Acoustic Experiments Research Articles

The enhancement of DNA fragmentation in a bench top ultrasonic water bath with needle-induced air bubbles: Simulation and experimental investigation.

Shearing DNA to a certain size is the first step in many medical and biological applications, especially in next-generation gene sequencing technology. In this article, we introduced a highly efficient ultrasonic DNA fragmentation method enhanced by needle-induced air bubbles, which is easy to operate with high throughput. The principle of the bubble-enhanced sonication system is introduced and verified by flow field and acoustic simulations and experiments. Lambda DNA long chains and mouse genomic DNA short chains are used in the experiments for testing the performance of the bubble-enhanced ultrasonic DNA fragmentation system. Air bubbles are an effective enhancement agent for ultrasonic DNA fragmentation; they can obviously improve the sound pressure level in the whole solution, thus, achieving better absorption of ultrasound energy. Growing bubbles also have a stretched function on DNA molecule chains and form a huge pressure gradient in the solution, which is beneficial to DNA fragmentation. Purified λDNA is cut from 48.5 to 2 kbp in 5 min and cut to 300 bp in 30 min. Mouse genomic DNA (≈1400 bp) decreases to 400 bp in 5 min and then reduces to 200 bp in 30 min. This bubble-enhanced ultrasonic method enables widespread access to genomic DNA fragmentation in a standard ultrasonic water bath for many virus sequencing demands even without good medical facilities.

Tonotopic Selectivity in Cats and Humans: Electrophysiology and Psychophysics

We describe a scalp-recorded measure of tonotopic selectivity, the “cortical onset response” (COR) and compare the results between humans and cats. The COR results, in turn, were compared with psychophysical masked-detection thresholds obtained using similar stimuli and obtained from both species. The COR consisted of averaged responses elicited by 50-ms tone-burst probes presented at 1-s intervals against a continuous noise masker. The noise masker had a bandwidth of 1 or 1/8th octave, geometrically centred on 4000 Hz for humans and on 8000 Hz for cats. The probe frequency was either − 0.5, − 0.25, 0, 0.25 or 0.5 octaves re the masker centre frequency. The COR was larger for probe frequencies more distant from the centre frequency of the masker, and this effect was greater for the 1/8th-octave than for the 1-octave masker. This pattern broadly reflected the masked excitation patterns obtained psychophysically with similar stimuli in both species. However, the positive signal-to-noise ratio used to obtain reliable COR measures meant that some aspects of the data differed from those obtained psychophysically, in a way that could be partly explained by the upward spread of the probe’s excitation pattern. Our psychophysical measurements also showed that the auditory filter width obtained at 8000 Hz using notched-noise maskers was slightly wider in cat than previous measures from humans. We argue that although conclusions from COR measures differ in some ways from conclusions based on psychophysics, the COR measures provide an objective, noninvasive, valid measure of tonotopic selectivity that does not require training and that may be applied to acoustic and cochlear-implant experiments in humans and laboratory animals.

Research on acoustic logging while drilling transmitting technologies

Abstract Acoustic logging while drilling (LWD) technology plays an important role in oil and gas exploration and development. Compared to traditional wireline logging, LWD must address more additional crucial problems, such as great noise confusions. This paper studies a series of technologies to improve the transmitting performances of LWD tools. First, we verified that the shear wave remote detection technology successfully adopted in wireline logging was also suitable for LWD, which could significantly expand its detection range. In addition, we calculated its dominant excitation frequency bands, which were different with wireline logging. Second, a class AB push–pull excitation circuit was designed. The results demonstrated that this circuit could obtain ideal excitation signals for LWD transmitting transducers. Furthermore, the signal shapes, excitation frequencies and cycle amounts are easily to adjust. In this study, we proposed a broadband impedance matching technology to solve the impedance mismatching problem between the excitation circuits and the excitation transducer. Acoustic experiments showed that this technology improved emitting powers of LWD transducers significantly.

