College of Computer Science Northeastern University COM3525: Wireless Networks

Winter 2002 February 20^th, 2002

Assignment 3 (Due February 28^th, 2002)

A mobile terminal is communicating with a base station using a carrier frequency f_c = 1500MHz. The communication antennas have gain G = 1. The data rate of the communication is 100Kbps and the transmission power is 1W. We assume that the noise power density is N₀ = 10^-11 W/Hz and that there is no other source of interference. The modulation is BPSK and is coherently demodulated.

• What is the E_b/N₀ as a function of the distance d between the mobile and the base station? Show a graph for d = 0 m to 5 Kms (use MATLAB).
• What is the bit error rate (BER) as a function of d? Show a graph (display the BER in logarithmic form).
• Assume that the data stream can be fragmented into frames of length L. The maximal packet size is 10000 bits. The fragmentation overhead is OH = 200 bits. What is the frame error rate? What is the expected throughput as a function of L and d.
• Write a program that finds the optimum frame size L_opt as a function of the d. It’s easier using Matlab but you can also use C/C++.
• Discuss if fragmentation can improve coverage and by how much.
• Assume that we can use 3 coding schemes: uncoded (UC), ½ convolutional code (½CC) and 1/3 convolutional code (1/3CC). The second coding scheme (½CC) allows a gain of 3dB at a cost of doubling the size of the data stream. The third coding scheme (1/3CC) allows a gain of 5dB at the cost of multiplying the size of the data stream by 3. Write a program that determines the optimal code and the optimal frame size.

Notes: in Matlab you can use the function erfc. If you use C/C++ you would have to input the Q function table in your program.

ERFC: Complementary error function.

Y = ERFC(X) is the complementary error function for each element

of X. X must be real. The complementary error function is

defined as:

erfc(x) = 2/sqrt(pi) * integral from x to inf of exp(-t^2) dt.

= 1 - erf(x).