Maximum Array Gain Research Articles

Integrated Sensing and Communications With Joint Beam-Squint and Beam-Split for mmWave/THz Massive MIMO

Integrated sensing and communications (ISAC) has attracted tremendous attention for the future 6G wireless communications systems. To improve the transmission rates and sensing accuracy, massive multi-input multi-output (MIMO) technique is leveraged with large transmission bandwidth in millimeter wave (mmWave)/terahertz (THz) band. However, the growing size of antenna array and transmission bandwidth results in the beam-squint effect, which hampers the performance of communications. Moreover, the time overhead of the traditional sensing algorithm is prohibitively high for practical systems. In this paper, instead of alleviating the beam-squint effect, we take advantage of joint beam-squint and beam-split effect and propose a novel integrated sensing and communications scheme for massive MIMO system. Specifically, with the beam-squint effect, the base station (BS) utilizes the true-time-delay (TTD) lines to steer the beams of different OFDM subcarriers towards distributive directions simultaneously. Different users then feedback their respective subcarrier frequency with the maximum array gain to BS, based on which BS could calculate the directions of the users. Moreover, by selecting sub-array with the inter-antenna spacing larger than half-wavelength, the beam-split effect can be introduced and exploited to expand the sensing range. The proposed sensing method operates over frequency-domain, and the intended sensing range is covered by all the subcarriers simultaneously, which significantly reduces the time overhead compared to the conventional sensing scheme. Simulation results have demonstrated the effectiveness as well as the superior performance of the proposed ISAC scheme.

79 GHz Multilayer Series-Fed Patch Antenna Array With Stacked Micro-Via Loading

A wideband compact series-fed patch subarray is proposed for 79 GHz multiple-input—multiple-output (MIMO) radar. The proposed subarray is, for the first time, loaded with stacked micro-vias (SMVs). Two sets of patches in the subarray are fed 180° out-of-phase. A low-cost, high-resolution multilayer printed circuit board (PCB) technology, called “any-layer PCB,” is used to implement the SMVs, which cannot be done by standard high-definition interconnect PCB technology. Moreover, the technology supports small SMVs on different layers; hence, thick machine-drilled vias can be avoided. For comparison, a series-fed patch subarray with no SMV loading is designed. It is shown that SMV loading facilitates a larger overlap of the impedance and gain bandwidths, leading to a larger operating bandwidth. The measured 10 dB impedance and 3 dB gain bandwidths are 15% and 9.6%, respectively. The sidelobe suppression is above 12.9 dB, and the maximum array gain is 12.67 dBi at 79.1 GHz. This subarray is suitable for MIMO radar, as its width is around half-wavelength and the SMVs around it mitigate the crosstalk between the transmitting and receiving arrays.

Circularly‐polarised end‐fire antenna and arrays for 5G millimetre‐wave beam‐steering systems

This study presents a circularly-polarised substrate-integrated waveguide end-fire antenna and four-antenna arrays for 5G beam-steering mobile devices at 28 GHz. Polarisation is achieved through implementation of a substrate-integrated waveguide notched-septum polariser. It is then loaded with a dielectric lens to improve gain, axial ratio bandwidth, and circular polarisation (CP) purity. To suppress the mutual coupling between array elements, vias are extended on either side of the lens. It also improves the single-element axial ratio and front-to-back ratio. The antenna's performance is found to be resilient to typical manufacturing tolerances for the lens and via extensions. The element and arrays are manufactured and measured. The prototypes demonstrated an impedance bandwidth of 11.4% with a maximum array gain of 10.5 dBi and a steering range of up to ± 35 ° (with reduced performance when steered to ± 45 ° ). Within this range, the antenna array demonstrates a gain variation of up to 3 dB and very good CP purity within the radiation half-power beamwidths (HPBWs). A wide single-element elevation HPBW of 95 ° is also demonstrated. Given its performance and ease of manufacture in a printed circuit board process, the proposed antenna could be a strong candidate for 5G millimetre-wave beam-steering systems.

A general superdirectivity model for arbitrary sensor arrays

This paper proposes a general model of superdirectivity to provide analytical and closed-form solutions for arbitrary sensor arrays. Based on the equivalence between the maximum directivity factor and the maximum array gain in the isotropic noise field, Gram-Schmidt orthogonalization is introduced and recursively transformed into a matrix form to conduct pre-whitening and matching operations that result in superdirectivity solutions. A Gram-Schmidt mode-beam decomposition and synthesis method is then presented to formally implement these solutions. Illustrative examples for different arrays are provided to demonstrate the feasibility of this method, and a reduced rank technique is used to deal with the practical array design for robust beamforming and acceptable high-order superdirectivity. Experimental results that are provided for a linear array consisting of nine hydrophones show the good performance of the technique. A superdirective beampattern with a beamwidth of 48.05° in the endfire direction is typically achieved when the inter-sensor spacing is only 0.09λ (λ is the wavelength), and the directivity index is up to 12 dB, which outperforms that of the conventional delay-and-sum counterpart by 6 dB.

