Class: 12/03/2010

• Spread spectrum receivers
• RAKE receiver

Class: 12/01/2010

• Finished OFDM synchronization
• Introduction to spread spectrum modulation

Class: 11/29/2010

• Further discussion of OFDM
• Began discussion on synchronization of OFDM

Class: 11/15/2010

• Mitigating fading by exploiting diversity
• Selection combining
• Maximal ratio combining

Class: 11/12/2010

• Further discussion on fading
• Probability of error on Rayleigh fading channels

Class: 11/05/2010

• Continued discussion of fading channels
• Coherence time
• Coherence bandwidth
• Doppler spread
• Delay spread

Class: 11/03/2010

• Introduction to fading channels
• Looked at deterministic multipath examples to develop intuition about stochastic descriptions of channels
• Frequency and time selectivity
• 
  

Class: 11/01/2010

• Adaptive blind equalizers
• Subspace based blind equalization

Class: 10/29/2010

• Practical matters with equalizer implementation
• Introduction to adaptive blind equalizers

Class: 10/27/2010

• Tomlinson-Harashima precoding
• Adaptive minimum bit error rate adaptive linear equalizers

Class: 10/25/2010

• Designing fixed decision feedback equalizers (DFE)
• Looked at DFE performance relative to linear equalizers and the Viterbi algorithm
• Considered adaptive DFE

Class: 10/22/2010

• Decision feedback equalizer

Class: 10/20/2010

• Adaptive RLS equalizer.

Class: 10/18/2010

• Adaptive zero forcing and LMS equalizers

Class: 10/14/2010

• Minimum mean squared error (MMSE) equalization
• ZF and MMSE equalizer examples

Class: 10/11/2010

• Developed time-domain model for fractionally spaced equalizers.

Class: 10/13/2010

• Zero forcing equalization
• Fractionally spaced and symbol spaced cases
• Noise amplification

Class: 10/08/2010

• Scaling for the BCJR algorithm.
• Started discussion of filter based equalization techniques.
• Discussed the differences between symbol rate and fractional spaced equalizers.

Class: 10/06/2010

• Developed forward-backward recursions for the BCJR algorithm.

Class: 10/04/2010

• Development of the BCJR algorithm.

Questions on HW 4

=======================
Question Problem #1:

You made the comment in lecture that the symbols are MSK encoded.  By this do you mean the using the constellation to encode for example pi/4 = 11, 3pi/4 = 01 5pi/4 = 00 and 7pi/4 = 10?  Then after they are encoding this way we up sample as done in com 1 and so on and so forth.  Am I seeing this correctly?

Response:

It was shown in Problem #3 in HW 3 that the MSK waveform has the form

s(t) = cos(2πf_ct)A_{2k−1} g(t − [2k − 1]T)(−1)^k − sin(2πf_ct)A_{2k} g(t − 2kT)(−1)^k

for nT ≤ t < (n + 1)T, where the encoded symbols A_n are given by

A_n = A_{n-1} I_n      (this is like differential encoding)

where I_n is the information symbol.  So, the information symbols I_n are encoded to A_n and then the even encoded symbols A_{2k} and odd encoded symbols A_{2k-1} are transmitted on the quadrature and in-phase carriers, respectively.  Also, note the (-1)^k.

=======================
Question Problem #4:

I am not sure how Proakis (in section 3.4 eq 3.4-15) goes from

G_k(f) = E[S_l(f;I_k)S^*_l(f;I_0)] to
 = E[I_kI^*_0|G(f)|^2]

Maybe I am forgetting something, but I do not see how he pulls the I_k/I_0 out of the S_l functions.  Can you elaborate on this for me?

Response:

He uses equation 3.4-14 which indicates that

s_l(t,I_n) = I_n g(t).

Then the Fourier transform is

S_l(t,I_n) = I_n G(f).  I don't have a problem with that part.  However, 3.4-14 does not seem to follow from 3.4-13  unless the pulses g(t) are time limited to one symbol period.

Here is a better way to solve this problem.

