1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Estimation of X in Gaussian Noise

  1. Nov 4, 2011 #1
    [itex]{X}=[x_1 x_2 ... x_n]^T[/itex] where [itex]{x_i} \in \{ 0, a_1, a_2, a_3 \}^n, a_i \in \mathbb{C}[/itex] and [itex]Z = \{z_1 z_2,...,z_n \}[/itex] where [itex]z_i ~ N(0,\sigma^2)[/itex] is a Complex Gaussian RV with mean 0 and variance [itex]sigma^2[/itex]. Suppose we observe [itex]Y[/itex]

    [itex]Y = HX+Z[/itex]

    where [itex]H[/itex] is known and its elements are independent complex Gaussian with mean 0 and variance 1 in [itex]\mathbb{C}[/itex] i.e. complex numbers. How can I estimate [itex]X[/itex] observing [itex]Y[/itex] when I only want to know whether [itex]x_i[/itex] is zero or non-zero? i.e. I don't want to distinguish between [itex]a_1, a_2, a_3[/itex] and only want to estimate whether [itex]x_i[/itex] was zero or non_zero?
    Is there any iterative way of finding this out?

    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads for Estimation Gaussian Noise
Estimating Eigenvalues from linear ODE