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Re: [Discuss-gnuradio] OFDM TX/RX


From: CEL
Subject: Re: [Discuss-gnuradio] OFDM TX/RX
Date: Tue, 27 Mar 2018 09:09:40 +0000

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

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