How LoRa Modulation really works - long range communication using chirps
ฝัง
- เผยแพร่เมื่อ 2 พ.ค. 2024
- LoRa (LoRaWAN) is a new modulation technique optimised for long range, low power, low bitrate communication. You'll often hear people say LoRa uses "Chirp Spread Spectrum', but this alone is only a small part of the story. LoRa uses an elegant mathematical trick to allow more efficient receivers. In this video, I outline how LoRa modulation works - it is incredibly unique. I was amazed how LoRa can communicate well beneath the noise floor. I tested the performance of LoRa with a Matlab livescript demonstration.
00:00 Introduction
01:00 Chirps as the basis for LoRa
04:20 Towards a mathematical description of the LoRa symbol
09:00 Correlation
12:34 Our first attempt at a receiver
13:12 Towards a more efficient receiver using a "mathematical trick"
16:40 Performance of LoRa
18:54 Matlab code to simulate a LoRa system
26:32 Summary - วิทยาศาสตร์และเทคโนโลยี
Which modulation scheme should I cover next? 🤔
I thought FT8, JT65, JT9, etc, were the best low noise schemes because of the very narrow bandwidth, which means you can use very narrow filters and get rid of almost all the noise.
This one....but after reading what Shannon limit is and Eb/N0...
Then you will compare apple to apples....
GPS Signals also come below the noise floor. They also have a correlation receiver type.
The descriptions of it, that I found, did not brought me insight how it really works on the modulation level.
I only understood that upper layer, there it receives from the 4 or more satellites their precise realtime and precise in space position, albeit the last digits of these numbers are enciphered for intentionally reducing the precision on non-military receivers.
I agree with Zach..894, any of the digital modes created by Dr. Joe Taylor. Use FT8 as your search term.
Go for WCDMA so you can compare processing gain against LoRa.
This is possibly the best explanation of Lora modulation I’ve seen ever…
It's like all of signal processing topics in one video! Exciting to learn about a robust platform with so much room for a lot of creative micro modulations.
No it is not !!
@@imlassuomcould you link to a better one? I’d love to see that one too.
Why?
This is possibly the best explanation of anything I've ever seen.
“You can always detect a sine wave in noise….if you are willing to “wait” long enough” - E.J. Swanson
I’m a ham operator. I setup a LoRa base station using the lora ham shield that runs on top of an arduino. With that arduino plugged into my raspberry pi at home, and another arduino with lora hsm shield running in my car. I was able to TX/RX short text messages first try back/forth about 9 miles apart. This was at only 1 watt or less power output, on 440 mhz. I was dumbfounded. It took some pass band filters, and good antennas, but still… Able to communicate well beyond any voice, digital voice, or digital modes on UHF from a very tough location to another, separated by multiple freeways, high rise buildings, trees, cars, etc, etc…
That is impressive.
Have a tutorial? I would be interested in your project 👍🏽
@paddler-sn7ub I don't sorry. It was an old project based on the LoRaChat program, and lora hamshield. The youtube channel was run by username inductive twig or something, and the arduino code for LoRaChat is on his github page.
The key to making these cheap single board transceivers communicate much further than what is possible, is by using band pass filters to block out all the other RF noise. So I used very tight, 435 to 450 mhz band pass filters when experimenting. Also very good coax and antennas. My base station during that test had 1/2" hardline running up to a good folded dipole 15' above my roof. So just reducing the losses. Especially at the receive side.
This wasn't really emphasized but usually more bits per symbol means worse performance for a given SNR, but in LoRas case, a higher SF also greatly increases the symbol's duration (as well as the bits per symbol), increasing SF by 1 means 1 more bit per symbol but it also doubles the symbol length, so that gives you more effective spreading, and lets you go to lower SNRs.
Yes, you explain it well.
I was confused by this at first because I'm so used to more bits per symbol meaning worse performance, but this makes it clear, thanks!
Thanks for adding this crucial comment. I'm not sure why longer symbols give more effective spreading?
This is an extremely important point that confused me at first. Since the symbol duration doubles with each increase in the spreading factor by one, the symbol duration increases exponentially with the SF. However, the number of bits per symbol increases linearly with the SF. Consequently, the overall data rate decreases with an increased SF. There's no magic there; a lower data rate improves the permissible signal-to-noise ratio.