Low-frequency and broadband muffler via cascaded labyrinthine metasurfaces

We theoretically and experimentally demonstrate an approach to design a kind of broadband muffler with functionalities of sound insulation and ventilation at low frequencies. By using a bypass space coiling tunnel connected to a central open hole, a large bandgap at low frequencies is discovered in the periodic system. Due to the tunability of the tunnel, the labyrinthine metasurface possesses a strong ability to control the performance and the bandwidth of sound insulation. Through a cascaded array of the metasurfaces, the muffler can exhibit the properties of large transmission loss (TL) with broad bandwidth. A cylindrical muffler of height 15.6 cm and diameter 10 cm composed of a simple array of metasurfaces with exactly the same parameters is observed to produce broadband transmission loss (TL) with a peak of 75 dB at 300 Hz. Through optimization in different metasurfaces, TL in the whole spectrum from 198 to 412 Hz can be enhanced to be over 15 dB. This theory is verified by both band structure analysis and acoustic experiment. Our findings open an approach for low-frequency and wideband noise control in general exhaust systems.

Effect of bat pinna on sensing using acoustic finite difference time domain simulation.

The practicality of the finite-difference time-domain (FDTD) method was confirmed by comparing head-related transfer functions obtained from a three-dimensional (3D) digital model of a bat (Rhinolophus ferrumequinum nippon) head with acoustic experiments using a 3D printed physical model. Furthermore, we simulated the auditory directionality using a 3D digital model that was modified based on the pinna movement of a bat during echolocation and found that the alternating movements of the left and right pinna result in a binaural sound pressure difference for vertical sources. Using the FDTD method, suitable for simulating acoustics in large spaces, we could analyze in detail the binaural echoes that bats receive and the acoustic cues they use for echolocation.

Complicated Fault Characterization and Its Influence on Shale Gas Preservation in the Southern Margin of the Sichuan Basin, China

Abstract The southern margin of the Sichuan Basin is characterized by strong structural deformation, complex fault structure styles and scales, and multistaged geological evolution stages, which together have created various shale gas preservation conditions. Taking Jianwu (JW)–Luochang (LC)–Shuanglong (SL) synclines as an example, the fault development characteristics and structural styles of the Longmaxi Formation were studied based on fine seismic interpretation and microscopic tests (rock acoustic emission experiments and fracture-filling inclusion tests), and the effects of the fault stage, fault class and scale, and fracture development degree on shale gas preservation conditions were analysed. Basement-involved faults, detachment faults, and intraformational microfaults are mainly developed from southeast to northwest. These fault structural types have affected the JW Syncline in the southeastern part, where faults are developed from the bottom of the Cambrian to the Wufeng–Longmaxi Formation and from the Wufeng–Longmaxi Formation to the Permian (Triassic). The SL-LC region in the northwestern part is dominated by the faults from the Wufeng–Longmaxi Formation to the Permian (Triassic). This region is dominated by NE-trending main control faults, supplemented by NW-trending, approximately EW-trending, SN-trending, and other small-scale regulating faults. Fault development can be divided into three stages, corresponding to the early, middle, and late Himalayan tectonic movements. In the early stage, a few small-scale approximately EW-trending faults had little impact on shale gas preservation. In the intermediate stage, the large number of large-scale NE-trending main control faults significantly impacted shale gas preservation. The JW Syncline mainly developed three types of faults with a high-filling degree, weak upwards penetration, and small-scale relevant fractures, which together created favourable conditions for shale gas preservation. The western and northern parts are dominated by I and II faults with large structural deformation, a low-filling degree, a large-scale, and strong penetration of related fractures, which have created unfavourable conditions for shale gas preservation. During the late stage, approximately SN- and NW-trending strike-slip reverse faults developed, and strong shear and fracture zones formed near the faults, producing unfavourable conditions for shale gas preservation. This research has clarified the characterization method of fault characteristics and stages and has established the influence of complex faults on shale gas preservation, which has an important reference value for the exploration and evaluation of shale gas reserves in complex tectonic regions.

Ray-based blind deconvolution with maximum kurtosis phase correction.

Ray-based blind deconvolution (RBD) is a method that estimates the source waveform and channel impulse response (CIR) using the ray arrival in an underwater environment. The RBD estimates the phase of the source waveform by using beamforming. However, low sampling, array shape deformation, and other factors can cause phase errors in the beamforming results. In this paper, phase correction is applied to the beamforming estimated source phase to improve RBD performance. The impulsiveness of the CIR was used as additional information to correct the initially estimated source phase. Kurtosis was used to measure impulsiveness, and the phase correction that maximized the kurtosis of the CIRs was calculated through optimization. The proposed approach is called ray-based blind deconvolution with maximum kurtosis phase correction (RBD-MKPC) and is based on a single-input multiple-output system. The RBD-MKPC was tested with several CIRs and source waveform combinations in the shallow-water acoustic variability experiment 2015 using broadband high-frequency pulses (11-31 kHz) as the source and a sparse vertical 16-element line array as receivers. The results indicate that the RBD-MKPC improves the estimation performance. In addition, from an optimization point of view and compared with other initialization methods, the proposed method showed superior convergence speed and estimation performance.

