add module 3

_layouts/page.html

@@ -87,11 +87,11 @@
         const nextHeadingTop = headings[i+1].offsetTop;
         const nextHeadingHeight = headings[i+1].offsetHeight;
 
-        console.log('Heading:', heading.id, 'Top:', headingTop, 'Height:', headingHeight, 'Scroll:', scrollPosition, 'Half screen height:', halfScreenHeight);
+        // console.log('Heading:', heading.id, 'Top:', headingTop, 'Height:', headingHeight, 'Scroll:', scrollPosition, 'Half screen height:', halfScreenHeight); // Debugging
 
         // Check if the scroll position is within the current heading
         if (scrollPosition + halfScreenHeight >= headingTop - headingHeight && (scrollPosition < headingTop - headingHeight || scrollPosition + halfScreenHeight < nextHeadingTop - nextHeadingHeight)) {
-            console.log('Found active link', heading.id); // Debugging
+            // console.log('Found active link', heading.id); // Debugging
             const activeLink = document.querySelector(`#toc-container a[href="#${heading.id}"]`);
             activeLink.classList.add('active');
             foundActive = true;

morea/01-introduction/experience-introduce-yourself.md

@@ -4,7 +4,7 @@ published: true
 morea_id: experience-introduce-yourself
 morea_type: experience
 morea_summary: "Get started with the EE 643 Discord server"
-morea_sort_order: 3
+morea_sort_order: 10
 morea_start_date: "2024-01-08T23:00"
 morea_labels:
 ---

morea/01-introduction/module-introduction.md

@@ -15,7 +15,7 @@ morea_icon_url: /morea/01-introduction/introduction.jpg
 morea_start_date: "2024-01-07"
 morea_end_date: "2024-01-08T23:00"
 morea_labels:
-morea_sort_order: 10
+morea_sort_order: 1
 ---
 
 Overview of EE 643 (Communication System Performance), and some simple initial tasks to get oriented and ready for the course.

morea/01-introduction/outcome-course-structure.md

@@ -3,7 +3,7 @@ title: "Understand how to succeed in EE 643"
 published: true
 morea_id: outcome-course-structure
 morea_type: outcome
-morea_sort_order: 1
+morea_sort_order: 10
 ---
 
   * You get familiar with the Moreal framework, which enables moduled-based learning.

morea/02-overview/module-overview.md

@@ -18,7 +18,7 @@ morea_icon_url: /morea/02-overview/02-Wireless-vs-Wired.jpeg
 morea_start_date: "2024-01-08"
 morea_end_date: "2024-01-09"
 morea_labels:
-morea_sort_order: 21
+morea_sort_order: 2
 ---
 
 Overview of the key differences between wireless and wired communication systems

morea/02-overview/outcome-overview.md

@@ -3,7 +3,7 @@ title: "Key features of wireless channels and wireless communication systems"
 published: true
 morea_id: outcome-overview
 morea_type: outcome
-morea_sort_order: 10
+morea_sort_order: 20
 ---
 
   * You understand the two key differences between wireless channels and wired channels.

morea/02-overview/reading-building-blocks.md

@@ -6,6 +6,7 @@ morea_summary: "Building blocks of a typical communication system"
 # morea_url: https://github.com/airbnb/javascript
 morea_type: reading
 morea_labels:
+morea_sort_order: 20
 ---
 
 # Basic building blocks

morea/02-overview/reading-fading-interference.md

@@ -6,12 +6,13 @@ morea_summary: "Wireless communication systems need to combat fading and interfe
 # morea_url: https://github.com/airbnb/javascript
 morea_type: reading
 morea_labels:
+morea_sort_order: 21
 ---
 
 # Key Challenges in Wireless Communications
 
 There are two key challenges in wireless communications:
-- *Fading*: The wireless channel is very random. A change of weather or a sudden change in the environment (e.g., people moving around) will change the channel condition. This changes happen in milliseconds or less.
+- *Fading*: The wireless channel is very random. A change of weather or a sudden change in the environment (e.g., people moving around) will change the channel condition. These changes happen in milliseconds or less.
 - *Interference*: The signals propagate in the open space, instead of through a conduit such as a cable. Therefore, the receiver gets signals intended for someone else, which are interference to its own communication.
 
 Both challenges are *unique* in wireless communications.

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

@@ -0,0 +1,26 @@
+---
+title: "Physical Models of Wireless Channels"
+published: true
+morea_coming_soon: false
+morea_id: module-wireless-channel-physical-model
+morea_prerequisites:
+morea_outcomes:
+  - outcome-wireless-channenl-physical-model
+morea_readings:
+  - reading-03-roadmap
+  - reading-03-free-space-fixed-antenna
+  - reading-03-free-space-moving-antenna
+  - reading-03-reflecting-wall-fixed-antenna
+morea_experiences:
+  # - experience-CHANGE-ME
+morea_assessments:
+  # - assessment-CHANGE-ME
+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_end_date: "2024-01-17"
+morea_labels:
+morea_sort_order: 3
+---
+
+We discuss physical models of wireless channels through some simplified examples, which reveal some key features of wireless channels.

morea/03-wireless-channel-physical-model/outcome-wireless-channenl-physical-model.md

@@ -0,0 +1,10 @@
+---
+title: "Physical models of wireless channels"
+published: true
+morea_id: outcome-wireless-channenl-physical-model
+morea_type: outcome
+morea_sort_order: 30
+---
+
+  * You have a sense of how to develop the physical model of wireless channels.
+  * You understand some key features of a wireless channel.

