Question 1 (100 marks)

Introduction

An ideal MIMO (Multiple Input Multiple Output) Wi-Fi system works by assigning a transformation to the transmitted signals:

X WXˆ ?

where X is the original information, W is the transformation matrix and Xˆ the transmitted signal. At the receiver end, the signals are then transformed back so that the original information is obtained.

A test received signal has been obtained from a source with an unknown transformation matrix. Determine the characteristics of the MIMO system (deduce which transformation matrix) if the original information and received signals are:

? ?? ??1 ˆ ??? 10 i???

X?? ?1 , X ?? ?

The potential transformation matrices are:

1 ?1 1 ? 1 ? 1 1 ? 1 ? 1 1 ? 1 ? 1 1 ?

W1 ? ??e0 ?e0?? , W2 ? 2 ??ei?4 ?ei?4?? , W3 ? 2 ??ei?2 ?ei?2?? , W4 ? 2 ??e3 4i? ?e3 4i? ??

A second signal is received:

Xˆ ?????2.133.56?1.08i???

Find the second value of X.

Requirements

For this assessment item, you must perform hand calculations:

1. Determines which transformation matrix produces the correct X based on the given Xˆ .

2. Determines the second value of X given the second value of Xˆ . For this assessment item, you must produce MATLAB code which:

3. Repeats the calculations of Requirements 1 and 2 and verifies the results.

4. Outputs to the MATLAB Command Window which matrix was used and the results of the tests to prove that the selection was correct.

5. Outputs to the MATLAB Command Window the second value of X.

6. Has appropriate comments throughout.

Submit a short video highlighting what part of the code you found most challenging and what part you are most proud of.

Assessment Criteria

Your code will be assessed using the following scheme.

Quality of hand calculations 25 marks

Quality of header(s) and comments 10 marks

Determination of correct transformation matrix based on known Xˆ 25 marks

Determination of second value of X 10 marks

Quality of verifications 5 marks

Quality of reporting 10 marks

Quality of the code 10 marks

Submission of video 5 marks

Question 2 (100 marks)

Introduction

The text file ‘makeupass2q2_in.txt’ contains data on the vapour pressure p of water (in kPa) at different temperatures T (in K). The first column in ‘makeupass2q2_in.txt’ gives the temperature data, and the second column gives the corresponding vapour pressure data. We expect the data to follow a relationship

?? = ??. ????/??

where A and B are two constants that can be identified via curve fitting. Based on the data in ‘makeupass2q2_in.txt’, use MATLAB to determine appropriate values of A and B and then use the above function to deduce the value of vapour pressure at 285 K and at 300 K.

Requirements

For this assessment item, you must perform hand calculations:

1. Estimate A and B based on the first two entries of ‘makeupass2q2_in.txt’ and calculate the error of using these values as a curve-fit for all the data.

For this assessment item, you must produce MATLAB code which:

2. Loads the data from the text file ‘makeupass2q2_in.txt’

3. Verifies that the data in the text file has been successfully loaded by checking the first 5 values.

4. Identifies the values of A and B using an appropriate curve fitting process

5. Outputs the values of A and B to the MATLAB Command Window, along with appropriate error reporting

6. Verifies the method by computing A and B using the same data as Requirement 1

7. Produces a plot of the given data with the chosen curve-fit

8. Outputs the required values of vapour pressure to the MATLAB Command Window

9. Has appropriate comments throughout.

Submit a short video highlighting what part of the code you found most challenging and what part you are most proud of.

Assessment Criteria

Your code will be assessed using the following scheme. Note that you are marked based on how well you perform for each category, so the correct answer determined in a basic way will receive half marks and the correct answer determined using an excellent method/code will receive full marks.

Quality of hand calculations 20 marks

Quality of header(s) and comments 10 marks

Quality of data load verification 5 marks

Quality of determination of curve-fit 25 marks

Quality of verification 5 marks

Quality of plots (e.g., axis labels, titles) 10 marks

Quality of vapour pressure calculation and reporting 10 marks

Quality of the code 10 marks

Submission of video 5 marks

Question 3 (100 marks)

Introduction

The following data has been collected from a Proctor compaction test to determine the dry-unit weight of soil based on the water content.

