Consider the wireless channel model given as y(n) = hx(n) + w(n). Show that the least square channel estimate ĥ, represented as h= = arg min ||y(P) - hx(p)||² h has an optimal solution given by h (x(p)) Hy(p) = where x(p), y(p) are the vectors of length ||x(p)||2 L corresponding to the transmitted and the received pilot symbols. Here (.) corresponds to the hermitian operator.
Consider the wireless channel model given as y(n) = hx(n) + w(n). Show that the least square channel estimate ĥ, represented as h= = arg min ||y(P) - hx(p)||² h has an optimal solution given by h (x(p)) Hy(p) = where x(p), y(p) are the vectors of length ||x(p)||2 L corresponding to the transmitted and the received pilot symbols. Here (.) corresponds to the hermitian operator.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Q7.
Consider the wireless channel model given as y(n) = hx(n) + w(n). Show that the least
square channel estimate ĥ, represented as
h = arg min ||y(P) - hx(p)||²
h
(x(p)) Hy(p)
||x (p)||2
where x(p), y(p) are the vectors of length
L corresponding to the transmitted and the received pilot symbols. Here (.) corresponds
to the hermitian operator.
has an optimal solution given by :
=
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