So how does the performance versus the bit energy to noise density ratio (Eb/No) compare to other modulation schemes and how does it change with SF?
It absolutely blew my mind how clearly you have explained the LoRa modulation despite the complex maths behind it.
Thanks!
Man, your explanation is awesome. I really liked the way you added the paper information and brought a nice explanation. Please, keep going with these kind of videos.
Regards,
Pedro.
This is what I call well-balanced video making and editing: normal transitions, clear presentation, voice level fairly constant, background tune merely present and allows or even helps one to get immersed in the topic without being disturbed either by its loudness or a crappy tune choice.
Your explanation is pretty good and shows you have a good understanding of the principles, but math is my weak side so I mostly skip over calculus and differential equations.
If he'd encoded the music using LoRa it could have been turned down to below the noise floor! /s
Great video!
Just one comment: The LoRa demodulator is basically a correlator plus a bank of filters, the latter being implemented using FFT. And, the LoRa symbols are basically time shifted versions of each other.
Conceptually it is very similar to an FMCW radar that also uses a similar demodulator. Instead of the symbols, the radar receives time delayed versions of the chirp waveform depending on the location of the target. The correlator output is a sine wave (for a single point target) whose frequency is proportional to the time delay (i.e. the range). Bank of filters (i.e. FFT) can thus be used to discriminate targets.
Are matched filters used to sense each frequency component?
The FFT by its nature is a matched filter to the fundamental sin/cos waves@@eswnl1
@@eswnl1 The FFT IS the bank of matched filters. Each FFT bin is computing how well the input signal matches the frequency for that bin. For CSS, the highest bin number is the symbol. For FMCW radar, the highest bin number is the range.
Perfect material for our LoRa APRS group!
Wonderful video. Amazing. I'm working with LoRA modeling on my thesis. Great job and great explanation.
Excellent video mate, cheers for that! Good to see matlab getting used as well, it is invaluable in so many ways.
What a great video and details explanation!
That helps me a lot with my project in LoRa IoT!
Thank you very much!
Dont know what amazed me more - the LoRa protocol or your explaination. Thanks for the video.
Truly wonderful and comprehensive explanation. Thanks a lot!
I've been very impressed with the performance I've been getting with LoRa, and this was a wonderful addition to the documentation from Semtec. They make it easy enough to use, but this understanding is invaluable.
This is a really good video you did explaining LoRa "mathematics', i.e. the magic of decoding a symbol where signal is less than noise i.e. SNR negative 8-) and the Matlab code is really useful. Thank you!
Really good explanation! Again this shows the power of FFT. OFDM uses a similar mathimatical trick with the FFT btw.
Brilliant video, this has demystified how the modulation and below noise floor parts work for me far better than any other video I've watched.
Well done. It would be interesting to add information about the bandwidth of the signal vs SF. This relates directly to the received noise and hence the S/N ratio. This will perhaps also shed a light on your question how far one can go by increasing the SF.
Excellent ! Really helped me to grasp the intution about LoRa !
This is a super valuable video! Simple and to the point. Thanks!
Incredible explanation! Thanks!
Many thanks for posting this video. I had no idea how LoRa worked beforehand but your video clearly explained it. It took a while to figure out how convert your Matlab code into Octave code and correct my typos. But the final result worked exactly like your demo showed.
Can you pls share your octave version?
Thanks for the video and very clear explanation.
As a graduated in electronic engineering at the Padua university ( the same of Lorenzo Evangelista) I studied spread spectrum in the nineties but at the time I didn't catched the concept: too much theory and few concrete examples. At the time spread spectrum modulation was probably used only by military and hardware was not able to support the computation needed.
After this video I want to go deeper on how Lora works, I think I will take the mathlab simulation you have developed to play a bit by myself.
Great Vid! Although I mostly forgot university maths, I got to understand the principle of spreading factor and symbols on LORA.
Brilliant explanation. Thank you
Fantastic explanation!
Absolutely nailed it!!!!!!!
at 4:09 you put up both down chirps. Thanks for the lecture
Thanks for explaining this what I always considered RF wizardry. Even though I don't have the mathematical fundament to stand on to understand it thoroughly, I have the feeling that I'm a lot smarter than before the video
Signed up! Love so deep math analysis.
Life, the Universe and Everything.
Excellent Teaching.
Amazing video. Thank you!