Water content (w) (% by weight) Dry-unit weight (?d) (lb/ft3)

0 80.85

2 82.93

4 90.61

6 100.88

8 110.70

10 117.06

12 116.94

14 107.30

Part (a)

You must determine the value of the optimum moisture content (the value of w which gives the largest value of ?d) for the following interpolation schemes:

i. linear

ii. spline

iii. pchip

Part (b)

Using a density of water of 998 kg/m3, determine the smallest value of w outside the values in the table where:

? ?? ?d ?w???d ?w?0?

is equal to the increase in ?d due to the water addition (i.e. the value of ?d is based on no interaction between the soil and water, as opposed to the tabulated data). Solve for the following extrapolation schemes:

i. linear

ii. spline

iii. pchip

Requirements

For this assessment item, you must produce MATLAB code which:

1. Uses linear interpolation to determine the value of ?d(w = 9.5%) and verifies that this result is correct by calculating the same value by hand.

2. Determines the value of w which gives the maximum value of dry-unit weight using the three interpolation schemes, with appropriate reporting of results that includes a specification of the accuracy of the answer for w.

3. Plots the data for dry-unit weight with the curve-fits from part (a), also indicating the optimum point for each method.

4. ***Extrapolates from the given data to determine where ?d intersects with ?d(w = 0) + ?w (this sum is the dry-unit weight of just the soil plus the contributing weight of water).

5. ***Plots the data with its interpolations/extrapolations, indicating the intersection point of each method.

6. Appropriately reports the results from part (b).

7. Displays a message in the Command Window with a brief discussion on which method you think is best and justify your selection.

8. Has appropriate comments throughout.

Submit a short video highlighting what part of the code you found most challenging and what part you are most proud of.

Assessment Criteria

Your code will be assessed using the following scheme. Note that you are marked based on how well you perform for each category, so the correct answer determined in a basic way will receive half marks and the correct answer determined using an excellent method/code will receive full marks.

Quality of header(s) and comments 10 marks

Quality of calculation of part (a) 30 marks

Quality of calculation of part (b) 25 marks

Quality of plots (e.g., axis labels, titles) 10 marks

Quality of reporting 5 marks

Quality of discussion 5 marks

Quality of the code 10 marks

Submission of video 5 marks

Submission

Submit your assignment by the due date to the StudyDesk.

Note that:

• you should also submit the file ‘makeupass2q2_in.txt’.

• only code appearing in *.m files will be marked.

• you MUST upload all of your code in a *.zip file. The following are the only file types that can be submitted: o *.zip o *.pdf o *.doc

o *.docx

Reference

Khan, F 2009, LTE for 4G Mobile Broadband, Cambridge University Press.

Introduction

An ideal MIMO (Multiple Input Multiple Output) Wi-Fi system works by assigning a transformation to the transmitted signals:

X WXˆ ?

where X is the original information, W is the transformation matrix and Xˆ the transmitted signal. At the receiver end, the signals are then transformed back so that the original information is obtained.

A test received signal has been obtained from a source with an unknown transformation matrix. Determine the characteristics of the MIMO system (deduce which transformation matrix) if the original information and received signals are:

? ?? ??1 ˆ ??? 10 i???

X?? ?1 , X ?? ?

The potential transformation matrices are:

1 ?1 1 ? 1 ? 1 1 ? 1 ? 1 1 ? 1 ? 1 1 ?

W1 ? ??e0 ?e0?? , W2 ? 2 ??ei?4 ?ei?4?? , W3 ? 2 ??ei?2 ?ei?2?? , W4 ? 2 ??e3 4i? ?e3 4i? ??

A second signal is received:

Xˆ ?????2.133.56?1.08i???

Find the second value of X.

Requirements

For this assessment item, you must perform hand calculations:

1. Determines which transformation matrix produces the correct X based on the given Xˆ .

2. Determines the second value of X given the second value of Xˆ . For this assessment item, you must produce MATLAB code which:

3. Repeats the calculations of Requirements 1 and 2 and verifies the results.

4. Outputs to the MATLAB Command Window which matrix was used and the results of the tests to prove that the selection was correct.

5. Outputs to the MATLAB Command Window the second value of X.

6. Has appropriate comments throughout.

Submit a short video highlighting what part of the code you found most challenging and what part you are most proud of.

Assessment Criteria

Your code will be assessed using the following scheme.

Quality of hand calculations 25 marks

Quality of header(s) and comments 10 marks

Determination of correct transformation matrix based on known Xˆ 25 marks

Determination of second value of X 10 marks

Quality of verifications 5 marks

Quality of reporting 10 marks

Quality of the code 10 marks

Submission of video 5 marks

Question 2 (100 marks)

Introduction

The text file ‘makeupass2q2_in.txt’ contains data on the vapour pressure p of water (in kPa) at different temperatures T (in K). The first column in ‘makeupass2q2_in.txt’ gives the temperature data, and the second column gives the corresponding vapour pressure data. We expect the data to follow a relationship

?? = ??. ????/??

where A and B are two constants that can be identified via curve fitting. Based on the data in ‘makeupass2q2_in.txt’, use MATLAB to determine appropriate values of A and B and then use the above function to deduce the value of vapour pressure at 285 K and at 300 K.

