cis022-2 assignment 1 modulation report ver.2.2 complete.pdf

Mr. Lee Garner 1818623

ASSIGNMENT TOP SHEET

Faculty of Creative Arts, Technologies & Science Department of Computing Science & Technology

Student Ref. No 1818623 Unit Code

CIS022-2

Unit Name Wireless Communications and Networks

Deadline for Submission(s)

Tuesday 22nd March 2019

Student's name: Lee Garner

Student's ID: 1818623

Unit Leader's Name

Dr. Enjie Liu

Assignment Details: Assignment 1

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Signature (Print Name):.Lee Garner.......................................... Date: ...20/03/2019......................

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Abstract: This Document contains information and performance analysis detailing on two types of modulation techniques: 16-QAM and 16-PSK. Implementation of these modulation strategies in wireless communication system has been investigated theoretically and in terms of a mathematical descriptive. Based on the mathematical analysis of the Bit Error Rate (BER), expressions of 16-phase-shift keying (PSK) and 16-quadrature amplitude modulation (QAM) are analytically obtained in the presence of a phase error. By averaging the statistics of the phase error, the performance penalty can be analytically examined as a function of the phase error variance. There using Matlab to show the corresponding performance of phase modulation and amplitude modulation techniques, the Matlab codes for 16-PSK and 16-QAM have been generated and the results of the simulations have been plotted and explained in Constellation Diagrams. To reflect the performance of the two types of modulation with respect to BER are also analysed and shown respectively.


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Contents

Abstract: ........................................................................................................................................................ 1

Table of Figures: ............................................................................................................................................ 3

1. Introduction: ........................................................................................................................................ 4

2. 16-Phase Shift Keying (16-PSK): ........................................................................................................... 4

2.1. QPSK Signal Generation: ............................................................................................................... 5

2.2. Constellation Diagram-1: ................................................................................................................... 6

2.2. Mathematical Description -1: ....................................................................................................... 6

3. Quadrature Amplitude Modulation (QAM): ........................................................................................ 8

3.1. Constellation Diagram-2: .............................................................................................................. 8

3.3. Mathematical Description-2: ............................................................................................................. 9

Matlab Simulation Results: ..................................................................................................................... 10

4.1. 16-PSK Simulation Results: .............................................................................................................. 10

4.2. 16-QAM Simulation Results: ............................................................................................................ 12

4.3. Comparison of BER in 16-PSK and 16-QAM Simulation Results: ..................................................... 14

4. Advantages & Drawbacks of 16-PSK and 16-QAM in Wireless Communication: .............................. 15

5. Conclusions of the 16-PSk Vs 16-QAM: .............................................................................................. 16

References .................................................................................................................................................. 17

Appendixes:................................................................................................................................................. 19

Matlab 16-PSK Code 16-PSK Matlab Code: ............................................................................................ 19

Matlab 16-QAM Code 16-QAM Matlab Code: ....................................................................................... 20

Matlab Code Comparison of BER in 16-PSK and 16-QAM: ..................................................................... 21


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Table of Figures: Figure 1. Adaptive Modulation (sami s, 2016) .............................................................................................. 4

Figure 2. Schematic Representation of PSK (M, n.d.) ................................................................................... 5

Figure 3. Generation of 16-PSK signal (G, 2019) ........................................................................................... 5

Figure 4. Constellation diagram for 16-QAM AND 16-PSK (Teruo K, 2006). ................................................. 6

Figure 5. Constellation diagram for 16-PSK (S, 2008) ................................................................................... 7

Figure 6. Constellation diagram for 16-QAM (P, 1995) ................................................................................ 8

Figure 7. Generated Random bits in 16-PSK in Matlab simulation ............................................................. 10

Figure 8. Random symbols generated in 16-PSK in Matlab simulation ...................................................... 10

Figure 9. Constellation diagram of 16-PSK in Matlab simulation ............................................................... 11

Figure 10. Generated Random bits in 16-QAM in Matlab simulation ........................................................ 12

Figure 11. Random symbols generated in 16-QAM in Matlab simulation.................................................. 12

Figure 12. Constellation diagram of 16-QAM in Matlab simulation. .......................................................... 13

