[Discuss-gnuradio] Costas Loop implemented on FPGA?

[Reid N Kleckner]

Hey all,

I'm looking at using the FPGA on the USRP to improve the performance in some of
what my lab is doing.  To learn about the Verilog code already written for the
FPGA, I'm trying to do phase recovery with the Costas loop at the end of the
rx_chain.  First of all, is this a good project?  It may not be good to have it
in the codebase for general purpose gnuradio since it's only relevant for
certain protocols, but is there anything wrong with this approach that makes it
brain dead?  I've read that the FPGA is using 90% of its logic cells with it's
current implementation, and that turning off a tx_chain or an rx_chain could
solve that problem, but I'm not there yet.

I've been hacking at it for a bit, and I drafted up a simple vlog file here:
http://web.mit.edu/~rnk/www/costas_loop.v
and a slightly modified rx_chain here:
http://web.mit.edu/~rnk/www/rx_chain.v
I'm new to FPGAs and signals (So why am I working on this?  To learn.), so I
have a few questions.

1. I need to store the phase shift somewhere as I correct the guess with the
error term.  I assume that the phase accumulator in phase_acc.v needs to do
something similar, but I don't understand how it stores its information.

2. The original C implementation of costas loop has two error terms you can
choose from:
((sample.real()>0 ? 1.0 : -1.0) * sample.imag() -
 (sample.imag()>0 ? 1.0 : -1.0) * sample.real());
and:
(sample.real()*sample.imag());
I chose the simpler because it involved one less multiply, and I didn't
understand what the other was doing.  The point of software radio is to allow
you to make these decisions in software, but if I had to hardcode one in the
FPGA, which would it be?  I'm definitely not complicating this further by
trying to get that info via USB.

3. For alpha and beta, I was just going to use a bitshift to scale the error
term.  That'd also be hardcoded in the vlog code, but what would reasonable
constants be?  I've seen this question asked before, and I looked at the paper
here:
http://i.cmpnet.com/chipcenter/dsp/images/dspsourced/DSP010531F1.pdf
and it said alpha is around 0.01 or less, so I figure a bitshift by seven places
makes alpha about 1/128, or 0.0078125, and the paper doesn't mention beta, so I
said eight places.

4. What's the difference between the code in gr_pll_carriertracking_cc.cc and
gr_costas_loop_cc.cc?  They seem to do the same stuff, but maybe they're subtly
different?

That's all.

Cheers,
Reid