EE290Q Homework 3

Due Thursday 2/26/2009

1. Using information from Figure 2 of Cook’s
“chapter 6” document

a. Which modulation scheme requires the lowest energy per
bit, and which the highest? What is
the difference in energy per bit?
Bits per second per Hertz?
Why might one prefer one over the other?

b. What is the minimum bandwidth
required, minimum SNR, and the theoretical sensitivity limit for a 1Mbps FSK
radio? A 1 Mbps 64-QAM radio
(similar to 802.11g)? A 1 Mbps QPSK
radio (similar to 802.15.4)?

2. Using the information from Figure 14 of Cook,

a. What is the overhead power
and the PA efficiency in the transmitter?

b. Assuming 2-FSK and the BW as indicated (500kHz), what is the maximum data rate and minimum
sensitivity possible with this receiver?

3. In the “radio basics” handout, the caption
of Figure 3 asks you to note a few things and compare them. Write down what you note and compare,
and then use that phase vs. time information to label a phase constellation
plot with the corresponding times.

4. You are designing a radio in CMOS, and need your LO to
be tuneable from 902 MHz to 928 MHz. You’ve designed a nominal 10nH
inductor. Due to process variation,
the inductor and capacitor values that you get back can vary by as much as
±5% from run to run.

a. What is the nominal range of capacitance values that
you need to cover to allow your LO to tune over the
whole band?

b. With process variation, what is the total range of
capacitance that you need to design to?

Do ONE of the following matlab
problems.

1)
You have two
antennas with a ground separation d above a ground plane at heights h1 and
h2. For the two-ray fading model,
assume that the reflected wave has 180 degree phase shift.

a. Calculate the power at receiving antenna as a function
of distance assuming a transmit power PT and isotropic antennas.

b. Calculate the approximate electric field of the direct
path as a function of ground separation d.

c.
Approximate the
path length difference between the direct and reflected paths.

d. Approximate the reflected-path electric field
strength, and the sum of the two fields, and then the received power.

e.
Use matlab to solve this problem exactly assuming h1=h2=1m,f=2.44GHz, and d=0 to 1km.

f.
Extra for
enthusiasts: assume dipole antennas in various orientations, or non-ideal
ground reflection.

2)
Use matlab to explore connectivity between motes.

a. Generate 10 uniformly distributed random mote
locations in a two-dimensional area 1km square.

b. Assume a transmit power of 0dBm, a receive sensitivity
of 90dBm, isotropic antennas, and a path loss model given by either

i.
the Friis equation from 0 to 1m, and then R3.7 attenuation
beyond 1m (IEEE model)

ii.
the Friis equation plus a constant uniformly distributed random
loss between 0 and 40 dB (the official Pister Hack model)

c.
Calculate the
connectivity matrix, Cij, which represents which
motes are connected. (Draw a plot
of mote locations with arrows connecting them if you want to be fancy)

d. Pick the first mote in your list as the gateway, and
calculate how many motes are connected to it via one or more hops.

e.
Increase the
number of motes until your network is fully connected.

f.
Plot % of
connected motes vs. the number of motes in the network for each of the two path
loss models.

g.
Which path loss
model gives better connectivity?
Why?

3)
Use matlab to generate IEEE 802.15.4 2.4GHz OQPSK-HSS modulated
waveforms and demodulate them.

a. Create a function [ichan, qchan, t] = iqmodulate(ichips,qchips,fc,fs) which takes the input vectors ichips and qchips and modulates
them onto a carrier at frequency fc, with a time
sampling rate of fs, returning the I and Q outputs as
well as the time vector.

b. Create the function [iout, qout] = iqdemod(Vant, fc,
fs) which takes the input antenna voltage signal Vant sampled at frequency fs and
demodulates it assuming a carrier frequency fc.