morea/03-wireless-channel-physical-model/reading-03-free-space-fixed-antenna.md

@@ -0,0 +1,48 @@
+---
+title: "Case 1: Fixed antennas in the free space"
+published: true
+morea_id: reading-03-free-space-fixed-antenna
+morea_summary: "Two antennas in the space of nothingness"
+# morea_url: https://github.com/airbnb/javascript
+morea_type: reading
+morea_labels:
+morea_sort_order: 31
+---
+
+# Case 1: Fixed antennas in the free space
+
+## The simplest environment
+We start with the simpliest propagation model. Consider a transmitter anteanna, radiating into *free space*, and a receiver antenna in the *far field* (i.e., far away from the transmitter). There is nothing else in the space, so that the only propagation path for the signal is the line-of-sight (LOS) path from the transmitter to the receiver.
+
+To make things even simpler, we let the transmitter send a sinusoid at frequency \\(f\\):
+\\[ 
+  \cos 2 \pi f t.
+\\]
+
+We can create an 3-dimensional (3D) coordination system with the transmitter antenna at the origin. Then the location of the receiver antenna can be described by a triple \\(\mathbf{u} = (r, \theta, \phi)\\), where \\(r\\) is the distance between the antennas, \\(\theta\\) is the vertical angle, and \\(\phi\\) is the horizontal angle.
+
+In this simplest possible environment, we can analytically determine the received signal as
+\\[
+  E_r(f,t,\mathbf{u}) = \frac{\alpha(\theta,\phi,f) \cos 2 \pi f (t - r/c)}{r},
+\\]
+where \\(c = 3 \times 10^8\\)m/s is the speed of light.
+
+## Breakdown
+Now let us break down the above equation.
+  * First, the received signal is still a sinusoid with the same frequency \\(f\\). But the phase is delayed by \\(2 \pi f r / c\\), which happened because the signal traveled across a distance of \\(r\\) at the speed \\(c\\).
+  * Second, the magnitude of the received signal depends on the function \\(\alpha(\theta,\phi,f)\\), which represents the antenna gain. The technical term is *radiation pattern* of the antenna, which usually looks like this:
+
+    <figure style="text-align: center;">
+      <img src="03-radiation-pattern.svg" alt="A typical radiation pattern" width="500">
+      <figcaption>By Timothy Truckle; Link: https://commons.wikimedia.org/w/index.php?curid=4245213</figcaption>
+    </figure>
+
+    + We can see that the antenna magnifies the signal at different levels depending on the angles. Since both the transmitter antenna and the receiver antenna have radiation patterns, the function \\(\alpha(\theta,\phi,f) = \alpha_s(\theta,\phi,f) \cdot \alpha_r(\theta,\phi,f)\\) is the product of the transmitter antenna radiation pattern \\(\alpha_s(\theta,\phi,f)\\) and the receiver antenna radiation pattern \\(\alpha_r(\theta,\phi,f)\\).
+    + We will not talk much about the radiation pattern in this course, because they are fixed and known.
+
+  * Third, the magnitude of the received signal is inverse propotional to the distance \\(r\\). This indicates that the power of the signal decreases as \\(r^{-2}\\). This is the *large-scale fading*. Note that the power law may change with the actual environment (i.e., raining or existence of other objects in the environment).
+
+## Take-away
+In summary, in a free space, the received signal attenuates by \\(r^{-2}\\). The frequency \\(f\\) does not change. The phase is delayed due to the distance. Nothing particularly interesting here.
+
+We will see something more interesting in more complicated environments.

morea/03-wireless-channel-physical-model/reading-03-free-space-moving-antenna.md

@@ -0,0 +1,32 @@
+---
+title: "Case 2: The antennas start moving..."
+published: true
+morea_id: reading-03-free-space-moving-antenna
+morea_summary: "Moving antennas create Doppler shift"
+# morea_url: https://github.com/airbnb/javascript
+morea_type: reading
+morea_labels:
+morea_sort_order: 32
+---
+
+# Case 2: Moving antennas in the free space
+
+## Analytical expression
+Consider the same two antennas in a free space. But now the receiver is moving *away* at the speed \\(v\\) in the direct opposite direction. In this case, the location of the receiver antenna is time-varying, namely
+\\[
+  \mathbf{u}(t) = \left( r(t), \theta, \phi \right), ~\text{with}~ r(t) = r_0 + vt,
+\\]
+where \\(r_0\\) is the initial distance at time \\(t=0\\).
+
+Compared to the case of fixed antennas, the only change is the distance \\(r(t)\\). Therefore, the received signal is
+\\[
+  E_r(f,t,(r(t), \theta, \phi)) = \frac{\alpha(\theta,\phi,f) \cos 2 \pi f \left[t - (r_0 + vt)/c\right]}{r_0 + vt} = \frac{\alpha(\theta,\phi,f) \cos 2 \pi f \left[(1-v/c)t - r_0/c\right]}{r_0 + vt}.
+\\]
+
+## Doppler shift
+The key observation is that *the frequency of the received signal changes*! In particular, the frequency changes by \\(- (v/c) \cdot f\\), which is proportional to the moving speed \\(v\\).
+* We may have experienced this in daily life. A siren has a higher frequency (i.e., a higher pitch) when the ambulance is moving towards us, and a lower frequency (i.e., a lower pitch) when the ambulance is moving away. 
+
+This phenomenon, where the signal frequency changes when the transmitter and/or the receiver is moving, is called **Doppler shift**.
+
+In wireless communication systems, we need to take into account the Doppler shift when the moving speed is high. For example, in a high-speed train, it is more challenging to maintain a high-speed wireless connection, partly due to the Doppler shift.