Re: [Discuss-gnuradio] how does Doppler shift increment in flat fading channel GNU radio

[Kelvin Augustin]

Hi Bastian,

 

The Doppler Frequency per sinusoid is distributed according to that U-shaped thing you see everywhere.

Now, instead of rolling the dice once during initialisation and sticking to that Doppler frequency forever, this implementation is doing something like a random walk through the Doppler Spectrum.

alpha_n is going back and forth between -pi and pi (plus some initial phase offset), so fDTs * cos(alpha_n), the normalised Doppler Frequency, follows this U-distribution.

Exactly. The dynamic channel in GNURadio models the Doppler spectrum accurately.

What I don’t get (and what I asked in the other thread) is why this is multiplied with d_m. I think that, per sample, the current Doppler Frequency should be used to calculate an incremental angle to the previous value.

To answer this, I would consider of the correspondence (via a Fourier Transform) of a Doppler shift in the time domain; A shift in frequency corresponds to a "time" dependant phase shift in the time domain. Thus a Doppler shift of Fd in the time domain corresponds to exp(j*2*pi*Fd*t). And since Dynamic channel model(flat_fader to be precise) in GNURadio models the Doppler in the time domain, the d_m could be a way to model the time.

I would also ask a supplementing question that I am having problems understanding. I would expect the Doppler shift to be modelled by a complex exponential(cos[2*pi*Fd*t*cos(alpha)] + i sin [2*pi*Fd*t*cos(alpha)]) which corroborates what we know from the Fourier correspondence of a Doppler shift. Why then, in the Dynamic channel model in GNURadio (flat_fader to be precise), the Doppler is modelled by (cos[2*pi*Fd*t*cos(alpha)] + i cos [2*pi*Fd*t*sin(alpha)]) ?? I.e why is the imaginary part a cos ? Any hints?
 

On 22 Feb 2016, at 06:41, Nasi <address@hidden> wrote:

Hello,

The question is about how does the given Doppler shift progress, or how is the Doppler induced phase shift implemented.

I select a simple frequency selective fading block and feed in it some gr_complex(1, 0) values. For simplicity I run one fader (num of sinusoids).
in file:
https://github.com/osh/gnuradio.old/blob/master/gr-channels/lib/flat_fader_impl.cc 
in the code below,

#elif FASTSINCOS == 2
	float s_i = scale_sin*d_table.cos(2*M_PI*d_fDTs*d_m*d_table.cos(alpha_n)+d_psi[n+1]);
	float s_q = scale_sin*d_table.cos(2*M_PI*d_fDTs*d_m*d_table.sin(alpha_n)+d_phi[n+1]);
	#else

 d_m shows that the Doppler shift must progress sequencially. However, the value of "2*M_PI*d_fDTs*d_m*d_table.cos(alpha_n)" as a whole, produces floating point numbers which results in kind of random values out of d_table.cos() function in file
https://github.com/osh/gnuradio.old/blob/master/gr-channels/lib/sincostable.h

Some more explanation:
the value: 2*M_PI*d_fDTs*d_m*d_table.cos(alpha_n) gets in as x below (in file .../lib/sincostable.h)
(((int)(x*d_scale)) + d_sz) % d_sz; - this is a random integer value (may be not, can you please help me with that?)
therefore it returns a random cos value as: return d_cos[idx];

The issue arises when that floating point values inside cos() function is converted to integers as given above.

Now, my question is, did you do that random phase shift/Doppler shift on purpose? If yes, what is the reasoning behind that.
As far as I know, the Doppler shift should be somehow linear progressive.

--
NE

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Ph.D. scholar: Kelvin Chelli
OFDM based wireless systems
Telecommunications Lab, Uni Saarland
Campus C6 3, Room  10.07
66123 Saarbrücken, Germany.