EE161  Spring 2012
San Jos State University
e
Solution of Midterm Exam # 1
Problem 1 (40 points) A binary communication system uses two orthonormal pulses given by
1 (t) =
2
t
cos
,
Tb
Tb
2 (t) =
2
t
sin
,
Tb
Tb
0 t Tb .
(Note: These are half period of c
EE161  Spring 2012
San Jos State University
e
Solution of Midterm Exam 2
Problem 1 (35 points) The generator matrix of a binary (5,2,3) singleerrorcorrecting code C is
1
0
G=
0
1
1
0
1
1
1
1
.
(a) Find the paritycheck matrix H of C .
(b) Find the code
EE161 Spring 2012
San Jos State University
e
Solution of Homework # 9
1. (a) BER curves:
Error performance of (3,2,2) code with BPSK modulation over a flat Rayleigh Fading channel
1
10
(3,2,2) code
BPSK
2
Bit Error Rate
10
3
10
4
10
0
2
4
6
8
10
Eb/N0 (dB
EE161 Spring 2012
San Jos State University
e
Solution of Homework # 6
1. (a) It is easy to verify that
X f
n=
n
T
= T.
Therefore, Nyquist criterion for ISIfree communication is satised by X (f ).
(b) Write this Lego spectrum as
X (f ) =
T
2
Tf
1+
+
Tf
1
EE161 Spring 2012
San Jos State University
e
Solution of Homework # 8
1. (a) Wavelength at 500 MHz: = 0.6 m. Doppler shift:
fD =
v
100 103
=
= 46.3 Hz.
0.6 3600
(b) Not covered in class.
(c) Doppler spread:
Bd = 2fD  = 92.6 Hz.
2. (a) Channel impulse r
EE161 Spring 2012
San Jos State University
e
Solution of Homework # 7
1. (a) From the simulation results below, the SNR gain of 3DQ modulation over QPSK
modulation, at a BER of 103 , is approximately equal to 0.75 dB. As explained in
class, the gain G is
EE161 Spring 2012
San Jos State University
e
Solution of Homework # 4
4
1. (a)
s1 (t)s2 (t) dt = 0.
0
(b) The basis signals are
sn (t)
n (t) = ,
3
n = 1, 2.
Signal constellation:
(c) Since s1 (t) and s2 (t) are orthogonal by part (a), the GrammSchmidt pr
EE161 Spring 2012
San Jos State University
e
Solution of Homework # 10
1. Fournger RAKE demodulator
Spreadspectrum BPSK modulation with a fourfinger RAKE receiver
MRC
EGC
1
BER
10
0
1
2
3
4
5
E/N0 (dB)
6
7
8
9
10
As expected, maximumratio combining (MRC
EE161 Spring 2012
San Jos State University
e
Solution of Homework # 3
1. For OOK modulation, the bit error probability expression is the same as for unipolar
mapping and given by
Eb
Pb = Q
= 103 .
N0
From this it follows that
Eb
= Q1 103
N0
2
= 9.55,
and
EE161 Spring 2012
San Jos State University
e
Solution of Homework # 5
1. See the solution of midterm exam 1.
2. Computer simulation results of QPSK modulation:
Simulation of QPSK modulation over an AWGN channel SJSU EE 161
Simulation (Natural)
Union bound
EE161 Spring 2012
Homework # 3
San Jos State University
e
Due: Thu. 2/23/12
1. A binary communication system uses OOK modulation. The bit rate is 100 kbps and
the bandwidth 500 kHz. The probability of a bit error is required to be less than 103 .
Determin
EE161 Spring 2012
San Jos State University
e
Solution of Homework # 1
1. (a) Use the modulation theorem:
X (f ) = (f + 5) + (f 5) .
(b) Again, using the modulation theorem:
1
[X (f + 5) + X (f 5)]
2
1
1
=
(f + 10) + (f ) + (f 10) .
2
2
Y (f ) =
2. Sketch
EE161 Spring 2012
Homework # 9
San Jos State University
e
Due date: Thu. 4/26/12
1. Dowload the MATLAB script SimRayleigh322vsBPSKD2.m from the web page of the
course. This script simulates the performance of a wireless communication system using
a (3,2,2
EE161 Spring 2012
Homework # 10
San Jos State University
e
Due: Tue. 5/15/12
1. MATLAB/Simulink experiment of a fournger RAKE demodulator
Download both the script run rake.m and the model RAKE SS 4F.mdl from the webpage of the course1 . The model simulat
EE161 Spring 2012
Homework # 4
San Jos State University
e
Due: Thu. 3/1/12
1. The two signals depicted in the gure below are used in binary orthogonal modulation.
s1(t)
s2(t)
1
1
1
2
3
4
t
1
2
3
4
t

1

1
(a) Show that s1
EE161 Spring 2012
Homework # 5
San Jos State University
e
Due: Thu. 3/15/12
1. A 100kbps wireless system with a center frequency of 13.56 MHz is to be designed
using binary modulation. The signal energytonoise ratio is Es /N0 = 5 dB.
(a) Compare the pe
EE161 Spring 2012
Homework # 7
San Jos State University
e
Due date: Thu. 4/5/12
1. The MATLAB script sim3DQ.m is available in the course web page. This simulates
the threedimensional quaternary (3DQ) modulation introduced in class, and twodimensional QPS
EE161 Spring 2012
Homework # 8
San Jos State University
e
Due date: Thu. 4/12/12
1. Solve problem 11.1 of the textbook, with the following change: The carrier frequency
is 500 MHz instead of 1 GHz.
2. A wireless channel has the following propagation delay
EE161 Spring 2012
Homework # 2
San Jos State University
e
Due: Tue. 2/14/12
1. Let cfw_Bk = cfw_1, 1, 0, 1 be a bit sequence to be transmitted through a channel. Sketch
the mapper output sequence cfw_Ak , signal s(t), correlator output (without noise) y
EE161 Spring 2012
Homework # 6
San Jos State University
e
Due date: Thu. 3/22/12
1. Consider the following overall response spectrum:
X(f)
T
T/2
f

(1+)/2T

(1
)/2T
(1
)/2T
(1+)/2T = W
(a) Show that X (f ) satises Nyquist criterion f
EE161 Spring 2012
Homework # 1
San Jos State University
e
Due: Thu. 2/2/12
1. Find expression of the Fourier transforms of the following signals
(a) x(t) = 2sinc(t) cos(10t)
(b) y (t) = x(t) cos(10t)
2. Sketch carefully the Fourier transforms found in pro