MidTerm2005

A what condition must hold for the vector v such that

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Unformatted text preview: * What condition must hold for the vector v such that y 2 im fH g? In the following assume that y 62 im H . Now consider the following optimization problem: min ky , Hxk2 ; 2 x b* How is the solution x of the optimization problem given in 2 called? 2 Name: Matr.-Nr.: 2 Let us now consider instead the following optimization problem: min J x x 3 xopt = H HW HWH ,1H HW HWy 4 where J x = kWy , WHxk2 and W 2 C mm is a positive de nite matrix. 2 @J x = 0, the solution to the optimization problem given in c* Show that by solving @ x 3 can be expressed as follows: Name: d* Compute Jmin = J xopt . Matr.-Nr.: 3 Name: Matr.-Nr.: 4 Task 26 pts Consider the following AWGN additive white Gaussian noise channel s with y n y =s+n 5 where s; n; y 2 C M with the transmitted signal s having zero mean and being uncorrelated with theon...
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