DOI: https://doi.org/10.3103/S0735272718060031
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### Odd symmetry of weights vector of symmetrical antenna arrays with linear constraints

Victor I. Djigan

#### Abstract

The paper provides proof of the odd symmetry of the vector of weight coefficients obtained on the basis of the least squares criterion in the linear antenna array with linear constraints and desired signal. Pairs of symmetrical elements of such vector are complex-conjugate to one another. For ensuring this property, the vector of constrained parameters (array pattern values in the directions of interest) must be real-valued, but need not be symmetrical. The odd symmetry of the antenna array vectors of input signals and weights makes it possible for such array to develop adaptive algorithms based on real-valued arithmetic. In this case, such algorithms have the number of arithmetic operations per iteration two or four times less as compared to the equivalent number of real-valued arithmetic operations of similar algorithms in the complex-valued arithmetic. The paper presents the results of comparative simulation of algorithms in the complex-valued and real-valued arithmetic. These results indicate that an adaptive algorithm using the real-valued arithmetic ensures (1.5–2)-fold shorter transient and deeper (by 2–3 dB) valleys in the steady state of the array pattern in the directions of sources of adaptively suppressed interferences as compared to the algorithm using the complex-valued arithmetic.

#### Keywords

adaptive antenna array; AAA; adaptive filtering algorithm; odd symmetry; recursive least mean squares; recursive least squares; RLS; linear constraints; linearly constrained; LC; radiation pattern; RP; weight coefficients; weights

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