Small-scale Fading Statistics Research Articles

Performance Analysis of IRS-Assisted THz Communication Systems over α-μ Fading Channels with Pointing Errors.

In this paper, we analyze the performance of an intelligent reflecting surface (IRS)-aided terahertz (THz) wireless communication system with pointing errors. Specifically, we derive closed-form analytical expressions for the upper bounded ergodic capacity and approximate expression of the outage probability. We adopt an α-μ fading channel model for our analysis that is experimentally demonstrated to be a good fit for THz small-scale fading statistics, especially in indoor communication scenarios. In the proposed analysis, the statistical distribution of the α-μ fading channel is used to derive analytical expressions for the ergodic capacity and outage probability. Our proposed analysis considers not only the IRS reflected channels, but also the direct channel between the communication nodes. The results of the derived analytical expressions are validated through Monte Carlo simulations. Through simulations, it has been noticed that pointing errors degrade the performance of the IRS-assisted THz wireless communication system which can be compensated by deploying an IRS having a large number of reflecting elements.

A measurement data-based investigation of fading modeling for indoor THz wireless systems

The terahertz (THz) band offers a vast amount of still unallocated bandwidth, which makes it a promising enabler for future sixth generation wireless systems. The high frequencies of the THz band lead to a significantly reduced multipath richness of the propagating THz signals. However, there are still paths that can carry a significant amount of power. As a result, the THz band small-scale fading characterization is of particular interest and the appropriate stochastic distributions that best fit the empirical channels need to be identified. This work investigates the suitability of the 'alpha-mu', Rice and Nakagami-m distributions to adequately model the small-scale fading statistics of the channel gain measurements of various Line-of-Sight (LoS) and Non-Line-of-Sight (NLoS) indoor THz wireless links. The fitting accuracy of the examined analytical distributions is validated by means of the Kolmogorov-Smirnov test, the Kullback-Leibler divergence, the logarithmic Kolmogorov-Smirnov test and the root-mean-square-error. Also, the ergodic capacity based on the channel gain measurements as well as on the 'alpha-mu', Rice and Nakagami-m distributions is presented. Based on the fitting accuracy metrics the Rice and 'alpha-mu' yield the best fit for the LoS and NLoS links, respectively. The Nakagami-m does not fit the empirical distributions for any of the presented links. Furthermore, insights are provided for the ranges of the extracted values of the analytical distributions in LoS and NLoS transmission conditions.

Millimeter-Wave System for High-Speed Train Communications Between Train and Trackside: System Design and Channel Measurements

This paper introduces the design of a 41 GHz mmWave system dedicated for high-speed train communications between train and trackside. A novel frame structure is provided for the acquirement of channel state information as well as for the transmission of user data. Based on the proposed design principles, a system prototype has been established and employed in extensive measurement campaigns. The channel measurement results obtained from a recent measurement campaign under high-speed mobile conditions where the relative velocity between the transmitter and the receiver reaches 170 km/h are presented in this paper. Channel characteristics, including the power delay profile, RMS delay spread, fade depth, small-scale fading statistics, Ricean K factor, autocovariance function, coherence time, level crossing rate, and average fading duration are analyzed in detail. Moreover, the bit-error-rate performance for the proposed system under the channel whose characteristics are obtained from the measurements is simulated. Based on the simulation results, the key parameters for the proposed frame structure are determined to improve the system's robustness in fast varying channels and in the mean time achieve high spectrum efficiency. Besides, the throughput of the system prototype recorded during the transmission of three high-definition video streams is presented. Finally, the outage probability as a function of transmission distance and path loss exponent is estimated based on the channel measurement results.

Investigating Validity of Wide-Sense Stationary Assumption in Millimeter Wave Radio Channels

In this paper, impact of antenna directivity and bandwidth on the small scale fading statistics have been analyzed for millimeter-wave (mmWave) radio channels. For this purpose, small-scale fading measurements at the mmWave frequency band (58-62 GHz) are carried out using transmit and receive antennas with different antenna directivities (emulated beamforming gains). Measurements emulate a non line-of-sight scenario when the communication between transmit and receive antennas is possible only through a single multipath cluster. In order to compare results, measurements in a line-of-sight scenario with omni-directional antennas are also carried out for reference purpose. Considering two main mmWave system features i.e., high antenna directivity and higher system bandwidth, we report the following results: 1) Randomness/fading in the received signal magnitude vanishes with an increase in bandwidth. 2) The channel impulse response h (t, τ) does not remain a wide-sense stationary (WSS) random process in the slow-time domain i.e., along t, where, the fast-time domain refers to the dimension along τ. 3) Measured channels are WSS in the frequency domain and the coherence bandwidth increases when propagation channels are illuminated with high gain antennas.