Figure 13. Constellation diagram of BER Probability 16-QAM and 16-PSK in Matlab simulation .............. 14

FIGURE 14. CONSTELLATION DIAGRAMS 16-PSK AND 16-QAM (R5)...................................................................... 16


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1. Introduction:

With the increasing development of communication techniques, the main process of carrying digital

signals or messages is communally known as modulation. For achieving higher bandwidth efficiency or

better throughput more bits are sent per unit using different modulations, to achieve different

throughputs / efficiencies. In the QAM system, two amplitude-modulated (AM) signals are combined into

a single channel, thereby doubling the effective bandwidth, thus showing the need to increase the higher

throughput.

FIGURE 1. ADAPTIVE MODULATION (SAMI S, 2016)

If you compare QPSK and QAM, they are identical systems in terms of constellation points. But if you compare 16-PSK with 16-QAM, the 16-QAM has the greatest distance from point to points, thus showing the need for very linear amplification. 16-PSK has less precise linearity requirements, and for that it has less spacing between each constellation points, confirming it is more affected by noise. Hence you see that the distance between the constellation points in the QAM system is greater. This document defines the differences and shows such in a constellation diagram.

2. 16-Phase Shift Keying (16-PSK):

The important divergent of phase key shifting (PSK) is the QPSK falls under the strategy of Double-

sideband suppressed-carrier transmission. Showing the differences between them, BPSK is able to

transmit one bit per symbol, while QPSK transmits two bits per symbol. So QPSK can be used to double

the data rate and still use the same bandwidth or to halve the bandwidth for the same data rate.

Looking at a time without using a second carrier frequency two bits digital information are sent in this

strategy. This oversees the difference of QPSK with respect to BPSK, thus using a mathematical formula

we can transpose to 16-psk, explained in this document.


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FIGURE 2. SCHEMATIC REPRESENTATION OF PSK (M, N.D.)

2.1. QPSK Signal Generation:

Mathematical implementation of the QPSK scheme is represented in the following diagram:

FIGURE 3. GENERATION OF 16-PSK

SIGNAL (G, 2019)

A ‘bit-splitter’ strips the even bits

from the data stream at the input

point. In 16-PSK, the carrier

undergoes four changes in phase. The

phase change can be represented by

four binary bits of data. The point of

this is that the carrier can transmit four bits of data instead of two, so the bandwidth of the transmission

has effectively doubled, but to express the distance of the mapping point of 16-PSK and 16-QAM we

look at the following constellation diagrams below.


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2.2. Constellation Diagram-1:

16-PSK & 16-QAM uses sixteen points on the constellation diagram, shown as a graphical representation

of the complex points paced around a circle. Thus displaying points on an X and Y axis within the

diagram displayed as the in phase as the X axis. Showing the distance between the mapped points

shows how different the waveform modulations are. Thus proving that a receiver can differentiate from

the points when radon white noise is found.

FIGURE 4. CONSTELLATION DIAGRAM FOR 16-QAM AND 16-PSK (TERUO K, 2006).

Therefor the BER is correlative to the distance separating the nearest points, showing that this

modulation if densely packed is therefore less efficient than a modulation that is scattered.

2.2. Mathematical Description -1:

The theoretical bit error rate probability for 16-PSK modulation we use Gray coded mapping. The

primary feature of Gray code is that the adjacent symbols differ by only one bit. Having proved that the

symbol error rate for an M-PSK modulation Shown is,

(1) (S, 2008)

Seeing from the constellation plot, for a 16-PSK modulation, each symbol transmits K = 4bits. In general,

for an M-PSK modulation the number bits in each constellation point, K = log₂ (M) since each symbol

consists of (K) bits, the symbol to noise ratio is K times the bit to noise ratio, i.e.

