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madmike159
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Homework Statement
Base station transmits signal t which is received by two antennas such that:
x = h1t + n1
y = h2t + n2
where n1 and n2 are independent additive white Gaussian noise with variances σ21 and σ22 respectively.
h1 is the channel gain between the base station and receive antenna 1 and h2 is the gain between the base station and receive antenna 2.
The receive terminal combines the signals x and y as follows:
z = αx + βy
Find the optimal values of α and β.
What is the resulting SNR of z? How does this compare to the SNR of x and y?
Homework Equations
The only hint given was that k = α/β and that
SNRz = f(k)
The Attempt at a Solution
I have tried finding the power of each signal since the variance is the power of the noise, and then trying to find a ratio of α/β to give a constant which should allow α and β to be adjusted to find the optimal values.
However I haven't come to a solution that actually expresses SNR of z, x or y. Some of the calculations I have made are lengthy and don't arrive at a solution, but I could upload them if you wish.
Any help or pointers would be greatly appreciated.
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