Fall 2015-2016

Dr. Dina Serhal ECE Department

CCEE 525, Wireless Communications

Homework 1: Due Monday, Sep.21

1. (2.1) Under a free space path loss model, find the transmit power

required to obtain a received power of 1 dBm for a wireless system

with isotropic antennas ( ) and a carrier frequency , assuming a distance . Repeat for .

2. (2.2) For a two-path propagation model with transmitter-receiver

separation , , and , find the delay spread between the two signals.

3. (2.8) [Matlab] Directional antennas are a powerful tool to reduce

the effects of multipath as well as interference. In particular,

directional antennas along the LOS path for the two-ray model can

reduce the attenuation effect of the ground wave cancellation, as will

be illustrated in this problem. Plot the dB power ( ) versus log distance ( ) for the two-ray model with the parameters , , , , , and the following values for and (i.e. and , respectively). Each of the 4 plots should range in distance from to .

Also calculate and mark the critical distance on each plot, and normalize the plots to start at approximately 0dB. Finally,

show the piecewise linear model with flat power falloff up to distance

, falloff for , and falloff

for . (On the power loss versus log distance plot the piecewise linear curve becomes a set of three straight lines with slope 0, 2, and

4, respectively). Note that at large distances it becomes increasingly

difficult to have since it requires extremely precise angular directivity in the antennas.

Fall 2015-2016

Dr. Dina Serhal ECE Department

4. (2.13) Consider a receiver with noise power within the signal bandwidth of interest. Assume a simplified path loss model

with , obtained from the free space path loss formula, and . For a transmit power of , find the maximum distance between the transmitter and receiver such that the received

signal-to-noise power ratio is .