PLEASE PLEASE HELP WITH ALL PARTS. Thanks in advance! 7.20 The signal vector in

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PLEASE PLEASE HELP WITH ALL PARTS. Thanks in advance!

7.20 The signal vector in a detection problem is given by 2 2 The noise has zero mean and a covariance matrix of the form 1 p CN o CHAPTER 7 where 2 t 2 and p 1/v2. (a) Find the explicit form of the decision rule as a function of the parameter (b) The contour for the density of the received vector when no signal is present is defined by Ho) constant XIH From (7.47) this is equivalent to requiring a C ar m constant Carefully sketch or plot this contour in the z1 plane. You can set the constant equal to 1. Hint To put the equation for the contour in the simplest form, consider rotating the coordinate system by the transformation yi (r1 +r2)/ 2 and 2 T2 -ari)/ 2 (i.e., yi and y2 become the new coordinate axes) (c) Sketch or plot the contour for the density of X when the signal is present. Hint: The form of the contour is the same except for a shift in the mean

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A vector signal analyzer is an instrument that measures the magnitude and phase of the input signal at a single frequency within the IF bandwidth of the instrument. The primary use is to make in-channel measurements, such as error vector magnitude, code domain power, and spectral flatness, on known signals.

Vector signal analyzers are useful in measuring and demodulating digitally modulated signals like W-CDMA, LTE, and WLAN.[1] These measurements are used to determine the quality of modulation and can be used for design validation and compliance testing of electronic devices.

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