opportunistic relaying for low-altitude UAV swarm secure communications with multiple eavesdroppers

In this study, we investigate the secrecy outage performance achieved by opportunistic relaying for a low-altitude unmanned aerial vehicle (UAV) swarm secure communication system in the presence of multiple UAV-eavesdroppers. In the primary channel, multiple UAV-transmitters are connected to a ground station via the ground-to-air (G2A) wireless backhaul and a UAV-transmitter and UAV-relay are selected to transmit the source signal to a far ground destination under air-to-air and air-to-ground Nakagami-m fading links. In the eavesdropping channel, maximum ratio combining is applied across multiple UAV-eavesdroppers for intercepting the legitimate transmissions from both the selected UAV-transmitter and UAV-relay. The backhaul reliability and eavesdropping probability are introduced to reflect the practical constraints on the G2A wireless backhaul and UAV-eavesdropper cooperation, respectively. The closed-form expression for the secrecy outage probability is derived in terms of the UAV cooperation, backhaul reliability, eavesdropping probability, and Nakagami-m fading parameters. In the high signal-to-noise ratio region, the asymptotic secrecy outage probability is also derived. It is shown that the secrecy diversity gain achieved by opportunistic relaying is jointly determined by the UAV cooperation and shape factors of Nakagami-m fading links in the primary channel. The analytical secrecy outage metrics achieved by opportunistic relaying are verified by Monte Carlo simulation results.

Capacity Analysis of MIMO in Non-Uniform Nakagami Channel with Linear Receiver

ABSTRACTMultiple-input–multiple-output (MIMO) systems have emerged as a promising solution to provide high data rate wireless services in a rich scattering environment. This paper deals with the performance analysis of the MIMO system in correlated non-uniform phase distributed Nakagami-m channel with linear receiver. Authors have considered spatial diversity scheme i.e, vertical bell laboratories layered space-time (V-BLAST) systems in correlated MIMO Nakagami-m fading channels with equal power distribution among the transmitter side antennas. Also, they consider that the channel state information (CSI) is available only at the receiver. The paper presents a detailed analysis of the channel capacity in correlated and uncorrelated channel condition and validated the result with appropriate mathematical model. The effect of Doppler shift and Nakagami-m fading parameter m on the channel ergodic and outage capacity has been analyzed here.

Outage Performance for DF Two-Way Relaying with Co-Channel Interference over Nakagami-m Fading

In this paper, we investigate the outage performance of a two-way decode-and-forward relaying network in an interference-limited Nakagami-m fading environment. More specifically, assuming the presence of Nakagami-m faded multiple co-channel interferers at the source/destination terminals, the closed-form approximate expression for the outage probability is derived by using moment-based estimators attaining the appropriate Nakagami-m fading parameter. Simulation results demonstrate that our analytical result is in excellent agreement with the Monte Carlo simulation.

BER Evaluation of IEEE 802.15.4 Compliant Wireless Sensor Networks Under Various Fading Channels

This paper presents bit error rate (BER) analysis of wireless sensor networks (WSNs) consisting of sensor nodes based on an IEEE 802.15.4 RF transceiver. Closed-form expressions for BER are obtained for WSNs operating over AWGN, Rayleigh and Nakagami-m fading channels. For the purpose of analysis, we consider an IEEE 802.15.4 RF transceiver using direct sequence spread spectrum-offset quadrature phase shift keying (DSSS-OQPSK) modulation under 2.4 GHz frequency band in a WSN. Analytical expressions for BER are derived for a wireless link between sensor nodes that act as a transmitter unit and a base station without considering the effect of interferers in the wireless environment. Numerical results for BER are obtained by varying the IEEE 802.15.4 standard specific physical layer parameters, such as number of bits used to represent a Zigbee symbol, number of modulation levels used in an OQPSK modulator, and various values of Rayleigh and Nakagami-m fading parameters, denoted as $$\alpha $$ ? and $$m$$ m , respectively. Moreover, optimum values of physical layer parameters are identified for improved system performance. It is found that error performance analysis of WSN shows improvement when lower number of bits is used to represent a Zigbee symbol. Specifically, under a Rayleigh fading channel which reflects a real-time WSN environment, the network exhibits better performance only when it is operated at high SNR values, i.e., BER of order $$10^{-2}$$ 10 - 2 is achieved when SNR lies in the range 5---15 dB. Also, the effect of fading parameters on network performance shows that better results are obtained for higher values of $$\alpha $$ ? and $$m$$ m for Rayleigh and Nakagami-m fading channels, respectively.