Requirements

For this assessment item, you must perform hand calculations:

1. Estimate A and B based on the first two entries of ‘makeupass2q2_in.txt’ and calculate the error of using these values as a curve-fit for all the data.

For this assessment item, you must produce MATLAB code which:

2. Loads the data from the text file ‘makeupass2q2_in.txt’

3. Verifies that the data in the text file has been successfully loaded by checking the first 5 values.

4. Identifies the values of A and B using an appropriate curve fitting process

5. Outputs the values of A and B to the MATLAB Command Window, along with appropriate error reporting

6. Verifies the method by computing A and B using the same data as Requirement 1

7. Produces a plot of the given data with the chosen curve-fit

8. Outputs the required values of vapour pressure to the MATLAB Command Window

9. Has appropriate comments throughout.

Submit a short video highlighting what part of the code you found most challenging and what part you are most proud of.

Assessment Criteria

Your code will be assessed using the following scheme. Note that you are marked based on how well you perform for each category, so the correct answer determined in a basic way will receive half marks and the correct answer determined using an excellent method/code will receive full marks.

Quality of hand calculations 20 marks

Quality of header(s) and comments 10 marks

Quality of data load verification 5 marks

Quality of determination of curve-fit 25 marks

Quality of verification 5 marks

Quality of plots (e.g., axis labels, titles) 10 marks

Quality of vapour pressure calculation and reporting 10 marks

Quality of the code 10 marks

Submission of video 5 marks

Question 3 (100 marks)

Introduction

The following data has been collected from a Proctor compaction test to determine the dry-unit weight of soil based on the water content.

Water content (w) (% by weight) Dry-unit weight (?d) (lb/ft3)

0 80.85

2 82.93

4 90.61

6 100.88

8 110.70

10 117.06

12 116.94

14 107.30

Part (a)

You must determine the value of the optimum moisture content (the value of w which gives the largest value of ?d) for the following interpolation schemes:

i. linear

ii. spline

iii. pchip

Part (b)

Using a density of water of 998 kg/m3, determine the smallest value of w outside the values in the table where:

? ?? ?d ?w???d ?w?0?

is equal to the increase in ?d due to the water addition (i.e. the value of ?d is based on no interaction between the soil and water, as opposed to the tabulated data). Solve for the following extrapolation schemes:

i. linear

ii. spline

iii. pchip

Requirements

For this assessment item, you must produce MATLAB code which:

1. Uses linear interpolation to determine the value of ?d(w = 9.5%) and verifies that this result is correct by calculating the same value by hand.

2. Determines the value of w which gives the maximum value of dry-unit weight using the three interpolation schemes, with appropriate reporting of results that includes a specification of the accuracy of the answer for w.

3. Plots the data for dry-unit weight with the curve-fits from part (a), also indicating the optimum point for each method.

4. ***Extrapolates from the given data to determine where ?d intersects with ?d(w = 0) + ?w (this sum is the dry-unit weight of just the soil plus the contributing weight of water).

5. ***Plots the data with its interpolations/extrapolations, indicating the intersection point of each method.

6. Appropriately reports the results from part (b).

7. Displays a message in the Command Window with a brief discussion on which method you think is best and justify your selection.

8. Has appropriate comments throughout.

Submit a short video highlighting what part of the code you found most challenging and what part you are most proud of.

Assessment Criteria

Your code will be assessed using the following scheme. Note that you are marked based on how well you perform for each category, so the correct answer determined in a basic way will receive half marks and the correct answer determined using an excellent method/code will receive full marks.

Quality of header(s) and comments 10 marks

Quality of calculation of part (a) 30 marks

Quality of calculation of part (b) 25 marks

Quality of plots (e.g., axis labels, titles) 10 marks

Quality of reporting 5 marks

Quality of discussion 5 marks

Quality of the code 10 marks

Submission of video 5 marks

Submission

Submit your assignment by the due date to the StudyDesk.

Note that:

• you should also submit the file ‘makeupass2q2_in.txt’.

• only code appearing in *.m files will be marked.

• you MUST upload all of your code in a *.zip file. The following are the only file types that can be submitted: o *.zip o *.pdf o *.doc

o *.docx

Reference

Khan, F 2009, LTE for 4G Mobile Broadband, Cambridge University Press.

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