TY - JOUR
T1 - Peak sidelobe level gumbel distribution of antenna arrays with random phase centers
AU - Krishnamurthy, Siddhartha
AU - Bliss, Daniel W.
AU - Richmond, Christ D.
AU - Tarokh, Vahid
N1 - Funding Information:
Manuscript received April 9, 2017; revised March 17, 2019; accepted April 26, 2019. Date of publication May 23, 2019; date of current version August 12, 2019. This work was supported by the United States Air Force under Contract FA8721-05-C-0002. (Corresponding author: Siddhartha Krishnamurthy.) S. Krishnamurthy is with the Structural Acoustics Branch, NASA Langley Research Center, Hampton, VA 23681 USA (e-mail: siddharthak@ieee.org).
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2019/8
Y1 - 2019/8
N2 - The maximum value of an antenna array's sidelobe beampattern, or radiation pattern in the power domain, is an important parameter determining its performance. In this paper, when array antenna elements have random phase centers, we approximate the maximum sidelobe value, or peak sidelobe level, as a Gumbel distribution using the extreme value theory (EVT). Before the EVT result, an expression for the beampattern distribution at each angle in the array field of view is found. From this expression, the pointwise convergence of the difference between the beampattern and exponential distributions in the limit of a large number of antennas is obtained. Using the exponential distribution approximation, EVT is applied with samples of the beampattern. A bound is given for the difference between the beampattern sample maximum and its true maximum in the sidelobe region.
AB - The maximum value of an antenna array's sidelobe beampattern, or radiation pattern in the power domain, is an important parameter determining its performance. In this paper, when array antenna elements have random phase centers, we approximate the maximum sidelobe value, or peak sidelobe level, as a Gumbel distribution using the extreme value theory (EVT). Before the EVT result, an expression for the beampattern distribution at each angle in the array field of view is found. From this expression, the pointwise convergence of the difference between the beampattern and exponential distributions in the limit of a large number of antennas is obtained. Using the exponential distribution approximation, EVT is applied with samples of the beampattern. A bound is given for the difference between the beampattern sample maximum and its true maximum in the sidelobe region.
KW - Antenna arrays
KW - antenna radiation patterns
KW - array signal processing
KW - linear antenna arrays
KW - phased arrays
KW - probability
KW - probability distribution
KW - random variables
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U2 - 10.1109/TAP.2019.2917469
DO - 10.1109/TAP.2019.2917469
M3 - Article
AN - SCOPUS:85070632749
SN - 0018-926X
VL - 67
SP - 5399
EP - 5410
JO - IEEE Transactions on Antennas and Propagation
JF - IEEE Transactions on Antennas and Propagation
IS - 8
M1 - 8721244
ER -