xG's Misleading WiFi Comparison

One of xG's demonstrations of xMax was to send digital video over a short (100 foot) path using only 300 nanowatts of power. They said this was up to 3 million times less power than 802.11 WiFi.

This is an extremely misleading statement. The fact is that on xG's controlled and highly benign test link, WiFi could be adjusted to operate with the same low power, or even less. xG is implying that xMax represents a breakthrough in modulation and coding that requires vastly smaller amounts of transmitter power. And this is simply untrue.

Most WiFi units do not use automatic transmitter power control; they transmit a constant, relatively high power level (see footnote 1) to provide "link margin" to maximize range, penetrate walls and diffract around obstacles. This means that they often operate with much more power than required. 802.11 does automatically vary its data rate according to the received signal-to-noise ratio, with 802.11g ranging between 1 Mb/s and 54 Mb/s, and this can be seen as another form of automatic transmitter power control. But this only covers a 21 dB range (see footnote 2), and real-world links vary over a much larger range.

Although the lack of automatic transmitter power control is a definite 802.11 drawback, it certainly isn't the fault of its modulation and coding schemes.

802.11g Link Budget

In this section I will compute the link budget for 802.11 over the same link that xG used for its xMax test to find the power that 802.11 would require for the same data rate. Although 802.11b/g WiFi operates on 2.4 GHz, to give an apples-apples comparison I will perform the calculations for the 902-928 MHz frequency band that xMax uses.

xG's reports do not include all of the test parameters, particularly the antennas, but we can make some reasonable estimates that actually bias the calculation in favor of xMax.

WiFi equipment performance varies by manufacturer, but we can use a representative example: the Ruckus Wireless 802.11b/g WiFi transceivers. They specify a receive sensitivity of -96 dBm for the 6 Mb/s speed of 802.11g. This is the closest 802.11g speed that exceeds the specified 3.7 Mb/s speed of the xG xMax radio. Lower speeds are available in the 802.11b mode set, but since 802.11g uses convolutional error control coding while 802.11b does not, most of the 802.11b speeds require as much or more power as 802.11g's 6 Mb/s speed even though they're slower.

The path loss between two isotropic antennas is

path_loss(db) = 20log10(4 π d/λ), where
d = distance
λ = wavelength in same units as distance
100 feet is about 30 meters, and the wavelength of 915 MHz (the center of the 902-928 MHz band) is 32.8 cm. The path loss is therefore
20log10(4 π 30 / .328)
= 61.2 dB
The required transmitter power over a 30 meter path between isotropic antennas to give a received power of -96 dBm is therefore
Ptx(db) = -96 dBm + 61.2 dB
= -34.8 dBm, or about 331 nanowatts.
This is almost exactly the same as xG's much-touted figure of 300 nanowatts -- and for nearly twice the data rate (6 Mb/s vs 3.7 Mb/s). If we normalize the WiFi data rate to xMax's speed, the WiFi power drops to only 204 nanowatts.

Furthermore, isotropic antennas do not exist; they are just a benchmark for comparison. All real antennas have gain over isotropic, so while we don't know what antennas xG used for their test, their received signal strength was undoubtedly higher than we've assumed here for WiFi. So it's reasonable to conclude that 802.11g would require even less than 204 nW to carry data over the same link and at the same rate as xMax.

Conclusion

This is no surprise to those familiar with digital modulation and coding. The Shannon Channel Capacity Theorem places a firm upper limit on the error-free data rate that can be achieved over a noisy, bandwidth-limited radio channel (as all radio channels are). The current state of the art, Turbo coding, is only 0.5 dB away from the Shannon limit, that is, Turbo coding can already achieve 89% of the absolute limit. Even though 802.11g uses an older code (k=7 convolutional coding with Viterbi decoding) that's perhaps 5 dB from the Shannon limit, there simply isn't much room for additional improvement, and there is no chance for the kind of dramatic breakthroughs implied by xG's statement that xMax is 3,000,000 times more power efficient than WiFi. Such numbers can be achieved only in artificial comparisons to systems that are operated with extreme inefficiency.

Footnote 1

3,000,000 times 300 nanowatts is 900 mW. Apparently xG assumes that all WiFi units operate near the FCC Part 15.247 limit of 1W. But nearly all units operate with much less. E.g., the popular Linksys WRT54G base station transmits 60 mW. That's only 200,000 times 300 nW.

Footnote 2

21 dB is the sensitivity range for the Ruckus Wireless 802.11g units used as a reference. The 1 Mb/s rate requires -99 dBm while the 54 Mb/s rate requires -78 dBm. This power range (21 dB) is larger than the range of data rates (54:1 or 17.3 dB) because the higher rates must use less power-efficient modulation and coding to fit in the same bandwidth as the lower rate signals. This is as expected from the Shannon channel capacity theorem; power efficiency and bandwidth efficiency are conflicting goals in modem design.

Phil Karn, 7 June 2007; revised 29 June 2007