1. Define the symbols to be I(n).
2. Define the pulse to be g(t).
3. The transmitted pulse train is s(t)=sum_n I(n) g(t-nT).  This is an infinite sum.
4. The autocorrelation function of s(t) is R(t;t-v) = E{s(t) s^*(t-v)}.  Show that this is a periodic function with period equal to the symbol period T.
5. Define the averaged autocorrelation function S(v) = (1/T) int_0^T R(t;t-v) dt, where int_A^B f(t) dt is the integral of f(t) on the interval (A,B).
6. Let P(f) be the continuous-time (CT) Fourier transform of S(v).  Interchange integrals and sums, do a few changes of variables and you will find that

P(f) = DTFT{autocorrelation function of the symbols evaluated at fT} |G(f)|^2 where f is continuous frequency in Hz.

Hope this helps.

Class: 9/29/2010

• Programming the Viterbi algorithm

Class: 9/27/2010

• Discussed homework assignment 4.
• Discussed C-based implementation of Viterbi algorithm.
• No class on Friday, 1 October 2010.

Class: 9/24/2010

Worked out Viterbi algorithm example in detail.

Class: 9/22/2010

• Discussed several homework problems
• Homework due date extended to Friday
• Continued development the Viterbi algorithm
• (audio went out part way through class, sorry)

Class: 9/20/2010

• Set up for maximum likelihood sequence estimation via the Viterbi algorithm
• The channel acts like a state machine, state transition diagrams, trellis diagrams
• Input sequences of symbols are in one-to-one correspondence with paths through the trellis
• Decomposition and simplification of the joint likelihood function

Class: 9/17/2010

• Intersymbol interference (ISI)
• Nyquist's criterion review
• Frequency selective channel impairments and examples
• Introduction to equalization

Class: 9/15/2010

• CPFSK, modulation index, MSK, MSK/OQPSK equivalence
• Non-coherent detection of FSK
• QPSK, non-coherent detection of differentially encoded QPSK, and DQPSK

Class: 9/13/2010

• Generation of FSK and CPFSK
• Phase trajectories
• Pulse shapes
• Spectral properties of CPFSK

Class: 9/10/2010

Derived the probability of bit error (in terms of Eb/N0) for (orthogonal, coherent) M-FSK.  Do the non-coherent case for homework.

Class: 9/8/2010

Devoted the whole hour to deriving and discussing the characteristics of complex low-pass noise given that the real bandpass noise characterization.  For WSS bandpass noise, the cross-correlation of the real and imaginary parts is odd while the auto-correlations are the same.  For white Gaussian bandpass noise, the real and imaginary parts of the low-pass noise are uncorrelated (and independent).  There is twice as much total power in the low-pass noise as in the bandpass noise.  If the bandpass noise is "white" and Gaussian with PSD N0/2 for |f-fc|<W, then the low pass noise is "white" and Gaussian with PSD 2N0 for |f|<W.

Do you want us to turn homework into the box in the breakroom?

9/3/2010

The following topics were discussed.

• Frequency shift keying.
• Minimum frequency separation for orthogonality: 1/T (low pass), 1/(2T) (bandpass).
• Bandwidth efficiency of FSK compared to PSK, QAM.
• Receiver structure for optimal (coherent and noncoherent) detection of FSK transmitted over AWGN channel.

Class: 9/1/2010

The discussion in class today focused on the following topics.

• Low pass equivalent signals and systems.
• Two ways to convert band pass signals to low pass: sin/cosine modulation + low pass filtering, Hilbert transform + complex down conversion.
• Low pass to band pass conversion.
• Band pass and low pass signal spaces.
• QAM has two dimensional band pass signal space, but one dimensional low pass signal space.

Class: 8/30/2010

First day of class. Topics covered include the following.

• Classroom administration, syllabus, blog, assignment format, etc.
• Started discussing low-pass equivalent signals.
• Look at the first four or five problems on the homework assignment.
• Read Chapter 2 in the Proakis text.

Welcome

Greetings.  In ECE 6670, we shall try using this blog as a means for communicating among the teacher and members of the class. I encourage the use of this blog for at least the following purposes.

• Each day after we meet for class, I will (try) to post a list of what I thought were the most important topics that we covered that day.
• If you have questions, this blog would be a good place to post them. Questions could be about material that we covered (or didn't cover) in class, the homework or computer programming assignments, etc.
• This blog would be a good place to raise points for discussion. I'll try to stay abreast of what is going on in the blog and address in class issues that are raised here. 
• What did I miss?