(S, 2008) The reasonable symbol to noise ratio , (S, 2008) the symbol will be in

error when noise causes the symbol to fall in the adjacent symbol bin. Now thanks to the Grey coded


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mapping, even if the symbol goes into the adjacent symbol there will be only 1 bit in error from the

bits. So, the relation between symbol error and bit error is. (S, 2008)

For low symbol to noise ratio, the noise can cause the symbol to fall into the non-adjacent symbol bin. This may cause more than 1 bit error for each symbol error. However, we can ignore this as we are interested only in reasonably high values of symbol to noise ratio Probability of bit error for M-PSK modulation, Combining the above two equations, the bit error probability for a general M-PSK modulation is shown as,

. (S, 2008)

FIGURE 5. CONSTELLATION DIAGRAM FOR 16-PSK (S, 2008)


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3. Quadrature Amplitude Modulation (QAM):

Quantization, defined in mathematics as well as digital signal processing, is the mapping process of

looking at values from a set of input points often expressed as a continuous set of values in a

measurable smaller set, expressed as a finite set of elements. But we have to round as well as truncation

be typical examples of the quantization processes. QAM makes extensive use of constellation diagrams.

Thus in digital modulation the number of grid points is power of 2. Therefore the most common QAM

are 16-QAM, 64-QAM and 256-QAM. But in case of the same constellation a higher order will require

closer positioning of the grid points in the output constellation diagram. This in turn will result in a

higher possibility of noise in the output diagram. Hence higher order QAM will be able to deliver larger

data. But reliability of these data will be lesser due to increased probability of bit-error for equal energy

in the constellation. Higher SNR is required to maintain lower BER with higher order QAM. We can

achieve this in two ways by reducing noise level or by increasing the energy of the signal or using both

these adjustments together.

3.1. Constellation Diagram-2:

Displayed is a representation of a signal modulated by a modulation technique as QAM thus displaying

the signal as a two-dimensional X-Y-plane scatter diagram the first rectangular QAM constellation we

usually encounter is the 16-QAM, the diagram for which is shown here. Including the mapping points

index

FIGURE 6. CONSTELLATION DIAGRAM FOR 16-QAM (P, 1995)

https://en.m.wikipedia.org/wiki/Truncation


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3.3. Mathematical Description-2:

Rectangular QAM’s (such as 16-QAM) the symbol error rate can be expressed in terms of a complicated

expression. For this reason it is a common practice to express BER per carrier using the following, Gray

coded bit mapping in 16-QAM modulation

The Binary to Gray code for 16-QAM, the 4 bits in each constellation point can be considered as two bits

each on independent 4-PAM modulation on I-axis and Q-axis respectively.

With gray code bit mapping adjacent constellation symbols differ by only one bit. So, if the noise causes

the constellation to cross the decision threshold, only 1 out (K) of bits will be in error. So the relation

value of it may so happen between bit error and symbol error is, for very low

that the noise causes the constellation to fall near a diagonally located constellation point. In that case,

the each symbol error will cause two bit errors. Hence the need for approximate operator in the above

equation. However, for reasonably high value of the chances of such events are negligible.

The Bit error rate for 16PSK, since each symbol consists of K bits, the symbol to noise ratio k times the

bit to noise ratio i.e.

Where, (2) (S, 2008)

16-QAM Bit Error Rate, from describing the derivation of the 16-QAM Symbol error rate, we know that

the symbol error is. . (3) (S, 2008)

Combining the above two equations, the bit error rate for Grey coded 16QAM in Additive White

Gaussian Noise is. . (4) (S, 2008)


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Matlab Simulation Results:

4.1. 16-PSK Simulation Results:

In 16-PSK simulation constellation size is fixed to 4 and 30000 bits are processed through 16-PSK

simulation. Following figure represents generated random bits. It can be observed that binary values are

distributed randomly over bit indexes.

FIGURE 7. GENERATED RANDOM BITS IN 16-PSK IN MATLAB SIMULATION

Then the binary values are converted to corresponding integer values lying in between 0 – 3. Following

figure represents random symbols generated in 16-PSK simulation.

FIGURE 8. RANDOM SYMBOLS GENERATED IN 16-PSK IN MATLAB SIMULATION


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FIGURE 9. CONSTELLATION DIAGRAM OF 16-PSK IN MATLAB SIMULATION

To observe the impact of variation of power of transmitted signal, total number of bits is varied and the

corresponding BER are monitored. Given thus the table represents these observations:

It can be clearly monitored that with increased power of transmitted signal BER for Gray and Binary

coding increases in 16-PSK scheme.


