[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
Quantization and Resolution
Quantization is a methodology of carrying out signal modulation by the process of mapping input values from an infinitely long set of continuous values to a smaller set of finite values. Quantization forms the basic algorithm for lossy compression algorithms and represents a given analog signal into digital signals. In other words, these algorithms form the base of an analog-to-digital converter. Devices that process the algorithm of quantization are known as a quantizer. These devices aid in rounding off (approximation) the errors of an input function called the quantized value.
Probability of Error
This topic is widely taught in many undergraduate and postgraduate degree courses of:
![[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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2df24b46-1f35-45c2-9a6b-667b76c49399%2F67d17eea-a9d0-478c-ab4b-d33271098a4e%2F1lwq84h_processed.jpeg&w=3840&q=75)
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