Statistical patterns of a general array

Howard, J.

doi:10.1109/tap.1967.1138851

Cited by 10 publications

(4 citation statements)

References 12 publications

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“…In spite of the fact that the spacing is only 0.6 A, a grating lobe not predicted by linear array theory appears, as shown in Fig. 20 [33]. This grating lobe appears around looo, where the radiation of the last few elements tend to add in phase; most of the others are not visible from that direction.…”

Section: (25)mentioning

confidence: 90%

Basic array theory

Kummer¹

1992

Proc. IEEE

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This paper outlines basic antenna array theory with major emphasis on pattern analysis and synthesis for periodic linear and planar arrays, phased arrays, and conformal arrays. Extension is made to synthesis techniques which use computer algorithms. These include arbitrary side lobe control, shaped beams, and phase-only null steering. The subjects of random errors and phased array quantization errors are outlined.

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Section: (25)mentioning

confidence: 90%

Basic array theory

Kummer¹

1992

Proc. IEEE

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“…If (20), (21) do not hold, (8) does not apply, the array gain at d = mλ/2, m = 1, 2, 3..., is not G = n anymore and some additional assumptions traditionally made (sometimes implicitly) in the array analysis cease to hold (e.g. the array pattern becomes a function of distance) [14]- [17].…”

Section: Limitations Of Asymptotic Analysismentioning

confidence: 99%

On physically-based normalization of MIMO channel matrices

Loyka

Levin

2009

IEEE Trans. Wireless Commun.

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Abstract-Various normalizations of the MIMO channel matrix are discussed from a physical perspective. It is demonstrated that the physics of antenna arrays and propagation channel should be taken into account when normalization is chosen, so that SNR has proper physical meaning, the conclusions are physical and correspond to realistic systems. The antenna array geometry and the transmission strategy (coherent/non-coherent) limits the choice of normalization and determines how the capacity and other performance metrics scale with the number of antennas, which is more pronounced for densely-populated antenna arrays. This is especially important for an asymptotic analysis, when the number of antennas increases to infinity. Limitations of such analysis from the physical perspective are pointed out.

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“…The effect of random errors in data-independent beamforming with conventional arrays has been investigated for many decades [1,5,[23][24][25][26][27][28][29][30][31][32][33][34], leading to equations for the calculation of the moments of the ABP (or of specific ABP portions, especially the side-lobe region) and, with different levels of approximation, to knowledge of the PDF of the ABP modulus. In many cases the studies are limited to gain and phase errors, considered constant with respect to frequency, neglecting errors in the positions of the array elements.…”

Section: Introduction N Data-independent Beamformingmentioning

confidence: 99%

“…The statistical moments of the ABP modulus in the presence of correlated random errors, as well as the directivity reduction and steering direction fluctuation, have been investigated in[27,28,33].…”

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confidence: 99%

The Statistics of Superdirective Beam Patterns

Trucco

2022

IEEE Trans. Signal Process.

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Superdirective arrays have been extensively studied because of their considerable potential accompanied, unfortunately, by a high sensitivity to random errors that affect the responses and positions of array elements. However, the statistics of their actual beam pattern (BP) has never been systematically investigated. This paper shows that the Rician probability density function (PDF), sometimes adopted to study the impact of errors in conventional arrays, is a valid approximation for superdirective BP statistics only where some mathematical terms are negligible. The paper also shows that this is the case for all linear end-fire arrays considered. A similar study is proposed concerning the correlation between BP lobes, showing that for the superdirective arrays considered the lobes, especially non-adjacent ones, are almost independent. Furthermore, knowledge of the PDF of the actual BP allows one to define quantile BP functions, whose probability of being exceeded, at any point, is fixed. Combining the lobes' independence with quantile BP functions, an empirical equation for the probability that the entire actual BP will not exceed a quantile function over an interval larger than a given size is obtained. This new knowledge and these tools make it possible to devise new methods to design robust superdirective arrays via optimization goals with clearer and more relevant statistical meaning.

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Statistical patterns of a general array

Cited by 10 publications

References 12 publications

Basic array theory

Basic array theory

On physically-based normalization of MIMO channel matrices

The Statistics of Superdirective Beam Patterns

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