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4.2. 16-QAM Simulation Results:

In 16-QAM simulation constellation size is fixed to 16 and 30000 bits are processed through 16-QAM

simulation. Following figure represents generated random bits. It can be observed that binary values are

distributed randomly over bit indexes.

FIGURE 10. GENERATED RANDOM BITS IN 16-QAM IN MATLAB SIMULATION

Then the binary values are converted to corresponding integer values lying in between 0 – 40.

The Following figure represents random symbols generated in 16-QAM simulation. 0 – 10.

FIGURE 11. RANDOM SYMBOLS GENERATED IN 16-QAM IN MATLAB SIMULATION


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FIGURE 12. CONSTELLATION DIAGRAM OF 16-QAM IN MATLAB SIMULATION.

To observe the impact of variation of power of transmitted signal, total number of bits is varied and corresponding bit error rate are observed. Following table represents the observations:

It can be clearly observed that with increased power of transmitted signal BER for Gray and binary

coding increases in 16-QAM scheme.


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4.3. Comparison of BER in 16-PSK and 16-QAM Simulation Results:

FIGURE 13. CONSTELLATION DIAGRAM OF BER PROBABILITY 16-QAM AND 16-PSK IN MATLAB SIMULATION

Figure 13 shows the 16-PSK Vs 16-QAM the BER vs EbN0, dB plots for modulation techniques which

have been used in this document. For low Eb/No values, we can see that the 16-PSK bit error rate is

slightly higher than that expected by the 16-QAM.


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4. Advantages & Drawbacks of 16-PSK and 16-QAM in Wireless Communication:

(Wireless World , 2012)

(Wireless World , 2012)


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5. Conclusions of the 16-PSk Vs 16-QAM:

Investigations of the two modulation schemes 16-PSK and 16-QAM through literature and Matlab

suggests that both these schemes have their individual advantages and drawbacks. But in general it is

concluded that for a reduced Bit Error Rate 16-PSK can be adopted while for higher data rate 16-QAM

can be adopted in wireless communication using 4 bits per carrier for 16-QAM and 6 bits for 64QAM,

but using QAM the transmitter this cannot operate at max power all of the time.

FIGURE 14. CONSTELLATION DIAGRAMS 16-PSK AND 16-QAM (R5)

The main purpose of wireless communication is to pass data as efficiently as possible through a window

of limited bandwidth, some information bits may be lost in somewhat most of the packets and the

original signal initially sent will encounter degradation or fading. To minimize the effect of signal fading

in wireless channels, the BER should be at a set minimal level, with the Eb/No raised significantly high. In

this document, the 16-QAM was analyzed in order to evaluate their BER performances in this Channel.

The document research revealed that 16-QAM modulation has a better BER performance than higher bit

QAM, but with lower Spectral efficiency (i.e. 4Bits/Symbol).

The 64-QAM has a higher Spectral efficiency than the lower QAM, but has shown has poor BER

performance. This is because the higher QAM modulation techniques are vulnerable to errors even thou

their high spectral proficiency. QAM is a prominent modulation technique with vast practical

applications, including current and future wireless technologies. So to sum up and In conclusion, M-

QAM can provide better BER performance over M-PSK.


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References Ahmed. Toaha, A. K. S., 2008. performance analysis of digital modulations on AWGN and fading channel.

In: performance analysis of digital modulations on AWGN and fading channel. s.l.:Lambert, p. 52.

Federal Communications Commission, 2015. Wireless services. [Online]

Available at: https://www.fcc.gov/spectrum

[Accessed 15 March 2019].

Forouzan, B., 2013. Global Edition. In: Data communications and networking fith edition. s.l.:mc graw

hill, p. 1226.

G, L., 2019. Viso block qpsk signal generation. st neots: s.n.

IEEE, 2012. Standard for Air Interface for Broadband Wireless Access Systems.. In: IEEE, ed. IEEE Std

802.16™. s.l.:IEEE, p. 1292.

Islam, I. a. H. S., 2005. Comparison of trac performance of QPSK and 16-QAM modulation techniques for

OFDM system. [Online]

Available at:

https://www.researchgate.net/publication/242235342_Comparison_of_trac_performance_of_QPSK_an

d_16-QAM_modulation_techniques_for_OFDM_system


M, A., 2006. Wireless Communications. In: I. Press, ed. Wireless Communications. s.l.:Wiley & Sons, p.

