means to detect a signal in the presence of additive noise gaussiskt and a detector using the method

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 MIL/MI MO⁡/MO MROW MO(/MO MIX/MI MO)/MO /MROW /MROW MO=/MO MROW MFRAC MN1/MN MROW MN2/MN MO⁢/MO MIpi/MI /MROW /MFRAC MO⁢/MO MROW MSUBSUP MO∫/MO MROW MO-/MO MIpi/MI /MROW MIpi/MI /MSUBSUP MO⁢/MO MROW MROW MSUB MIL/MI MIϕ/MI /MSUB MO⁡/MO MROW MO(/MO MIX/MI MO)/MO /MROW /MROW MO⁢/MO MSTYLE MTEXT /MTEXT /MSTYLE MO⁢/MO MROW MOⅆ/MO MIϕ/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.