On the Ergodic Capacity of Amplify-and-Forward Relay Channels with Interference in Nakagami-m Fading

Integrating relaying techniques into cellular communications sheds new light on higher capacity and broader coverage. However, applying relaying techniques in practice has to take into account important issues such as co-channel interference (CCI). In this work, a generalized framework for the ergodic capacity analysis of dual-hop fixed-gain amplify and forward (AF) relaying systems in the presence of interference is presented. New expressions for the ergodic capacity are derived considering transmissions over independent but not necessarily identically distributed Nakagami-m fading channels in the presence of a finite number of co-channel interferers. Our results establish that the ergodic capacity is dominated by the source-relay interference power and that it improves slowly with the average signal-to-noise ratio (SNR) increasing. It slightly deteriorates, however, with a larger Nakagami-m fading parameter for interference channels. Furthermore, our results offer an analytical insight into the key impact of relay placement on performance. Our new ergodic capacity expressions could therefore provide a very practical/low-cost performance optimization tool for relayed-communication system designers.

Symbol Error Rate of Space–Time Network Coding in Nakagami- $m$ Fading

In this paper, we analyze the symbol error rate (SER) of space-time network coding (STNC) in a distributed cooperative network over independent but not necessarily identically distributed (i.n.i.d.) Nakagami-m fading channels. In this network, multiple sources communicate with a single destination with the assistance of multiple decode-and-forward (DF) relays. We first derive new exact closed-form expressions for the SER with M-ary phase-shift keying modulation (M-PSK) and M-ary quadrature-amplitude modulation (M-QAM). We then derive new compact expressions for the asymptotic SER to offer valuable insights into the network behavior in the high signal-to-noise ratio (SNR) regime. Importantly, we demonstrate that STNC guarantees full diversity order, which is determined by the Nakagami-m fading parameters of all the channels but independent of the number of sources. Based on the new expressions, we examine the impact of the number of relays, relay location, Nakagami-m fading parameters, power allocation, and nonorthogonal codes on the SER.

Error Performance of Multi-Antenna Receivers in a Poisson Field of Interferers: A Stochastic Geometry Approach

In this paper, we introduce an analytical framework for performance analysis and design of Single-Input-Multiple-Output (SIMO) wireless systems in the presence of noise, fading, and radio frequency interference produced by randomly distributed active interferers surrounding an intended probe receiver. The framework leverages recent application of stochastic geometry and Poisson Point Processes (PPPs) theory to network interference modeling. To assess the impact of spatial dependence across multiple receive-antennas, three models of network interference are studied: i) the isotropic model, where all receive-antennas see interferers belonging to the same PPP; ii) the independent model, where each receive—antenna sees interferers belonging to an independent PPP; and iii) the mixture model, which is a superposition of isotropic and independent interferences. Depending on the fading distribution of the interferers, the Nakagami-m fading parameter of the probe link, and the number of receive-antennas, either exact or upper-bound formulas of the error probability averaged over noise, fading, and spatial interference are given. Our analysis shows that, depending on the interference model, performance can either improve or get worse with multiple antennas at the receiver. The proposed analytical methodology is applicable to single- and multi-PPPs interference environments.

