Mulitply PN sequence to real and convert output to complex - Question

GNU Radio
1

hi friends,

To convert this complex signal to a real, one has to do
this according to the following formula, isn’t it?

x(t) = Y(t)Cos(2pifct) - Y(t)Sin(2pifct) where
Y(t) -> Complex signal,fc -> Carrier frequency, x(t) -> real signal.

I looked at the block “complex_to_real” and it outputs the Inphase
component
as the real signal. Is it because, “fc” is 0Hz as the signal being at
baseband? I think this sounds right.

I want to mulitply this real signal with a PN sequence and then pass the
result
on to a costas loop which takes a complex input. I want to know how can
we
get a complex signal from a real one. Is there a block that does that?

The book “Communication Systems” by Simon Haykin 2nd edition says,

  • The complex envelope g_complex(t) equals a frequency shifted version
    of the pre-envelope g+(t) as shown
    g_complex(t) = g+(t)exp(-j2pifct), where fc->
    carrier frequency.
    and the pre-envelop is defined as, g+(t) = g_real(t) + j*g_hilbert(t).

I suppose this is what I need to do to get what I want. Is there a
block that does it all?

Thanks,
Peng.

P.S. - I am sorry but I thought to make sure before I go ahead so that
I don’t spend time doing things that may be unnecessary.

2

sorry a correction,

3

Sir:

Welcome to GnuRadio and happy to have a newcomer. Let me spend some
time on netiquette here. Asking the same question, many times in many
different ways is a sure fired way to get LESS help and for it to be
delayed by an irritation factor.

To convert a complex signal to real, it depends on where you are doing
it. You are writing what looks like C/C++. There are gr_complex types
for GnuRadio in C++. Let us assume you have a complex number X. Then
X.re() is the real part.

Your x(t) is not “making the signal real”, it is modulating the complex
signal Y at baseband by the complex carrier exp(j 2pi t fc).

This gives

Yc(t)Cos(2pifct) - Yi(t)Sin(2pifct)

as the REAL PART of that modulation process.

Yc(t)Sin(2pifct) + Yi(t)Cos(2pifct) is the imaginary part of that
complex modulation process.

This is not taking the real part, or “making it real”, it is making a
passband signal out of a baseband signal.

Your question is somewhat ill posed. Assuming that you meant modulating
the signal away from zero frequency by
the carrier frequency fc, and taking the real part to get a passband
signal, then the answer to your question is yes, you did it right.

Bob

Peng Huo wrote:

Thanks,

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4

First of all thank you very much for replying and I will refrain from
posing
questions that way.

I still have some doubts about this. I will be thankful to you if you
clear
these.

I want to de-spread a spread spectrum signal. I have a transmitter that
transmits data spread using PN sequence. These can be any type such as
m-sequence or gold sequence. I want to strip the PN sequence from the
received spread spectrum signal. We get complex baseband signal from
USRP_source. I want to write C++ blocks to do this.

a. How can I multiply this to this received complex baseband? Can I do
it
directly on this complex representation?
b. The output of this needs to be input to the costas loop for carrier
tracking and I want the result of the above step in complex.

Thanks,
Peng.