Small-Scale Fading Statistics of Emerging 3-D Mobile Radio Cellular Propagation Channels

Small-Scale Fading Statistics of Emerging 3-D Mobile Radio Cellular Propagation Channels

Small-Scale Fading Statistics of Emerging 3-D Mobile Radio Cellular Propagation Channels

In delivering fifth generation (5G) communication networks, the fundamental advancements in the scale of antenna arrays, density of networks, mobility of communicating nodes, size of cells, and range of frequencies necessitate the derivation of an appropriate and reliable channel model. A tunable three dimensional (3-D) geometric channel model comprehending the mobility of user terminal together with high degree of flexibility in modelling the shape, orientation, and scale of the scattering region is proposed. Characterization of Doppler spectrum, quantization of multipath dispersion in angular domain, and second order fading statistics of the radio propagation channel is presented. Mathematical expressions for joint and marginal probability density function of Doppler shift and multipath power are derived for this advanced 3-D hollow geometric scattering model. Next, an analysis on the Doppler spectrum is presented, where the impact of various physical channel parameters on its statistical characteristics is analyzed. Since, the quantification of multipath dispersion in 3-D angular domain is of vital importance for designing large scale planner antenna arrays with very high directional resolution for emerging 5G communications, therefore, a thorough analysis on the multipath shape factors (SFs) of the proposed analytical 3-D channel model is conducted. Finally, the analysis on SFs is extended for characterization of second order fading statistics of multipath channels.

Propagation modeling for outdoor-to-indoor and indoor-to-indoor wireless links in high-speed train

Nowadays telecommunication companies have shown a great interest in deploying broadband mobile wireless networks in high-speed trains (HSTs) with the aim of supporting both passenger services provisioning as well as automatic train control and signaling. The train carriage, as a confined steel structure, has specific propagation characteristics, which motivates the study of the indoor-to-indoor and outdoor-to-indoor radio propagation characteristics for broadband wireless communication systems in high-speed railways, constituting the main contribution of this work. This study has been performed by means of measurements considering an actual Long Term Evolution (LTE) network deployment, as well as a portable test transmitter and different configurations of antennas and receivers at 2.4, 2.6 and 5.7GHz in a commercial high-speed rail line in Spain. The results show that radio waves incur obvious waveguiding effects inside the HST car. Moreover, for the propagation from the railway station to a mobile receiver inside the HST car, waves at higher frequencies experience less attenuation through the train carriage, by better propagating through windows. Although the railway station and train interior contain objects that induce a rich set of multipath components, the analysis of small-scale fading statistics shows that the channel still has a dominant path. Also, the LTE coverage tests for Base Transceiver Station (BTS)-Train and BTS-Mobile links were conducted and with internal and external antennas on board the train. We found that there was a strong signal penetration loss of approximately 26dB caused by the train carriage structure. The final results constitute an initial model for the propagation incurred by a relay-based communications system for fourth generation (4G) network in railways.

Human Body Affected Small-Scale Fading for Indoor UWB Channel

This paper deals with the small-scale fading distribution for UWB channels in the absence and presence of human bodies in indoor line-of-sight (LOS) environments and performance analysis of UWB systems considering the small-scale fading distribution. To obtain small-scale fading statistics, the channel measurements are performed in five representative environments that have different structure and size while locating the receiver (Rx) antenna on 49 (7×7 grid) local points with a fixed transmitter (Tx) antenna in each environment. The measured channel data are processed by a vector network analyzer and the target frequency bands range from 3 to 4.6GHz. From the measured data, we find the best fitted channel model among several typical theoretical distribution models such as Lognormal, Nakagami, and Weibull distributions, showing good agreement with the empirical channel data. We analyze the amplitude variation of the small-scale fading distribution in the absence and presence of human bodies. The results show that the small-scale fading statistics are best described by Weibull distribution and the two parameters of the distribution that determine the shape and the scale of the distribution depend on whether or not human bodies exist. We modeled and analyzed two parameters at different excess delays for all environments. Based on the measured small-scale fading distribution, this paper deals with the performance of UWB system using Rake receivers and also compares the performance with the existing channel model. The results suggest that the small-scale fading distribution in the absence and the presence of human bodies in indoor LOS environments should be considered when assessing the performance of UWB systems.

