2. Consider a narrow band fading channel with bandwidth B = 1Hz for which the SNR y has probability mass function for Y₁ = 72 = 3,0 = 21 probability 10 (a) (b) (c) (d) 10° 1 - P[y=₁] = P[y=72] = 0, In other words, 7 = ₁ = with probability and y = 72 = 3 with 10 Compute the Shannon capacity with CSI known at the receiver only. Compute the loss in rate between the capacity in point 2a and the capacity of the channel without fading and same average SNR as the channel in point 2a. Compute the Shannon capacity with CSI at the receiver and at the transmitter. Compute the capacity with truncated channel inversion (find the cutoff value that achieves maximum capacity). Redo (e) point 2c by considering 1 - P[y=₁] = P[y=72] = 0 € [0, 1] as parameter. Find the maximum value of such the optimal water-filling power allocation assigns strictly positive power on both channel gains.
2. Consider a narrow band fading channel with bandwidth B = 1Hz for which the SNR y has probability mass function for Y₁ = 72 = 3,0 = 21 probability 10 (a) (b) (c) (d) 10° 1 - P[y=₁] = P[y=72] = 0, In other words, 7 = ₁ = with probability and y = 72 = 3 with 10 Compute the Shannon capacity with CSI known at the receiver only. Compute the loss in rate between the capacity in point 2a and the capacity of the channel without fading and same average SNR as the channel in point 2a. Compute the Shannon capacity with CSI at the receiver and at the transmitter. Compute the capacity with truncated channel inversion (find the cutoff value that achieves maximum capacity). Redo (e) point 2c by considering 1 - P[y=₁] = P[y=72] = 0 € [0, 1] as parameter. Find the maximum value of such the optimal water-filling power allocation assigns strictly positive power on both channel gains.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Parts
C and D
![2. Consider a narrow band fading channel with bandwidth B = 1Hz for which the SNR y has probability
mass function
1 - P[y = ₁] = P[y = √₂] = 0,
for ₁ = 72 = 3,0 = 1. In other words, y = ₁= with probability and y = 72 = 3 with
probability 10.
1
(a)
(b)
(c)
(d)
Compute the Shannon capacity with CSI known at the receiver only.
Compute the loss in rate between the capacity in point 2a and the capacity of the
channel without fading and same average SNR as the channel in point 2a.
Compute the Shannon capacity with CSI at the receiver and at the transmitter.
Compute the capacity with truncated channel inversion (find the cutoff value that
achieves maximum capacity).
(e)
Redo
point 2c by considering 1 - P[y = 1] = P[y = 72] = 0 = [0, 1] as parameter. Find the maximum
value of such the optimal water-filling power allocation assigns strictly positive power on both
channel gains.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c70b4b7-660c-4d2d-84c0-c0a2ffc3ff9d%2Fcc9d798d-73ea-465f-8a2a-b7c1c9d8fb26%2Flh1fap_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Consider a narrow band fading channel with bandwidth B = 1Hz for which the SNR y has probability
mass function
1 - P[y = ₁] = P[y = √₂] = 0,
for ₁ = 72 = 3,0 = 1. In other words, y = ₁= with probability and y = 72 = 3 with
probability 10.
1
(a)
(b)
(c)
(d)
Compute the Shannon capacity with CSI known at the receiver only.
Compute the loss in rate between the capacity in point 2a and the capacity of the
channel without fading and same average SNR as the channel in point 2a.
Compute the Shannon capacity with CSI at the receiver and at the transmitter.
Compute the capacity with truncated channel inversion (find the cutoff value that
achieves maximum capacity).
(e)
Redo
point 2c by considering 1 - P[y = 1] = P[y = 72] = 0 = [0, 1] as parameter. Find the maximum
value of such the optimal water-filling power allocation assigns strictly positive power on both
channel gains.
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