EEEN 3009J作业代做、Matlab实验作业代写、代做BPSK System作业、代写Matlab语言程序作业
Assignment - Simulation of a Hamming-coded BPSK
System
Digital Communications (EEEN 3009J)
You are required to write, in MATLAB, a time domain simulation of a communication
system which uses coded binary phase shift keying (BPSK) modulation. The code used is
a (7, 4) linear block code called a Hamming code. The system model is shown in Figure 1
below. The channel model uses symbol rate sampling and the only channel impairment is
additive white Gaussian noise (AWGN).
BPSK
MODULATOR
AWGN
CODE
BITS
DATA
ESTIMATES
DATA BIT
ENCODER
HAMMING
DECODER
HAMMING
DEMODULATOR
(HARD DECISION)
BITS
Figure 1: Block Diagram of the Hamming-coded BPSK system to be simulated.
The (7, 4) Hamming code has the following generator matrix:
G =

P Ik

=
1 1 0 1 0 0 0
0 1 1 0 1 0 0
1 1 1 0 0 1 0
1 0 1 0 0 0 1
. (1)
Note that the matrix G is in systematic form. Therefore, from class notes, the parity-check
matrix is given by H =

Ink P
T

. Given that the received vector may be written as
r = c + e, where c denotes the transmitted codeword and e the error vector, decoding of
this code proceeds by using the received vector r to form the syndrome s = rHT = eHT
.
The maximum-likelihood error vector e may then be identified via Table 1 below.
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Table 1: Decoding table for the (7, 4) Hamming code.
Syndrome s Error Vector e
000 0000000
001 0010000
010 0100000
011 0000100
100 1000000
101 0000001
110 0001000
111 0000010
The following are the requirements:
Use your simulation to plot the bit error rate (BER) versus Eb/N0 curve for the system.
Plot BER on a log scale and Eb/N0 in dB.
On the same graph, plot the theoretical BER curve for uncoded BPSK.
From the curves, estimate the value of Eb/N0 above which the Hamming code offers
improved performance over an uncoded system, i.e., find the values of BER and Eb/N0
at which the two curves cross over each other.
From the curves find the coding gain (in dB) at a BER of 10 5
.
Your program should consist of a single m-file script, and should be appropriately
annotated with comments. You should not use any procedures from the MATLAB
communications toolbox.
The m-file script should be saved in the following format: yourfirstname_yourUCDID.m.
General comments about the methods you used and the results obtained should be
included in comments at the end of your program. Any other relevant points should
also be clearly indicated in the these comments.
The answers to the questions asked above should also be stated clearly as part of these
comments.
The working m-file, together with the relevant graphs of results, should be uploaded
via Blackboard.
The deadline is 5pm on Friday 30th November 2018.
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And most importantly: The program you submit should be your own work.
Programs will be scrutinized for evidence of copying. Programs in which copying is
found will be awarded 0 marks.
You may find the following MATLAB tips useful:
The function rand generates a random number which is uniformly distributed between
0 and 1. Thus for example, b = rand < 0.5 generates a random bit b.
The function randn generates a Gaussian-distributed random number with mean 0
and variance 1. Thus, multiplying this number by σ produces a Gaussian-distributed
random number with mean 0 and variance σ2.
The function semilogy(x,y) plots x against y, rather like plot(x,y), except that it
uses a log scale for the y-axis.

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