Tracking Valley Topology with Synthetic Weyl Paths.

Inspired by the newly emergent valleytronics, great interest has been attracted to the topological valley transport in classical metacrystals. The presence of nontrivial domain-wall states is interpreted with a concept of valley Chern number, which is well defined only in the limit of small band gap. Here, we propose a new visual angle to track the intricate valley topology in classical systems. Benefiting from the controllability of our acoustic metacrystals, we construct Weyl points in synthetic three-dimensional momentum space through introducing an extra structural parameter (rotation angle here). As such, the two-dimensional valley-projected band topology can be tracked with the strictly quantized topological charge in three-dimensional Weyl crystal, which features open surface arcs connecting the synthetic Weyl points and gapless chiral surface states along specific Weyl paths. All theoretical predictions are conclusively identified by our acoustic experiments. Our findings may promote the development of topological valley physics, which is less well defined yet under hot debate in multiple physical disciplines.

Research on a method of conveying material sensations through sound effects

Material sound effects are widely used in virtual reality and games to convey specific material sensations to the audience and improve the immersion experience. However, systematic research on parametrically controlling the material sensations evoked by sound effects is lacking. This study presents a new method of sound design regarding the control of parameters – pitch, waveform, attenuation time and artificial harmonics. The acoustic semantic experiments demonstrate that these sound effects can convey virtual material sensations with a 78% understanding rate with only auditory cues. This study can broaden our thinking regarding sound effects, music production and related disciplines .

Lamb Waves Propagation Characteristics in Functionally Graded Sandwich Plates.

Functionally graded materials (FGM) have received extensive attention in recent years due to their excellent mechanical properties. In this research, the theoretical process of calculating the propagation characteristics of Lamb waves in FGM sandwich plates is deduced by combining the FGM volume fraction curve and Legendre polynomial series expansion method. In this proposed method, the FGM plate does not have to be sliced into multiple layers. Numerical results are given in detail, and the Lamb wave dispersion curves are extracted. For comparison, the Lamb wave dispersion curve of the sliced layer model for the FGM sandwich plate is obtained by the global matrix method. Meanwhile, the FGM sandwich plate was subjected to finite element simulation, also based on the layered-plate model. The acoustic characteristics detection experiment was performed by simulation through a defocusing measurement. Thus, the Lamb wave dispersion curves were obtained by V(f, z) analysis. Finally, the influence of the change in the gradient function on the Lamb wave dispersion curves will be discussed.

Effects of Fracture Formation Stage on Shale Gas Preservation Conditions and Enrichment in Complex Structural Areas in the Southern Sichuan Basin, China

Fractures have significantly impacted the preservation, enrichment, and productivity of shale gas in the Longmaxi Formation in the complex structural area of the southern Sichuan Basin. Based on outcrop, core, imaging logging, inclusion analysis, acoustic emission experiments, and burial and thermal evolution history data, the formation stage, evolution and preservation conditions of structural fractures were comprehensively studied. Shear fractures are the main features of tectonic origin and are characterized by small widths, wide spacing, and high filling degrees. The structural fractures of the Longmaxi Formation can be divided into three groups in terms of their formation stage. The first-stage fractures were formed in the middle-late period of the Yanshanian tectonic movement (86.2–68.5 Ma), when the palaeotectonic stress was 68.33–71.82 MPa; and the homogenization temperature of the fluid inclusions in the corresponding fracture fillings is 150–178°C. The second-stage fractures were formed at the end of the Yanshanian -early Himalayan tectonic movement (68.5–35.2 Ma), when the palaeotectonic stress was 85.2–100.5 MPa; the homogenization temperature of the corresponding fluid inclusions is 123–148°C. The third-stage tectonic fractures formed during the middle-late period of the Himalayan tectonic movement (35.2–0 Ma), when the palaeotectonic stress was 55.6–63.8 MPa; fillings are scarce in these fractures, but the measured homogenization temperature of the corresponding fluid inclusions is 90–110°C. Shale gas preservation conditions were affected by the fracture formation stage, maximum horizontal crustal stress, fault scale, structural burial depth, formation pressure coefficient, etc. Three types of favourable preservation conditions were identified. The Type I target area is the low slope area in the middle of the syncline, which occurs more than 2.0 km from the fault. The research results have guiding significance for the evaluation of the preservation conditions of deep shale gas in the study area and similar areas.

