Laboratory 4
Data transmission through a
noise-limited communication channel
1. Review and Preparation
This lab builds on Lab 3. The important concepts studied in this experiment are signal
corruption by additive noise, signal-to-noise ratio, and effect of noise on bit errors.
In Lab 3 (data transmission through a bandwidth-limited communication channel), we
learned that if the channel bandwidth is smaller than the signal bandwidth, the received
signal is distorted, and such distortion causes bit errors. In this lab, the channel’s
bandwidth is larger than the signal bandwidth, but the channel adds a noise signal to the
data signal. This noise causes bit errors at the receiver.
In communications channels, noise is a random signal n(t) created by various effects
(thermal agitation, nonlinearity in electronics, inter-channel interference, etc.). Noise
typically adds to the information signal. So, if si(t) is the transmitted information signal,
then at the output of the channel the received signal is sot)= si(t) + n(t). Fig. 1 shows a
data signal corrupted with additive noise, resulting in 2 bit errors.
Fig. 1: Data transmission with noise
In communications theory, noise is assumed to be ideally white. White noise has a
frequency spectrum across all frequencies (it’s the worst type of noise). A simulated
white noise is given in Fig. 2[1].
Fig. 2: Simulated white noise
In ASCII text transmission, bit errors in an ASCII code translates into errors in
characters. For example, consider letter B, with ASCII code 1000010 (without parity bit).
See ASCII table in [2]. If a bit error occurs in the LSB bit, the received code is 1000011,
which is letter C. But if a bit error occurs in the 3rd bit from the left, the received code is
1000110 which is letter F. In the case of 4 bit errors occurring within the code as follows:
0100101, then the received character is the symbol #.
The probability that a bit is received in error, or bit error rate (BER), is an important
characteristic of a communication channel. The BER increases if the noise power
increases with respect to the signal power, that is, if the signal-to-noise ratio (SNR)
decreases. The SNR is defined as the ratio of signal power to noise power. An SNR=1000
is typical in a telephone line. The variation of BER with SNR is depicted in Fig. 3. A
BER of 10-4 in a metallic channel is reasonable (i.e., 1 bit in 10,000 bits will be in error,
on the average).
BER
1
0
10
SNR
Fig. 2: BER versus SNR
The capacity (in bits/sec) of a channel of bandwidth W Hz is given by Shannon’s
formula:
C  W log 2 (1  SNR)
(1)
We can now state the second basic principle of communications:
If data is transmitted through a noisy channel at a bit rate R<C, then the BER can be
made reasonably small.
If data is transmitted through a noisy channel at a bit rate R>C, then the BER cannot be
made small (i.e., will be around 1).
The main purpose of this experiment is to connect 2 PC’s via the low-pass channel circuit
(used in the previous experiment), and add a noise signal to the data signal by a summing
circuit, as shown in Fig. 4. The complete circuit showing the low-pass channel, the adder
circuit for the noise is given in Fig.5. The channel is implemented by the 1st order RC
low-pass filter, and the summing circuit is realized by the 2 opamps and the 4 resistors,
R. This complete circuit is already built on the lab board. The labels “point V1, point V2,
point V3, point V4” correspond to the points marked on the lab board. A picture of the
lab board is given in Picture 1 (note points V1, V2, V3, and V4). A picture of the board
hooked up to the oscilloscope and other equipment is given in Picture 2.
Data signal
received
Noise signal
PC1
PC2
+
adder
Lowpass filter
channel
Data signal sent
Fig. 4: Transmission through channel + noise
To noise
source
(point V2)
To TD pin
of PC1
(point V1)
R
R
R
-
R
-
R
+
+
To RD pin
of PC2
(point V4)
R variable
C
Fig. 5: Circuit for low-pass channel plus additive noise
Point V3
Preparation: give answers in the lab sheet
1. Show that the signal, S3, at point V3 in Fig. 4 is the sum of the signals S1 and S2,
at points V1 and V2, respectively. The opamps are assumed ideal.
2. The SNR of a typical dial-up telephone line using modems is 1000. The
bandwidth of such line is W=4000 Hz.
Calculate the capacity (bits/sec) of such dial-up line.
3. Shannon’s formula is based on white noise. White noise in the channel has a
constant
power spectrum density (PSD), No. The noise power at the receiver is thus
N=NoW, where W is the channel bandwidth in Hertz. If S represents the signal
power, then the SNR=S/NoW. Rewrite the formula for C in Eq. (1). Let No =
2x10-8 Watt/Hz, and S= 8x10-2 =0.08 Watt. Find the value of C when W goes to
infinity.
Picture 1: Circuit Board for Comm Labs
Picture 2: Circuit board and setup for labs
2. Lab Experiment
2.1 Objective: Transmit serial data from one PC to another across a low-pass
channel with ample bandwidth, but with additive noise. By varying the strength of the
noise, we observe the effect of noise on the character errors on the receiving PC.
2.2 Apparatus: Lab board, 2 PC’s, 2 RS232 cables, oscilloscope, signal source,
noise source.
2.3 Procedure
1. Verify that the TD pin of PC1 (input) is connected to point V1 on the board.
Verify that the RD pin of PC2 (output) is connected to point V4 on the board.
Apply the noise signal to point V2 on the board. For noise, use a noise source if
one is available. If not, apply a square-wave or triangular signal with a some low
frequency (e.g., 100Hz) and a low amplitude around 1V. Such signal may affect
the data signal but should not be strong enough to destroy it.
Set the bit-rate on both PC’s to 300 bps, and adjust the resistance of the filter
(channel) to a value such that the bandwidth is W=600Hz (answer in lab-sheet).
Using Hyperterminal transmit a text file from PC1 to PC2. The text should appear
error-free on PC2; if not, reduce the noise signal until you see no errors
2. Increase the frequency or the amplitude of the noise. Retransmit the text file from
PC1 to PC2. Repeat this step until character errors appear in PC2. Capture screens
of both PC’s.
Note: if the amplitude of the noise signal is high enough, the opamps may
saturate, and the output signal may be completely garbled. To check this
condition, connect the scope at the output of the opamps and view the signal.
3. Repeat Step 2 until you see extensive character errors. Capture screens of both
PC’s. See Note above.
3. Lab Answer Sheet
Preparation:
1. Give derivation of S3=S1+S2.
2. For SNR=1000, W=4000Hz
Calculate the capacity (bits/sec) of such dial-up line.
Answer: C= …………….
3. Let No = 2x10-8 Watt/Hz, and S= 8x10-2 =0.08 Watt. Find the value of C when W
goes
to infinity.
Answer: ……………… bps
Experiment:
Step 1:
What noise source have you used?
If signal generator, what signal have you used?
Step 2:
Give the captured PC screens. Discuss the errors observed.
Step 3:
Give the captured screens. Discuss the errors observed
4. References
[1]. http://tcts.fpms.ac.be/cours/1005-08/speech/projects/2001/delfabro_henry_poitoux/
[2]. http://www.asciitable.com/