This is my first post in the AllWize blog and the first of a series of experiments using AllWize K1 and K2 boards. We will try to answer some of the usual questions when using a new LPWAN technology: battery constraints, message retrieval or what we will be exploring in this post: how far does it reach?
Theory
Theory is more or less the same as the Olympus: the place where perfect beings live and look over how we, mere mortals, try to resemble them.
The main concept here is the “link budget”, this is the balance between the receiver sensitivity and the different gains and losses of the radio transmission. A general equation, taken from M. Barbiroli et al., “Smart Metering Wireless Networks at 169 MHz”, June 2017, is:
Where the different variables stand for (please note we are using [] instead of subindexes due to a limitation of the editor):
S[RX]: sensitivity of the receiver, sometimes referred as receiver power or P[RX], this is a negative value meaning “down to” that many dBm
P[TX]: radiated power of the transmitter, this is a positive value that sums up to the budget
G[TX]: gain of the transmitter antenna
G[RX]: gain of the receiver antenna
L: average losses due to different factors, these are all negative values meaning the subtract from the link budget:
PL[A]: average outdoors (on air) path loss
PL[B]: average building penetration loss
IL: installation loss (due to antenna connections, installation cases,...)
MF: a fading margin due to propagation effects and EM noise
Sensitivity and losses are negative values, while transmitting power and gains are positive values.
There are a lot of things to take into account and some of them are hard to determine, like loss due to the installation or the propagation noise. Others can be easily found in the datasheet of the radio module we are using. Since we are using the RC1701HP-WIZE module by Radiocrafts in our AllWize K1 and K2 boards, we will head over to its datasheet.
The sensitivity of the receiver S[RX] depends on the data rate. For slow data rates (2.4 kbps) the S[RX] is -119 dBm. Note that these are slow compared to the other available options in the Wize protocol (4.8 and 6.4 kbps), but it is still several times faster than Sigfox (100 to 600 bps) and in the same order of magnitude as the fastest LoRa data rates (SF7BW125 transmits at 5.5 kbps aprox).
Of course, sensitivity gets worse if we increase the data rate. As a rule of thumb we will lose 4 dBm every time we duplicate the speed. So we should expect a -115 dBm receiver sensitivity for 4.8 kbps and around -113 dBm for 6.4 kbps, for instance. This is coherent with the common sense idea of “talk slower if you want to be understood”.
Also, in the RC1701HP-WIZE datasheet, we can read that it lets you define the transmitting power P[TX] in several different steps from +14 dBm to +27 dBm.
To get the antenna gains (both for the transmitting antenna and the receiving one) you have to check their datasheet also. It’s important to note that antenna gains are always directional, after all they cannot transmit more power that what the receive. They just focus the power they transmit in certain directions. The gain is then represented as the relative difference with an ideal antenna with a spherical radiation pattern where all incoming energy is radiated out.
Monopole and dipole antennas have a donut-like radiation pattern with positive gains in the plane perpendicular to the antenna. More gain means a more flat pattern and thus less coverage in directions not in the perpendicular plane to the antenna. Constraints in the antenna length and ground plane size for monopole antennas translate into typical gains of -9 to 0 dBi, relative to that ideal sphere.
Another interesting value is the pathloss (L). It is actually a sum of different impacts on the radio signal where the main one is the PL[A], i.e. the signal loss as it travels through air. The formula for this value depends on a couple of factors and it’s mostly experimental:
Where R is the link distance, n takes into account the average amount of obstruction suffered by the wireless channel and P[0] is the pathloss at 1m and is accounting for major link parameters as the wavelength and the height of the antennas.
Based on the Radiocraft’s “AN021: RF modules range calculations and test” by By T.A.Lunder and P.M.Evjen, values for P[0] might range from -12 to -20 dBm with an average, statistical, value of -17 dBm for 169 MHz (based on this formula: P[0] = 20·log(𝛌) - 21.98). The slope of the curve (n) depends on the environment. Here you have some approximate, experimental, values:
So, for free space areas, you can see the effect of the air path loss as 6 dB to double the distance. Whilst the worst case scenario for indoor propagation would be almost 20 dB to double the distance.
All this results in a power curve similar to the one below. If after all the losses and gains we are still over the sensitivity of the receiving device we are good:
Experimental setup
We set our base station almost on top of the Tibidabo mountain, the hill that dominates over Barcelona city, at 433 m altitude and with great sights. I stayed there with the receiver while Marc started a motorbike tour all around the city and whereabouts. The goal was to test the radio link between places from 6 to 12 km far away, to get some performance numbers in the urban environment.
We used two AllWize K1 shields on top of two Arduino Leonardo, both tuned to the same channel, same data rate (2400 bps) and max output power in the transmitter node, which is 27 dBm.
The antenna is one of the critical points when using 169 MHz. On one hand, typical quarter length antennas would be 44 cm long for 169 MHz (!!) so we need really big antennas to get similar performances to other technologies. On the other hand, the small ground plane area compared to the carrier wavelength translates into worse performances. This is something that affects all prototyping boards up to some extent, not only the K2.
During the experiment we tested different combinations with 3 different antennas.
A 2J0819-C708N antenna, the same you will get with the AllWize K2, by 2J Antenna Conceptor. This is a small 7 cm, <2:1 VSWR antenna. The gain is not specified so it is assumed to be around -9 dBi.
A H169-SMA antenna, by EAD. At 14 cm is twice the length of the previous one. Again no gain specification but <1.5:1 VSWR.
A Taoglass FW.80.SMA.M Meteor antenna. This is a 35 cm whip antenna with 0 dBi max gain (-3.9dBi average).
The receiver was connected to my computer and I was logging all incoming packets sent by the transmitter with an autoincrement payload, along with the RSSI and the timestamp of the message. During the test we decided to use only the H169-SMA antenna on the receiver and use the 3 different ones on the transmitter.
Here you have the results:
These results are compatible with an antenna gain of -18 dBi (both RX and TX summed up), a default P[0] of -17 dBm and a path loss slope of between 2 and 2.2 which corresponds to the medium where the experiment took place.
The relation between different antennas also falls in the expected range, with 4.5 dBi difference between the smaller and the bigger one. Remember we don’t have gain values for all the antennas, but the whip antenna (the big one) has an average gain of -3.9 and the minimum theoretical gain for a 169 MHz monopole antenna is -9 dBi.
Here you have a couple of pictures so you can get an idea of the distances. The first picture was taken from Tibidabo. You can see Barcelona and the Mediterranean Sea and the small hill of Montjuïc. At the top of the hill there is a castle from where Marc was sending packets. The distance is 7.76 km.
The second picture was taken by Marc from La Conreria, a specific zone in the Marina Mountains, north of Barcelona. You can spot the Tibidabo in the center of the image 11.94 km away from there.
You might have notice we had a fabulous day for mid November. Mostly sunny, dry and no wind. The weather station in the Tibidabo repored 17.8º Celsius and 54% relative humidity at noon. Best testing conditions.
Conclusions
Experimental results are compatible with the theoretical values and confirm a distance range comparable to that of other LPWA technologies. This is good since it confirms Wize can compete with LoRa or Sigfox on distance, even with relatively small antennas compared to the carrier wavelength. This is quite important since antenna size and cost have always been a handicap for low frequencies.
Now we can hop to test one of the strongest points of Wize: the extra penetration capability of the 169 MHz frequency over the 868 MHz used by those others on the European Union.