This contribution provides experimental evidence for the two-wave with diffuse power (TWDP) fading model. We have conducted two indoor millimetre wave measurement campaigns with directive horn antennas at both link ends. One horn antenna is mounted in a corner of our laboratory, while the other is steerable and scans azimuth and elevation. Our first measurement campaign is based on scalar network analysis with 7 GHz of bandwidth. Our second measurement campaign obtains magnitude and phase information, additionally sampled directionally at several positions in space. This second measurement campaign is limited to 2 GHz bandwidth. We apply Akaike's information criterion to decide whether Rician fading sufficiently explains the data or the generalized TWDP fading model is necessary. Our results indicate that the TWDP fading hypothesis is favoured over Rician fading in situations where the steerable antenna is pointing towards reflecting objects or is slightly misaligned at line-of-sight. We demonstrate TWDP fading in several different domains, namely, frequency, space, and time.
TWDP fading has already successfully been applied to describe @math ,GHz near body shadowing @cite_11 . Furthermore, as quoted above, TWDP must be considered for arrays, as they act as spatial filters @cite_43 @cite_78 . While theoretical work on TWDP fading is already advanced @cite_32 @cite_51 @cite_79 @cite_36 @cite_13 @cite_52 @cite_83 , experimental evidence, especially at millimetre waves, is still limited. For enclosed structures, such as aircraft cabins and buses, the applicability of the TWDP model is demonstrated by Frolik @cite_38 @cite_21 @cite_34 @cite_9 @cite_53 . A deterministic two ray behaviour in ray tracing data of mmWave train-to-infrastructure communications is shown in @cite_85 . A further extension of the TWDP -fading model, the so called fluctuating two-ray fading model, was also successfully applied to fit mmWave measurement data @cite_13 .
@cite_13 @cite_38 @cite_78 @cite_36 @cite_9 @cite_21 @cite_53 @cite_32 @cite_52 @cite_85 @cite_43 @cite_79 @cite_83 @cite_34 @cite_51 @cite_11
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This work is motivated by the problem of characterizing small-scale radio propagation environments for wireless sensor networks. If sensors are statically deployed near the ground or within structures, temporal fading may not exist but the channel may nevertheless experience severe frequency-selective behavior. The work presents real-world, frequency-selective fading data measured for in-vehicle wireless sensor applications. This fading data often exhibit statistics more severe than predicted by the Rayleigh fading model; a scenario referred herein as to as being hyper-Rayleigh. A two-ray, small-scale model is proposed as a new worst-case for this application space. 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. A two-ray, small-scale fading model was recently proposed as a worst-case fading scenario for certain wireless sensor applications. Empirical data motivated this development for fading was found to be more severe than predicted by Rayleigh fading statistics, a behavior referred to as hyper-Rayleigh fading. Based on the two-ray model, we study the benefits of M-branch diversity in the context of signal-to-noise ratio (SNR) and bit-error rate (BER) performance metrics. While these results are well-known for Rayleigh fading, this work is the first analysis of diversity for the hyper-Rayleigh regime. A detailed study is presented of some statistical properties of the stochastic process, that consists of the sum of two sine waves of unknown relative phase and a normal process. Since none of the statistics investigated seem to yield a closed-form expression, all the derivations are cast in a form that is particularly suitable for machine computation. Specifically, results are presented for the probability density function (pdf) of the envelope and the instantaneous value, the moments of these distributions, and the relative cumulative density function (cdf). The analysis hinges on expanding the functions of interest in a way that allows computation by means of recursive relations. Specifically, all the expansions are expressed in terms of sums of products of Gaussian hypergeometric functions and Laguerre polynomials. Computer results obtained on a CDC 6600 are presented. If a and b are the amplitudes of the two sine waves, normalized to the rms noise level, the expansions presented are useful up to values of a,b of about 17 dB, in double precision on the CDC 6600. A different approximation is also given for the case of very high SNR. In this letter, we revisit single-user multiple-input single-output beamforming with imperfect channel state information (CSI) at the transmitter. We present a CSI estimation model that is suitable for finite-scatterer directional channel models with uncertainty in the relative phase shifts of the scattering components. We show that in this case the distribution of the effective beamformed channel does not follow one of the well-known channel fading distributions and leads to complicated outage calculations. We show that the presented model generalizes popular existing models and we relate our investigations for the special cases of one and two specular components to existing results. We furthermore consider signal outage optimal beamforming for the case of two specular components. The two-ray model has been used for modelling of wireless channels already for decades. However, since researchers and industry are pushing forward to unlock the millimeter wave bands, we revisited this model. We re-derive the break point distance based on a generalized first Fresnel zone. The simplified approximation formula — four times the product of antenna heights scaled by wavelength — is especially accurate for millimeter waves, but difficult to verify. We then demonstrate that the two-ray ground-reflection model can be observed within many vehicular scenarios and fit ray-tracing data with the two-ray model. Finally we devise a measurement strategy as well as the usage of an l 1 algorithm for piecewise linear fitting slopes to the model data. Thereby we are able to show that the break point distance is indeed a valid modelling parameter and can be determined accurately. This paper presents new envelope probability density functions (PDFs) that describe small-scale, local area fading experienced by narrow-band wireless receivers. The paper also develops novel PDFs that describe the local area fading of two specular multipath components in the presence of other diffusely propagating waves. These PDFs are studied in the context of classical fading PDFs such as the Rayleigh, Rician, and other distributions. Two infinite series expressions are derived for the TWDP fading PDF and CDF. The derived series are shown to rapidly converge over the range of practical TWDP fading parameters. An efficient low-complexity algorithm is also proposed for evaluation of these series. Infinite series solution are derived for the TWDP moments, and the integral of the TWDP fading PDF against the complementary error function for performance analysis purposes. The BER of a BPSK system operating in TWDP fading is evaluated as an application of the results. Recent propagation measurements conducted for emerging applications such as vehicle-to-vehicle communications and wireless sensor systems have illustrated that present worst-case channel models are not sufficient to characterize the small-scale propagation effects seen. New theoretical models have thus been proposed but existing emulation environments do not create sufficiently severe channel conditions. In this work we present the design of a compact, reconfigurable channel emulator (CRCE) specifically designed to create Ricean, Rayleigh and hyper-Rayleigh fading environments in a repeatable manner. The bench-top sized chamber leverages concepts seen in reverberation chambers but in addition to a mechanical stirrer varies the multipath environment through the use of multiple antennas. Emulated channels illustrating space-, time- and frequency-selective behaviors are presented.