Re: [Discuss-gnuradio] Changing channel width and its relation with interpolation/decimation rate and bit rate

[Anand Prabhu Subramanian]

Dear Brain,

Thank you very much for the reply. I didnt get this point.

> GMSK only rotates
> ~pi/4 for every bit, so +/-(symbol_rate/2) ends up being your
> bandwidth.

Can you please explain it a little bit. I am sorry my DSP background
is very less. I am still learning. Thanks for your help.

-Anand
PhD Candidate,
Wireless Networking and Simulations Lab,
Stony Brook University

On Wed, Sep 3, 2008 at 5:27 PM, Brian Padalino <address@hidden> wrote:
> On Wed, Sep 3, 2008 at 5:12 PM, Anand Prabhu Subramanian
> <address@hidden> wrote:
>> Folks,
>>
>>  I am trying to change the channel width used for a transmission using
>> the benchmark_tx.py program. I use the default modulation scheme
>> (gmsk) and on the receive side, I am running the usrp_fft.py to see
>> the spectrum and understand how wide the channel is used.
>>
>> If I use an interpolation rate of 128, I see a channel width of 500kHz
>> showing high energy in the spectrum. Similarly, if I change it to 64,
>> I see about 1MHz occupied. I read in one of the docs that the
>> interpolation rate could be varied from [4, 512] and it should be a
>> multiple of 4. I tried it but I was able to vary only from 16 to 512.
>> I notice the channel width = 64MHz/interpolation rate. Please correct
>> me if I am wrong. The bits/symbol always seems to be 1, so if I use a
>> 500KHz channel, the bit rate is set to 500Kbps.
>>
>> On the receive side, if use the benchmark_rx.py, a decimation rate of
>> 64 corresponds to 500Kbps bitrate while on the transmit side an
>> interpolation rate of 128 corresponds to 500kbps. Also, if I fix the
>> bitrate to 500kbps, I do not see the relation channel width =
>> 64Mhz/interpolation rate to hold. Channel width seems to be 500kHz for
>> different interpolation rates.
>>
>> It would be very helpful if someone can help me understand the
>> relationship between channel width, bit rate and the
>> interpolation/decimation rates. I want to be able tune the channel
>> width for each transmission dynamically by playing with these
>> parameters. Thanks a lot for your time and consideration.
>
> You're close.  The USRP always transmits samples at a rate of 128Msps
> (Mega-samples/second).  The USRP samples at 64Msps.  GMSK has a
> spectral efficiency of 1 bit/sec/Hz.  At 1 sample/symbol and an
> interpolation rate of 128, approximately 1MHz worth of bandwidth is
> used.  If you are running at 2 samples/symbol, you are running at
> 500kHz worth of bandwidth.
>
> Working through the math for TX, you come up with 128Msps / 128
> (interpolation rate) / 2 samples/symbol = 500ksps (kilosymbols/sec).
>
> On the receive side, just work in that samples are at 64Msps instead of 128.
>
> The actual bandwidth of your signal is determined by the modulation
> type and the type of filtering done beforehand.  GMSK only rotates
> ~pi/4 for every bit, so +/-(symbol_rate/2) ends up being your
> bandwidth.  CPM is all about trajectory, but that's a little
> off-topic.
>
> Hope this was helpful.
>
> Brian
>