# A fundamental question on LTE/OFDM sampling rates

Started by September 2, 2011
```Hi,

I've a few fundamental question. I was going through the LTE specs.
It said the fundamental symbol duration was .67us

1. If 30.72Mhz is the sampling rate (15khz subcarrier spacing*2048 sub
carriers) , how does LTE support bandwidths greater than 15.36, the spec
specifies bandwidths upto 20Mhz. Even if I assume only 100 RBs are used, it
still leaves me with a bandwidth of 18 Mhz. Doesn't this violate nyquist
sampling theorem ?

2.How would one define sampling rate in case of a system that uses OFDM as
the modulation scheme ? Is merely carrier spacing * number of carriers or
is it the reciprocal of (symbol duration divided by number of carriers).
How can i express or derive this mathematically ?

```
```Hi,

it's complex-valued samples, the Nyquist bandwidth equals your sampling
rate. In other words, there is no 1/2 factor, as in real-valued sampling.
Your IFFT output "controls" a bandwidth of 30.72 MHz, if you use 2048k at
30.72Msps. Of that, a bandwidth of 18 MHz is used, 2 M are guard bands.

You can sample your OFDM signal at any rate you like.
For example, if I use a 2049-size FFT, I'll get one extra sample over the
body length.

BTW I dug out some old piece of code that's supposed to generate an OFDM
signal with raised-cosine windowing, maybe it's useful.
http://www.dsprelated.com/blogimages/MarkusNentwig/comp.dsp/generateGenericOFDM.m
Once you delete away the first and last lines, there isn't any toolbox
magic etc, just basic vector manipulation.

```
```>> Of that, a bandwidth of 18 MHz is used, 2 M are guard bands.

.. and in an implementation we need the remaining 10.72 MHz for the
low-pass filter that reconstructs a continuous-time waveform (anti-aliasing
filter).

```
```please i'd like to ask u about choice of band with when we use 1.4 ; 3; 5; 10; 15 ;20. I'd like to now the advantages an disadvantages of bandwidth choice.
thank you
```
```On Thu, 10 Jan 2013 03:38:50 -0800 (PST), mensimedmehdi@gmail.com
wrote:

>please i'd like to ask u about choice of band with when we use 1.4 ; 3; 5; 10; 15 ;20. I'd like to now the advantages an disadvantages of bandwidth choice.
>thank you

Wider bandwidth has higher throughput potential, but results in
decreased range for the same transmit power and occupies more spectrum
(so fewer channels are available).

Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com
```