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Consider the use of the differential BPSK scheme proposed in Section 3.1.3 for the Rayleigh flat fading channel. 1. Find a natural non-coherent scheme to detect um based on ym−1 and ym, assuming the...

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Consider the use of the differential BPSK scheme proposed in Section 3.1.3 for the Rayleigh flat fading channel.

1. Find a natural non-coherent scheme to detect um based on ym−1 and ym, assuming the channel is constant across the two symbol times. Your scheme does not have to be the ML detector.

2. Analyze the performance of your detector at high SNR. You may need to make some approximations. How does the high SNR performance of your detector compare to that of the coherent detector?

3. Repeat your analysis for differential QPSK.

 

 

Answered 316 days After Nov 28, 2021

Solution

Banasree answered on Oct 11 2022
75 Votes
Ans.
1. Let assume a system model for Ralyleigh channel with co efficient constant for two symbol line as
X[m] = u[m] x[m-1]
Whereas u[m] = +/- 1
For the generalized case,
X[m] = u[m] * x[m-1]/|x[m-1]|        normalized upto x[m]
System model out put
Y[m] = h* u[m] * x[m-1]/|x[m-1]| + n(m)…………………….a
Where n(m) = noise
Then
Y[m-1] = h * x[m-1] + n[m-1]…………………………………………
A simple non coherent detector for the above condition can be obtained from the quantities y[m], y[m-1] are:
Y[m]y * [m-1] = |h2| u[m] |x[m-1] + h*n[m] x * [m-1] + n[m] n*[m-1] + hn* [m-1] u [m] x[m-1]/ |x[m-1]|
At high SNR, n[m] n*[m-1]...
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