Question

1. Let $h \sim CN(0, 5)$ where $h = h_1 + jh_2$. Find $P(h_1 > 2)$ in terms of $Q$ function with positive arguments. 2. Consider a scalar AWGN channel: $y = u + w$ where the transmit symbol $u$ takes values $+3$ and $+6$ with probabilities $1/3$ and $2/3$, respectively and $w \sim N(0, 1)$. Determine the MAP decision rule, and compute its probability of error.

          1.
Let $h \sim CN(0, 5)$ where $h = h_1 + jh_2$. Find $P(h_1 > 2)$ in terms of $Q$ function with positive
arguments.

2.
Consider a scalar AWGN channel: $y = u + w$ where the transmit symbol $u$ takes values $+3$ and $+6$
with probabilities $1/3$ and $2/3$, respectively and $w \sim N(0, 1)$. Determine the MAP decision rule,
and compute its probability of error.

1.
Let h ∼ CN(0, 5) where h = h1 + jh2. Find P(h1 > 2) in terms of Q function with positive
arguments.

2.
Consider a scalar AWGN channel: y = u + w where the transmit symbol u takes values +3 and +6
with probabilities 1/3 and 2/3, respectively and w ∼ N(0, 1). Determine the MAP decision rule,
and compute its probability of error.

Added by Jerry S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

06/17/2023

Step 1

We can write $h = h_1 + jh_2$, where $h_1$ and $h_2$ are independent real Gaussian random variables with mean 0 and variance 5/2. Therefore, $h_1 \sim N(0, 5/2)$. Show more…

Show all steps

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1. Let $h \sim CN(0, 5)$ where $h = h_1 + jh_2$. Find $P(h_1 > 2)$ in terms of Q function with positive arguments. 2. Consider a scalar AWGN channel: $y = u + w$ where the transmit symbol $u$ takes values $+3$ and $+6$ with probabilities $1/3$ and $2/3$, respectively and $w \sim N(0, 1)$. Determine the MAP decision rule, and compute its probability of error.