622.

mathuranathan.V, 2018. Wirless Communication Systems in MatLab. In: mathuranathan.V, ed. Wirless

Communication Systems in MatLab. s.l.:mathuranathan.V, p. 344.

Molisch, A., 2005. Wireless Communications. In: IEEE, ed. Wireless Communications second edition.

s.l.:Wily, p. 817.

M, R. F., n.d. Adaptive Modulation (QPSK, QAM), Pakistan: National University of Sciences and

Technology.

P, J., 1995. Quadrature amplitude modulation. Digital Communications, Volume 3rd.

Rappaport, T., n.d. wireless Communications. In: wireless Communications principles and practice.

s.l.:Pearson, p. 709.

Rfwireles-world.com, 2012. QAM-Quadrature Amplitude Modulation. [Online]

Available at: http://www.rfwireless-world.com/Terminology/QAM.html


Rfwireles-world.com, 2015. QPSK-Quadrature Phase Shift Keying. [Online]

Available at: http://www.rfwireless-world.com/Terminology/QPSK.html


sami s, a. a. m. s. a. m., 2016. Implementation of adaptive modulation for broadband wireless access

networks using cognitive radio approaches. Implementation of Adaptive Modulation for Broadband, p. 6.


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S, K., 2008. DspLog Signal Processing for Communication. [Online]

Available at: http://www.dsplog.com/2008/05/18/bit-error-rate-for-16psk-modulation-using-gray-

mapping/


Teruo K, Y. K. K. H. M. S., 2006. Ninth International Symposium on Spread Spectrum Techniques and

Applications. Comparisons of 16QAM Modulation Schemes Considering PAPR, Volume nine, p. 5.

Wireless World , 2012. Home of RF and Wireless Vendors and Resources. [Online]

Available at: http://www.rfwireless-world.com/Terminology/Advantages-and-Disadvantages-of-QAM-

types.html



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Appendixes: Matlab 16-PSK Code 16-PSK Matlab Code:

% 16-PSK Matlab Code: clc; Z = 16; % signal constellation size n = 30000; % Number of bits to process k = log2(Z); % per symbol number of bits OversamplingFactor = 1; rng default % Generation of random number Indata = randi([0 1],n,1); % Generation of binary data vector figure; stem(Indata(1:40),'filled'); ylabel('Binary Value'); xlabel('Bit Index'); title('Generated Random Bits');

IndataMatrix = reshape(Indata,length(Indata)/4,4); % Reshaping to binary 4-

tuples IndataSymbols = bi2de(IndataMatrix); % Conversion to integer figure; stem(IndataSymbols(1:10)); ylabel('Integer Value'); xlabel('Symbol Index'); title('Random Symbols');

Moddata = pskmod(IndataSymbols,Z,0); % Phase offset = 0 for Binary

coding ModGdata = pskmod(IndataSymbols,Z,0,'gray'); % Phase offset = 0 for Gray

coding EbNo = 10; snr = EbNo + 10*log10(k) - 10*log10(OversamplingFactor);

Signalreceived = awgn(Moddata,snr,'measured'); SignalGreceived = awgn(ModGdata,snr,'measured');

sPlotFig = scatterplot(Signalreceived,1,0,'g.'); hold on scatterplot(Moddata,1,0,'k*',sPlotFig) OutdataSymbols = pskdemod(Signalreceived,Z); OutGdataSymbols = pskdemod(SignalGreceived,Z,0,'gray');

OutdataMatrix = de2bi(OutdataSymbols, k); Outdata = OutdataMatrix(:); % Returns column vector data OutdataMatrixG = de2bi(OutGdataSymbols, k); OutdataG = OutdataMatrixG(:); % Returns column vector data [numErrorsG,berG] = biterr(Indata,OutdataG); fprintf('\nThe bit error rate of Gray coding = %5.2e, with %d errors\n', ... berG,numErrorsG) [numErrors,ber] = biterr(Indata,Outdata); fprintf('\nThe bit error rate of binary coding = %5.2e, with %d

errors\n', ...