Generalized Method of Moments Estimation of the Nakagami-m Fading Parameter

The generalized method of moments (GMM) is introduced in the framework of estimating the Nakagami-m fading parameter. This GMM approach provides a systematic procedure for finding the moment-based m parameter estimators. Using the multivariate delta method, we present a derivation for the asymptotic variance of the GMM Nakagami m parameter estimators. Monte Carlo simulation results show that the GMM approach can lead to estimators outperforming existing moment-based m parameter estimators over a wide range of channel conditions. It is shown that the asymptotic performance of these GMM estimators are close to that of the maximum-likelihood based estimator. The proposed method can be easily applied to both noiseless and noisy environments.

Cooperative AF Relaying in Spectrum-Sharing Systems: Performance Analysis under Average Interference Power Constraints and Nakagami-m Fading

Since the electromagnetic spectrum resource is becoming more and more scarce, improving spectral efficiency is becoming extremely important for the sustainable development of wireless communication systems and services. Integrating cooperative relaying techniques into spectrum-sharing cognitive radio systems sheds new light on higher spectral efficiency. In this paper, we analyze the end-to-end performance of cooperative amplify-and-forward (AF) relaying in spectrum-sharing systems. In order to achieve the optimal end-to-end performance, the transmit powers of the secondary source and the relays are optimized with respect to average interference power constraints at primary users and Nakagami-m fading parameters of interference channels (for mathematical tractability, the desired channels from secondary source to relay and from relay to secondary destination are assumed to be subject to Rayleigh fading). Also, both partial and opportunistic relay-selection strategies are exploited to further enhance system performance. Based on the exact distribution functions of the end-to-end signal-to-noise ratio (SNR) obtained herein, the outage probability, average symbol error probability, diversity order, and ergodic capacity of the system under study are analytically investigated. Our results show that system performance is dominated by the resource constraints and it improves slowly with increasing average SNR. Furthermore, larger Nakagami-m fading parameter on interference channels deteriorates system performance slightly. On the other hand, when interference power constraints are stringent, opportunistic relay selection can be exploited to improve system performance significantly. All analytical results are corroborated by simulation results and they are shown to be efficient tools for exact evaluation of system performance

On the Capacity of Nakagami-m Fading Channels with Full Channel State Information at Low SNR

The capacity of flat Rayleigh fading channels with full channel state information (CSI) at the transmitter and at the receiver at asymptotically low SNR has been recently shown to scale essentially as SNR log(1/SNR). In this paper, we investigate the Nakagami-m fading channel capacity with full CSI, and show that the capacity of this channel scales essentially as Ω/m SNR log (1/SNR), where m is the Nakagami-m fading parameter and where Ω is the channel mean-square. We also show that one-bit CSI at the transmitter is enough to achieve this asymptotic capacity using an On-Off power control scheme. Our framework may be seen as a generalization of previous works as it captures the Rayleigh fading channel as a special case by taking m = 1.

Accurate BER Analysis of OFDM Systems Over Static Frequency-Selective Multipath Fading Channels

Bit error rate (BER) analysis of orthogonal frequency division multiplexing (OFDM) systems over frequency-selective Nakagami-m fading channels is considered in this work. The provided analyses are applicable for multipath channels with any number of taps and the Nakagami-m fading parameter can be finite or infinite. The results obtained demonstrate that the Gaussian approximation (GA) can be inaccurate if the number of channel taps is less than five. The analytical results confirmed by simulation demonstrated that the probability distribution functions for infinite fading parameter m are substantially different from those where m is finite. It was also found that the effect of m depends on the number of multipath components L. For even values of L, increasing m decreases the BER while the opposite happens for odd L values. Therefore, the worst case scenario for even L values occurs for m = 1, while for odd L values it occurs for m = ∞, i.e., the amplitudes of the multipath components are constants and equal.

