ECE4513 Digital Communication Systems
Laboratory
Dennis Silage, PhD
silage@temple.edu
BER of Bi-Phase-L with Optimum Receiver
The performance of a digital communication system in the presence of additive
white Gaussian noise (AWGN) can be assessed by the measurement of the bit
error rate (BER). The bi-phase (Manchester or sometimes also called split phase
RZ) line code is to be used here.
MS Figure 4.20 (Fig420.slx on Canvas) contains the bi-phase-L (or split phase RZ)
baseband transmit signal generator (lower right) and three other signals which can
be simplified and used here. The bi-phase-L (or split phase RZ) signal is shown in
MS Figure 4.21 with an output amplitude of ±1 for the binary bit stream
111001001….
MS Figure 4.20 AMI NRZ and RZ and split-phase RZ line code
binary data generators (Fig420.slx).
Bi-phase-L is a symmetrical baseband signal. The binary rectangular symmetrical
pulse amplitude modulated (PAM) NRZ digital communication system with BER
analysis and the optimum correlation receiver is shown in MS Figure 2.34
(Fig234.slx on Canvas). This model forms the basis for the bi-phase-L digital
communication system to be designed by you here.
The optimum correlation receiver reference signal in MS Figure 2.34 is a
rectangular pulse with a near 100% duty cycle or a constant value. The reference
signal and the receiver structure must be altered here to accommodate the biphase-L (or split-phase RZ) signal. A single correlation function receive structure
is to be used.
MS Figure 4.21 Split Phase RZ (Bi-Phase-L)
MS Figure 2.34. A binary rectangular symmetrical PAM digital communication
system with BER analysis and the optimum correlation receiver (Fig234.slx).
In the Simulink model Fig234.slx the parameters of the Random Integer Generator
block data source and the rectangular PAM transmitter is a rate of rb = 1 kb/sec, M
= 2 levels (binary) and a resulting amplitude of 0 and 1 V. The transmitter offset
(TX offset) and gain (TX Gain) of 10 implies that the transmitted pulse is ± 5 V.
Your task is to modify this Simulink model Fig234.slx with new parameters and
reconfigured transmitter and receiver.
The bi-phase-L (or split phase RZ) baseband transmit signal generator from a
portion of MS Figure 4.20 replaces the binary rectangular PAM signal generator of
MS Figure 2.34. Your transmitter design will utilize baseband amplitudes of ±Vs
and a data rate rb b/sec derived from the transmitter gain (TX Gain) and bit time Tb
assigned to you:
The transmitter gain (TX Gain, 10 in the Simulink model, resulting in ± 5V) =
[sum of the 2nd through 4th digits of your TU ID]/10
The bit time (Tb = 1 msec in the Simulink model) =
[sum of the 3rd, 4th, and 6th digits of your TU ID]/100 in milliseconds (msec)
In this Laboratory you are to assess the BER performance of the Bi-phase-L
baseband signal with an optimum receiver. You must choose an appropriate
simulation step time TS. This data rate is somewhat higher than the Simulink model
in MS Figure 2.34 (1 kb/sec) which used a 20 µsec simulation step time TS or a
simulation frequency fS = 1/ TS = 50 kHz resulting in 50 sample points per bit time,
which is a reasonable simulation resolution.
Therefore the simulation step time TS = 1/ fS and the parameters of the Data Rate
Translation blocks, the receiver correlation reference Pulse Generator blocks, the
Integrate and Dump block, the optimal threshold values for the receiver binary data
detection and the delay between the transmitted and received bits in the Error Rate
Calculation block must all be carefully chosen for the simulation in this Laboratory
to be correct.
Obtaining 0 BER with no AWGN for each of the Laboratory simulations is crucial
since all other reported measurements will be incorrect if this is not met. If a nonzero BER with no AWGN is obtained, timing parameters and delays are the usual
problems that can cause this performance error and could be different in each of
the simulations specified.
The Laboratory tasks are as follows:
1. Run the simulation of the binary rectangular symmetrical PAM NRZ
Simulink model Fig234.slx with the standard model parameters to
familiarize yourself with the BER analysis before starting your project.
MS Table 2.8 shows the observed and theoretical BER performance for
fixed steps in the value of Eb/No for a sequence of 10 000 random, equally
likely data bits for a binary rectangular symmetrical PAM binary data
signal.
2. Configure a single correlator receiver in a Simulink simulation with a
receiver reference source that you will develop as φ2
^
(t). Note that the NS
text has the signals as s2(t) (binary 1) and s0(t) (binary 0).
Show the determination of φ2
^
(t) and its implementation as a signal
source. Plot the signal for several bit times in Simulink to verify its
performance.
Strict scaling of the single correlator by the denominator term of φ2
^
(t) is
not required because of the Simulink Sign block in the receiver structure.
The threshold T = 0 since the bi-phase-L (or split phase RZ) baseband
signal is symmetrical and with equally likely binary data with P1 = P2.
3. Configure the single correlator receiver with this receiver reference source
φ2
^
(t) as shown below. The Simulink model Fig234.slx is a rectangular
symmetrical pulse amplitude modulated (PAM) binary baseband digital
communication system with an AWGN channel and the optimum
correlation receiver and provides a template here.
4. Calculate the power in your bi-phase-L transmitted signal assuming
equally likely binary data and compute the SNR in dB in the standard
range ∞, 10, 8, 6, 4, 2 and 0 dB by first determining Eb then setting the
AWGN channel appropriately. Here use the Eb/No ratio for the noise
generated by the AWGN channel as described in the MS text and not the
noise variance σ2
.
2 2
( -1)
= − = s ( ) d ( 1) 0,1
b
b
iT
j
b j b b
i T
E γ t t i T t iT j
MS Eq. 2.28
j 0 1
b j b 0 b 1 b
j
P P P P P P P = = + MS Eq. 2.30
5. Run your simulation for your bi-phase-L binary data signal. Does your
implementation of the bi-phase-L binary system in AWGN produces
similar BER tabular results as in MS Table 2.8 using the theoretical
probability of bit error Pb for a symmetrical binary signal and the energy
per bit Eb shown below?
Note that it is not reasonable in digital communications to even report a
BER greater than approximately 0.1 (1 in 10 bits in error).
2
Q
b
b
o
E
P
N
=
MS Eq. 2.31
Table 2.8 Observed BER and theoretical Pb as a function of Eb/No in a binary
symmetrical rectangular PAM digital communication system with optimum
correlation receiver.
Eb/No dB BER Pb
0 0
10 0 4.05 × 10-6
8 0 2.06 × 10-4
6 2.5 × 10-3 2.43 × 10-3
4 1.35 × 10-2 1.25 × 10-2
2 3.95 × 10-2 3.75 × 10-2
0 8.09 × 10-2 7.93 × 10-2
6. Produce a table of your BER for the bi-phase-L digital communication
system and compare that to MS Table 2.8 for a binary symmetrical
rectangular PAM binary data signal. Comment on any apparent
differences.
Your report should be submitted using the posted Laboratory Report Format on
Canvas.
This Laboratory is for the two weeks starting February 28th and March 7th due no
later than Sunday March 14th at 11:59 PM with an upload to Canvas. Note that
this two week Lab 4 is graded as 200 points. You may be required to demonstrate
all Laboratories during the semester so your Model and Report should be
maintained.
Spring 2021
