In Part 2 of this blog series, we start by looking into the receiver part of an orthogonal frequency-division multiplexing (OFDM) transceiver. First, let’s recall the conclusion from Part 1: OFDM is a sum of windowed-modulated exponential functions. We can write this statement in the form of a formula:

So now, at the receiver, how do we separate one subcarrier from the other for symbol extraction? We simply multiply the received signal y (t) by the conjugate of the subcarrier that we want to extract. By the fact that the subcarriers are orthogonal between each other, the conjugate of the subcarrier  is orthogonal to the other subcarriers, except  (and so on for the other subcarriers). But again, the orthogonality holds in a specific interval of length Tsym, which means that at the receiver, we have a prototype filter pR (t) that is also a rectangular pulse of length Tsym:

This block diagram is valid for both OFDM and FBMC and the difference between both lies in the choice of the prototype filters pT (t) and pR (t) and the symbol spacing T. It’s now time to bring the new variable T into the discussion. From the beginning, we worked with Tsym which is the length of an OFDM symbol. It’s a fact that in practice, the actual length of an OFDM symbol is T = Tsym Tcp , where Tcp is the length of the cyclic prefix. That brings us to the point that OFDM doesn’t have the maximum bandwidth efficiency in practice, as the bandwidth efficiency of OFDM is

To summarize, OFDM has a lot of advantages but its prototype filters aren’t optimal for narrow band multicarrier communications and, in practice, it doesn’t provide the maximum bandwidth efficiency. The goal of FBMC is to solve both problems.

In FBMC, a set of parallel data symbols are transmitted through a bank of modulated filters, just like in OFDM. The main difference lays in the choice of the prototype filters. However, this selection depends on the modulation technique. For example, some FBMC systems are designed to transmit complex-valued (i.e., QAM) data symbols and others are limited real-valued data symbols. Both of these methods have their roots in the early development of digital communication systems, before OFDM.

FBMC systems are still an active research subject and there are many ways to implement them. In

[1], one can find detailed tutorials on some FBMC systems. Another good implementation that I found is the PHYDYAS (PHYsical layer for DYnamic AccesS and cognitive radio) project (http://www.ict-phydyas.org/). Their implementation is very interesting, with the goal of proposing an FBMC physical layer that is more efficient than OFDM and which includes FFT and IFFT. This is interesting since they were able to ‘upgrade’ their original OFDM PHY with FBMC and make it more suited for dynamic spectrum access and cognitive radio. Also, the fact that they use FFT and IFFT makes their approach easy to implement.

In conclusion, FBMC is one of the potential candidates for PHY layer technology in 5G. However, other technologies are also being investigated like Generalized Frequency Division Multiplexing (GFDM) as potential candidate for 5G. 5GNOW is currently investigating this technology and even provides some MATLAB code for comparison with OFDM. Check out their website at www.5gnow.eu.

## Reference

[1] Behrouz Farhang-Boroujney, “OFDM Versus Filter Bank Multicarrier”, IEEE Signal Processing Magazine, May 2011, p. 92- 112.