College of Computer & Information Science Fall 2007 Northeastern University Handout 2 CSG250: Wireless Networks 21 September 2007

Problem Set 2 (due Tuesday, October 2)

(Problem numbers indicated below refer to the problems in the second edition of the course text. The problem numbers in parentheses refer to the problems in the first edition of the course text.)

1. (10 points) Frequency-hopping spread spectrum Problem 7.4 (Chapter 7, Problem 4).

2. (6 points) Spreading codes in CDMA Problem 7.7 (Chapter 7, Problem 7).

3. (4 points) Generation of m-sequences Problem 7.12 (Chapter 7, Problem 12).

4. (4 points) Parity codes Consider a simple (3,1) linear block code where each codeword consists of three data bits and one parity bit.

(a) Find all codewords in this code.

(b) Find the minimum distance of the code.

5. (4 points) Walsh codes Demonstrate that codes in a 8 × 8 Walsh matrix are orthogonal to each other. What are the advantages and limitations of using Walsh codes in spread spectrum applications?

6. (10 points) Convolutional encoding Consider the convolutional encoder with n = 3, k = 1, and K = 3, defined by v_{n1} = u_{n}, v_{n2} = u_{n} ⊕ u_{n−1} ⊕ u_{n−2}, and v_{n3} = u_{n} ⊕ u_{n−2}.

(a) Draw a shift-register diagram for the encoder.

(a) Draw a trellis diagram for the encoder.

7. (4 points) Block error correction codes Problem 8.11 (Chapter 8, Problem 11).

8. (8 points) Interleaving Problem 8.19 (Chapter 8, Problem 19).