Question 2.

a) To solve this question, we need download communications Toolbox first

in matlab.

Find the function:

The berawgn function returns the bit error rate (BER) and symbol error
rate (SER) in an additive white Gaussian noise (AWGN) channel for
uncoded data using various modulation schemes. The first input
argument, EbNo, is the ratio of bit energy to noise power spectral density
in dB (Eb/N0). Values in the output ber and ser vectors correspond to the
theoretical error rate at the specified Eb/N0 levels for a Gray-coded signal
constellation.
The result of the graph is as follows：

Explain why the performance of 16QAM is worse than QPSK?

The QPSK constellation diagram consists of four points on equidistant

circles. The dots are well separated, making it easier to distinguish the
symbols. The 16QAM constellation diagram consists of 16 points arranged
in a coordinate system.The signalling states in the constellation diagram
of QPSK have greater separation than 16QAM,the required Eb/N0 for a
fixed BER of 16QAM is higher than QPSK which indicate the signalling
states within the constellation become closer together requiring higher Bb
for reliable detection(As Eb increases, efficiency decreases).

b) Same as last question,we need use communications Toolbox:

use function ‘pskmod’ to modulate,

use function ‘awgn’ to add AWGN,

use function ‘pskdemod’ to demodulate,

use function ‘biterr’ to calculate ber,

To complete the code,we should definite the initial data(the range of

Eb/N0,number of bit),than we can begin to simulation.
First,we should create some random data to be transmitted.
Second,use function ‘pskmod’ to modulate.
Third,use function ‘awgn’ to add AWGN.
Forth,use function ‘pskdemod’ to demodulate.
Finally,plot the figure.
Parametres:EbNo: the range of Eb/N0;numBits: number of bits;ber : bit
error rate; data: random data;modData: the data after modulation;
awData:the data after add awgn;demodData:the data after demodulation.
The result of the graph is as follows：

c) To solve this question, we used function ‘berfading’,

So,Theoretical BER for QPSK in Rayleigh fading => berfading(EbNo,
‘oqpsk’,1);
Theoretical BER for 16QAM in Rayleigh fading => berfading(EbNo,
‘qam’,16,1).
The result of the graph is as follows：

Concept:
Rayleigh Fading: In wireless communication channels, due to multipath
propagation of signals, the field strength at the receiving point comes
from different propagation paths, the delay time of each path is different,
and the superposition of component waves in each direction , and a
standing wave field strength is generated, resulting in fast signal fading
called Rayleigh fading. Rayleigh fading is a small-scale fading effect, which
is always superimposed on large-scale fading effects such as shadows and
attenuation.
Rician fading: refers to the phenomenon that in wireless communications,
the signal weakens as the distance increases during transmission. This
attenuation is due to the signal attenuation caused by the influence of air,
terrain and other physical factors during the transmission of radio waves.

Difference:
The difference between Rayleigh fading and Rician fading is: when there is
no main static signal component in the multipath component of the
received signal, the channel is a Rayleigh fading channel, otherwise it is a
Rician fading channel.

d) Use the same function as in the previous problem:

The result of the graph is as follows：

There are two kinds of diversity methods in common use: macro diversity
and differential set.
macro diversity:
Macro diversity, also known as "multi-base station diversity", is a diversity
technology mainly used in cellular systems. In the macro concentration,
multiple base stations are set in different geographical locations and
different directions, and at the same time communicate with a mobile
station in the cell. As long as the signal propagation in all directions is not
affected by the shadow effect or terrain at the same time, there is a
serious slow fading, this method can ensure that the communication will
not be interrupted. It is a technique for reducing slow fading.

Differential diversity:
Differential diversity is a diversity technique to reduce the effect of fast
fading, which is often used in various wireless communication systems.
The main technologies of differential set are space diversity, polarization
diversity, frequency diversity, field component diversity, Angle diversity,
time diversity and so on.

(1) Spatial diversity

The basic principle of spatial diversity is that the same signal is received
at any two different positions. As long as the distance between the two
positions is large to a certain extent, the signal fading received at the two
places is not correlated, that is to say, the fast fading has spatial
independence.
Spatial diversity, also known as antenna diversity, is the most widely used
diversity technique in wireless communication.
Spatial diversity requires at least two antennas, and the distance is d, and
the interval distance d is related to the working wavelength, ground
objects and antenna height. In mobile communication, it is usually taken
as: urban d=0.5, suburban d=0.8, the greater the value of d, the weaker
the correlation.

