Midterm 2 study guide:
Review sections:
5.1, 5.3-6,
6. 11,
7.1-2, 7.10-12
8.3, 8.7
MacKay’s treatment of I(x), H(x) 4.1-3
Here’s a start at some test-style sub-problems. Obviously, not all of them will fit on a
single test. I’ll answer many of these during our review on Tuesday. I’ll also hand
calculate many of them and post the solutions online.
1 Given m = 5, taps = [ 5 1 ], initialized with all zeros except for a single one at
the far right, compute the first 6 values of this maximal length sequence.
2 How long is the PN code in (1)?
3 What does it look like if you correlate the sequence from (1) against a
continuously repeating copy of itself? How high and how far apart are any
unusual parts of that correlation?
4 If the processing gain in a spread spectrum system is 100, and there are eleven
users in the system, what is the SIR?
5 Draw a picture of the frequency-domain representation of the signal in (4)
before and after spreading and despreading.
6 Draw a picture of the impact of despreading on a narrow-band interferer.
7 Use the following repeating sequence [ 1 1 -1 1 -1 -1 1 ] to spread the
following bit stream [ 1 0 ].
8 Draw a time-domain picture of the spread sequence from (6).
9 Encode [ 0 1 0 0 1 1 1 0 ] using the (7,4) Hamming code.
10 Decode the following symbol stream [ -.3 -.9 .8 -1.1 -.9 -1.0 -1.2 ] using the
Hamming (7,4) code. (Note the syndrome look-up table is [ 3 2 5 1 7 4 6 ].)
11 What’s the likeliest bit to detect incorrectly in (9)?
12 Compute a pdf and cdf from measured data as shown on Midterm #2 from
2005.
13 Determine if a channel is frequency selective given sigma_T or Bc and Ts or
Rs or Rb.
14 Determine if a channel exhibits fast fading given Ts or Bs or Rs and the
velocity and wavelength of the user or the maximum Doppler.
15 Recommend a mitigation to frequency selective fading.
16 Recommend a mitigation to slow fading.
17 Given five branches of receive diversity, compute the probability that
SNR_instantaneous / SNR_average < -8 dB under selection combining.
18 Given instantaneous SNRs on five diversity branches of 10, 12, 8, 3, and 7
dB, compute the output SNR under selection combining.
19 Compute the output SNR for (18) under maximal-ratio combining.
20 Indicate the coding gain given curves for the BER, SER and decoded BER.
21 Indicate the relative impact of code rate on BER
