| 摘要 |
A method for detecting a single or multi dimensional signal contaminated by additive Gaussian noise, and a detector using the method. The signal is an amplitude modulated sinusoid with known, but arbitrary, envelope and carrier frequency, but unknown uniform phase angle. The method comprises the step of calculating the integral for the likelihood ratio <maths id="MATH-US-00001" num="1"> <MATH OVERFLOW="SCROLL"> <MROW> <MROW> <MI>L</MI> <MO></MO> <MROW> <MO>(</MO> <MI>X</MI> <MO>)</MO> </MROW> </MROW> <MO>=</MO> <MROW> <MFRAC> <MN>1</MN> <MROW> <MN>2</MN> <MO></MO> <MI>pi</MI> </MROW> </MFRAC> <MO></MO> <MROW> <MSUBSUP> <MO>∫</MO> <MROW> <MO>-</MO> <MI>pi</MI> </MROW> <MI>pi</MI> </MSUBSUP> <MO></MO> <MROW> <MROW> <MSUB> <MI>L</MI> <MI>ϕ</MI> </MSUB> <MO></MO> <MROW> <MO>(</MO> <MI>X</MI> <MO>)</MO> </MROW> </MROW> <MO></MO> <MSTYLE> <MTEXT> </MTEXT> </MSTYLE> <MO></MO> <MROW> <MO>ⅆ</MO> <MI>ϕ</MI> </MROW> </MROW> </MROW> </MROW> </MROW> </MATH> </MATHS> analytically or numerically without limiting assumptions, and to make a comparison with a threshold value for deciding the question of detection.
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