MIMO Radar Transmit Beampattern Matching Design

Abstract

In this paper, a novel transmit beampattern matching design method is proposed for a multiple-input multiple-output (MIMO) radar system. Whereas previous approaches first solve the correlation matrix <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$R$</tex></formula> and then use <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$R$</tex></formula> to design the transmit signal <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$S$</tex></formula> , the proposed one-step method obtains the transmit signal <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$S$</tex></formula> directly through solving the waveform matrix <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$P$</tex></formula> . Since MIMO radar transmit beampattern matching design is an inverse problem of the transmit beampattern, in this paper, we first discuss some important properties of the transmit beampattern and standardize the beampattern matching design problem. We then theoretically explain the value of the signal waveform matrix <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$P$</tex></formula> , followed by an unconstrained optimization problem to solve <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$P$</tex></formula> . Numerical examples demonstrate the advantages of the proposed one-step method for the MIMO radar transmit beampattern matching design problem, including uniform and non-uniform linear arrays.