Re: [Discuss-gnuradio] OFDM TX/RX

CCDF (Complementary Cumulative Distribution Function) is often used to show PAPR probability. Here's what the GNU Radio DVB-T2 transmitter looks like at 32K (27841 active) carriers with an without tone reservation PAPR reduction.

Ron

On 03/27/2018 02:09 AM, Müller, Marcus (CEL) wrote:

On Fri, 2018-03-23 at 14:21 -0700, Martin Braun wrote:  

If you've  increased the number of carriers, PAPR also goes up (a bit).  

  Yep, by the same factor as you increase the number of carriers (proof  idea: time-symbol with worst PAPR is the discrete dirac over the vector  of FFT length N. That has a PAPR of N/1 = N if freq domain samples were  amplitude-limited to 1.)    The probability to hit a PAPR that bad is, however, limited.  Considering an M-PSK modulation on the N subcarriers. Then there's a  total of M^N possible time-domain OFDM symbols, but only M·N of these  are worst-PAPR, so  P(worst PAPR for N carriers) = M·N/M^N = N / M^(N-1)  assuming equally likely symbols. Since M^N pretty certainly grows  faster than N, your likelihood of ending up in the "worst PAPR"  scenario actually drops with N.    The story looks a bit different if you're not interested in the worst-  PAPR-symbol, but in all symbols that have a PAPR worse than some  threshold, e.g. 20dB. Especially for LTE, there's a lot of  simulative/monte carlo PAPR>threshold curves, as things like trading  clipping for amplifier efficiency plays a very commercially relevant  role there.    Best regards,    Marcus