Detection of Bessel components of a received PM signal

Hi

My current work involves estimation of modulation index for a PM signal
with or without subcarriers. I have found articles to do the same without
subcarriers, but I am yet to find something which might work when
subcarriers are included. An important method to estimate the modulation
index (which I believe can be extended for subcarriers later) is to detect
the Bessel components and find corresponding modulation index for the same
(from a lookup table etc.). The thing is that in the demodulation block I
still haven't understood how I can arrive at the Bessel components directly
from the received signal (assuming for the time being that it is
noiseless). Most literature talks of how using a known modulation index b,
one can find the Bessel components J0(b), J1(b) etc. I need to do the
reverse. But to do so, I need info on the Bessel components.

Could someone please help me urgently in this regard.

Thanks in advance
MS

mayanksharma wrote:
> Hi
> 
> My current work involves estimation of modulation index for a PM signal
> with or without subcarriers.

What is the purpose of that? Would you describe the entire problem?

> I have found articles to do the same without
> subcarriers, but I am yet to find something which might work when
> subcarriers are included. An important method to estimate the modulation
> index (which I believe can be extended for subcarriers later) is to detect
> the Bessel components and find corresponding modulation index for the same
> (from a lookup table etc.). The thing is that in the demodulation block I
> still haven't understood how I can arrive at the Bessel components directly
> from the received signal (assuming for the time being that it is
> noiseless). Most literature talks of how using a known modulation index b,
> one can find the Bessel components J0(b), J1(b) etc. I need to do the
> reverse. But to do so, I need info on the Bessel components.

I can think of several approaches to that, but why can't you simply 
demodulate the signal and then figure out the modulation index and the 
components?

> Could someone please help me urgently in this regard.

Sure. Send me money right now.

> Thanks in advance

Your "thanks" sure means a lot.

VLV

mayanksharma wrote:
> Hi
> 
> My current work involves estimation of modulation index for a PM signal
> with or without subcarriers. I have found articles to do the same without
> subcarriers, but I am yet to find something which might work when
> subcarriers are included. An important method to estimate the modulation
> index (which I believe can be extended for subcarriers later) is to detect
> the Bessel components and find corresponding modulation index for the same
> (from a lookup table etc.). The thing is that in the demodulation block I
> still haven't understood how I can arrive at the Bessel components directly
> from the received signal (assuming for the time being that it is
> noiseless). Most literature talks of how using a known modulation index b,
> one can find the Bessel components J0(b), J1(b) etc. I need to do the
> reverse. But to do so, I need info on the Bessel components.
> 
> Could someone please help me urgently in this regard.

Pity drives me to this.

Context leads me to believe that you refer to frequency-, not 
phase-modulation index. (Bessel functions are irrelevant to amplitude 
modulation.)

For FM, the modulation index is 
(carrier_deviation)/(modulating_frequency). It is defined only when the 
modulation is a single frequency. In that case, the sidebands are 
symmetric. In general, they are not. I don't think your question makes 
any sense.

Jerry

P.S. to Vladimir: Surely you wouldn't accept a commission for an 
impossible job?
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Vladimir Vassilevsky  <nospam@nowhere.com> wrote:

>mayanksharma wrote:

>> Hi

>> My current work involves estimation of modulation index for
>> a PM signal with or without subcarriers.

> What is the purpose of that? Would you describe the entire problem?

Sounds like spook work to me.


S.

Jerry Avins wrote:

> For FM, the modulation index is 
> (carrier_deviation)/(modulating_frequency). It is defined only when the 
> modulation is a single frequency. In that case, the sidebands are 
> symmetric. In general, they are not. I don't think your question makes 
> any sense.

I can think about the variety of the sensible scenarios; however it is 
not clear what did the OP really mean. It could be anything from the FM 
pilot tone to the equalization of the OFDM over FM.

> Jerry
> 
> P.S. to Vladimir: Surely you wouldn't accept a commission for an 
> impossible job?

There is no challenge in the solving of the soluable problems. This is 
what Matlab does :-) Anyway the question looks a lot like a homework 
assignment.

VLV

Vladimir Vassilevsky wrote:
> 
> 
> Jerry Avins wrote:
> 
>> For FM, the modulation index is 
>> (carrier_deviation)/(modulating_frequency). It is defined only when 
>> the modulation is a single frequency. In that case, the sidebands are 
>> symmetric. In general, they are not. I don't think your question makes 
>> any sense.
> 
> I can think about the variety of the sensible scenarios; however it is 
> not clear what did the OP really mean. It could be anything from the FM 
> pilot tone to the equalization of the OFDM over FM.
> 
>> Jerry
>>
>> P.S. to Vladimir: Surely you wouldn't accept a commission for an 
>> impossible job?
> 
> There is no challenge in the solving of the soluable problems. This is 
> what Matlab does :-) Anyway the question looks a lot like a homework 
> assignment.