Dual-hop DF relaying systems with multiple interferers and subject to arbitrary Nakagami- m fading

The outage performance of dual-hop decode-and-forward relaying systems with multiple co-channel interferers at both nodes, namely relay and destination, and subject to arbitrary Nakagami-m fading is investigated. More specifically, an indeed highly accurate closed-form approximate expression for the end-to-end outage probability is derived that is simple to calculate and yields results instantaneously independently of the number of interferers, thus circumventing the intricacy and the computationally inefficiency of the exact formulation. Simulation results are shown that corroborate the tightness of the proposed approximations. It is noteworthy that the results apply to general operating scenarios with distinct, non-integer Nakagami-m fading parameters and unequal average fading powers between hops.

Interference-Limited Relaying Transmissions in Dual-Hop Cooperative Networks over Nakagami-m Fading

In this letter, we investigate the outage performance of dual-hop decode-and-forward (DF) cooperative systems in an interference-limited Nakagami-m fading environment. More specifically, assuming the presence of Nakagami-m faded multiple co-channel interferers at the DF relay and a noisy destination, simple accurate closed-form approximations for the end-to-end outage probability are derived. To this end, moment-based estimators are used to attain the appropriate Nakagami-m fading parameters. Simulation results are presented in order to confirm the accuracy of the proposed approximations.

Cooperative dual-hop relaying systems with beamforming over nakagami-m fading channels

In this paper, we investigate the end-to-end performance of dual-hop relaying systems with beamforming over Nakagami-m fading channels. Our analysis considers semiblind (fixed-gain) relays with single antennas, and source and destination nodes equipped with multiple antennas. Closed-form expressions for the outage probability (OP), moment generating function (MGF), and generalized moments of the end-to-end signal-to-noise ratio (SNR) are derived. The proposed expressions apply to general operating scenarios with distinct Nakagamim fading parameters and average SNRs between the hops. The influence of the power imbalance, fading parameters, and antenna configurations on the overall system performance are analyzed and discussed through representative numerical examples. Furthermore, the exactness of our formulations is validated by means of Monte Carlo simulations.

Precise Analysis and Evaluation of OFDM Systems over a Mobile Frequency-Selective Nakagami-m Fading Channels

In this article, the symbol error probability (SEP) of OFDM systems using M-ary coherent demodulation communicating over time-varying sum of Nakagami-m fading channels is analyzed. The focus of this article is on the evaluation of OFDM signals in mobile radio applications, such as IEEE 802.11a, IEEE 802.16a, and digital video broadcasting (DVB) systems. The time variations of the channel during one OFDM symbol interval destroy the orthogonality of the adjacent subcarriers and generate power leakage among the subcarrier, known as inter-carrier interference (ICI). We first present an integral solution for the probability density function (PDF) of the sum of Nakagami-m random vectors (RVs). Second, we used this PDF expression to obtain an exact closed form for the error probability. The error rate analysis is then extended to systems using multichannel reception with maximal ratio combining (MRC). Based on Jakes’ model for Doppler effects, and an exponential multipath intensity profile, numerical results for the error probability are illustrated for several mobile speeds. An interesting observation was concluded that depending on the number of the channel taps, the error rate performance does not necessarily improve with increasing Nakagami-m fading parameter.

Accurate error-rate performance analysis of OFDM on frequency-selective Nakagami-m fading channels

Error rates of orthogonal frequency-division multiplexing (OFDM) signals in multipath slow fading Nakagami-m fading channels are considered. The exact probability density function of a sum of Nakagami-m random phase vectors is used to derive a closed-form expression for the error rates of OFDM signals. The precise error-rate analysis is extended to a system using multichannel reception with maximal ratio combining. An asymptotic error-rate analysis is also provided. For a two-tap channel with finite values of Nakagami-m fading parameters, our analysis and numerical results show that the asymptotic error-rate performance of an OFDM signal is similar to that of a single carrier signal transmitted over a Rayleigh fading channel. On the other hand, our analysis further shows that a frequency-selective channel that can be represented by two constant taps has similar asymptotic error-rate performance to that of a one-sided Gaussian fading channel. It is observed that, depending on the number of channel taps, the error-rate performance does not necessarily improve with increasing Nakagami-m fading parameters.