Today, we’ll talk about SC-FDMA, or *single-carrier frequency-division multiple access*. But first let’s review some basic concepts of OFDM that will help you understand the why and how of SC-FDMA.

As discussed in my previous post, in an OFDM system the data to be transmitted, X(0), X(1), … X(N-1), is first modulated, typically using quadrature phase shift keying (QPSK) or a quadrature amplitude modulation (QAM). The resulting data is then transformed using an N-point inverse fast Fourier transform (IFFT), and the resulting samples, x(0), x(1), …, x(N-1), are transmitted over the air.

Mathematically, a single sample, x(k), can be described using the following equation:

It’s interesting to note that for a single sample in time, the signal being transmitted is composed of the summation of all symbols, each multiplied by a phasor term. With a little bit of mathematics, it’s easy to demonstrate that this summation leads to a *peak-to-average power ratio* (PAPR) that’s proportional to N, the number of subcarriers. A typical OFDM system uses hundreds or even thousands of subcarriers, which leads to a system with a very high PAPR. This is known to be the major drawback of OFDM, imposing many challenges on the power amplifier (PA) designer.

Real PAs are linear only for a small operating range. When the input signal becomes too strong, a PA enters into its saturation region, where the output power is no longer proportional to the input level. This means that when a peak arises, it causes distortion. This distortion breaks the orthogonality between the subcarriers, causing inter-carrier interference (ICI).

The idea of SC-FDMA is to add an M-point fast Fourier transform block before the N-point inverse fast Fourier transform of the OFDM system. Usually, M is chosen to be much smaller N, so that the FFT only partially cancels the final IFFT, resulting in a single carrier type of signal with, obviously, a lower PAPR.

## Single Carrier, Frequency Domain Equalizer (SC-FDE) Systems

In the special case where M is equal to N, the two blocks cancel each other completely and are therefore no longer required in the transmitter, but they’re kept in the receiver to allow the implementation of the frequency domain equalizer. These systems are called SC-FDE.

The structure of the SC-FDMA receiver is similar to the one for OFDMA except that this time, it is a subcarrier demapper block and an M-point IFFT block that are inserted after the N-point FFT.

## Localized and Interleaved SC-FDMA Mappings

There are basically two ways to map the M symbols that are output by the FFT to the input of the IFFT. The first solution, which is called *localized SC-FDMA*, is to use M consecutive subcarriers of the IFFT and zero-pad the other ones. The second option, called d*istributed SC-FDMA*, distributes the subcarriers over the entire bandwidth and again uses zeros for the unused bins. *Interleaved SC-FDMA* is a special case of the distributed version where the subcarriers are evenly distributed over the whole bandwidth. In that case, the separation between each subcarrier is typically equal to the number users.

There are many studies (see References, below) that compare the pros and cons of each mapping method, but we can generally conclude that interleaved SC-FDMA leads to lower PAPR and also naturally benefits from more frequency diversity than localized SC-FDMA. However, by using an intelligent resource allocation that assigns the subcarriers with the best propagation conditions for each terminal, it is possible to achieve better performance using localized SC-FDMA.

The fact that SC-FMDA has a lower PAPR with performance very close to that of OFDMA explains why this scheme has been selected by the 3GPP as the uplink multiple access scheme in LTE. By more efficiently using the power amplifier, LTE terminals are able to increase coverage and reduce their power consumption, which is extremely important in battery powered devices.

**References**

Myung, Hyung G. 2007. “Introduction to Single Carrier FDMA”. 15th European Signal Processing Conference (EUSIPCO). Poznan, Poland. http://www.eurasip.org/Proceedings/Eusipco/Eusipco2007/Papers/d3l-a01.pdf

Surgiewicz, Rafal, Niklas Ström, Amser. Ahmed, Yun. Ai. 2013. “LTE Uplink Transmission Scheme.” Project paper submitted to California State University, Bakersfield. http://www.mehrpouyan.info/Projects/Group%201.pdf

Burcu Hanta. 2009. “SC-FDMA and LTE Uplink Physical Layer Design”. Seminar LTE: Der Mobilfunk der Zukunft, University of Erlangen-Nuremberg, LMK. http://www.lmk.lnt.de/fileadmin/Lehre/Seminar09/Ausarbeitungen/Ausarbeitung_Hanta.pdf