Introduction/Abstract
Faster than Nyquist (FTN) signaling is a signaling scheme alternative to the current industry standard which accelerates data transfer while keeping all other properties of the signal the same. There are several advantages to an FTN system, but perhaps the most notable is that the capacity (the maximum rate at which communication can be performed reliably) of an FTN channel is greater than the capacity of other commonly used channels. Unfortunately, there is no such thing as a free lunch in engineering, meaning trade-offs must be made to achieve this performance. The paragraphs that follow will discuss in some detail the current state of the art followed by an introduction to FTN signaling, how it improves on the current technology, and the trade-offs made related to the current standards to achieve these improvements.
This document serves as a primer for a project a friend and I are currently in the middle of where we seek to design one of these FTN systems. While there is one currently existing for Software Defined Radios (SDRs) [2], we are interested in a more analog approach. My responsibilities will primarily be designing the physical system whereas my friend will lean towards creating simulations (at the datalink layer, not the physical layer). Updates on this project will be posted about in a similar level of detail or finer as it progresses.
Current Practices in Communications
Figure 1 below shows the most basic model of communications we use today. As can be seen, the basic structure of a system is intuitive/straightforward. We have some information source generating a message, which we then send out over some medium called the channel. Eventually, the information reaches the receiver, who then delivers the message to the ultimate destination.
A good example of this model in action is when we talk with one another. If I am talking with a friend about something, we can think of our interaction as a communication system where my brain is the information source, my vocal cords and mouth are the transmitter, the air is the channel, my friend’s ears are the receiver, and their brain is the destination.
Continuing the analogy, when we speak, it is obvious that if I could somehow speak multiple words at the same time, then it would be harder for us to communicate. Similarly, in a communication system, each bit of information we send should be sent such that the symbols representing that information do not interfere with one another. To put a technical term to this idea, we would say that we want the symbols to be “orthogonal” (or at right angles) to one another. Perhaps at this point it seems surprising that geometry is suddenly involved. For now, we won’t worry about the underlying mathematics and move forward with our current understanding.
We incorporate this principle into a communication systems design by sending pulses at Nyquist Rate, or transmitting a “nice” pulse of some bandwidth W Hz every T=1/(2W) seconds or longer. We will discuss in a later blog what constitutes “nice”. For now, I want to briefly provide a very high-level understanding of what bandwidth is and its relationship to the pulse.
To get an intuitive understanding of bandwidth, we can continue our analogy of speaking with a friend. If I speak slowly with my friend, it doesn’t require all that much of their attention. If I speak at a normal speed, it requires a normal amount of attention. Finally, if I speak very quickly, they must spend a lot of their attention to keep pace with what I’m saying. The attention of my friend represents bandwidth and the speed I speak at represents the data rate. In other words, higher data rates require higher bandwidths. To connect this back to the statement in the previous paragraph, a higher data rate also means that the width of the symbols representing the data need to be shorter. So, a shorter symbol time requires a higher bandwidth. Feel free to plug some numbers into the equations to see how things change. Once we put all of these concepts together, we have a start for principles to follow for communication systems. We design the transmitter and receiver with these assumptions in mind, allowing for a simple communication system free of interference (disregarding noise). Of course, things are not this simple in practice. As we follow the FTN system project, we will discuss many things which add complexity to the system and incorporate those complexities in the designs
A Brief Aside
This part of the blog is tangential to the main content being presented, but I want to include a brief aside on the design process because I think it will resonate or serve as much-needed advice for current engineers. If you are an aspiring engineer, it could also act as guideline for you. As previously stated, we are interested in starting from basics and building up complexity as we go through the project. This practice is, in general, the best way to approach a design problem. We have all jumped right into a project, guns blazing, with all its complexities already in mind in the past. We also have all (or at least most of us) come to realize that this is not usually the best way to go about the design process. That approach often leads to confusion and unnecessarily complicated solutions. Instead, we start at the most fundamental level we can and work with a trivial “toy” problem, adding or removing constraints one at a time. This allows us to work on problems which more and more closely resemble the problem we are trying to solve until, eventually, we do solve it. In doing the design process this way, we often find that solving this series of “toy” problems leads to a solution far more elegant than previously thought. It is in this spirit that I do all my design work, and I encourage the reader to take on a similar approach themselves.
FTN Signaling
In light of our aside, the extra step in complexity FTN signaling brings to a communication system is lifting our “no interference” constraint. We do this by maintaining the same bandwidth of W Hz (and thus the same symbol time), but now send a pulse every TFTN = τT seconds. τ here is a real number between 0 and 1 and serves to accelerate the signaling rate (how often we send a pulse). Figures 2 and 3 below shows graphically what happens to some message waveform with rectangular pulses
As can be seen, with the range of τ we are given, our symbols/pulses start to interfere with one another (which will increase the overall system complexity), but allow us to communicate faster. In Figure 2, with a τ of 0.8, the FTN signal ends a little after the 2s mark, and adjacent symbols add when they overlap. For the standard system, the message finishes transmitting around 2.5s.
