1.
An ideal MIMO (Multiple Input Multiple Output) Wi-Fi system works by assigning a transformation to the transmitted signals:ˆ
X = WX
where X is the original information, W is the transformation matrix and X 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:
Requirements
For this assessment item, you must perform hand calculations:ˆ
- Determines which transformation matrix produces the correct Xbased on the given X.ˆ
- Determines the second value of Xgiven the second value of X.
For this assessment item, you must produce MATLAB code which:
- Repeats the calculations of Requirements 1 and 2 and verifies the results.
- Outputs to the MATLAB Command Window which matrix was used and the results of the tests to prove that the selection was correct.
- Outputs to the MATLAB Command Window the second value of X.
- Has appropriate comments throughout.
2.
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
p= A .e B ⁄T
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:
- Estimate Aand 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.
- Loads the data from the text file ‘makeupass2q2_in.txt’
- Verifies that the data in the text file has been successfully loaded by checking the first 5 values.
- Identifies the values of Aand B using an appropriate curve fitting process
- Outputs the values of Aand B to the MATLAB Command Window, along with appropriate error reporting
- Verifies the method by computing Aand B using the same data as Requirement 1
- Produces a plot of the given data with the chosen curve-fit
- Outputs the required values of vapour pressure to the MATLAB Command Window
- Has appropriate comments throughout.
3.
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 (yd) (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:
- linear
- spline
- 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:
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:
- linear
- spline
- pchip
Requirements
For this assessment item, you must produce MATLAB code which:
- Uses linear interpolation to determine the value of yd(w= 9.5%) and verifies that this result is correct by calculating the same value by hand.
- Determines the value of wwhich 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.
- Plots the data for dry-unit weight with the curve-fits from part (a), also indicating the optimum point for each method.
- Extrapolates from the given data to determine where dintersects with d(w = 0) + w (this sum is the dry-unit weight of just the soil plus the contributing weight of water).
- Plots the data with its interpolations/extrapolations, indicating the intersection point of each method.
- Appropriately reports the results from part (b).
- Displays a message in the Command Window with a brief discussion on which method you think is best and justify your selection.
- Has appropriate comments throughout.