5.8 GHz propagation of low‐height wireless links in sea port scenario

Experimental fading measurements were performed in Cadiz Bay, Spain, for a variety of operational scenarios over the sea at the unlicensed 5.8 GHz frequency band. Measurements are based on continuous wave (CW) transmissions with both the transmitter and the receiver installed in typical low-height maritime platforms, such as oceanographic buoys, military ships and boats. Based on the measurements, large-scale and small-scale fading statistics are characterised by cumulative distribution functions (CDFs) and key wireless channel parameters are estimated and discussed. Results show, first, that large-scale fading can be modelled using classical log-normal path-loss models and, secondly, that small-scale fading statistics fits the extreme value distribution (EVD) function when they are expressed in decibel units. This study can be used for practical planning of wireless communications in maritime applications and as an experimental basis for further simulation works.

SEP calculations for coherent M-ary FSK in different fading channels with MRC diversity

In this paper, the authors derive symbol error probability (SEP) expressions for coherent M-ary frequency shift keying (MFSK) modulation schemes in multipath fading channels. The multipath or small-scale fading process is assumed to be slow and frequency non-selective. In addition, the channel is also subjected to the usual degradation caused by the additive white Gaussian noise (AWGN). Different small-scale fading statistics such as Rayleigh, Rician (Nakagami-n), Hoyt (Nakagami-q), and Nakagami-m have been considered to portray diverse wireless environments. Further, to mitigate fading effects through space diversity, the receiver front-end is assumed to be equipped with multiple antennas. Independent and identically distributed (IID) as well as uncorrelated signal replicas received through all these antennas are combined with a linear combiner before successive demodulation. As the detection is coherent in nature and thus involves phase estimation, optimum phase-coherent combining algorithms, such as predetection maximal ratio combining (MRC), may be used without any added complexity to the receiver. In the current text, utilizing the alternate expressions for integer powers (1≤n≤4) of Gaussian Q function, SEP values of coherent MFSK are obtained through moment generating function (MGF) approach for all the fading models (with or without MRC diversity) described above. The derived end expressions are composed of finite range integrals, which can be numerically computed with ease, dispenses with the need of individual expressions for different M, and gives exact values up to M=5. When the constellation size becomes bigger (M≥6), the same SEP expressions provide a quite realistic approximation, much tighter than the bounds found in previous literatures. Error probabilities are graphically displayed for each fading model with different values of constellation size M, diversity order L, and for corresponding fading parameters (K, q, or m). To validate the proposed approximation method extensive Monte-Carlo simulations were also performed, which show a close match with the analytical results deduced in the paper. Both these theoretical and simulation results offer valuable insight to assess the efficacy of relatively less studied coherent MFSK in the context of the optimum modulation choice in wireless communication. Copyright © 2010 John Wiley & Sons, Ltd.

Non-Stationary Narrowband MIMO Inter-Vehicle Channel Characterization in the 5-GHz Band

In this paper, we describe measurements and models of 30 × 30 narrowband multiple-input-multiple-output (MIMO) vehicle-to-vehicle (V2V) radio propagation channels at 5.3 GHz. Four environments were considered: a campus, a highway, a suburban area, and an urban area. Since the scattering environment may rapidly change in V2V communications, we first investigate the validity of the wide-sense stationarity (WSS) assumption for such channels using the correlation matrix distance (CMD), which is a metric for the characterization of the MIMO channel nonstationarity. Moreover, statistical channel models were developed for these environments, which take into account the non-stationary behavior of the measured V2V channels. The large-scale fading was found to be lognormally distributed, whereas the small-scale fading was characterized by the flexible Weibull distribution. Finally, the non-stationary behavior of both large-scale fading and small-scale fading statistics was investigated.

Three-dimensional multipath shape factors for spatial modeling of wireless channels

This paper develops a generalized theory of multipath shape factors used to study the small-scale fading statistics in three-dimensional non-omnidirectional multipath channels. Previous results for horizontal propagation channels are special cases of the present framework when the multipath angular power density (APD) and the travel direction of the mobile unit are confined to a plane. The three-dimensional multipath shape factors are derived in terms of the first three degrees of unnormalized spherical harmonics of the APD. Based on the so derived shape factors, analytical expressions for the level crossing rate, average fade duration and approximate envelope correlation are derived for a Rayleigh fading three-dimensional channel.