Non-classical mechanical states guided in a phononic waveguide

The ability to create, manipulate and detect non-classical states of light has been key for many recent achievements in quantum physics and for developing quantum technologies. Achieving the same level of control over phonons, the quanta of vibrations, could have a similar impact, in particular on the fields of quantum sensing and quantum information processing. Here we present a crucial step towards this level of control and realize a single-mode waveguide for individual phonons in a suspended silicon microstructure. We use a cavity–waveguide architecture, where the cavity is used as a source and detector for the mechanical excitations while the waveguide has a free-standing end to reflect the phonons. This enables us to observe multiple round trips of phonons between the source and the reflector. The long mechanical lifetime of almost 100 μs demonstrates the possibility of nearly lossless transmission of single phonons over, in principle, tens of centimetres. Our experiment demonstrates full on-chip control over travelling single phonons strongly confined in the directions transverse to the propagation axis, potentially enabling a time-encoded multimode quantum memory at telecommunications wavelength and advanced quantum acoustics experiments. Non-classical vibrations are generated and transmitted along a mechanical waveguide, providing a platform for distributing quantum information and realizing hybrid quantum devices using phonons in a solid-state system.

Coupling relationship between current in-situ stress and natural fractures of continental tight sandstone oil reservoirs

We have integrated rock mechanics and acoustic experiments, full-wave array acoustic testing, formation microscanner image logging, and hydraulic-fracturing data to evaluate the coupling relationship between current in-situ stress and natural fractures. We used the data of the Yanchang Formation in the DL block of the western Ordos Basin, China, as an example. Our results find that the Yanchang Formation mainly develops high-angle fractures and vertical fractures. Furthermore, the in-situ stress state of the target sandstone strata satisfies [Formula: see text]. Nearly vertical and high-angle fractures are formed in the environment when [Formula: see text] is the maximum principal stress. Therefore, the current in-situ stress state of the target layer matches the induced fractures (longitudinal tensile-induced fractures) and natural fractures. As the buried depth increases, the difference between the horizontal maximum and minimum stresses ([Formula: see text]) has a tendency to first decrease and then increase, and its conversion depth is approximately 2000 m. Natural fractures are not developed in the distributary bay (the lowest horizontal stress area) and the thick sand area in the middle of the main river channel (the largest horizontal stress area). Natural fractures are mainly developed on the two wings of the main channel, and their horizontal stress is approximately 2–4 MPa lower than the central part of the main channel. We determined a correlation between fractures and sedimentary facies, and we have an important reference value for improving the drilling success rate of tight oil reservoirs. Furthermore, our study provides insights into the prediction of fractures and sweet spots for further exploration and hydraulic fracturing activities in the studied area and elsewhere in continental tight sandstone reservoirs.

Among-individual differences in auditory and physical cognitive abilities in zebra finches.

Among-individual variation in performance on cognitive tasks is ubiquitous across species that have been examined, and understanding the evolution of cognitive abilities requires investigating among-individual variation because natural selection acts on individual differences. However, relatively little is known about the extent to which individual differences in cognition are determined by domain-specific compared with domain-general cognitive abilities. We examined individual differences in learning speed of zebra finches across seven different tasks to determine the extent of domain-specific versus domain-general learning abilities, as well as the relationship between learning speed and learning generalization. Thirty-two zebra finches completed a foraging board experiment that included visual and structural discriminations, and then these same birds went through an acoustic operant discrimination experiment that required discriminating between different natural categories of acoustic stimuli. We found evidence of domain-general learning abilities as birds’ relative performance on the seven learning tasks was weakly repeatable and a principal components analysis found a first principal component that explained 36% of the variance in performance across tasks with all tasks loading unidirectionally on this component. However, the few significant correlations between tasks and high repeatability within each experiment suggest the potential for domain-specific abilities. Learning speed did not influence an individual’s ability to generalize learning. These results suggest that zebra finch performance across visual, structural, and auditory learning relies upon some common mechanism; some might call this evidence of “general intelligence”(g), but it is also possible that this finding is due to other noncognitive mechanisms such as motivation.Supplementary InformationThe online version contains supplementary material available at 10.3758/s13420-022-00520-w.