Well produced! I'll investigate more with MatLab; very inspiring!
This video is simply unbelievable, very clever explanation!
Thanks!
Thanks for such a well presented and clear description of the modulation scheme used.
In response to your question, the LoRa modulation scheme is still subject to the Shannon limit, the maximum information rate is a function of channel SNR and bandwidth.
If you increase the spreading factor in a channel where the SNR is constant, you will need more bandwidth to maintain the received symbol error rate.
As bandwidth is usually fixed for a given channel, the SF can be varied to optimise information throughput for a given channel SNR. This can be done adaptively as the SNR varies over time, due to radio fading and interference sources.
Excellent explanation. Excellent content. Excellent topic. Keep up the good work.
impressive explaination, perfectly explained
Incredible!
I'm new to radio staff. But I have basic knowledge of signal processing from my university studied 30 years ago. That is best described LoRa that I really understood. Keep up with a great job spreading knowledge and understanding!!! 🙏🙏🙏
Truly amazing work . Thanks for your efforts. Inspiring ❤
Super explanation, many thanks!
For as little as I do know about wireless, and even wired signal communications, this honestly feels like it fills a lot of gaps in my brain
Since TH-cam has trouble with comments on Shorts, if there are any here that are unrelated, @ me so I can just delete them
Great video. I love learning the theory behind stuff like LoRa. Keep it up.
Thank you for this good explanation!
Years ago with a friend i did a equivalent experiment using GNU-Radio.
Not related to LoRa but the target was using width bandwidth spreadspectrum to get a signal over a long distance 100 - 200 km (60-100Mi)
I also added a noise generator to see what happened....
it's long ago, but you retriggered my interest.
Thank you for this excellent explanation !
Really good explanation
Explanation is great. Subscribed
Very well presented! In thinking about the limits to the number of symbols, as the symbol duration increases distortions in propagation will modulate the baseband coordinates and increase the error rate. This is not ‘noise’ and will not show up in simulation. A noise driven delay modulation term would cover this.
Let me see, as stated in some comments, if the SF increases by 1, the symbol length (and window) doubles. That effectively lowers the bitrate, which makes total sense.
Then, why the chirp at all? You could do exactly the same with nFSK, just have more possible values per symbol, over a longer time with a lower bitrate.
For this to work so well, the chirp has to provide some important benefit. Perhaps less reliance in the oscillator stability?
I'd love to see a comparison between LoRa and an equivalent nFSK in Matlab.
BTW awesome video!
I guess the nFSK system would fail much sooner due to frequency selective multipath or constant carrier interference. That interference won't match the chirp rate. The difference wouldn't show in a simulation using AGWN like in this video. Just a guess, this video is the only real research I've done into LoRa.
@realsolarcars I guess, but you could address those problems in nFSK in an upper level of spreading and FEC, no one said the FSK should be simple and straight, after all LoRa isn't. I think what I try to say is that there is no real need for the continuous shifting in frequency, you could instead do discrete jumping between the n subcarriers. The reason could very well be making it patentable. Anyway I am just guessing. Regards!
The benefit is each symbol is spread across the entire bandwidth, so no symbol can be lost in a multipath null, unlike what could happen with nFSK. When you DONT use forward error correction this has big advantage!
Amazing lecture indeed. Would you make more tutorials on LoRaWAN implementation, hacking, and defending?
Wow - great explanation - usually there are 3 features but youre only allowed 2 of them - here you can choose 3 simultanously :) Low Bitrate, Low Power and Long Range :) - great idea :)))
Well technically the desirable traits are High Bitrate, Low Power and Long Range. Power and bitrate are low to begin with. Each time you increment the spreading factor, symbol duration has to double, but so does the number of bits per symbol. I think the trade-off there is in the processing power needed by the larger FFT in the receiver.
Although I wasn't able to follow most of the parts related to the mathematical bases, but I got the concept behind and I've learned something new and interesting. I am sure I will never use it... but thanks :)
Thank you, that's really interesting
This video really explains not only LoRa protocol. But Modulation/Demodulation process in general. Nice!