Microphone cross-array beamformer processing to reduce noise and reverberation

Hands-free audio communication systems that are designed to allow audio and speech communication between remote parties are known to be sensitive to room reverberation and noise when the source is distant from the microphone. A common solution to the problem of room reverberation is to use an array of microphones to spatially filter the acoustic field. The maximum array gain is only attainable with specific microphone geometries and the gain of realizable microphone arrays is typically significantly lower than the maximum. The algorithm described in this talk attempts to address the rather slow growth in linear processing directional gain as a function of the number of microphones. One possible approach to attain higher directive gain is to use a processing scheme based on nonlinear multiplicative processing. An obvious candidate is the coherence function since it is a bounded and normalized multiplicative measure. A technique is presented for reverberation reduction processing using at least two beamforming microphones and a function of the estimated short-time coherence between the beamformer outputs. Each beamformer should have a different directional response or spatial position, or both, but with overlapping responses in the direction of the desired source.

Characterization of the radiation from single-walled zig-zag carbon nanotubes at terahertz range

This paper investigates the radiation characteristics of metal single-walled zig-zag carbon nanotubes as a dipole antenna at terahertz wave range. The current distribution, input impedance and mutual impedance are calculated for various geometrical parameters of vertically-aligned carbon nanotubes. The numerical results demonstrate the properties of the antenna depending strongly on the geometrical parameters such as the radius, the lengths of carbon nantobues, and the spacing between nanotubes. It is found that the zig-zag carbon nanotubes exhibit very high input impedance and the mutual impedances for antenna array applications. These unique high impedance properties are different from the conventional metal thin wire antenna. The far-field patterns and gain of antenna array are also calculated. The maximum gain of array of 100-element array is up to 20.0 dB, which is larger than the gain of 0.598 dB of single dipole antenna at distance d = 0.5λ.

Directionality of generalized acoustic sensors of arbitrary order

For several decades there has been a great deal of interest in acoustic sensors that can make multiple measurements at a single point in the ocean. The order of such sensors has been defined by linking it to the order of the Taylor series approximation of the pressure field at that point. Following this definition, the pressure, vector, and dyadic sensor is of order zero, one, and two, respectively. For this theoretical study, a multichannel three-dimensional spatial filter is derived for a directional acoustic sensor of arbitrary order. Explicit formulas are found for the filter coefficients that maximize the array gain (directivity index) of the filter as well as an explicit expression for the maximum array gain (directivity index). This process is repeated for the case of a first-order null placed in the direction opposite to the look direction of the multichannel filter. Finally, an example is presented which tracks the array gain and beamwidth of a third-order acoustic sensor as the order of the null is assigned values 0, 1, 2, and 3.

Array optimization applied in the near field of a microphone array

This paper describes the application of array optimization techniques in the near-field of a microphone array. It is shown that the optimum weights obtained for microphone spacing equal to a half wavelength are real, aside from the propagation delay, and inversely proportional to the distance from each microphone to the focal point. When the microphone spacing is less than a half wavelength, the optimum weights are super-directive requiring both an amplitude and phase adjustment in addition to delay-and-sum beamforming. In the super directive regime, the maximum array gain increases as the distance to the focal points decreases. The technique is suitable for applications where the source of interest is located in the near-field region but interfering sources are located farther from the array.

Mutual coupling, gain and directivity of an array of two identical antennas

It is shown that there is an optimum nonzero value of mutual coupling and passive reflection coefficient that is a function of only the embedded element pattern and element spacing. Optimum is defined as yielding maximum array gain. For closely spaced arrays, the optimum mutual coupling and passive reflection coefficient are quite large, but tend to cancel in the active mode to produce a low active reflection coefficient. A smaller value of mutual coupling would give lower gain than the optimum case. This again demonstrates that mutual coupling is a natural and desirable effect in array behavior. It is well known that it is possible to achieve array superdirectivity, in the sense that the directivity of an array of " <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> " elements is greater than " <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> " times the embedded element directivity; however, in this case the mutual coupling and passive reflection produce an active reflection coefficient that results in an array gain lower than " <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> " times the embedded element gain. In fact, higher superdirectivity always implies lower gain, relative to embedded element gain.

Influence of input quantizer step sizes on the processing gain of digital beamformers

Utilizing a formulation of output power of a digital beamformer with input quantizers of unequal input and output step sizes given previously, the optimum quantizer step sizes which yield maximum processing gain for a typical array were searched by the method of “steepest ascent” with a digital computer. For the case of two-bit /channel quantization with small input SNR (⩽ − 10 dB), the array gain surface as a function of two independent step variables exhibits a maximum which is only slightly greater than the maximum array gain achievable with uniform input quantizers. For larger input SNR, the array gain surface tends to be concave upward, and the performance of uniform quantizers can at the best be a suboptimum. The high theoretical processing gain in the limiting case of very large step sizes is attributed to a threshold effect of the input quantizers. Except for these latter conditions, the optimum uniform quantizing condition previously reported by the author represents essentially valid optimum design.