Experiments in a Large Boundary Layer Wind Tunnel: Propagation of Noise through the Turbulent Boundary Layer

A series of acoustic propagation experiments was conducted in the University of Florida Boundary Layer Wind Tunnel (UFBLWT) to investigate tornadic infrasound propagation in the turbulent atmosphere. A synthetic acoustic wave was generated within a boundary layer wind field using a speaker, and distorted by the surrounding turbulent atmosphere as it propagated along the UFBLWT fetch where it was measured by an acoustic microphone 22 m downwind of the speaker. The wind tunnel operating speed and the configuration of the mechanical turbulence generating roughness elements were varied between experiments to alter the turbulence characteristics and thus the distortion of the acoustic wave. The wind field turbulence data were obtained by three Cobra probes mounted on an actuated and automated gantry. The turbulence-induced distortion of the acoustic wave was captured by analyzing the signal at its source and as-measured downwind. Data were characterized, organized, and curated into four stages.

A Prototype System With Custom-Designed RX ICs for Contrast-Enhanced Ultrasound Imaging

This work presents a prototype system based on a multichannel receiving (RX) integrated circuit (IC) for contrast-enhanced ultrasound (CEUS) imaging. The RX IC is implemented in a 40-nm low-voltage CMOS technology and is designed to interface to a capacitive micromachined ultrasonic transducer array. To enable a direct connection of the RX electronics to the transducer, an analog multiplexer with on-chip protection circuitry is developed. Stress tests confirm the reliability of this arrangement when combined with a high-voltage pulser. The RX IC is equipped with a highly programmable bandpass filter to capture harmonic signals from ultrasound contrast agents (UCAs) while suppressing fundamental components. In order to examine the impact of analog front-end (AFE) bandpass filtering, in vitro acoustic experiments are performed with UCAs. A spatial resolution analysis suggests that the AFE bandpass filtering combined with a pulse inversion (PI) technique can improve the lateral resolution by 38% or 9% compared to the original full-bandwidth approach or a stand-alone PI approach, respectively, while the impact on axial resolution is negligible. A phantom study shows that compared to digital bandpass filtering, the AFE bandpass filtering enables better use of the dynamic range of the RX electronics, resulting in better generalized contrast-to-noise ratio from 0.44/0.53 to 0.57/0.68 without or with PI.

Comprehensive Evaluation of Rock Mechanical Properties and in-situ Stress in Tight Sandstone Oil Reservoirs

Comprehensive research on reservoir rock mechanics and in-situ stress properties combined with petrophysical experiments, logging models and numerical simulation is an important means to achieve efficient development of tight sandstone oil reservoirs. In this study, a large number of rock mechanics and acoustic experiments, full-wave train array acoustic wave tests, hydraulic fracturing data and three-dimensional finite element simulations were used to study the rock mechanical properties and in-situ stress characteristics of continental tight oil reservoirs in the Yanchang Formation. The results show that under uniaxial conditions, the tight sandstone samples mainly suffer from tensional ruptures. With the increase of confining pressure, the tight sandstone samples undergo obvious shear ruptures. When the confining pressure is loaded to 35 MPa, a typical vertical shear fracture will be formed. The hydraulic fracturing calculation results show that the in-situ stress state of the target layer satisfies σv (vertical principal stress)>σH (maximum horizontal principal stress)>σh (minimum horizontal principal stress). Based on the results of rock mechanics and acoustic tests, we have constructed the dynamic and static mechanical parameter conversion models of tight oil reservoirs and the logging interpretation model of current in-situ stress. Furthermore, the finite element method is used to simulate the three-dimensional structural stress field of the target layer. The simulations show that the horizontal principal stress distribution in the work area is consistent with the applied environmental stress. The σH of the target layer is mainly distributed in 32–50 MPa, and the σh is mainly distributed in 20–34 MPa. Both σH and σh are relatively high in the southern uplift of the work area; among them, σH is usually greater than 44 MPa, and σh is usually greater than 24 MPa. The northern part of the study area developed several grooved areas with relatively low stress values. The regions with high stress values are often distributed in bands, which may be related to the compression caused by the deformation of the strata. For shear stress, left-handed and right-handed regions usually alternate with each other. However, the extent of the left-handed area in the southern uplift area is larger than that of the right-handed area, indicating that the tight oil reservoirs in the study area are mainly affected by left-handed activities.