If we want to continue our analogy from earlier, we can think of τ as a factor that represents how much faster we speak when we use contractions. For example, if we wanted to say the words “do not” to our friend, we can say them separately or we could contract the words together and say “don’t” instead. The FTN system takes this contraction idea to the extreme and meshes all of the words in the sentence together into one giant contraction. Admittedly, our analogy starts to break down here as we don’t generally speak like that, but I believe the principle of the idea is apparent.
This idea gained a lot of traction resulting from a paper written by J.E. Mazo in 1975 [1]. The question Mazo asked (and the question that we want to ask right now) is if it is even worth it to do something like this.
As it turns out, it can be worth it. Mazo’s seminal work showed that sacrificing orthogonality does not necessarily degrade the system performance (the metric being bit error rate). In fact, taking values of τ from 1 down to around 0.8 were shown to not sacrifice performance at all. Later work revealed that the channel capacity, the maximum rate at which communication can be performed reliably, of the FTN scheme is greater than the capacity of the Nyquist rate scheme. So, if our primary design aspect of interest is having the fastest possible communication rate, it could be worth it to design an FTN communication system.
The benefits of an FTN system, however, are not limited to how fast you can communicate. We can also find benefits in terms of bit error rate (BER) performance and bandwidth.
When achieving the optimal performance of a communication system in terms of BER, we have to take a brief detour into a field of communications called Coding Theory. In a nutshell, Coding Theory is the study of coming up with ways to add redundancy to your messages with the goal of achieving the smallest amount of bit errors possible at the receiver with the smallest amount of overhead (extra bits) added to the message. Luckily for us, we can apply Coding Theory to FTN systems in the exact same way we do for Nyquist rate systems. So, a clever thing we can do is use the same code that we use in the currently existing technology, but add on more redundancy bits to make the overall message transmission time the same as the Nyquist rate system. To give a brief example, if τ = 0.9, the overall transmission time of an FTN system is 90% of a Nyquist rate system. We could either take that shortened transmission time as is, or we can fill that extra 10% with more redundancy bits, communicating information at the same speed, but doing so more reliably. Additionally, if we are careful about it, we may be able to achieve both a faster overall transmission time as well as a better BER at the same time. This goal, however, is something we’ll have to tackle way down the line due to the sheer number of other things we must do first and its difficulty.
As far as advantages concerning bandwidth go, there are two: one is resistance to noise and the other is spectral efficiency. Noise exists at all frequencies, but we only care about noise present where our signal is present (i.e. in our band). So, having a wider bandwidth means our signal can be affected more by noise. This can be a problem if we want to transmit data faster in a Nyquist rate system, since smaller pulse widths would necessitate larger bandwidths. For FTN systems, though, we can decrease that overall transmission time, but keep that same bandwidth. This last point is relevant to spectral efficiency as well. An intuitive, albeit loose, way to think about it is that we are getting more than 1 symbol in any given symbol time due to the packing of the symbols, making us more efficient within our band.
As mentioned in the intro, these advantages are not free. We have to trade these benefits off with increased complexity in the communication system and more processing time (in the form of more mathematical operations done by the receiver) to remove the effects of the interference on received signals.
A Final Design-Related Note
A lot of communication systems won’t need this signaling scheme, and that determination is made based on a system’s requirements. For example, when dealing with a basic hobby project where everything is wired and speed isn’t much of a priority, it is not worth it to implement an FTN communication system; it adds on way too much complexity for a design that doesn’t need it. An FTN system could find use, however, when dealing with something cutting-edge like the 5G standard. Each subsequent generation of the wireless cellular network demands faster and more reliable communication, so a FTN signaling scheme (at least at face value) is a good way to achieve those ends. Having done research in my undergrad on the FTN scheme (with a paper hopefully to be published), I do believe that next generation wireless networks like 6G and beyond or the internet are likely to be first place these kinds of systems go, if they are implemented at all.
Thank you for reading! If you have any thoughts please feel free to share them below.
Acknowledgements
Thanks to a friend of mine, Xander Good, for helping in proofreading this blog to better ensure this work can be understood by a general audience. His website can be found here:
https://goodxander.wordpress.com
I’d also like to thank another one of my friends and partner on this project, Morrison, who is working on simulations and design work.
References
[1] J. E. Mazo, “Faster-than-nyquist signaling,” in The Bell System Technical Journal, vol. 54, no. 8, pp. 1451-1462, Oct. 1975, doi: 10.1002/j.1538-7305.1975.tb02043.x.
[2] G. Dzhezyan, M. Kulhandjian, H. Kulhandjian, “Implementation of Faster-than- Nyquist Signaling using Software Defined Radios,” in Proc. of the GNU Radio Conference (GRCon), Washington, DC, Sept. 2022.
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