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ber,numErrors)

Matlab 16-QAM Code 16-QAM Matlab Code: % Matlab 16-QAM Code 16-QAM Matlab Code: clc; Z = 16; % signal constellation size n = 300000; % Number of bits to process k = log2(Z); % per symbol number of bits OversamplingFactor = 1;

rng default % Generation of random number Indata = randi([0 1],n,1); % Generation of binary data vector

figure; stem(Indata(1:40),'filled'); ylabel('Binary Value'); xlabel('Bit Index'); title('Generated Random Bits'); IndataMatrix = reshape(Indata,length(Indata)/4,4); % Reshaping to binary 4-

tuples IndataSymbols = bi2de(IndataMatrix); % Conversion to integer

figure; stem(IndataSymbols(1:10)); ylabel('Integer Value'); xlabel('Symbol Index'); title('Random Symbols');

Moddata = qammod(IndataSymbols,Z); % Phase offset = 0 for Binary

coding ModGdata = qammod(IndataSymbols,Z,'gray'); % Phase offset = 0 for Gray coding

EbNo = 10; snr = EbNo + 10*log10(k) - 10*log10(OversamplingFactor);

Signalreceived = awgn(Moddata,snr,'measured'); SignalGreceived = awgn(ModGdata,snr,'measured');

sPlotFig = scatterplot(Signalreceived,1,0,'g.'); hold on scatterplot(Moddata,1,0,'k*',sPlotFig)

OutdataSymbols = qamdemod(Signalreceived,Z); OutGdataSymbols = qamdemod(SignalGreceived,Z,'gray');

OutdataMatrix = de2bi(OutdataSymbols,k); Outdata = OutdataMatrix(:); % Returns column vector data OutdataMatrixG = de2bi(OutGdataSymbols,k); OutdataG = OutdataMatrixG(:); % Returns column vector data [numErrorsG,berG] = biterr(Indata,OutdataG); fprintf('\nThe bit error rate of Gray coding = %5.2e, with %d errors\n', ... berG,numErrorsG) [numErrors,ber] = biterr(Indata,Outdata);


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fprintf('\nThe bit error rate of binary coding = %5.2e, with %d

errors\n', ... ber,numErrors)

Matlab Code Comparison of BER in 16-PSK and 16-QAM:

% Matlab code for comparing the bit error rate (BER) for 16PSK and 16QAM

modulation clear M = 16; EbN0_dB = [0:25]; % multiple EbN0(dB) values Theory_16PSK = erfc(sqrt(10.^(EbN0_dB/10))*sin(pi/M)); Theory_16QAM = 3/2*erfc(sqrt(0.1*(10.^(EbN0_dB/10)))); close all figure semilogy(EbN0_dB,Theory_16PSK,'bs-','LineWidth',2); hold on semilogy(EbN0_dB,Theory_16QAM,'mx-','LineWidth',2); axis([0 25 10^-5 1]) grid on legend('16PSK', '16QAM'); xlabel('EbN0, dB') ylabel('Bit Error Rate') title('Bit error probability curve for 16PSK and 16QAM modulation')


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CIS022-2 Wireless Communication and Networks, Assignment 2

Name: Lee Garner

Student number: 1818623

Names of other members of your group:

None

What is your part of work; please list the task number as indicated in the assignment brief:

ALL OF THE WORK WAS DONE BY MYSELF LEE GARNER

Tick one of the options below:

(1) I believe that the workload was equally shared and all members of the team contributed to the final report of the assignment

(2) The workload was not shared equally and some team members did not contribute to the final report

(3) I have no specific opinion about if team members had contributed to the final report

x (4) None of the above

If you ticked option (2), (3) or (4) please explain below how workload was distributed. Please feel free to

provide as many details as possible to allow fair marking. Please note that this form is only a

recommendation to the marker; the unit team reserves the right to further discuss with individual

students of the team if clarification is needed.

The work has been done by myself, due to the fact that no groups were put together, and as the older

student, the other students are already known to each other and mixed, hence I was not part of the

younger click.

cis022-2 assignment 1 modulation report ver.2.2 complete.pdf

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