Quantizer functions and their use in the analyses of digital beamformer performance

The formulation of output autocorrelation function of a digital beamformer into an infinite series leads naturally to the introduction of “quantizer functions” of various orders as a convenient vehicle in the evaluation of beamformer performance corresponding to different input quantizer designs. For arrays operating in a Gaussian ambient noise field, the quantizer function of a general nonuniform quantizer is defined and evaluated in terms of “reduced Hermite polynomials,” which facilitate less costly machine computation via their unique recursion formulae. A rigorous proof of the convergence of the series of quantizer functions is given to ensure confidence in numerical results. Examples of the use of quantizer functions given are (i) determination of optimum step sizes of 2-, 3-, and 4-bit uniform quantizers which yield maximum array gain for a typical array, (ii) calculation of directivity patterns of digital beamformer with input signals of arbitrary bandwidth, and (iii) evaluation of the effect of post filtering on the directivity patterns of digital beamformers. The special case of 1 bit per channel quantization (DIMUS) was especially discussed in detail with respect to both array gain and directivity patterns. The use of quantizer functions can also be extended to the solution of active-sonar problems involving sine-wave signals, and a brief example was given to illustrate the partial recovering of clipping loss in DIMUS by post filtering.

Influence of Input Quantizer Step Sizes on the Processing Gain of Digital Beamformers

Utilizing a formulation of output power of a digital beamformer with input quantizers of unequal input and output step sizes reported elsewhere [H. S. C. Wang, Quantizer Functions and Their Use in the Analyses of Digital Beamformer Performance (to be published); also see J. Acoust. Soc. Amer. 51, 135(A) (1972)], the optimum quantizer step sizes that yield maximum processing gain are searched by the method of “steepest ascent” with a digital computer. For the case of 2 bits/channel quantization with small input S/N (&amp;lt; −10 dB), the array gain surface as a function of two independent step variables exhibits a maximum that is somewhat greater than the maximum array gain achievable with uniform input quantizers. For larger input S/N (&amp;gt; −10 dB), no maximum can be found, and, as the input S/N exceeds −4 dB, the array gain increases monotonically with respect to both input and output step variables. These phenomena were clarified by a numerical study of a “3-level quantizer” as a limiting case. The large theoretical processing gain at large step sizes is attributed to a threshold effect of the input quantizers.

Effect of Spatially Uncorrelated Noise on the Maximum Array Gain Processor

Several authors have shown that large array gains may be obtained by weighting individual elements with the optimum amplitude and phase factors. It is known that spatially uncorrelated noise, α, such as electronic noise, will decrease this maximum array gain. The purpose of this study is to obtain a quantitative value for this loss. Vertical, linear, equally spaced arrays from two to 10 elements are analyzed for both an isotropic and a surface generated noise field. Calculations on each array with elements spaced from one eighth to one wavelength have been made showing: (1) array gain as a function of the direction of “look” for several values of α, (2) array gain versus α for various spacing intervals, and (3) array gain versus the number of elements for given values of α. The loss of array gain increases as the number of elements increases for a given α. However, for the worst case of 10 elements spaced one-eighth wavelength apart, α could be 20 dB below the ambient noise level and still give much better results than conventional processing.

Maximum Array Gain Versus Optimum Pattern

In the design of arrays, there is a tradeoff between obtaining the maximum array gain on one hand and an optimum pattern on the other. An array was chosen, and the amplitude shading coefficients were calculated to produce the maximum array gain. Next the Tchebyscheff polynomials were used to obtain the amplitude shading coefficients which result in an optimum intensity pattern. Then the array gains and intensity patterns were calculated for each procedure and for a surface generated ambient and an isotropic noise field. The beam width of the patterns (for the same side lobe levels) and the array gains, as obtained by the two methods, were compared at each element spacing. For the cases of a linear, five-element, evenly spaced array at spacings of d/λ=1/8, 2/8, ⋯, 6/8 and both noise models, the two procedures produced minor differences. The maximum differences were that the Tchebyscheff procedure produced a main beam about 112° narrower but resulted in 12 dB less of array gain. For d/λ=7/8 and 1, differences were greater.

Optimum directional pattern synthesis of circular arrays

An attempt is made to deduce rules for designing circular arrays which produce desired directional patterns. The paper considers circular arrays consisting of equally spaced radiators distributed on the whole circumference or on a coherent part of it.First the general relation between the desired far-field amplitude distribution and the complex input amplitudes of the individual radiators is deduced. The results can be written as a linear system of equations. Its order depends only on the ratio of diameter to wavelength. This form permits a clear and simple numerical treatment of the task by means of a digital computer. Additionally, practical hints are given for the realization of the array feed function. There by it is found that a problem of the directional pattern synthesis can be reduced to a synthesis of linear networks.In a second step the actual optimizing problem is dealt with. It is intended to find, for a given ratio of circular array diameter to wavelength, the design for which the maximum array gain is obtainable with simultaneous maximum attenuation of side-lobes. The result shows that there exists a theoretical limit for the obtainable attenuation of the dominating side-lobe, a limitation which is independent of the ratio of circular array diameter to wavelength. In the investigated case this boundary is at −26-43 dB. The array gain increases in a nearly linear mannerwith the indicated ratio and there seems to be no theoretical limit to any desired increase of the gain.All considerations are valid for transmission and for reception. The correctness of the treatment has been confirmed by a laboratory experiment.