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Project 3: OFDM Modulation (10%)

In this project,  students are required to  design  a program to  simulate the OFDM transmitter shown in Page 50 of Lecture 9. Suppose that there are N=16 subcarriers. Note that in Matlab and Pathon, there is a function to perform IDFT. You are not allowed to call this function. Please design your code for IDFT based on Page 31 Lecture 9.

Step 1: Generating N=16 modulated samples, i.e., [d0,…,d15], from QPSK. First, you can randomly generate 2N=32 bits. For every two bits, you use a QPSK sample to modulate them. Therefore, N=16 QPSK samples will be generated based on your bits. The modulation codebook is as follows (Page 18 of Lecture 6):

If the two bits are 00, then d=1 (in-phase component is 1, quadrature

component is 0)

If the two bits are 01, then d=j (in-phase component is 0, quadrature

component is 1)

If the two bits are 11, then d=- 1 (in-phase component is - 1, quadrature

component is 0)

If the two bits are 10, then d=-j (in-phase component is 0, quadrature

component is - 1)

Step 2: Generating N=16 OFDM samples, i.e., [s0,…,s15], based on IDFT. You can implement IDFT on [d0,…,d15] to get the OFDM samples based on Page 32 of Lecture 9.

Step 3: Inserting the cyclic prefix. Suppose that the length of the cyclic prefix is Q=5. Generate the cyclic prefix based on Page 50 of Lecture 9.

Step 4: Calculating Peak-to-Average Power Ratio (PAPR) of your OFDM samples.

PAPR is defined in Page 55 of Lecture 9. For the expectation of |sk|, you may use ∑k(1)0 |sk |/16  to approximate it.

Submission Checklist:

1.   Your Matlab or Pathon code

2.   A report covering

2.1 Your name and student ID

2.2 32 random bits generated by you in Step 1, and the corresponding 16 QPSK samples [d0,…,d15]

2.3 16 OFDM samples [s0,…,s15] generated in Step 2

2.4 The OFDM signal after inserting the cyclic prefix

2.5 PAPR of the OFDM signal generated by you

Submission Deadline:

1. 11:59pm, March 28, 2023

2. Visit  the  website  of our  course  at  blackboard.  On  the  left  tool  bar,  click  on “Assessment” . You will see an item Please submit Homework 3 here” . Attach your code and report there.

TA Information:

1. Wang Qipeng:[email protected]