Chirp Spread Spectrum: The Jell-O of Non-Coherent M-ary Modulation

We have asserted textbook style categories for Low-Power, Wide-Area (LPWA) connectivity Blog 1: Categories of LPWA Modulation Schemes.  Then we went back to basics to get some framework and vocabulary in place to discuss these various schemes in Blog 2: Back to Basics – The Shannon-Hartley Theorem, where we introduced the critical concepts of spectral efficiency (η), Eb/No, and how a point of diminishing returns can be reached in the quest to reach the Shannon Limit.

Based on this framework, what I would like to discuss here is why Chirp Spread Spectrum (CSS) can be treated more generically as Non-Coherent M-ary Modulation (NC-MM). The title of this blog likely makes you ask what could CSS possibly have to do with Jell-O?  With brilliant marketing, Jell-O has eclipsed the more generic terminology of “gelatin” defined as “protein obtained by boiling skin, tendons, ligaments, and/or bones with water.”  Non-Coherent M-ary Modulation (NC-MM) is analogous to “gelatin”; LoRa™(CSS) is analogous to “Jell-O”.  It is actually a compliment to the marketing around LoRa (CSS). As you can imagine, if you want to study the science behind Jell-O, you would have better luck starting with “gelatin”.  The same is true with understanding LoRa(CSS).

But first, we must justify why we’re lumping CSS into the NC-MM category.  There are two parts to the argument:

1. It’s the same math. The mathematical operations for demodulation are identical to other well-known NC-MM waveforms – particularly M-ary FSK.
2. If it looks like a duck, swims like a duck… CSS has the same performance as other NC-MM waveforms (again particularly M-ary FSK), and that is further proof that it’s best to treat CSS more generically as NC-MM.

I will back up the two arguments below.

It’s the Same Math

Please take a look at the figure below – it is the demodulation engine of 2-ary FSK.  If you added M-2 more elements, this could be turned into a demodulation engine for M-ary FSK.  And, most critically, if the set of waveforms in the figure Φ are sinusoids, it is an FSK demodulator, and if Φ is an orthogonal set of chirp waveforms, it’s CSS.  As long as the set of waveforms Φ are an orthogonal set, the performance of this demodulator will be 100% identical regardless of the particular orthogonal set Φ.

If it Looks Like a Duck, Swims Like a Duck…

Beware the straw man argument! Taking a look at the document entitled “LoRa Modulation Basics”, they do a comparison of the LoRa modulation (also known as CSS) against FSK and make the claim of an impressive sensitivity improvement of 15 dB for the SF = 12 LoRa mode over FSK (There is an obvious typo in the equivalent bit rate column in SFs 6 through 9 where the data rate is expressed in b/s as opposed to the stated kb/s.)

First, we need to talk about the relationship between SF and spectral efficiency.  For un-coded Non-Coherent M-ary Modulation (NC-MM) the expression for η = (SF)2^-SF (in other words a non-coherent symbol yields SF bits of information and that non-coherent symbol is of duration 2^SF.)    If channel coding as added into the mix (like in the LoRa waveform), this expression becomes η = R(SF)2^-SF where R is the code rate (typically rate ½).

On face value, that makes the claim that the math is the same rather dubious.   However, as discussed in Blog 2: Back to Basics – The Shannon-Hartley Theorem, there are several reasons why similar modulations may achieve different sensitivity.

• Increased data rate means reduced receive sensitivity even with the same spectral efficiency (η).
• Increased spectral efficiency means reduced Eb/No which reduces sensitivity.
• Almost all modern communication theory approaches include channel coding. An apples-to-apples comparison would be consistent relative to whether channel coding was implemented.  A very popular and effective channel coding is convolutional encoding coupled with a Viterbi decoder (invented and named after the same individual that is on our advisory board).

As it turns out, relatively higher data rate, spectrally efficient, un-coded 2-ary FSK is fairly easy to beat up on in terms of sensitivity.  A more accurate comparison point would be the coded 7-ary FSK that a company called Sensus uses.  The Sensus flavor of FSK is more of an apples-to-apples comparison because 7-ary FSK has a lower spectrally efficiency (η) which allows for better Eb/No.

Thus, from a fundamental technology viewpoint, the well-marketed LoRa (CSS) is really no different than the Sensus 7-FSK approach that has been around in the utility space for years. The Sensus technology is known to be very low capacity, typically appropriate for meter billing reads only, and requiring licensed spectrum to operate robustly. The Sensus technology is certainly not a WAN as we define it.       

In the table above, notice many of the LoRa modes have η << 0.01.  Is that bad in terms of capacity?  Not necessarily, is the general answer.  What’s not explored in the Shannon-Hartley theorem is the ability to send simultaneous links over the same bandwidth.  That is potentially a bit of a “loophole” in the theory. Does LoRa leverage this “loophole”?  What about RPMA?  I’ll explore that in more detail in Blog 4: “Spreading” – A Shannon-Hartley Loophole?.

And finally, I’ll get back into the real world and test whether this discussion is even useful in Blog 5: The Economics of Receiver Sensitivity and Spectral Efficiency to attempt to quantify the commercial value of that which is discussed on these blogs.

At any point, if you’re interested in a more in-depth treatment of these topics, please download, How RPMA Works:  The Making of RPMA.