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unit02_propagation/lab_prop_modeling.mlx

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unit02_propagation/lab_prop_modeling_partial.m

1	-	%% Lab: Fitting Propagation Models from Ray Tracing Data
2	-	% Ray tracing is a widely-used method for predicting wireless coverage
3	-	% in complex indoor and outdoor environments. Ray tracers take a 3D model
4	-	% of some region along with locations of transmitters and can predict the
5	-	% path characteristics from the transmitter locations to specified receiver
6	-	% locations. Ray tracing requires certain assumptions (such as building
7	-	% materials to make the material), so they may not be exact. Nevertheless,
8	-	% they provide an excellent approximation and are often used by cellular
9	-	% carriers to select sites for deploying cells. In this lab, we will use
10	-	% ray tracing outputs to generate a collection of path data from which
11	-	% we can fit analytic models. Ray tracing can provide much more data than
12	-	% would be possible with time-consuming real measurements.
13	-	%
14	-	% In going through this data, you will learn to:
15	-	%
16	-	% * Load and describe ray tracing data produced from a commercial ray
17	-	% tracing tool
18	-	% * Compute the omni-directional path loss from the ray tracing data
19	-	% * Determine if links are in outage (no path), LOS or NLOS
20	-	% * Visualize the path loss and link state as a function of distance
21	-	% * Fit simple models for the path loss and link state using machine
22	-	% learning tools
23	-	%
24	-	% Submission: Complete all the sections marked \|TODO\|, and run the cells
25	-	% to make sure your scipt is working. When you are satisfied with the
26	-	% results, <https://www.mathworks.com/help/matlab/matlab_prog/publishing-matlab-code.html
27	-	% publish your code> to generate an html file. Print the html file to
28	-	% PDF and submit the PDF.
29	-
30	-
31	-
32	-	%% Data from Remcom
33	-	% The data is in this lab was created by NYU MS student Sravan Chintareddy
34	-	% and Research Scientist Marco Mezzavilla. They used a widely-used and
35	-	% powerful commercial ray tracer from <https://www.remcom.com/ Remcom>.
36	-	% Remcom is one of the best ray tracing tools in the industry. Although
37	-	% we will illustrate the concepts at 1.9 GHz carrier, the Remcomm tool is
38	-	% particularly excellent for mmWave studies. Remcom has generously
39	-	% provided their software to NYU for purpose of generating the data for
40	-	% this lab and other research.
41	-	%
42	-	% The data was in this lab comes from a simulation of a section of
43	-	% Reston, VA. In this simulation, a number of transmitters were placed in
44	-	% the area in location similar to possible micro-cellular sites. The
45	-	% receivers were placed on street levels similar to pedestrians (UEs).
46	-	% We can plot the area and the sites with the following.
47	-	A = imread('map.png');
48	-	imshow(A, 'InitialMagnification', 40);
49	-
50	-	%% Loading the data
51	-	% We can load the data with the following command.
52	-	% This will create three variables in your workspace.
53	-	%
54	-	% * txpos: A trx x 3 array of the positions of the transmitters
55	-	% * rxpos: An nrx x 3 array of the positions of the receivers
56	-	% * pathTable: A table of all the paths
57	-	load pathData;
58	-
59	-	% TODO: Find nrx, ntx and npath
60	-
61	-	% TODO: Plot the locations of the TX and RX on the x-y plane.
62	-	% You can ignore the z coordinate of both in the plot. Use different
63	-	% markers (e.g. 'o' and 's' for the TX and RXs).
64	-
65	-
66	-	%% Determine omni-directional path loss and minimum path delay
67	-	% The table, pathTable, has one row for each path found in the ray tracer.
68	-	% Each path has a TXID and RXID and key statistics like the RX power
69	-	% and delay. Due to multi-path, a (TXID,RXID) pair may have more than
70	-	% one path.
71	-
72	-	% TODO: Use the head command to print the first few rows of the path
73	-	% table.
74	-
75	-	% TODO: Loop through the paths and create the following arrays,
76	-	% such that for each RXID i and TXID j:
77	-	% pathExists(i,j) = 1 if there exists at least one path
78	-	% totRx(i,j) = total RX power in linear scale
79	-	% minDly(i,j) = minimum path delay (taken from the toa_sec column)
80	-
81	-
82	-
83	-	% TODO: For each link (i,j), compute the omni-directional path loss,
84	-	% which is defined as the txPowdBm - total received power (dBm).
85	-	% In this dataset, txPowdBm = 36
86	-	txPowdBm = 36;
87	-
88	-
89	-	%% Plot the path loss vs. distance
90	-	% Just to get an idea of the path losses, we plot the omni directional path
91	-	% losses as a function of distance and compare against the FSPL.
92	-
93	-
94	-	% TODO: Using the arrays rxpos and txpos, compute
95	-	% dist(i,j) = distance between RX i and TX j in meters.
96	-	% Do this without for loops.
97	-
98	-	% At this point, you should have nrx x ntx matrices such as dist,
99	-	% plomni, minDly and pathExists. For the subsequent analysis, it is
100	-	% useful to convert these to nrx*ntx x 1 vectors.
101	-	%
102	-	% TODO: Convert dist, plomni, minDly and pathExists to vectors
103	-	% dist1, plomni1, ...
104	-
105	-	% TODO: Compute the free-space path loss for 100 points from dmin to dmax.
