# SC-FDMA vs single carrier signal PAPR

Why is the PAPR of a single user SC-FDMA signal different than the PAPR of a conventional single carrier signal if they both use the same modulation? Aren't they both single carrier signals?

Consider some actual use cases for further insight:

Unmodulated Carrier: The peak to average ratio is 3 dB given the relationship between the rms and peak level of a sine wave.

Unfiltered Single-Carrier BPSK or QPSK: This would be the modulation of rectangular shaped symbols, so would have a 3 dB peak to average ratio just as in the case of an unmodulated carrier. Great for peak-average ratio but terrible for bandwidth constraint. Given we have to share bandwidth efficiently (in terrestrial communications) we don't have this luxury. GPS is an example where the signal can be essentially unfiltered and we have the benefit of power efficiency.

Root-Raised Cosine BPSK or QPSK: This is what is traditionally done but the tighter the filtering (smaller $$\alpha$$ in the filter design) results in more overshoot of the symbol transitions and slower trajectories that may go through the origin resulting in a higher peak-average ratios.

pi/4 QPSK: This modulation changes phase by $$\pi/4$$ between symbols thus avoiding having the slower transitions from filtering from ever going through the origin (Meaning minimizing the lowest instantaneous power in the signal envelope, increasing the average relative to the peak). This modulation is therefore considered for lower power (battery operated) applications since we are able to drive the transmit power amplifier further into saturation meaning higher efficiency.

GMSK: Gaussian Minimum Shift Keying and other constant-envelope modulations have a 0 dB peak-average ratio and offer moderate bandwidth efficiency so are an excellent choice for power efficient (battery operated) applications.

OFDM: To the extent each bin in the FFT representation of an OFDM symbol is independent and in consideration of each other randomly generated, the resulting signal as the summation of multiple independent identically distributed random processes will be well approximated by a Gaussian distribution given the central limit theorem. A Gaussian distribution has a relatively high peak to average ratio, and we need to decide on a significance to establish what is the "peak" (usually on a distortion criteria from clipping anything beyond the established peak). In SC-OFDM we do have some control over the association of the signals in each bin, allowing for lower peak-average ratios than MC-OFDM where each bin can represent a different data source.

SC-FDMA is not actually a single carrier signal. SC-FDMA is sometimes also known as DFT-spread OFDM or DFT-precoded OFDM, which I think is a better name to characterize it. It is still a multi-carrier signal, but with the DFT applied before the OFDM transmission. The DFT spreading helps to reduce PAPR compared to a normal OFDM signal, but that doesn't really make SC-FDMA a conventional single carrier signal, as you have noted.

• In a conventional SC signal every original symbol in time domain is represented by all frequencies in the available signal BW which is not the case for OFDM May 10 '20 at 7:51
• In SC FDMA since the DFT values are used to modulate the sinusoids instead of the original symbols themselves (as in OFDM) we find the same situation like in a conventional SC signal: every original time domain signal is represented by all sinusoids i.e. all available frequencies , so therefore it is also considered to be a SC signal, don't you agree? May 10 '20 at 7:56
• I understand what you are saying, and that is one reason why it is called SC-FDMA with "Single Carrier" as the prefix. But it is different from a conventional single carrier signal. In a conventional single carrier signal, at each time sample, the signal power will be bounded (e.g., within the amplitude A for a normal QPSK). In SC-FDMA, however, when you look at the signal coming out of the IFFT, it can be thought of as the sum of N sinosoids (for N point IFFT), and in the worse case, could all add in phase for a large peak power. May 10 '20 at 11:34
• The difference between OFDMA and SC-FDMA is that the input to the IFFT in the transmitter, is mapping one-to-one with the modulated data symbols, whereas in SC-FDMA, it is coming from multiple data symbols, "mixed" by the DFT. So the distribution of the peak power is not as bad in SC-FDMA as in OFDMA. But still, it is "worse" in SC-FDMA than a conventional single carrier signal. May 10 '20 at 11:37
• I do have one explanation for the lower PAPR in SC-FDMA: May 10 '20 at 18:51