I have only a high-school education. a total of 13 years of formal education, and no math beyond a semester of intro to algebra, but my fascination with RF led me to do a bit of research, and I ended up building a LowFER antenna and transmitter (175 kHz) transmitting BPSK ASCII using a computer program called Coherent, and with my transmitting beacon sending a short, repetitive text message, using crystal ovens at the beacon and in a homebrew receiver in my car, and averaging out the noise I was able to receive my beacon's text message, ( except for a couple of minutes in De Moines, Iowa, every foot of the way as I drove over a distance of 800 miles. It would have worked further, but I had not included sufficient front-end gain for copying the signal at great distances. I realized this because instead of my CRT screen printing out random characters, as it would with my transmitter turned off, in a low noise location it stopped displaying anything at all. Not enough gain. So, based on my simple experiments there is no SNR that a good modulation technique is incapable of receiving a signal through if the effective bandwidth is narrow enough, (i.e. a synchronized message repeated enough times to average out the noise.) The only limitation is how long you're willing to wait for the data to appear correctly. BTW, I estimated the EIRP of my transmit antenna to be 7 mW, which is very good for a LowFER antenna and 1 W transmitter. A friend took a receiver with him on his vacations each summer and received the beacon all over the western USA, day and night. So if chirp modulation can reduce the amount of time necessary to receive a given symbol and act in a manner similar to what we were doing with crystal ovens, BPSK, and Coherent, I'd say they have a winner.
Awesome explanation, thanks!
Glad it was helpful!
Wow, what a helpful video. Actually I'm doing some studies on LPWAN Technologies and tried to figure out where the limits of LoRa are. The other technology that I've tested is way weaker and loses connection at a SNR of like -2.
fascinating,thanks
Great Video! Thanks so much!
amazing video, thank you sir
As a visual learner - THANK YOU! I don't think I could have ever wrapped my head around this without your visual representation of time. All of it makes sense and, when you see how it works, it is one of those things that makes you go - yeah, why did it take so long for this to be figured out?! THANK YOU!!!
Perfect video. It's like a missed Digital Communications lecture that I finally found. Thank you.
Good explanation. Keep it up
wow. I'm totally not a EE or hardware guy but I find this so interesting. I'm surprising that a higher SF results in lower error rare since it seems to me that a higher SF actually means more data is transmitted (unless I'm misunderstanding or somehow the length of transmission is longer for compensate) but with lower error. very cool video!!!
You are correct, there is one thing: With a higher SF the chirps also get longer. So the bitrate goes down although there are more symbols.
What an extremely well presented video on a very complex subject. What I was wondering is what kind of bit rate you expect from this modulation scheme. You could always add a Foreward Error Correction protocol (FEC) to the original signal to improve the SNR. We use that extensively on high speed optical transmission systems
Overall great video. Good job extracting the bottom line information from the sinusoidal equations. Small correction needed: 20 db implies a magnitude of 100, not 10. Meaning the at -20db, the Noise is 100x the Signal magnitude, further driving the point of just how effective the signaling scheme is at handling noise, especially when you show the -10dB signal... just imagine 10x that.
I do wish that you explained the Y axis of the Err Rate vs SNR a little bit, because the way its graphed in the video (right to left) almost implies that the higher value on the Y axis is good, but for anyone viewing, having an error rate of 1 is of course unusable. Maybe a horizontal line on the graph that shows an acceptable error rate wouldve helped.
Oh, and thank you VERY much for providing a Matlab example
This the very original way in which knowledge should be conveyed. Structured, well articulated language and definitely accurate. Thank you for your time and effort. New subscriber.
Thanks
Great explanation. Here is the code if you want to play with it.
