Homework-1 solution-2021.pdf - ELEC 6099 Wireless...

ELEC 6099 Wireless Communication and Networking
Homework 1: Solution
March 13, 2021
Topic.1 Introduction and Transmission Fundamentals
1.1
Suppose a transmitter produces 100 W of power.
a. Express the transmit power in units of dBm and dBW.
b. If the transmitters power is applied to a unit gain antenna with a 900 MHz carrier frequency,
what is the received power in dBm at a free space distance of 500 m?
c. Repeat (b) for a distance of 5 km.
d. Repeat (c) but assume a receiver antenna gain of 2.
Solution:
1.2
Consider a transmitter transmitting a signal with power of 10 watt over a distance of 1 km
using a carrier of 2 . 4 GHz and an antenna with an effective aperture (area) of 1 . 2 m
2
. The
signal is received by an antenna with an effective aperture of 0 . 2 m
2
. Given the speed of light
c = 3 × 10
8
m/s, compute the received signal power in dBm.
1

2.1
A sine wave is to be used for two different signaling schemes: (a) PSK; (b) QPSK. The du-
ration of a signal element is 10
- 5
s. If the received signal is of the following form s ( t ) =
0 . 01 sin(2 π 10
6
t + θ