(2) Frequency diversity

The basic principle of frequency diversity is that the fading of two signals
whose frequency spacing is greater than the relevant bandwidth is not
correlated, so the same information can be transmitted at multiple
frequencies to achieve frequency diversity.
According to the definition of the relevant bandwidth, namely:

Where is delay extension. In urban areas, =0.3μs, where Bc=53kHz.

Frequency diversity requires two transmitters to transmit the same signal
and two receivers to receive the same signal.
This diversity technology is mainly used in line-of-sight microwave
communication in frequency division duplex (FDM) mode. Due to
propagation and refraction in the troposphere, deep fading sometimes
occurs during propagation.
In actual use, it is often called 1∶N protected switching mode. When
diversity is required, the corresponding traffic is switched to an alternate
free channel. The disadvantage is that not only standby switching is
required, but also a number of receivers equal to the number of channels
used in the frequency division set.

(3) polarization diversity

The basic principle of polarization diversity is that two electromagnetic
waves with different polarizations have independent fading, so the
sending end and the receiving end can send and receive signals with two
antennas that are close to each other but with different polarizations to
obtain the diversity effect.
Polarization diversity can be regarded as a special case of spatial diversity,
which also uses two antennas (double diversity case), but only by taking
advantage of the unrelated fading characteristics of electromagnetic
waves of different poles, thus shortening the distance between the
antennas.
In the polarization concentration, because the RF power is divided
between two different polarized antennas, the transmission power is lost
by about 3dB.

(4) Field component diversity

The E and H fields of electromagnetic wave contain the same information,
but the reflection mechanism is different.
The phase difference of the standing wave pattern of E and H waves
reflected by a scatterer is 90°, that is, when E wave is maximum, H wave
is minimum.
In the mobile channel, multiple E and H wave superposition, Ex, Hx, Hy
components are independent of each other, so by receiving 3 field
components, diversity can also be obtained.
Field component diversity does not require physical separation between
antennas and is therefore suitable for lower (100MHz) operating bands.
When the operating frequency is high (800 ~ 900MHz), spatial diversity is
structurally easy to achieve.

(5) Angle diversity

The method of Angle diversity is to make the radio wave through several
different paths and reach the receiving end at different angles, and the
receiving end can separate the signal components from different
directions by using multiple sharp directional receiving antennas. Because
these signal components have independent fading characteristics, the
Angle diversity can be realized and the anti-fading effect can be obtained.

(6) Time diversity

Fast fading in addition to space and frequency independence, but also has
time independence, that is, the same signal in different time, interval
multiple retransmission, as long as the time interval of each transmission
is large enough, then the decline of each transmission signal will be
independent of each other, the receiver will repeatedly receive the same
signal to merge, you can reduce the impact of fading.
Time diversity is mainly used to transmit digital signals in fading channels.

e) In question b) ,we write the code to perform a baseband simulation of

QPSK communication system in AWGN.The simulation results show that
with the increase of Eb/N0, the bit error rate is smaller and smaller than
the theoretical value.

In question c), we discuss the theoretical error rates for QPSK and 16QAM
under Rayleigh fading, and find that the error rates decrease with the
increase of Eb/N0, as expected.

In question d), we use different diversity sets to calculate the error rate in
Rayleigh fading state, and we find that the error rate decreases as the
diversity increases.

Other methods:
Diversity Technology:
In addition to spatial diversity, other types of diversity can be considered,
such as temporal diversity (by encoding or interleaving) or frequency
diversity (using multi-frequency channels or spread spectrum techniques).

Automatic Repeat Request (ARQ):

Implements an ARQ scheme in which the receiver requests retransmission
of a corrupted packet. This mechanism improves reliability by selectively
handling errors.

Adaptive Modulation Coding (AMC):

Dynamically adjust modulation and coding schemes based on
instantaneous channel conditions. This ensures the best data rate under
various fading conditions.
Question 1.3

Define 4 functions :
awgn_outage_capacity:
Function to compute outage capacity for AWGN channel.

rayleigh_outage_capacity:
Function to compute outage capacity for SISO Rayleigh fading channel.

mimo_outage_capacity:
Function to compute outage capacity for MIMO wireless channel.

special_mimo_outage_capacity:
Function to compute outage capacity for special MIMO system.

The result of the graph is as follows：

The final result(Q1):

The final result(Q2):