add assignment of module 04

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

@@ -8,14 +8,14 @@ morea_summary: "Physical models of wireless channels"
 morea_type: assessment
 morea_start_date: "2024-02-06T00:00"
 morea_end_date: "2024-02-12T23:55"
-morea_labels:
+morea_labels: Google Colab
 ---
 
 # Input/output models of wireless channels
 
 *Please submit your solutions in Laulima.*
 
-In this assessment, we look at a realistic channel model with its parameters determined by field measurements. Then we will implement a simplified version of this channel model.
+In this assessment, we look at a realistic channel model with its parameters determined by field measurements. Then we will implement a simplified version of this channel model in [this Google Colab notebook](https://colab.research.google.com/drive/1-Phfq-bfamIrVRMkTvJAtOFAIcUtPoEA?usp=sharing).
 
 One feature of the 5th-generation (5G) wireless communication systems is the usage of the millimeter-wave (mmWave) band at 60 GHz. Therefore, it is crucial to understand the mmWave channels. The Millimetre-Wave Evolution for Backhaul and Access (MiWEBA) project is one of the efforts toward this goal. If you are interested, you might want to take a look at [the complete project report](https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=e41ca51b3a590d267f5d09661b790c9002d3abbc).
 
@@ -24,19 +24,12 @@ For this assessment, we will only need to refer to [this paper](https://jwcn-eur
 We will implement a quasi-deterministic (Q-D) channel model, as illustrated in Fig. 8 of [the paper](https://jwcn-eurasipjournals.springeropen.com/articles/10.1186/s13638-016-0568-6). The Q-D channel consists of a few strong deterministic rays (D-rays) and some random rays (R-rays). Each ray or multipath is a cluster of rays with similar delays. You can look at Fig. 9 of [the paper](https://jwcn-eurasipjournals.springeropen.com/articles/10.1186/s13638-016-0568-6) for an example with two D-rays (i.e., the line-of-sight (LoS) path and the ground reflection path) and two R-rays (i.e., one path due to reflection from a car and the other due to reflection from a building). 
 
 Below are the list of tasks to do.
-* Please look at Fig. 3 and Fig. 4, and identify four major multipaths in terms of delay (in ns) and power (in dB).
-  - Note that a major multipath should have a relatively high power (i.e., less attenuation). In addition, peaks that are very close to each other can be clustered into one multipath.
-* Identify two D-rays and three R-rays. Specify the delay and the power.
-* Direct ray
-* Ground ray
-* Random ray that is reflected from a random reflector (e.g., a car)
-* a far wall ray that is reflected from a far reflector (e.g., a building far away from the receiver)
-
-<figure style="text-align: center;">
-  <img src="04-baseband-spectrum.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.
+* (4 points) Please look at Fig. 3 and Fig. 4, and identify four major multipaths in terms of delay (in ns) and power (in dB).
+  - Note that a major multipath should have a relatively high power (i.e., less attenuation).
+* (2 points) How would you assign each one of the four major multipaths to the LoS D-ray, the ground reflection D-ray, and two R-rays?
+* (2 points) Fill in the power delay profile above in [the Google Colab notebook](https://colab.research.google.com/drive/1-Phfq-bfamIrVRMkTvJAtOFAIcUtPoEA?usp=sharing). Then calculate the following quantities.
+  - Calculate the excess delays of the multipaths relative to the LoS path. For example, if the delays are 100 ns, 150 ns, 250 ns, 300ns, the excess delays should be 0 ns, (150-100 = 50) ns, (250-100 = 150) ns, (300-100 = 200) ns. Then convert the excess delays in seconds to excess delays in time slots according to the sampling rate.
+  - Convert the power in dB to the power in the linear scale.
+* (1 point) Run the code to see the *power spectral density (PSD)* of the transmit signal and that of the received signal. Explain how the channel results in the difference between the two PSDs? *Hint: think about the delay spread of the channel.*
+  - Note that the PSD illustrates the spectrum of a *random* signal. It is defined as the Fourier transform of the *autocorrelation function* of the random signal. Unlike a deterministic signal, for a random signal, we compute the Fourier transform of its autocorrelation function, instead of the signal itself, because the autocorrelation function is deterministic.
 

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

@@ -15,7 +15,7 @@ morea_experiences:
   - experience-04-baseband-passband-conversion
   - experience-04-sampling-theorem
 morea_assessments:
-  # - assessment-04-input-output-model
+  - assessment-04-input-output-model
 morea_type: module
 morea_icon_url: /morea/04-wireless-channel-input-output-model/04-module-icon-multipath.png
 morea_start_date: "2024-01-22"