Question on gmsk mod block

GNU Radio
1

Hi,

I noticed that the Gaussian pulse is convolved with a rectangular window
in the GMSK modulator. Why is that so?

Thanks
Achilleas

2

If we need to truncate the Gaussian pulse, there are better windows!

Bob

Anastasopoulos Achilleas wrote:

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3

Anastasopoulos Achilleas wrote:

Hi,

I noticed that the Gaussian pulse is convolved with a rectangular window
in the GMSK modulator. Why is that so?

The pulse is convolved with a rectangular window because the incoming
data is not.

For example, if you wanted to send 1011 and had 4X interpolated data,
the data stream into the gaussian filter would look like:

1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1

however, the input to the block in question is:

1,0,0,0,-1,0,0,0,1,0,0,0,1,0,0,0

It was easier to precombine the zero-order hold with the gaussian filter
by convolving it rather than having 2 separate filters in the real-time
portion of the code.

Matt

4

I guess I am answering my own question here.
Just realized that GMSK is defined with pulses that are
indeed the convolution of Gaussian and square pulses.
What a missnomer…

Achilleas

5

This does not seem right to me:

The instantaneous frequency of GMSK signal is supposed to be:
fi(t)=h sum_k a_k g(t-kT)
where a_k is the symbol (say ±1), g(t) is the Gaussian pulse
T is the symbol interval and h is the modulation index.
In a discertized model with oversampling factor of Q (ie, Ts=T/Q)
this equation becomes:
fi(n Ts)=h sum_k a_k g((n-kQ)Ts)
or in discrete time notation
fi(n)=h sum_k a_k g(n-kQ) = h x(n) conv g(n)
where
x(n) = [a0 0 0 0 a1 0 0 0 a2 0 0 0…]

I don’t see where the need for the rectangular window is.
What am I missing?

Achilleas

6

Anastasopoulos Achilleas schrieb:

Hi,

I noticed that the Gaussian pulse is convolved with a rectangular window
in the GMSK modulator. Why is that so?

Usually you would shape (that is) convolute your pulses with a rectangle
to get nice symbols, as a single spike won’t be detected at the
receiver.
But rectangles produce infinite bandwidth sinc spectra. You really like
to limit your bandwith (and thus save you trouble with other people and
power). This can be achieved by convoluting your (now rectangle) signal
with a Gaussian shape. This is known to achieve maximum bandwidth
efficiency.

Gaussian has an second interpretation/origin: yiu get the same signal
with an optimized phase shift modulation.

Patrick

7

Achilleas A. wrote:

I guess I am answering my own question here.
Just realized that GMSK is defined with pulses that are
indeed the convolution of Gaussian and square pulses.
What a missnomer…

Yeah, I was bothered by that for a while.

Matt