clear all
SF = 7; %Spreading Factor
BW = 1000;% Bandwidth
Fs = 1000;%Sampling Frequency
s = 127; %send symbol '10'
SNR = -10;%Signal to Noise Ratio
%Generate a data symbol
num_samples =(2^SF)*Fs/BW;
k = s; %add s to k to start (defines the data symbol)
lora_symbol = zeros(1,num_samples);
for n=1:num_samples
if k>= (2^SF)
k = k-2^SF;
end
k = k+1;
lora_symbol(n) = (1/(sqrt(2^SF)))*exp(1i*2*pi*(k)*(k/(2^SF*2)));
end
loop = 100;
ind2 = zeros(1,loop);
for j=1:loop
%Add noise
lora_symbol_noisy = awgn(lora_symbol,SNR,'measured');
%Transmit
%Receiver below
% Generate the Base Down Chirp
base_down_chirp = zeros(1,num_samples);
k=0;
for n=1:num_samples
if k>= (2^SF)
k = k-2^SF;
end
k = k + 1;
base_down_chirp(n) = (1/(sqrt(2^SF)))*(exp(-1i*2*pi*(k)*(k/(2^SF*2))));
end
dechirped = lora_symbol_noisy.*(base_down_chirp);
corrs = (abs(fft(dechirped)).^2);
figure(1); plot(corrs)
[~, ind] = max(corrs);
ind2(j) = ind;
pause(0.01)
end
figure(2); histogram(ind2,2^SF)
symbol_error_rate = sum(ind2~=s+1)/j
figure(3); spectrogram(lora_symbol)
This video shows the mathematical basis for a trick used in the LoRa implementation
to reduce the complexity and power requirements of LoRa receivers. How LoRa works is
quite simple, it sends a fixed duration linear chirp between fixed low and high frequencies,
for each symbol to be transmitted, which symbol is determined by when the abrupt transiton
from the highest back to the lowest frequency of the chirp occurs. There is also an abrupt
transition between symbol boundaries. en.wikipedia.org/wiki/LoRa#LoRa_PHY
The core equation for the trick is a thick read if you're not an RF design engineer.
At 6:40 into the video, it shows Equation 2 from the original paper:
c(n*Ts+k*T) = 1/sqrt(2**SF)*e**(j*2*pi*((s(n*Ts)+k)mod(2**SF))*(k*T*B/(2**SF))
c(): The complex number result from the equation, to be evaluated at each moment in time
n*Ts+k*T: The time in seconds from time 0, when the k'th sample of the n'th symbol is sent
SF: The "Spreading Factor", which is the number of bits in each symbol.
k: An integer that increments up from 0 to (2**SF)-1 for each sample within a symbol
Ts: The time it takes to send each symbol, there are 2**SF samples in each symbol
n: An integer that increments up (starting from 0) with each symbol to be transmitted
s(n*Ts): The integer value of the n'th symbol to be transmitted, a value between 0 and (2**SF)-1
B: The bandwidth that the complete LoRa signal will occupy in Hz
pi: 3.14159265... (Ratio of the circumference over the diameter of a circle)
e: 2.71828... (Euler's constant)
j: The square root of -1 (some sources use the letter i instead of j)
This is the equation for a complex sine wave using Euler's formula
e**(j*2*pi*f*t) = cos(j*2*pi*f*t) + j*sin(j*2*pi*f*t)
Euler's formula converts what would be a trigonometric equation involving sines and cosines
into an exponential in the complex plane that is much easier to manipulate mathematically.
We are interested the real part cos(2*pi*f*t), equal to sin(2*pi*f*t) shifted 90 degrees.
In sin(2*pi*f*t), the sin() operator expects a value in radians, not in degrees.
There are 2*pi radians in a full cycle of 360 degrees, so 2*pi*f is the frequency
expressed in radians per second. Multiplying that by the time t in seconds we get the
number of radians that have passed since time zero, and can evaluate the sin() function
to determine the value (perhaps in Volts) of the sine wave at that moment. As t increases
to infinity, the result of sin(2*pi*f*t) repeatedly cycles through values between +1 and -1.
The complex conjugate of Equation 2 is: e**(-j*2*pi*f*t) = cos(j*2*pi*f*t) - j*sin(j*2*pi*f*t)
At 15:00 minutes into the video he multiplies Equation 2 by its complex conjugate while performing
the convolution, the imaginary parts involving j cancel out leaving only a real result.
The mathematical trick is that the complex conjugate can be broken down into two terms,
we need only multiply each incoming symbol by a base down-chirp (the complex conjugate of
a base up-chirp), and this will result in a different constant tone for each possible symbol.
The receiver must first be synchronized to the symbol boundaries by inspecting the preamble sequence.
But forget complex conjugates, let's evaluate the real part of Equation 2:
v(n*Ts + k*T) = 1/sqrt(2**SF) * sin(2*pi*((s(n*Ts)+k) mod(2**SF))*(k*T*B/(2**SF)))
The v(n*Ts + k*T) means that the formula gives a value (perhaps in Volts)
for the k'th sample of the n'th symbol to be transmitted.