Influence of internal wave induced sound speed variability on acoustic propagation in shallow waters of North West Bay of Bengal

This study focuses on the influence of internal wave induced sound speed variability on acoustic propagation parallel to the coast in shallow waters of North West Bay of Bengal (BoB). An acoustic transmission and reception experiment had been conducted at the site during February 2018 with simultaneous acquisition of oceanographic data, to examine propagation characteristics. The 950 Hz signal from an anchored vessel was received by an array of hydrophones moored 50 km away, with a loss of ∼ 80–95 dB with respect to the source position, receiver depth and sound speed variability. Sound speed variations in the acoustic environment were simulated using a shallow water internal wave model called WAVE to characterize the acoustic environment. Derived internal wave features from oceanographic and acoustic observations from study location during the experiment period were used to simulate the internal wave acoustic environment. Sound propagation using BELLHOP model was carried out with a simulated internal wave sound speed environment for 950 Hz source frequency. Model and observed temporal variability of transmission loss with sound speed at both source depth and thermocline depth has been addressed. Transmission loss features are comparable with field observations and model limitations are reflected in the results thus showing errors between two approaches. Range dependent bathymetry and other ocean acoustic parameters influence transmission loss at the study location. Temperature and salinity are major parameters influencing sound speed fluctuation in shallow waters, and corresponding variations are reflected in transmission loss and propagation. Finally this study provides a quantitative support in transmission loss in both modeling and experimental approaches at the study location.

Experimental measurements of monopole inner/outer collar waves and estimation of P wave velocity in acoustic LWD

Acoustic logging while drilling (LWD) technology is extensively applied for petroleum prospecting. It utilizes the acoustic characteristics of stratum to deduce the formation properties such as porosity, permeability, and oil saturation, etc., which can help to detect the location of oil reservoirs. In acoustic logging process, the formation longitudinal (P) and transverse (S) wave velocity is the primary factor of interest. Nevertheless, an accurate identification of P/S wave velocity in different formations is hard to be performed due to the influence of the collar waves, which has become an urgent problem in LWD measurements. To study this issue more practically, a small-sized measurement system based on the propagation mechanism of collar waves is established in our laboratory. With this system, we design and perform multiple sets of monopole acoustic LWD experiments with different models. After recording the experimental data, the attenuations of inner and outer collar waves received along the axial direction are compared and analyzed. The result shows that the collar waves have an exponential decay in amplitude by the expansion of source-receiver distance, but the outer collar wave decreases more rapidly. We also conduct experiments at different source frequencies (20–400 kHz) to quantitatively describe the relationship between the amplitude and frequency. The result suggests that the inner/outer collar waves and P/S waves have a similar frequency response, and it's difficult to remove collar waves from the full waveforms of LWD signals by only changing source frequency. Therefore, we present a new data processing method for extracting the formation wave velocities according to the energy distribution of the componential waves, and then apply it in the analysis of two borehole measurements. The inner and outer collar waves are almost removed from the processed time domain waveforms, which leads to a successful verification of formation P/S wave velocities. These experimental results prove the feasibility and repeatability of our method, and propose an alternative method for the LWD data explanations.

Long-Range Underwater Communication Based on Time Reversal Processing Using Various Diversity Methods.

Time reversal processing (TRP) exploits signal diversity methods, namely, spatial, temporal, beam, and frequency, to mitigate the distortion caused by multipath time delay. Using the same experimental data, this study compares the performance of communication utilizing TRP based on various diversity methods. In October 2018, the biomimetic long-range acoustic communication experiment 2018 (BLAC18) was conducted in the East Sea, east of Pohang, Korea. During the experiment, communication signals modulated by binary phase-shift keying were transmitted over a range of 60 km, and a vertical line array of 16 elements (with an aperture of ∼42 m) was utilized. The BLAC18 analysis showed that the performance of each diversity method depends on the order of diversity. When the order of diversity was one, the beam diversity method with the beamformed signal yielded the best performance. For the maximum order of diversity, however, the spatial diversity method delivered the best performance, owing to the high channel variability and large number of receivers.