Correlation receiver in digital communication

Lab Activity :Digital Communication Systems

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, 5 in the Simulink model) = [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] as 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 non- zero 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.

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 1b 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 bb

o

E P

N

  =   

  MS Eq. 2.31

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.

This Laboratory is for the two weeks starting October 1st and October 8th and due no later than Wednesday October 17th at 11:59 PM. You will be required to demonstrate all Laboratories during the semester, so your Model and Laboratory Report should be maintained.

Fall 2018