The 1/sqrt(2**SF) is a constant for the amplitude in Volts of the sine wave, which
scales with the power of the transmitter. This is arbitrary, and we can ignore this factor.
The remainder of the equation is: sin(2*pi*((s(n*Ts)+k) mod(2**SF))*(k*T*B/(2**SF)))
and we expect this to be of the form: sin(2*pi*f*t).
Since k is the number of steps and T is the seconds per step, then (k*T) is the
elapsed time since the start of the symbol, and thus equal to "t".
With that resolved, the remaining terms must be the frequency f in Hz:
f = ((s(n*Ts)+k) mod(2**SF))*(B/(2**SF))
Lets make this all a bit more concrete by specifying that SF=7,
so the symbols transmitted have 7 bits of information, and thus each symbol
can take any of the 128 integer values between 0 and 127. We will further assume
that the transmitter is continuously sending the same symbol of s(n*Ts) = 0.
The text above Equation 2 in the paper says LoRa (arbitrarily?) sets the bandwidth B equal
to the inverse of the sample time T, or B = 1/T. Let's assume a LoRa bandwidth of 10400 Hz,
(one of the standard choices) so the sample time is 1/10400 = 0.000096 seconds
When all the above substitutions are made, the equation for f in Hz simplifies to:
f = ((0+k) mod(128))*(10400Hz/(128))
With the symbol value held at 0, the mod(128) no longer has any effect
since it never sees an argument greater than 127:
f = k * 10400Hz/128
And now it is clear that the frequency varies from 0 to 10400*127/128 = 10318.75 Hz
with a step size of 10400/128 = 81.25 Hz as k increments from 0 to 127 during each symbol.
This is a baseband signal. The signal must later be translated up to the target center
frequency for transmission, in the US this would typically be in the 915 MHz ISM band.
It seems likely that the discrete frequencies given by equation 2 would be the frequency
at the center of each sample period, and that the frequency is varied continuously.
Given that, the bandwidth will indeed be 10400 Hz.
Each symbol in our example with SF=7 takes 128/10400 seconds to transmit,
giving us a data rate of 7/(128/10400) = 568.75 bits/second.
There will be overhead added to that for the preamble sequence used for synchronization,
a header to identify the transmitter, and the proprietary LoRa Forward Error Correction.
As others have noted in the comments, if we increase SF from 7 to 8 bits per symbol
then the time it takes to send one symbol goes up from 128 sample periods to 256.
Given the much longer time per bit spent transmitting, it is not surprising
that noise immunity improves.
Receiving signals below the noise floor has been done by radio amateurs for at least 50 years.
Other services likely had similar schemes long before that.
www.sigidwiki.com/images/a/a5/Coherent_CW_arrl.pdf
Somehow, I just knew the clever math trick would involve fourier transforms. Invariably in signals, compression, or other similar domains, converting between time and frequency domains opens up all sorts of interesting options for improving the efficiency of the process.
Great video, very enlightening! LoRa is no longer magic to me. I'd love to see you cover CDMA, especially the way code-based modulations are combined with other methods to provide efficient band sharing and tolerance for multipath interference.
Thank you
Really interesting video! :)
LoRa is incredible in that it can work below the noise floor
Amazing video! If i'm not wrong LoRa technique was used in Express LRS open source system used for example in FPV drones. You can get amazing range even at super small TinyWhoop like Mobula 7 1S ELRS. There is super tiny ceramic antenna and this system rocks in terms of penetration even on small transmitter power.
Thanks for the video-i’m an Amateur radio operator with an interest in digital modes and LORA. I’m not sophisticated enough to follow along with the calculations in the video, but I understood the scene behind interpreting the symbols based on your description.
Glad it was helpful!
"Spreading factor is between 7 and 12 in Lora"
Fascinating, I'll be sure to let her know.
Man, how have I not come across your channel before and how are your subscriber numbers not 10x?! Instant subscribe, super clear explanation thank you!!
This protocol is being used in Ukraine by both sides now, due to its resistance to jamming, range, and lack of the need for constant back-and-forth handshakes. I couldn't understand how jamming wouldn't work, but this explains it
Thanks for the clear explanation! I do wonder what happens if there are 2 LoRa transmitters in an area though, how would the receiver distinguish between them?
you deserve more subs and viewers
Fantastic analysis and explanation of the signal. So does this breakdown such that many of the newer SDR equipment could utilize this as a new digital mode as well? This could be a new mode to explore for ham radio.
