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.