On appropriate models for characterizing hyper-rayleigh fading

Recent work presented empirical data for which the small-scale fading statistics were more severe than Rayleigh; a phenomena deemed hyper-Rayleigh fading. This paper considers whether commonly utilized small-scale propagation models can be appropriately adapted to represent this class of fading. The work argues that the most meaningful model for the hyper- Rayleigh regime is based on a physical wave model (as opposed to stochastic); in particular, the TWDP model, where Deltaap1, holds the greatest promise. The crux of the argument is that the stochastic models significantly over-predict the amount of constructive interference in comparison to what is physically realizable.

Low Complexity Rake Receivers in Ultra-Wideband Channels

One of the major issues for the design of ultra-wideband (UWB) receivers is the need to recover the signal energy dispersed over many multipath components, while keeping the receiver complexity low. To this aim we consider two schemes for reduced-complexity UWB Rake receivers, both of which combine a subset of the available resolved multipath components. The first method, called partial Rake (PRake), combines theirs/ arriving multipath components. The second is known as selective Rake (SRake) and combines the instantaneously strongest multipath components. We evaluate and compare the link performance of these Rake receivers in different UWB channels, whose models are based on extensive propagation measurements. We quantify the effect of the channel characteristics on the receiver performance, analyzing in particular the influence of small-scale fading statistics. We find that for dense channels the performance of the simpler PRake receiver is almost as good as that of the SRake receiver, even for a small number of fingers. In sparse channels, however, the SRake outperforms the PRake significantly. We also show that for a fixed transmitted energy there is an optimum transmission bandwidth

Spatio-temporal ultrawideband indoor propagation modelling by reduced complexity geometric optics

A simple and efficient virtual-source ray-tracing technique for the simulation of indoor wideband radio and optical propagation channels is proposed. The parametric deterministic model considers the room geometry, transceiver locations, material properties and probe signal types. It is applied to the indoor ultrawideband channel in the FCC-allocated 3.1–10.6 GHz band, and a range of novel results are presented to illustrate several possible applications. The channel small-scale fading statistics and spatial variability are examined by synthesising a densely sampled aperture. Multiple-antenna array systems are simulated to evaluate multiple-input multiple-output performance. The multipath angular characteristics are analysed from the simulated azimuth-delay profile. The simulation results closely match previous channel measurement studies and statistical models, validating the proposed technique. It is shown that specular reflection is dominant, and power convergence is achieved with three reflections in a typical indoor environment. Thus, it is demonstrated that despite its simplicity, the model yields reliable and accurate results, and can therefore be a useful tool for indoor wireless network planning and performance prediction.

Indoor radio channel characterization and modeling for a 5.2-GHz bodyworn receiver

Wireless local area network applications may include the use of bodyworn or handportable terminals. For the first time, this paper compares measurements and simulations of a narrowband 5.2-GHz radio channel incorporating a fixed transmitter and a mobile bodyworn receiver. Two indoor environments were considered, an 18-m long corridor and a 42-m/sup 2/ office. The modeling technique was a site-specific ray-tracing simulator incorporating the radiation pattern of the bodyworn receiver. In the corridor, the measured body-shadowing effect was 5.4 dB, while it was 15.7 dB in the office. First- and second-order small-scale fading statistics for the measured and simulated results are presented and compared with theoretical Rayleigh and lognormal distributions. The root mean square error in the cumulative distributions for the simulated results was less than 0.74% for line-of-sight conditions and less than 1.4% for nonline-of-sight conditions.

Theory of multipath shape factors for small-scale fading wireless channels

This paper presents a new theory of multipath shape factors that greatly simplifies the description of small-scale fading statistics of a wireless receiver. A method is presented for reducing a multipath channel with arbitrary spatial complexity to three shape factors that have simple intuitive geometrical interpretations. Furthermore, these shape factors are shown to describe the statistics of received signal fluctuations in a fading multipath channel. Analytical expressions for level-crossing rate, average fade duration, envelope autocovariance, and coherence distance are all derived using the new shape factor theory and then applied to several classical examples for comparison.

Measurements and predictions of the local mean power and small-scale fading statistics in indoor wireless environments

In this letter, a comparison between measurements and simulations at 2.5 GHz carried out by the authors is presented in order to show that ray-tracing techniques make it possible to estimate with sufficient accuracy not only the signal mean level, but also its local statistics. ©2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 24: 329–331, 2000.