Everything about Lora is counterintuitive. Increasing the spreading factor which means increasing the possible symbols IMPROVES performance? Incredible how the maths proves the fact. Does make you think about what more advanced tech the military has hidden away
As noted in other comments, the data rate falls in relation to improvement in noise performance
Very good 🙌👏👏👏
Armsman Pham Trinli at the On-Off star would be very happy with this encoding scheme for his nanopower localizers...
Awesome. Thank you. +Subscribed. 🙂
Wow beautiful! From a new modulation concept with a complex maths expressions to a smart way of computational representation, that’s incredible! Cannot imagine how people invented this smart are!
Thanks! Yes, it is a smart idea with a lot of applications.
Well, done! I was having a discussion in a math class where I introduced "i" and Complex Numbers to my 9 & 10.5 year old grandsons! (Yes, great joy in doing that!).
I was immediately asked words to the effect of, "Well, that's all nice and consistent, and even beautiful if you wish, but it is all based on something that doesn't exist - the square root of negative one. How how can that have any practical value?" My answer then was (based on old analog oscillators I had studied early in EE in college) that when the complex roots of a quadratic equation have an imaginary component, the oscillator is unstable.) Neither a practical nor a very fascinating example for a 10-year old. But this!
You've given me the most practical use of complex numbers - even more than the FFT itself - to be the basis of communication with a signal well below the noise level.
As a long time amateur radio operator, liking CW (Morse code), we really appreciate digging a usable signal out of the noise. It can save lives. Some ham communications (lower frequency bands) bounce up and down off the ionosphere to make global communication with just milliwatts. Just subscribed. Will properly thank soon!
YOU ARE GREAT !!!
Wow, what a great video explanation. Thankyou. So if I get this correctly there is a signal hidden in the noise, you just need to know how to decode ... so wonder what the implications of something like this is for SETI and so on. Would the checks that SETI perform still just show noise as well.
LoRa, also can let you use a longer preamble. In just random noise, sometimes your whole message is messed up by the sync being thrown off. Most implementations allow a longer preample to help with this. If you really want to push the range, you can add error correction. Real word noise is a bit episodic. Error correction codes can take this into account.
For those who want to try this at home without having to get matlab, there is the option to use octave. Most anything that works in matlab, also works in octave. I haven't tried it but if anyone finds an issue, they can respond with a reply saying it happened and I will take a look.
Ty!
thanks for whatever this is... sounded informashunny and signal to noise wallacazam 4 Hz got it Thanks!
If I understand the modulation scheme correctly, then the spreading factor correlates with the symbol transmission time. This means that it falls entirely with the expected strategy for improving the probability of error, which is to either reduce the data rate (larger spreading factor) or to increase the transmission power. You could get even better error performance by (a priori) agreeing to only use a subset of the the symbols provided by a given spreading factor, since reducing the constellation size increases the distance between symbols and therefore reducing the probability of misinterpreting a symbol.
Excellent explanation of a highly technical subject. I guess I'm going to have to experiment more with Lora, if I can find a worthy use. Thanks for investing the time to show this.
Amazing explanation of LoRa modulation. I am trying to understand LoRa from scratch and I would like to know why we have that factor 1/sqrt(2^SF) at the beginning of the equation. And the same for the k/2^SF at the end. Thanks in advance.
2^SF is the number of symbols; 128 for 7. So a vector of k=0..127 rational-number elements each holding "k/127" makes it range from zero to one. That's a standard trick when doing a dot-product correlation, for both clarity (we like talking about unit-length vectors) and computational efficiency. The multiplication by 1/sqrt(2^SF) is a normalization factor of some sort: 1/sqrt(2^SF)=(2^SF)^-0.5=2^(-SF/ 2) which you can move into the exponent, making the values range from less than one to a smaller max value. I'm guessing this helps the fidelity of the FFT or avoids some floating point error.
I reversed the lorawan protocol in Python -- bit more fun to work with -- so can stretch the SF way beyond recommended (*beware time on air radio license restrictions)...but I'm installing sensors in far Canada north. When I hit a limitation in distance + antenna...I'm going to boost the spreading factor as high as needed & will let you know!
Another thing you can do is adding error correction and multiple packets. Depending on the noise source, it may be a pulse.