106	-	% Use the fspl() command.
107	-	dmin = 10;
108	-	dmax = 500;
109	-	fc = 1.9e9; % Carrier frequency
110	-
111	-	% TODO: Create a scatter plot of plomni1 vs. dist1 on the links
112	-	% for which there exists a path. On the same plot, plot the FSPL.
113	-	% Use semilogx to put the x axis in log scale. Label the axes.
114	-	% Add a legend.
115	-
116	-	% TODO: Plot the path losses
117	-
118	-
119	-
120	-	%% Classify points
121	-	% In many analyses of propagation models, it is useful to classify links as
122	-	% being in LOS, NLOS or outage. Outage means there is no path.
123	-
124	-	% TODO: Create a vector Ilink of size nrx*ntx x 1 where
125	-	% linkState(i) = losLink = 1: If the link has a LOS path
126	-	% linkState(i) = nlosLink = 2: If the link has only NLOS paths
127	-	% linkState = nrx*ntx;
128	-	losLink = 0;
129	-	nlosLink = 1;
130	-	outage = 2;
131	-
132	-
133	-	% TODO: Print the fraction of the links in each of the three states
134	-
135	-	%% Plot the path loss vs. distance for the NLOS and LOS links
136	-	% To get an idea for the variation of the path loss vs. distance,
137	-	% we will now plot the omni path loss vs. distance separately for the LOS
138	-	% and NLOS points. You should see that the LOS points are close to the
139	-	% FSPL, but the NLOS points have much higher path loss.
140	-
141	-	% TODO: Create a scatter plot of the omni path loss vs. distance
142	-	% using different markers for LOS and NLOS points. On the same graph,
143	-	% plot the FSPL. Label the axes and add a legend.
144	-
145	-
146	-	%% Linear fit for the path loss model
147	-	% We will now fit a simple linear model of the form,
148	-	%
149	-	% plomni = a + b10log10(dist) + xi, xi ~ N(0, sig^2)
150	-	%
151	-	% MATLAB has some basic tools for performing simple model fitting like this.
152	-	% The tools are not as good as sklearn in python, but they are OK.
153	-	% In this case, you can read about the fitlm() command to find the
154	-	% coefficients (a,b) and sig for the LOS and NLOS models. For sig, take
155	-	% the RMSE as the estimate, which is the root mean squared error.
156	-
157	-
158	-	% TODO: Fit linear models for the LOS and NLOS cases
159	-	% Print the parametrs (a,b,sig) for each model.
160	-
161	-
162	-	% TODO: Plot the path loss vs. distance for the points for the LOS and
163	-	% NLOS points as before along with the lines for the linear predicted
164	-	% average path loss, a + b10log10(dist).
165	-
166	-	%% Plotting the link state
167	-	% The final part of the modeling is to understand the probability of a link
168	-	% state as a function of the distance. To visualize this, divide
169	-	% the distances into bins with bin i being
170	-	%
171	-	% [(i-1)binwid, ibinwid], i = 1,...,nbins
172	-	%
173	-	% We will create an array nbins x 3 arrays:
174	-	%
175	-	% cnt(i,j) = number links whose distance is in bin i and linkState = j
176	-	% cntnorm(i,j)
177	-	% = cnt(i,j) / sum( cnt(i,:) )
178	-	% = fraction of links whose distance is in bin i and linkState = j
179	-	nbins = 10;
180	-	binwid = 50;
181	-	binlim = [0,nbins*binwid];
182	-	bincenter = ((0:nbins-1)' + 0.5)*binwid;
183	-
184	-	% TODO: Compute cnt and cntnorm as above. You may use the histcounts
185	-	% function.
186	-
187	-
188	-	% TODO: Plot cntnorm vs. bincenter using the bar() command with the
189	-	% 'stacked' option. Label the axes and add a legend
190	-
191	-
192	-	%% Predicting the link state
193	-	% We conclude by fitting a simple model for the probability.
194	-	% We will use a simple multi-class logistic model where, for each link i,
195	-	% the relative probability that linkState(i) == j is given by:
196	-	%
197	-	% log P(linkState(i) == j)/P(linkState(i) == 0)
198	-	% = -B(1,j)*dist1(i) - B(2,j)
199	-	%
200	-	% for j=1,2. Here, B is the matrix of coefficients of the model. So
201	-	% the probability that a link is in a state decays exponentially with
202	-	% distnace. 3GPP uses a slightly different model, but we use this model to
203	-	% make this simple.
204	-	%
205	-	% Fitting logistic models is discussed in the ML class. Here, we will use
206	-	% the MATLAB mnrfit routine.
207	-
208	-	% TODO: Use the mnrfit() method to find the coefficients B. You will need
209	-	% to set the response variable to y = linkState + 1 since it expects class
210	-	% labels starting at 1.
211	-
212	-
213	-	% TODO: Use the mnrval() method to predict the probabilties of each class
214	-	% as a function of distance.
215	-
216	-
217	-	% TODO: Plot the probabilities as a function of the distance.
218	-	% Label your graph.
219	-
220	-
221	-	%% Compare the link state
222	-	% Finally, to compare the predicted probabilties with the measured valued,
223	-	% plot the probabilities as a function of the distance on top of the bar
224	-	% graph in a way to see if they are aligned. You should see a good fit
225	-
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