[Q4] A baseband signal (band-limited to 5kHz) is sampled at 20% over the Nyquist rate and coded using a PCM system having a 128 levels quantizer. The binary data is sent through a 2.5km transmission channel after been modulated as MPSK. The bandwidth of this channel is set to be 78% of the operating binary rate. Assume the power spectral density of the noise is 2nW/Hz per km, calculate the required minimum r.m.s. power of the received signal (in dB) to ensure the operating BER is not worse than 78 error bits per second. (Use TB21.9). a ob (1+²1²

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[Q4] A baseband signal (band-limited to 5kHz) is sampled at 20% over the Nyquist rate
and coded using a PCM system having a 128 levels quantizer. The binary data is sent
through a 2.5km transmission channel after been modulated as MPSK. The bandwidth
of this channel is set to be 78% of the operating binary rate. Assume the power spectral
density of the noise is 2nW/Hz per km, calculate the required minimum r.m.s. power of
the received signal (in dB) to ensure the operating BER is not worse than 78 error bits
per second. (Use ToB≥ 1.9).
(1+5
The above question is similar to
this question, but with the
numbers changing, solve the
question in the same way and steps
(12) A baseband signal (band-limited to 4.5kHz) is sampled at 22% over Nyquist rate
and coded using PCM system having 256 levels quantizer. The resulting NRZ
unipolar binary data is planned to be sent through a 2km transmission channel
after been modulated with M-ary PSK. The bandwidth of this channel was set
to be 78% of the operating binary rate. If the channel is contaminated by a
Gaussian zero-mean white noise of PSD = 2.5nW/Hz per km, calculate the
required minimum r.m.s. power of the received signal (in dBm) to ensure the
operating BER is not worse than 120 error bits per second. (Use TB≥ 1.7).
Solution: R = lfs = 8 x 2.44 x 4.5 x 10³ = 87.84 kbps,
=
m
Bch = 0.78R = 68.5152kHz. To Bch = 1.7 Rg = 40.3031k symbols per
second, m =
Rb
R=2.17953 bits per symbol. → Rs = 29.28 k symbols
per second. P, =BER = 1.3661 x 10-3. n = 2 x 2.5 = 5nW/Hz.
→Q¹(2.0492 x 10-3) = 44.7285√S
>
25
mP = 2Q (√√x sin)
nRs
X
S = (287)² = 4.1171mW: S≥6.1459dBm
44.7285
The Q function can be approximated as:
Q(x) e(az²+bx+c)
For 0 ≤ x ≤ 8, the variables are: a = -0.4698, b=-0.5026, c= -0.8444.
Transcribed Image Text:[Q4] A baseband signal (band-limited to 5kHz) is sampled at 20% over the Nyquist rate and coded using a PCM system having a 128 levels quantizer. The binary data is sent through a 2.5km transmission channel after been modulated as MPSK. The bandwidth of this channel is set to be 78% of the operating binary rate. Assume the power spectral density of the noise is 2nW/Hz per km, calculate the required minimum r.m.s. power of the received signal (in dB) to ensure the operating BER is not worse than 78 error bits per second. (Use ToB≥ 1.9). (1+5 The above question is similar to this question, but with the numbers changing, solve the question in the same way and steps (12) A baseband signal (band-limited to 4.5kHz) is sampled at 22% over Nyquist rate and coded using PCM system having 256 levels quantizer. The resulting NRZ unipolar binary data is planned to be sent through a 2km transmission channel after been modulated with M-ary PSK. The bandwidth of this channel was set to be 78% of the operating binary rate. If the channel is contaminated by a Gaussian zero-mean white noise of PSD = 2.5nW/Hz per km, calculate the required minimum r.m.s. power of the received signal (in dBm) to ensure the operating BER is not worse than 120 error bits per second. (Use TB≥ 1.7). Solution: R = lfs = 8 x 2.44 x 4.5 x 10³ = 87.84 kbps, = m Bch = 0.78R = 68.5152kHz. To Bch = 1.7 Rg = 40.3031k symbols per second, m = Rb R=2.17953 bits per symbol. → Rs = 29.28 k symbols per second. P, =BER = 1.3661 x 10-3. n = 2 x 2.5 = 5nW/Hz. →Q¹(2.0492 x 10-3) = 44.7285√S > 25 mP = 2Q (√√x sin) nRs X S = (287)² = 4.1171mW: S≥6.1459dBm 44.7285 The Q function can be approximated as: Q(x) e(az²+bx+c) For 0 ≤ x ≤ 8, the variables are: a = -0.4698, b=-0.5026, c= -0.8444.
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