finish module 03

morea/03-wireless-channel-physical-model/assessment-03-physical-model.md

@@ -0,0 +1,45 @@
+---
+title: "Physical models"
+published: true
+morea_id: assessment-03-physical-model
+morea_summary: "Physical models of wireless channels"
+# morea_outcomes_assessed:
+ # - outcome-CHANGE-ME
+morea_type: assessment
+morea_start_date: "2024-01-24T00:00"
+morea_end_date: "2024-01-31T23:55"
+morea_labels:
+---
+# Physical models of wireless channels
+
+*Please submit your solutions in Laulima.*
+
+## A reflecting wall at the transmitter
+
+We have worked on examples where there is a perfectly reflective wall at the receiver. Now let us assume that the wall is at the transmitter.
+
+<figure style="text-align: center;">
+  <img src="03-moving-antenna-reflecting-wall-tx.png" alt="Moving antennas with a reflecting wall at the transmitter" width="600">
+</figure>
+
+* (1 point) Derive the analytical expression of the received signal using the ray tracing method.
+* (2 points) Following [the procedure here](reading-03-reflecting-wall-fixed-antenna.html), derive the coherence distance, the delay spread, and the coherence bandwidth. Compare them with the example when the wall is at the receiver.
+* (2 points) Following [the procedure here](reading-03-reflecting-wall-moving-antenna.html), derive the Doppler spread and the coherence time. Compare them with the example when the wall is at the receiver.
+
+## Reflecting on the ground plane
+
+Consider the scenario where the transmit and receive antennas are at different heights. There is a line-of-sight path and a path where the signal is reflected on the ground.
+
+<figure style="text-align: center;">
+  <img src="03-reflection-from-ground-plane.png" alt="Two antennas at different heights" width="500">
+</figure>
+
+* (1 point) Derive the analytical expression of the received signal using the ray tracing method.
+  * We can assume that the ground is a perfect reflector: it does not absorb energy and shifts the phase by \\(180^\circ\\).
+  * Please use the heights \\(h_s, h_r\\) and the *horizontal distance* \\(r\\) as the parameters in the expression.
+  * You would need to use some geometry to write \\(r_1\\) and \\(r_2\\) as a function of \\(h_s, h_r, r\\).
+* (2 points) Write a Python script to draw the energy of the received signal as a function of the horizontal distance \\(r\\) between the transmitter and the receiver. Verify that the power scaling law is roughly \\(r^{-4}\\).
+  * You can reuse our code in [the experiential learning](experience-03-fixed-antenna-reflecting-wall.html).
+  * You can set the heights of the transmitter and the receiver as \\(h_s=30\\)m and \\(h_r=1\\)m, respectively.
+  * Note that we derived the signal. For its power, we need to square it.
+  * To verify the scaling law, it may be easier to plot in the log scale.

morea/03-wireless-channel-physical-model/experience-03-fixed-antenna-reflecting-wall.md

@@ -1,5 +1,5 @@
 ---
-title: "Simulation on coherence distance and coherence bandwidth"
+title: "Coherence distance and coherence bandwidth"
 published: true
 morea_id: experience-03-fixed-antenna-reflecting-wall
 morea_type: experience

morea/03-wireless-channel-physical-model/experience-03-moving-antenna-reflecting-wall.md

@@ -1,5 +1,5 @@
 ---
-title: "Simulation on coherence time"
+title: "Doppler spread and coherence time"
 published: true
 morea_id: experience-03-moving-antenna-reflecting-wall
 morea_type: experience
@@ -8,7 +8,7 @@ morea_start_date:
 morea_labels: Google Colab
 ---
 
-# Simulation on coherence time
+# Simulation on Doppler spread and coherence time
 
 Using [this Google Colab notebook](https://colab.research.google.com/drive/1RckFUXT8-xSK6Yr25vMKTLz56sZBxU2m?usp=sharing), we can simulate the received signal in [the example of moving antennas with a reflecting wall](reading-03-reflecting-wall-moving-antenna.html).
 

morea/03-wireless-channel-physical-model/module-wireless-channel-physical-model.md

@@ -17,7 +17,7 @@ morea_experiences:
   - experience-03-fixed-antenna-reflecting-wall
   - experience-03-moving-antenna-reflecting-wall
 morea_assessments:
-  # - assessment-CHANGE-ME
+  - assessment-03-physical-model
 morea_type: module
 morea_icon_url: /morea/03-wireless-channel-physical-model/03-module-icon-ray-tracing.png
 morea_start_date: "2024-01-10"

morea/04-wireless-channel-input-output-model/module-wireless-channel-input-output-model.md

@@ -7,6 +7,7 @@ morea_prerequisites:
 morea_outcomes:
   - outcome-04-wireless-channel-input-output-model
 morea_readings:
+  - reading-04-roadmap
   - reading-04-linear-time-varying-system
 morea_experiences:
   # - experience-CHANGE-ME

morea/04-wireless-channel-input-output-model/reading-04-linear-time-varying-system.md

@@ -18,7 +18,7 @@ If we review the physical models in the previous module, we can find a pattern.
   \sum_{i} a_i(f,t) \phi(t - \tau_i(f,t)).
 \\]
 
-Take the most complex model, namely moving antennas with a perfectly reflecting wall, as an example. The received signal is
+Take the most complex model, namely moving antennas with a reflecting wall, as an example. The received signal is
 \\[
   E_r(f,t) = \frac{\alpha \cos 2 \pi f \left[(1-v/c) t - r_0 / c\right]}{r_0+vt} - \frac{\alpha \cos 2 \pi f \left[(1+v/c)t + (r_0-2d)/c\right]}{2d-r_0-vt}.
 \\]
@@ -35,7 +35,7 @@ where the \\(\frac{1}{2f}\\) term in \\(\tau(t)\\) comes from the \\(180^\circ\\
 
 In summary, the received signal is the weighted sum of sinusoids with different delays.
 
-In practice, the transmit signal is not a sinusoid. But any practical transmit signal can be viewed as a superpositon of sinusoids of different frequencies. Therefore, for any transmit signal \\(x(t)\\)), the above linear relationship is preserved. In other words, we can write the receive signal \\(y(t)\\) as
+In practice, the transmit signal is not a sinusoid. But any practical transmit signal can be viewed as a superpositon of sinusoids of different frequencies. Therefore, for any transmit signal \\(x(t)\\), the above linear relationship is preserved. In other words, we can write the receive signal \\(y(t)\\) as
 \\[
   y(t) = \sum_i a_i(t) x(t-\tau_i(t)).
 \\]