Question

3) Use the figure of Bit Error Probability $P_b$ versus ($E_b/N_0$) given below to answer the following two questions: a) At ($E_b/N_0$) = 9 dB, compare the Bit Error Probability $P_b$ for Bipolar and Unipolar baseband signaling. Clearly show how much advantage in performance will be obtained if we use one of those signaling techniques for a Digital Communication System (DCS). b) For a $P_b = 10^{-5}$, how much more or less power is required for Bipolar baseband signaling compared to Unipolar baseband signaling? Clearly show your measurements and calculations. 4) A binary communication system transmits signals $s_i(t)$ (i = 1, 2). The receiver test statistic $z(T) = a_i + n_0$, where the signal component $a_i$ is either $a_1 = +1$ or $a_2 = -1$ and the noise component $n_0$ is uniformly distributed, yielding the conditional density functions $p(z|s_i)$ given by $\qquad p(z|s_1) = \begin{cases} \frac{1}{2} & \text{for } -0.2 \le z \le 1.8\\ 0 & \text{otherwise} \end{cases}$ and $\qquad p(z|s_2) = \begin{cases} \frac{1}{2} & \text{for } -1.8 \le z \le 0.2\\ 0 & \text{otherwise} \end{cases}$ Find the probability of a bit error, $P_b$, for the case of equally likely signaling and the use of an optimum decision threshold.

          3)
Use the figure of Bit Error Probability $P_b$ versus ($E_b/N_0$) given below to answer the following
two questions:
a) At ($E_b/N_0$) = 9 dB, compare the Bit Error Probability $P_b$ for Bipolar and Unipolar baseband
signaling. Clearly show how much advantage in performance will be obtained if we use one of
those signaling techniques for a Digital Communication System (DCS).
b) For a $P_b = 10^{-5}$, how much more or less power is required for Bipolar baseband
signaling compared to Unipolar baseband signaling? Clearly show your measurements
and calculations.
4)
A binary communication system transmits signals $s_i(t)$ (i = 1, 2). The receiver test
statistic $z(T) = a_i + n_0$, where the signal component $a_i$ is either $a_1 = +1$ or $a_2 = -1$ and
the noise component $n_0$ is uniformly distributed, yielding the conditional density
functions $p(z|s_i)$ given by
$\qquad p(z|s_1) = \begin{cases} \frac{1}{2} & \text{for } -0.2 \le z \le 1.8\\ 0 & \text{otherwise} \end{cases}$
and
$\qquad p(z|s_2) = \begin{cases} \frac{1}{2} & \text{for } -1.8 \le z \le 0.2\\ 0 & \text{otherwise} \end{cases}$
Find the probability of a bit error, $P_b$, for the case of equally likely signaling and the
use of an optimum decision threshold.

3)
Use the figure of Bit Error Probability Pb versus (Eb/N0) given below to answer the following
two questions:
a) At (Eb/N0) = 9 dB, compare the Bit Error Probability Pb for Bipolar and Unipolar baseband
signaling. Clearly show how much advantage in performance will be obtained if we use one of
those signaling techniques for a Digital Communication System (DCS).
b) For a Pb = 10^-5, how much more or less power is required for Bipolar baseband
signaling compared to Unipolar baseband signaling? Clearly show your measurements
and calculations.
4)
A binary communication system transmits signals si(t) (i = 1, 2). The receiver test
statistic z(T) = ai + n0, where the signal component ai is either a1 = +1 or a2 = -1 and
the noise component n0 is uniformly distributed, yielding the conditional density
functions p(z|si) given by
p(z|s1) = (1)/(2) for -0.2 ≤ z ≤ 1.8
0 otherwise
and
p(z|s2) = (1)/(2) for -1.8 ≤ z ≤ 0.2
0 otherwise
Find the probability of a bit error, Pb, for the case of equally likely signaling and the
use of an optimum decision threshold.

Added by Jack P.

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