Spreading—A Shannon-Hartley Loophole?

by Ted Myers, Co-founder and CTO of Ingenu (originally posted here)

Quick Refresh

We have asserted textbook style categories for Low-Power, Wide-Area (LPWA) connectivity in 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. In Blog 3:Chirp Spread Spectrum (CSS): The Jell-O of Non-Coherent M-ary Modulation, I confirmed that CSS can be treated more generally as Non Coherent M-ary Modulation (NC-MM).

Spreading, the Love

So, what is “spreading”? From the most generic perspective, it is increasing receive sensitivity (thus, a longer range and more robust link) by reducing the data rate and keeping the same channel bandwidth. That underlined part is very important and represents a potential looming problem: the link data rate is becoming a trickle, and yet that link takes the same amount of valuable spectrum. The result is that the capacity could become vanishingly small. But the capacity does not have to — and therein lays the loophole.

Let’s use what we’ve learned to determine the capacity of a few well-known Low-Power, Wide-Area (LPWA) “spreading-based” connectivity technologies [LoRa™ (CSS) and RPMA®] highlighted in the table below and additionally, a well-marketed Ultra-Narrow Band (UNB) approach used as the Sigfox™ technology for comparison purposes.

Recall from Blog 3: Chirp Spread Spectrum (CSS): The Jell-O of Non-Coherent M-ary Modulation, we introduced the calculation of the individual link spectral efficiency (η) for LoRa. Let’s take that information and insert the Sigfox technology and RPMA for comparison. The Sigfox technology looks great and RPMA looks worse than even the meager spectral efficiency of LoRa. Uh oh…Looks like RPMA is off to a rough start.

But wait, this analysis is far from complete in terms of a capacity calculation. RPMA is a WAN that allows for simultaneous transmission of overlapping waveforms. That is the loophole. Recall that the Shannon-Hartley Theorem is applicable only to a single link.

The result is that for RPMA, there is no capacity benefit for an individual link being extremely spectrally inefficient. RPMA can use extreme variable spreading (or processing gain), result in an extremely sensitive modem (-145 dBm is best in the world), and not be hit with any capacity penalty.

RPMA can demodulate 1,000 signals simultaneously for a couple of fundamental reasons:

  1. Transmit power control is essential. Signals must arrive at the access point at very similar power levels for this multiple access capability to exist.
  2. There must be a mechanism such that the received waveforms can be individually resolved. Any individual waveform may not be correlated with any other waveform, or neither waveform will be resolvable. That is exactly what the RPMA access scheme was designed to do.

RPMA satisfies both of these requirements; LoRa only partially satisfies the second criteria. LoRa signals at different data rates have a chance of both being resolvable which results in incremental capacity benefit (< 30%), not the game-changing 1000x advantage that RPMA enables. Note that RPMA satisfies these requirements without the need for protocol overhead. This is a big differentiator from cellular technologies such as LTE (and the LPWA offshoots like NB-IOT) and I will discuss this in more depth in a future blog.

RPMA is a WAN that allows for simultaneous transmission of overlapping waveforms. That is the loophole. Recall that the Shannon-Hartley Theorem is applicable only to a single link.

As detailed in Appendix A-C of How RPMA Works: The Making of RPMA, there are other significant factors that influence the total amount of data that can be pushed through the spectrum (η_goodput )

  • Amount of Media Access Control (MAC) protocol overhead such as retransmissions and headers.
  • The effect of transmissions that are heard by multiple access points/base stations (known as other cell interference) and the corresponding reduction in capacity.
When you look at spectral efficiency from a multiple access standpoint, which is how these systems operate in the real world, RPMA is well above the competition.

And that’s not all! η_goodput is a per Hertz of bandwidth number, it still needs to be multiplied by the amount of spectrum available!

Since RPMA is at 2.4 GHz where 80 MHz is available, we can use significantly more spectrum than the fractured, regional subGHz bands that the Sigfox technology and LoRa use.

As you can see, RPMA has a massive advantage in the resultant goodput. That means a piece of RPMA network infrastructure (typically on a tower or rooftop) will be capable of servicing orders of magnitude more devices and devices with far greater data needs. We’ll crunch some numbers on this in Blog 5 — The Economics of Receiver Sensitivity and Spectral Efficiency.

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.

One clap, two clap, three clap, forty?

By clapping more or less, you can signal to us which stories really stand out.