Various papers define "modulation index" for broad-spectrum baseband in 
various ways. How do you suppose the OP defines it?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

>Vladimir Vassilevsky wrote:
>> 
>> 
>> Jerry Avins wrote:
>> 
>>> For FM, the modulation index is 
>>> (carrier_deviation)/(modulating_frequency). It is defined only when 
>>> the modulation is a single frequency. In that case, the sidebands are

>>> symmetric. In general, they are not. I don't think your question makes

>>> any sense.
>> 
>> I can think about the variety of the sensible scenarios; however it is

>> not clear what did the OP really mean. It could be anything from the FM

>> pilot tone to the equalization of the OFDM over FM.
>> 
>>> Jerry
>>>
>>> P.S. to Vladimir: Surely you wouldn't accept a commission for an 
>>> impossible job?
>> 
>> There is no challenge in the solving of the soluable problems. This is

>> what Matlab does :-) Anyway the question looks a lot like a homework 
>> assignment.
>
>Various papers define "modulation index" for broad-spectrum baseband in 
>various ways. How do you suppose the OP defines it?
>
>Jerry
>-- 
>Engineering is the art of making what you want from things you can get.
>???????????????????????????????????????????????????????????????????????
>

Ok. I am new to dsprelated, and did not expect such quick responses! Thank
you all for taking out your time, although it seems I might have skipped
some details. So here goes:
Context: The goal is to use blind estimation to estimate modulation index
for a PM signal (i.e. signal modulated using Phase Modulation explained in
equations below), with the aim of avoiding a complex FFT operation for the
same. Basically an operation which makes the task of implementation in an
FPGA easier and perhaps faster. This application is to be used for deep
space or satellite communications. I'd like to remind that it's not OFDM
that we use here.I have found an estimator which can work for a PM signal
modulated without a subcarrier, which does not require the knowledge of the
carrier frequency as well. The estimation is purely data-aided and done so
in the time domain (for further clarification refer
http://descanso.jpl.nasa.gov/Monograph/series9/Descanso9_03.pdf).
Theory: It is obviously not AM. It is PM with or without subcarriers
perhaps better explained with the following equations-
    mod_phase = cn*B*sin(2*pi*FREQ_sc*t+PH_sc);
    signal = sin(2*pi*FREQ_c*t + PH_c + mod_phase);

FREQ_c is the frequency of the main carrier
FREQ_sc is the frequency of 1 subcarrier
cn is the data +1 or -1
B is the modulation index
PH_c and PH_sc are the initial constant phases
For a system without subcarrier, one needs to remove the
"sin(2*pi*FREQ_sc*t+PH_sc)" term from mod_phase.

Now the thing is the estimator I have talked about in the paragraph above
works well for a system which does not use subcarriers for data. However
for a system with subcarriers (like in the equations above), I haven't
found a proper estimation scheme. Theoretically, the signal can be
decomposed into Bessel components, each of whose value depends only on the
modulation index. Hence, if i can estimate the value of a Bessel component
like J0 or J1, i can then know the value of the modulation index directly
from a lookup table. The big obstacle is to find the Bessel components
without FFT. Is that possible?

mayanksharma wrote:

Oh, my!

> Ok. I am new to dsprelated, and did not expect such quick responses! Thank
> you all for taking out your time, although it seems I might have skipped
> some details. So here goes:
> Context: The goal is to use blind estimation to estimate modulation index
> for a PM signal (i.e. signal modulated using Phase Modulation explained in
> equations below), with the aim of avoiding a complex FFT operation for the
> same. Basically an operation which makes the task of implementation in an
> FPGA easier and perhaps faster. This application is to be used for deep
> space or satellite communications. I'd like to remind that it's not OFDM
> that we use here.I have found an estimator which can work for a PM signal
> modulated without a subcarrier, which does not require the knowledge of the
> carrier frequency as well. The estimation is purely data-aided and done so
> in the time domain (for further clarification refer
> http://descanso.jpl.nasa.gov/Monograph/series9/Descanso9_03.pdf).
> Theory: It is obviously not AM. It is PM with or without subcarriers
> perhaps better explained with the following equations-
>     mod_phase = cn*B*sin(2*pi*FREQ_sc*t+PH_sc);
>     signal = sin(2*pi*FREQ_c*t + PH_c + mod_phase);
> 
> FREQ_c is the frequency of the main carrier
> FREQ_sc is the frequency of 1 subcarrier
> cn is the data +1 or -1
> B is the modulation index

What definition of modulation index do you use for PM?

> PH_c and PH_sc are the initial constant phases
> For a system without subcarrier, one needs to remove the
> "sin(2*pi*FREQ_sc*t+PH_sc)" term from mod_phase.
> 
> Now the thing is the estimator I have talked about in the paragraph above
> works well for a system which does not use subcarriers for data. However
> for a system with subcarriers (like in the equations above), I haven't
> found a proper estimation scheme. Theoretically, the signal can be
> decomposed into Bessel components, each of whose value depends only on the
> modulation index. Hence, if i can estimate the value of a Bessel component
> like J0 or J1, i can then know the value of the modulation index directly
> from a lookup table. The big obstacle is to find the Bessel components
> without FFT. Is that possible?

I think it is a mistake to talk about "Bessel components". What you have 
are sidebands whose amplitudes are determined by the superposition of 
the Bessel functions of the equivalent FM modulation indices /of each of 
the component modulating frequencies/. More than one modulationg 
frequency tends to make an intractable asymmetric mess.

Jerry
-- 
Engineering is the art of making what you want from things you can get.